� 2 Programmable Dynamical Systems Analog Devices x ′ � ′ � + c 1 x ′ � + c 2 x ′ � ′ � = 0 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 L ⋅ I ′ � ′ � + R ⋅ I ′ � + C − 1 ⋅ I = 0 528 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 · 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 Fig. 1. Poisson chemical reaction flux and Poisson electron flow in Fig. 1. Poisson chemical reaction flux and Poisson electron flow in sub-threshold transistors obey the same Boltzmann exponential laws of sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy thermodynamics, and are therefore mathematically similar [13]. Electron copy ES = k f ⋅ E ⋅ S − k r ⋅ ES number is analogous to molecular copy number and temperature represents number is analogous to molecular copy number and temperature represents Fig. 1. Poisson chemical reaction flux and Poisson electron flow in itself. itself. sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy single cell on a few chips and speedup multi-cell simulations single cell on a few chips and speedup multi-cell simulations number is analogous to molecular copy number and temperature represents on multi-chip electronic boards [13]. Therefore, we were moti- on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could vated to create a few fundamental molecular circuits that could itself. be composed and scaled to model large biochemical reaction be composed and scaled to model large biochemical reaction Fig. 2. Die micrograph of the Fig. 2. Die micrograph of the cytomorphic chip fabricated cytomorphic chip fabricated in an AMS BiCMOS process. The left inset is a layout screen capture in an AMS BiCMOS process. The left inset is a layout screen capture networks in the future. This paper describes these fundamental Fig. 1. Poisson chemical reaction flux and Poisson electron flow in networks in the future. This paper describes these fundamental Fig. 1. Poisson chemical reaction flux and Poisson electron flow in of one gene block (2x magnification). of one gene block (2x magnification). sub-threshold transistors obey the same Boltzmann exponential laws of building-block cytomorphic circuits. The paper focuses on building-block cytomorphic circuits. The paper focuses on sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy thermodynamics, and are therefore mathematically similar [13]. Electron copy x ′ � ′ � + ax ′ � + x + ax 2 = c 3 establishing quantitative agreement of the cytomorphic chip establishing quantitative agreement of the cytomorphic chip number is analogous to molecular copy number and temperature represents number is analogous to molecular copy number and temperature represents measurements with prior biological measurements and models. itself. measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog 6) A stochastics circuit intentionally amplifies analog itself. single cell on a few chips and speedup multi-cell simulations The building-block circuits may be classified into seven im- The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- Poisson noise in transistors to represent biological fluc- portant categories: portant categories: tuations in mRNA and protein concentrations at very tuations in mRNA and protein concentrations at very on multi-chip electronic boards [13]. Therefore, we were moti- single cell on a few chips and speedup multi-cell simulations 1) Basic BiCMOS current-mode analog circuits exploit the 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. low copy numbers and at relatively high noise levels. single cell on a few chips and speedup multi-cell simulations log-domain cytomorphic mapping to capture the exact dy- log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- The Poisson nature of biochemical reaction fluxes au- on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could namics of fundamental mass-action molecular kinetics namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at tomatically maps biological noise to electronic noise at vated to create a few fundamental molecular circuits that could be composed and scaled to model large biochemical reaction such as association, dissociation, and degradation. These Fig. 2. Die micrograph of the such as association, dissociation, and degradation. These Fig. 2. Die micrograph of the high copy numbers and relatively low noise levels [13]. cytomorphic chip fabricated high copy numbers and relatively low noise levels [13]. cytomorphic chip fabricated be composed and scaled to model large biochemical reaction be composed and scaled to model large biochemical reaction Fig. 2. Die micrograph of the cytomorphic chip fabricated in an AMS BiCMOS process. The left inset is a layout screen capture networks in the future. This paper describes these fundamental fundamental circuits are general enough to capture subtle fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling in an AMS Thus, these circuits are most useful for reliably modeling BiCMOS process. The left inset is a layout screen capture in an AMS networks in the future. This paper describes these fundamental BiCMOS process. The left inset is a layout screen capture of one gene block (2x magnification). networks in the future. This paper describes these fundamental of one gene block (2x magnification). building-block cytomorphic circuits. The paper focuses on effects such as loading, fan-out, feedback, and substrate de- effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios highly stochastic and relatively low signal-to-noise-ratios building-block cytomorphic circuits. The paper focuses on of one gene block (2x magnification). pletion through the use of a few explicit connections and pletion through the use of a few explicit connections and in biological cells. in biological cells. establishing quantitative agreement of the cytomorphic chip establishing quantitative agreement of the cytomorphic chip building-block cytomorphic circuits. The paper focuses on measurements with prior biological measurements and models. Kirchhoff’s current law. A wide dynamic range of opera- Kirchhoff’s current law. A wide dynamic range of opera- 6) A stochastics circuit intentionally amplifies analog 7) ADCs and DACs convert between analog currents and 7) ADCs and DACs convert between analog currents and measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog The building-block circuits may be classified into seven im- tion and low power consumption are achieved through the tion and low power consumption are achieved through the Poisson noise in transistors to represent biological fluc- digital bits to enable our chips to communicate with each digital bits to enable our chips to communicate with each The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- establishing quantitative agreement of the cytomorphic chip use of bipolar and subthreshold MOS transistors that func- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- other via digital input/output (I/O), and with off-chip dig- portant categories: tuations in mRNA and protein concentrations at very portant categories: tuations in mRNA and protein concentrations at very 1) Basic BiCMOS current-mode analog circuits exploit the tion at low current levels. tion at low current levels. ital processors and computers. low copy numbers and at relatively high noise levels. ital processors and computers. measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. 2) The ability to model cooperative binding is enabled by tun- 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our Off-chip digital processors synergistically interact with our log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- able Hill-function building-block circuits. namics of fundamental mass-action molecular kinetics able Hill-function building-block circuits. chips to carry out various functions: reading digital data from tomatically maps biological noise to electronic noise at chips to carry out various functions: reading digital data from The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at 3) An “ITD” block built by a composition of above cur- such as association, dissociation, and degradation. These 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital high copy numbers and relatively low noise levels [13]. the chips; decoding the data; performing high-speed digital such as association, dissociation, and degradation. These high copy numbers and relatively low noise levels [13]. portant categories: rent-mode circuits enables mapping of the exact differen- tuations in mRNA and protein concentrations at very rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time signal processing as necessary (e.g., scaling, diffusion, time fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling tial equations of inducer-transcription-factor binding effects such as loading, fan-out, feedback, and substrate de- tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or highly stochastic and relatively low signal-to-noise-ratios delay, and error correction); encoding the data to create or effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. and transcription-factor-DNA binding including for- pletion through the use of a few explicit connections and and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; in biological cells. modify molecular data packets via address and data strings; pletion through the use of a few explicit connections and in biological cells. ward and reverse reactions, degradation, protection from ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene storing the programmable address connectivity amongst gene Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- degradation of transcription factors bound to DNA, and tion and low power consumption are achieved through the degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips digital bits to enable our chips to communicate with each and protein circuits; and communicating data to other chips tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each the change in DNA binding affinity of transcription factors the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were or to a computer. For simplicity, the data in this paper were use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at when bound by an inducer. tion at low current levels. when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that ital processors and computers. collected with a data-acquisition board (NI PXI-6541) that tion at low current levels. ital processors and computers. 4) An “analogic” current-mode circuit determines the tran- 2) The ability to model cooperative binding is enabled by tun- 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A Off-chip digital processors synergistically interact with our interacted with our chip and with MATLAB on a computer. A such as association, dissociation, and degradation. These high copy numbers and relatively low noise levels [13]. 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our INTRODUCTION scription rate of genes based on the probability of mul- scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) high-performance FPGA (e.g., from the Xilinx Spartan family) able Hill-function building-block circuits. chips to carry out various functions: reading digital data from able Hill-function building-block circuits. chips to carry out various functions: reading digital data from fundamental circuits are general enough to capture subtle 3) An “ITD” block built by a composition of above cur- tiple transcription-factor DNA binding sites being occu- Thus, these circuits are most useful for reliably modeling tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift the chips; decoding the data; performing high-speed digital could perform all of these functions in the future as well. Shift 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital pied or unoccupied in a combinatorial fashion with the rel- rent-mode circuits enables mapping of the exact differen- pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable signal processing as necessary (e.g., scaling, diffusion, time registers, SRAM blocks, and switches on the chip enable rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time effects such as loading, fan-out, feedback, and substrate de- ative mRNA production rate of each such combinatorial highly stochastic and relatively low signal-to-noise-ratios ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- programmability of parameters (e.g., reaction rates, dissocia- tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or state programmable by the user. This strategy enables us and transcription-factor-DNA binding including for- state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as modify molecular data packets via address and data strings; tion constants, Hill coefficients, and time constants) as well as and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; pletion through the use of a few explicit connections and in biological cells. to implement any arbitrary “analogic promoter function” to implement any arbitrary “analogic promoter function” connectivity. connectivity. ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene that is capable of complex saturating digital logic or prob- degradation of transcription factors bound to DNA, and that is capable of complex saturating digital logic or prob- and protein circuits; and communicating data to other chips The organization of this paper is as follows: Section II de- The organization of this paper is as follows: Section II de- degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and abilistic analog behavior depending on the molecular con- the change in DNA binding affinity of transcription factors abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with or to a computer. For simplicity, the data in this paper were scribes the core building-block circuits of the chip along with the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were centration. centration. chip measurement data. Fig. 2 shows a die micrograph of the chip measurement data. Fig. 2 shows a die micrograph of the when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each 5) A current-mode low pass filter (LPF) circuit enables the 4) An “analogic” current-mode circuit determines the tran- 5) A current-mode low pass filter (LPF) circuit enables the interacted with our chip and with MATLAB on a computer. A chip that reveals the various building blocks. Section III dis- chip that reveals the various building blocks. Section III dis- 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A gain and dynamics of mRNA and protein production scription rate of genes based on the probability of mul- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- high-performance FPGA (e.g., from the Xilinx Spartan family) cusses design considerations that are important in BiCMOS cy- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) and degradation to be represented. and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic tomorphic chip design. Section IV discusses how cytomorphic tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift tion at low current levels. pied or unoccupied in a combinatorial fashion with the rel- ital processors and computers. registers, SRAM blocks, and switches on the chip enable pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as to implement any arbitrary “analogic promoter function” connectivity. to implement any arbitrary “analogic promoter function” connectivity. able Hill-function building-block circuits. chips to carry out various functions: reading digital data from that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital centration. chip measurement data. Fig. 2 shows a die micrograph of the centration. chip measurement data. Fig. 2 shows a die micrograph of the 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as to implement any arbitrary “analogic promoter function” connectivity. that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with centration. chip measurement data. Fig. 2 shows a die micrograph of the 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic
� 3 DYNAMICAL SYSTEMS MODEL THE PHYSICAL WORLD x ′ � ′ � + c 1 x ′ � + c 2 x ′ � ′ � = 0 L ⋅ I ′ � ′ � + R ⋅ I ′ � + C − 1 ⋅ I = 0 · ES = k f ⋅ E ⋅ S − k r ⋅ ES x ′ � ′ � + ax ′ � + x + ax 2 = c 3 INTRODUCTION
� 4 DYNAMICAL SYSTEMS MODEL BIOLOGICAL PROCESSES x ′ � ′ � + c 1 x ′ � + c 2 x ′ � ′ � = 0 L ⋅ I ′ � ′ � + R ⋅ I ′ � + C − 1 ⋅ I = 0 · ES = k f ⋅ E ⋅ S − k r ⋅ ES x ′ � ′ � + ax ′ � + x + ax 2 = c 3 INTRODUCTION
� 5 BIOLOGICAL DYNAMICAL SYSTEMS E = E 0 − ES E S = S 0 − ES S · E ES = k f ⋅ E ⋅ S − k r ⋅ ES S state variables model physical quantities INTRODUCTION
� 6 BIOLOGICAL DYNAMICAL SYSTEMS E = E 0 − ES S = S 0 − ES · ES = k f ⋅ E ⋅ S − k r ⋅ ES differential equations specify continuous dynamics of state variables over time INTRODUCTION
� 7 GOAL: SIMULATING BIOLOGICAL DYNAMICAL SYSTEMS E = E 0 − ES E 0 = 6800 S = S 0 − ES S 0 = 4400 · ES (0) = 0 ES = k f ⋅ E ⋅ S − k r ⋅ ES given initial state of system: compute values of state variables over time INTRODUCTION
� 8 GOAL: SIMULATING BIOLOGICAL DYNAMICAL SYSTEMS E = E 0 − ES E 0 = 6800 6000 molecules 4000 S = S 0 − ES S 0 = 4400 2000 · ES = k f ⋅ E ⋅ S − k r ⋅ ES 0 ES (0) = 0 0 2 4 6 8 10 time (su) plot molecule counts/concentrations of compounds over time INTRODUCTION
� 9 ANALOG COMPUTING CIRCA 1950 ‣ direct mapping ‣ variables → current, voltage ‣ dynamics → circuit physics ‣ straightforward simulation ‣ power up circuit ‣ measure current, voltage over time ‣ 1970-2010 : Age of Digital Computing ‣ Analog computes out of fashion INTRODUCTION
� 10 PROGRAMMABLE ANALOG DEVICES ‣ same computational model ‣ modernized hardware 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 ‣ modern semiconductor technologies 528 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 ‣ new capabilities 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 Fig. 1. Poisson chemical reaction flux and Poisson electron flow in Fig. 1. Poisson chemical reaction flux and Poisson electron flow in sub-threshold transistors obey the same Boltzmann exponential laws of sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy thermodynamics, and are therefore mathematically similar [13]. Electron copy number is analogous to molecular copy number and temperature represents number is analogous to molecular copy number and temperature represents Fig. 1. Poisson chemical reaction flux and Poisson electron flow in itself. itself. ‣ powerful, heavily optimized sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy single cell on a few chips and speedup multi-cell simulations single cell on a few chips and speedup multi-cell simulations number is analogous to molecular copy number and temperature represents on multi-chip electronic boards [13]. Therefore, we were moti- on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could vated to create a few fundamental molecular circuits that could itself. building blocks be composed and scaled to model large biochemical reaction be composed and scaled to model large biochemical reaction Fig. 2. Die micrograph of the Fig. 2. Die micrograph of the cytomorphic chip fabricated cytomorphic chip fabricated in an AMS BiCMOS process. The left inset is a layout screen capture in an AMS BiCMOS process. The left inset is a layout screen capture networks in the future. This paper describes these fundamental Fig. 1. Poisson chemical reaction flux and Poisson electron flow in networks in the future. This paper describes these fundamental Fig. 1. Poisson chemical reaction flux and Poisson electron flow in of one gene block (2x magnification). of one gene block (2x magnification). sub-threshold transistors obey the same Boltzmann exponential laws of building-block cytomorphic circuits. The paper focuses on building-block cytomorphic circuits. The paper focuses on sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy thermodynamics, and are therefore mathematically similar [13]. Electron copy establishing quantitative agreement of the cytomorphic chip establishing quantitative agreement of the cytomorphic chip number is analogous to molecular copy number and temperature represents number is analogous to molecular copy number and temperature represents measurements with prior biological measurements and models. itself. measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog 6) A stochastics circuit intentionally amplifies analog itself. single cell on a few chips and speedup multi-cell simulations The building-block circuits may be classified into seven im- The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- Poisson noise in transistors to represent biological fluc- portant categories: portant categories: tuations in mRNA and protein concentrations at very tuations in mRNA and protein concentrations at very on multi-chip electronic boards [13]. Therefore, we were moti- ‣ digital reprogrammability single cell on a few chips and speedup multi-cell simulations 1) Basic BiCMOS current-mode analog circuits exploit the 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. low copy numbers and at relatively high noise levels. single cell on a few chips and speedup multi-cell simulations log-domain cytomorphic mapping to capture the exact dy- log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- The Poisson nature of biochemical reaction fluxes au- on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could namics of fundamental mass-action molecular kinetics namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at tomatically maps biological noise to electronic noise at vated to create a few fundamental molecular circuits that could be composed and scaled to model large biochemical reaction such as association, dissociation, and degradation. These Fig. 2. Die micrograph of the such as association, dissociation, and degradation. These Fig. 2. Die micrograph of the high copy numbers and relatively low noise levels [13]. cytomorphic chip fabricated high copy numbers and relatively low noise levels [13]. cytomorphic chip fabricated be composed and scaled to model large biochemical reaction be composed and scaled to model large biochemical reaction Fig. 2. Die micrograph of the cytomorphic chip fabricated in an AMS BiCMOS process. The left inset is a layout screen capture networks in the future. This paper describes these fundamental fundamental circuits are general enough to capture subtle fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling in an AMS Thus, these circuits are most useful for reliably modeling BiCMOS process. The left inset is a layout screen capture in an AMS networks in the future. This paper describes these fundamental BiCMOS process. The left inset is a layout screen capture of one gene block (2x magnification). networks in the future. This paper describes these fundamental of one gene block (2x magnification). building-block cytomorphic circuits. The paper focuses on effects such as loading, fan-out, feedback, and substrate de- effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios highly stochastic and relatively low signal-to-noise-ratios building-block cytomorphic circuits. The paper focuses on of one gene block (2x magnification). pletion through the use of a few explicit connections and pletion through the use of a few explicit connections and in biological cells. in biological cells. establishing quantitative agreement of the cytomorphic chip establishing quantitative agreement of the cytomorphic chip building-block cytomorphic circuits. The paper focuses on measurements with prior biological measurements and models. Kirchhoff’s current law. A wide dynamic range of opera- Kirchhoff’s current law. A wide dynamic range of opera- 6) A stochastics circuit intentionally amplifies analog 7) ADCs and DACs convert between analog currents and 7) ADCs and DACs convert between analog currents and measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog ‣ exploit analog noise The building-block circuits may be classified into seven im- tion and low power consumption are achieved through the tion and low power consumption are achieved through the Poisson noise in transistors to represent biological fluc- digital bits to enable our chips to communicate with each digital bits to enable our chips to communicate with each The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- establishing quantitative agreement of the cytomorphic chip use of bipolar and subthreshold MOS transistors that func- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- other via digital input/output (I/O), and with off-chip dig- portant categories: tuations in mRNA and protein concentrations at very portant categories: tuations in mRNA and protein concentrations at very 1) Basic BiCMOS current-mode analog circuits exploit the tion at low current levels. tion at low current levels. low copy numbers and at relatively high noise levels. ital processors and computers. ital processors and computers. measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. 2) The ability to model cooperative binding is enabled by tun- 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our Off-chip digital processors synergistically interact with our log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- able Hill-function building-block circuits. namics of fundamental mass-action molecular kinetics able Hill-function building-block circuits. chips to carry out various functions: reading digital data from tomatically maps biological noise to electronic noise at chips to carry out various functions: reading digital data from The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at 3) An “ITD” block built by a composition of above cur- such as association, dissociation, and degradation. These 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital high copy numbers and relatively low noise levels [13]. the chips; decoding the data; performing high-speed digital such as association, dissociation, and degradation. These high copy numbers and relatively low noise levels [13]. portant categories: rent-mode circuits enables mapping of the exact differen- tuations in mRNA and protein concentrations at very rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time signal processing as necessary (e.g., scaling, diffusion, time fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling tial equations of inducer-transcription-factor binding effects such as loading, fan-out, feedback, and substrate de- tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or highly stochastic and relatively low signal-to-noise-ratios delay, and error correction); encoding the data to create or effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. and transcription-factor-DNA binding including for- pletion through the use of a few explicit connections and and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; in biological cells. modify molecular data packets via address and data strings; pletion through the use of a few explicit connections and in biological cells. ward and reverse reactions, degradation, protection from ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene storing the programmable address connectivity amongst gene Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- degradation of transcription factors bound to DNA, and tion and low power consumption are achieved through the degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips digital bits to enable our chips to communicate with each and protein circuits; and communicating data to other chips tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each the change in DNA binding affinity of transcription factors the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were or to a computer. For simplicity, the data in this paper were use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at when bound by an inducer. tion at low current levels. when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that ital processors and computers. collected with a data-acquisition board (NI PXI-6541) that tion at low current levels. ital processors and computers. 4) An “analogic” current-mode circuit determines the tran- 2) The ability to model cooperative binding is enabled by tun- 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A Off-chip digital processors synergistically interact with our interacted with our chip and with MATLAB on a computer. A such as association, dissociation, and degradation. These high copy numbers and relatively low noise levels [13]. 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our scription rate of genes based on the probability of mul- scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) high-performance FPGA (e.g., from the Xilinx Spartan family) able Hill-function building-block circuits. chips to carry out various functions: reading digital data from able Hill-function building-block circuits. chips to carry out various functions: reading digital data from fundamental circuits are general enough to capture subtle 3) An “ITD” block built by a composition of above cur- tiple transcription-factor DNA binding sites being occu- Thus, these circuits are most useful for reliably modeling tiple transcription-factor DNA binding sites being occu- the chips; decoding the data; performing high-speed digital could perform all of these functions in the future as well. Shift could perform all of these functions in the future as well. Shift 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital INTRODUCTION pied or unoccupied in a combinatorial fashion with the rel- rent-mode circuits enables mapping of the exact differen- pied or unoccupied in a combinatorial fashion with the rel- signal processing as necessary (e.g., scaling, diffusion, time registers, SRAM blocks, and switches on the chip enable registers, SRAM blocks, and switches on the chip enable rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time effects such as loading, fan-out, feedback, and substrate de- ative mRNA production rate of each such combinatorial highly stochastic and relatively low signal-to-noise-ratios ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- programmability of parameters (e.g., reaction rates, dissocia- tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or state programmable by the user. This strategy enables us and transcription-factor-DNA binding including for- state programmable by the user. This strategy enables us modify molecular data packets via address and data strings; tion constants, Hill coefficients, and time constants) as well as tion constants, Hill coefficients, and time constants) as well as and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; pletion through the use of a few explicit connections and in biological cells. to implement any arbitrary “analogic promoter function” to implement any arbitrary “analogic promoter function” connectivity. connectivity. ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene that is capable of complex saturating digital logic or prob- degradation of transcription factors bound to DNA, and that is capable of complex saturating digital logic or prob- and protein circuits; and communicating data to other chips The organization of this paper is as follows: Section II de- The organization of this paper is as follows: Section II de- degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and abilistic analog behavior depending on the molecular con- the change in DNA binding affinity of transcription factors abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with or to a computer. For simplicity, the data in this paper were scribes the core building-block circuits of the chip along with the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were centration. centration. chip measurement data. Fig. 2 shows a die micrograph of the chip measurement data. Fig. 2 shows a die micrograph of the when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each 5) A current-mode low pass filter (LPF) circuit enables the 4) An “analogic” current-mode circuit determines the tran- 5) A current-mode low pass filter (LPF) circuit enables the interacted with our chip and with MATLAB on a computer. A chip that reveals the various building blocks. Section III dis- chip that reveals the various building blocks. Section III dis- 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A gain and dynamics of mRNA and protein production scription rate of genes based on the probability of mul- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- high-performance FPGA (e.g., from the Xilinx Spartan family) cusses design considerations that are important in BiCMOS cy- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) and degradation to be represented. and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic tomorphic chip design. Section IV discusses how cytomorphic tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift tion at low current levels. pied or unoccupied in a combinatorial fashion with the rel- ital processors and computers. registers, SRAM blocks, and switches on the chip enable pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as to implement any arbitrary “analogic promoter function” connectivity. to implement any arbitrary “analogic promoter function” connectivity. able Hill-function building-block circuits. chips to carry out various functions: reading digital data from that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital centration. chip measurement data. Fig. 2 shows a die micrograph of the centration. chip measurement data. Fig. 2 shows a die micrograph of the 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as to implement any arbitrary “analogic promoter function” connectivity. that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with centration. chip measurement data. Fig. 2 shows a die micrograph of the 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic
� 11 PROGRAMMING CHALLENGES FOR ANALOG DEVICES ‣ physical behavior ‣ voltage/current operating ranges 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 ‣ circuit noise [thermal/shot/flicker] 528 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 ‣ complex building blocks ‣ non-linear, non-convex 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 Fig. 1. Poisson chemical reaction flux and Poisson electron flow in Fig. 1. Poisson chemical reaction flux and Poisson electron flow in sub-threshold transistors obey the same Boltzmann exponential laws of sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy thermodynamics, and are therefore mathematically similar [13]. Electron copy number is analogous to molecular copy number and temperature represents number is analogous to molecular copy number and temperature represents Fig. 1. Poisson chemical reaction flux and Poisson electron flow in itself. itself. sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy single cell on a few chips and speedup multi-cell simulations single cell on a few chips and speedup multi-cell simulations number is analogous to molecular copy number and temperature represents ‣ space limitations on multi-chip electronic boards [13]. Therefore, we were moti- on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could vated to create a few fundamental molecular circuits that could itself. be composed and scaled to model large biochemical reaction be composed and scaled to model large biochemical reaction Fig. 2. Die micrograph of the Fig. 2. Die micrograph of the cytomorphic chip fabricated cytomorphic chip fabricated in an AMS BiCMOS process. The left inset is a layout screen capture in an AMS BiCMOS process. The left inset is a layout screen capture networks in the future. This paper describes these fundamental Fig. 1. Poisson chemical reaction flux and Poisson electron flow in networks in the future. This paper describes these fundamental Fig. 1. Poisson chemical reaction flux and Poisson electron flow in of one gene block (2x magnification). of one gene block (2x magnification). sub-threshold transistors obey the same Boltzmann exponential laws of building-block cytomorphic circuits. The paper focuses on building-block cytomorphic circuits. The paper focuses on sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy thermodynamics, and are therefore mathematically similar [13]. Electron copy establishing quantitative agreement of the cytomorphic chip establishing quantitative agreement of the cytomorphic chip number is analogous to molecular copy number and temperature represents number is analogous to molecular copy number and temperature represents measurements with prior biological measurements and models. itself. measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog 6) A stochastics circuit intentionally amplifies analog itself. single cell on a few chips and speedup multi-cell simulations The building-block circuits may be classified into seven im- The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- Poisson noise in transistors to represent biological fluc- ‣ limitations on number of portant categories: portant categories: tuations in mRNA and protein concentrations at very tuations in mRNA and protein concentrations at very on multi-chip electronic boards [13]. Therefore, we were moti- single cell on a few chips and speedup multi-cell simulations 1) Basic BiCMOS current-mode analog circuits exploit the 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. low copy numbers and at relatively high noise levels. single cell on a few chips and speedup multi-cell simulations log-domain cytomorphic mapping to capture the exact dy- log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- The Poisson nature of biochemical reaction fluxes au- on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could namics of fundamental mass-action molecular kinetics namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at tomatically maps biological noise to electronic noise at vated to create a few fundamental molecular circuits that could be composed and scaled to model large biochemical reaction such as association, dissociation, and degradation. These Fig. 2. Die micrograph of the such as association, dissociation, and degradation. These Fig. 2. Die micrograph of the high copy numbers and relatively low noise levels [13]. cytomorphic chip fabricated high copy numbers and relatively low noise levels [13]. cytomorphic chip fabricated be composed and scaled to model large biochemical reaction be composed and scaled to model large biochemical reaction Fig. 2. Die micrograph of the cytomorphic chip fabricated available blocks and connections in an AMS BiCMOS process. The left inset is a layout screen capture networks in the future. This paper describes these fundamental fundamental circuits are general enough to capture subtle fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling in an AMS Thus, these circuits are most useful for reliably modeling BiCMOS process. The left inset is a layout screen capture in an AMS networks in the future. This paper describes these fundamental BiCMOS process. The left inset is a layout screen capture of one gene block (2x magnification). networks in the future. This paper describes these fundamental of one gene block (2x magnification). building-block cytomorphic circuits. The paper focuses on effects such as loading, fan-out, feedback, and substrate de- effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios highly stochastic and relatively low signal-to-noise-ratios building-block cytomorphic circuits. The paper focuses on of one gene block (2x magnification). pletion through the use of a few explicit connections and pletion through the use of a few explicit connections and in biological cells. in biological cells. establishing quantitative agreement of the cytomorphic chip establishing quantitative agreement of the cytomorphic chip building-block cytomorphic circuits. The paper focuses on measurements with prior biological measurements and models. Kirchhoff’s current law. A wide dynamic range of opera- Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and 6) A stochastics circuit intentionally amplifies analog 7) ADCs and DACs convert between analog currents and measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog The building-block circuits may be classified into seven im- tion and low power consumption are achieved through the tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each Poisson noise in transistors to represent biological fluc- digital bits to enable our chips to communicate with each The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- establishing quantitative agreement of the cytomorphic chip use of bipolar and subthreshold MOS transistors that func- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- other via digital input/output (I/O), and with off-chip dig- portant categories: tuations in mRNA and protein concentrations at very portant categories: tuations in mRNA and protein concentrations at very 1) Basic BiCMOS current-mode analog circuits exploit the tion at low current levels. tion at low current levels. ital processors and computers. low copy numbers and at relatively high noise levels. ital processors and computers. measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. 2) The ability to model cooperative binding is enabled by tun- 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our Off-chip digital processors synergistically interact with our log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- ‣ requires creativity when log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- able Hill-function building-block circuits. namics of fundamental mass-action molecular kinetics able Hill-function building-block circuits. chips to carry out various functions: reading digital data from tomatically maps biological noise to electronic noise at chips to carry out various functions: reading digital data from The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at 3) An “ITD” block built by a composition of above cur- such as association, dissociation, and degradation. These 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital high copy numbers and relatively low noise levels [13]. the chips; decoding the data; performing high-speed digital such as association, dissociation, and degradation. These high copy numbers and relatively low noise levels [13]. portant categories: rent-mode circuits enables mapping of the exact differen- tuations in mRNA and protein concentrations at very rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time signal processing as necessary (e.g., scaling, diffusion, time fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling tial equations of inducer-transcription-factor binding effects such as loading, fan-out, feedback, and substrate de- tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or highly stochastic and relatively low signal-to-noise-ratios delay, and error correction); encoding the data to create or effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. and transcription-factor-DNA binding including for- pletion through the use of a few explicit connections and and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; in biological cells. modify molecular data packets via address and data strings; configuring device pletion through the use of a few explicit connections and in biological cells. ward and reverse reactions, degradation, protection from ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene storing the programmable address connectivity amongst gene Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- degradation of transcription factors bound to DNA, and tion and low power consumption are achieved through the degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips digital bits to enable our chips to communicate with each and protein circuits; and communicating data to other chips tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each the change in DNA binding affinity of transcription factors the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were or to a computer. For simplicity, the data in this paper were use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at when bound by an inducer. tion at low current levels. when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that ital processors and computers. collected with a data-acquisition board (NI PXI-6541) that tion at low current levels. ital processors and computers. 4) An “analogic” current-mode circuit determines the tran- 2) The ability to model cooperative binding is enabled by tun- 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A Off-chip digital processors synergistically interact with our interacted with our chip and with MATLAB on a computer. A such as association, dissociation, and degradation. These high copy numbers and relatively low noise levels [13]. 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our scription rate of genes based on the probability of mul- scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) high-performance FPGA (e.g., from the Xilinx Spartan family) able Hill-function building-block circuits. chips to carry out various functions: reading digital data from able Hill-function building-block circuits. chips to carry out various functions: reading digital data from fundamental circuits are general enough to capture subtle 3) An “ITD” block built by a composition of above cur- tiple transcription-factor DNA binding sites being occu- Thus, these circuits are most useful for reliably modeling tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift the chips; decoding the data; performing high-speed digital could perform all of these functions in the future as well. Shift 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital INTRODUCTION pied or unoccupied in a combinatorial fashion with the rel- rent-mode circuits enables mapping of the exact differen- pied or unoccupied in a combinatorial fashion with the rel- signal processing as necessary (e.g., scaling, diffusion, time registers, SRAM blocks, and switches on the chip enable registers, SRAM blocks, and switches on the chip enable rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time effects such as loading, fan-out, feedback, and substrate de- ative mRNA production rate of each such combinatorial highly stochastic and relatively low signal-to-noise-ratios ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- programmability of parameters (e.g., reaction rates, dissocia- tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or state programmable by the user. This strategy enables us and transcription-factor-DNA binding including for- state programmable by the user. This strategy enables us modify molecular data packets via address and data strings; tion constants, Hill coefficients, and time constants) as well as tion constants, Hill coefficients, and time constants) as well as and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; pletion through the use of a few explicit connections and in biological cells. to implement any arbitrary “analogic promoter function” to implement any arbitrary “analogic promoter function” connectivity. connectivity. ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene that is capable of complex saturating digital logic or prob- degradation of transcription factors bound to DNA, and that is capable of complex saturating digital logic or prob- and protein circuits; and communicating data to other chips The organization of this paper is as follows: Section II de- The organization of this paper is as follows: Section II de- degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and abilistic analog behavior depending on the molecular con- the change in DNA binding affinity of transcription factors abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with or to a computer. For simplicity, the data in this paper were scribes the core building-block circuits of the chip along with the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were centration. centration. chip measurement data. Fig. 2 shows a die micrograph of the chip measurement data. Fig. 2 shows a die micrograph of the when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each 5) A current-mode low pass filter (LPF) circuit enables the 4) An “analogic” current-mode circuit determines the tran- 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- interacted with our chip and with MATLAB on a computer. A chip that reveals the various building blocks. Section III dis- 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A gain and dynamics of mRNA and protein production scription rate of genes based on the probability of mul- gain and dynamics of mRNA and protein production high-performance FPGA (e.g., from the Xilinx Spartan family) cusses design considerations that are important in BiCMOS cy- cusses design considerations that are important in BiCMOS cy- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) and degradation to be represented. and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic tomorphic chip design. Section IV discusses how cytomorphic tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift tion at low current levels. pied or unoccupied in a combinatorial fashion with the rel- ital processors and computers. registers, SRAM blocks, and switches on the chip enable pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as to implement any arbitrary “analogic promoter function” connectivity. to implement any arbitrary “analogic promoter function” connectivity. able Hill-function building-block circuits. chips to carry out various functions: reading digital data from that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital centration. chip measurement data. Fig. 2 shows a die micrograph of the centration. chip measurement data. Fig. 2 shows a die micrograph of the 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as to implement any arbitrary “analogic promoter function” connectivity. that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with centration. chip measurement data. Fig. 2 shows a die micrograph of the 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic
� 12 A COMPILER FOR PROGRAMMABLE ANALOG DEVICES 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 x ′ � ′ � + c 1 x ′ � + c 2 x ′ � ′ � = 0 528 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 L ⋅ I ′ � ′ � + R ⋅ I ′ � + C − 1 ⋅ I = 0 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 Fig. 1. Poisson chemical reaction flux and Poisson electron flow in Fig. 1. Poisson chemical reaction flux and Poisson electron flow in sub-threshold transistors obey the same Boltzmann exponential laws of sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy thermodynamics, and are therefore mathematically similar [13]. Electron copy number is analogous to molecular copy number and temperature represents number is analogous to molecular copy number and temperature represents · Fig. 1. Poisson chemical reaction flux and Poisson electron flow in itself. itself. sub-threshold transistors obey the same Boltzmann exponential laws of ES = k f ⋅ E ⋅ S − k r ⋅ ES thermodynamics, and are therefore mathematically similar [13]. Electron copy single cell on a few chips and speedup multi-cell simulations single cell on a few chips and speedup multi-cell simulations number is analogous to molecular copy number and temperature represents on multi-chip electronic boards [13]. Therefore, we were moti- on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could vated to create a few fundamental molecular circuits that could itself. be composed and scaled to model large biochemical reaction be composed and scaled to model large biochemical reaction Fig. 2. Die micrograph of the Fig. 2. Die micrograph of the cytomorphic chip fabricated cytomorphic chip fabricated in an AMS BiCMOS process. The left inset is a layout screen capture in an AMS BiCMOS process. The left inset is a layout screen capture networks in the future. This paper describes these fundamental Fig. 1. Poisson chemical reaction flux and Poisson electron flow in networks in the future. This paper describes these fundamental Fig. 1. Poisson chemical reaction flux and Poisson electron flow in of one gene block (2x magnification). of one gene block (2x magnification). sub-threshold transistors obey the same Boltzmann exponential laws of building-block cytomorphic circuits. The paper focuses on building-block cytomorphic circuits. The paper focuses on sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy thermodynamics, and are therefore mathematically similar [13]. Electron copy establishing quantitative agreement of the cytomorphic chip establishing quantitative agreement of the cytomorphic chip number is analogous to molecular copy number and temperature represents number is analogous to molecular copy number and temperature represents measurements with prior biological measurements and models. itself. measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog 6) A stochastics circuit intentionally amplifies analog itself. single cell on a few chips and speedup multi-cell simulations x ′ � ′ � + ax ′ � + x + ax 2 = c 3 The building-block circuits may be classified into seven im- The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- Poisson noise in transistors to represent biological fluc- portant categories: portant categories: tuations in mRNA and protein concentrations at very tuations in mRNA and protein concentrations at very on multi-chip electronic boards [13]. Therefore, we were moti- single cell on a few chips and speedup multi-cell simulations 1) Basic BiCMOS current-mode analog circuits exploit the 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. low copy numbers and at relatively high noise levels. single cell on a few chips and speedup multi-cell simulations log-domain cytomorphic mapping to capture the exact dy- log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- The Poisson nature of biochemical reaction fluxes au- on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could namics of fundamental mass-action molecular kinetics namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at tomatically maps biological noise to electronic noise at vated to create a few fundamental molecular circuits that could be composed and scaled to model large biochemical reaction such as association, dissociation, and degradation. These Fig. 2. Die micrograph of the such as association, dissociation, and degradation. These Fig. 2. Die micrograph of the high copy numbers and relatively low noise levels [13]. cytomorphic chip fabricated high copy numbers and relatively low noise levels [13]. cytomorphic chip fabricated be composed and scaled to model large biochemical reaction be composed and scaled to model large biochemical reaction Fig. 2. Die micrograph of the cytomorphic chip fabricated Programmable in an AMS BiCMOS process. The left inset is a layout screen capture networks in the future. This paper describes these fundamental fundamental circuits are general enough to capture subtle fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling in an AMS Thus, these circuits are most useful for reliably modeling BiCMOS process. The left inset is a layout screen capture in an AMS networks in the future. This paper describes these fundamental BiCMOS process. The left inset is a layout screen capture of one gene block (2x magnification). networks in the future. This paper describes these fundamental of one gene block (2x magnification). building-block cytomorphic circuits. The paper focuses on effects such as loading, fan-out, feedback, and substrate de- effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios highly stochastic and relatively low signal-to-noise-ratios building-block cytomorphic circuits. The paper focuses on of one gene block (2x magnification). pletion through the use of a few explicit connections and pletion through the use of a few explicit connections and in biological cells. in biological cells. establishing quantitative agreement of the cytomorphic chip establishing quantitative agreement of the cytomorphic chip building-block cytomorphic circuits. The paper focuses on measurements with prior biological measurements and models. Kirchhoff’s current law. A wide dynamic range of opera- Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and 6) A stochastics circuit intentionally amplifies analog 7) ADCs and DACs convert between analog currents and Dynamical Systems measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog The building-block circuits may be classified into seven im- tion and low power consumption are achieved through the tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each Poisson noise in transistors to represent biological fluc- digital bits to enable our chips to communicate with each The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- establishing quantitative agreement of the cytomorphic chip Analog Devices use of bipolar and subthreshold MOS transistors that func- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- other via digital input/output (I/O), and with off-chip dig- portant categories: tuations in mRNA and protein concentrations at very portant categories: tuations in mRNA and protein concentrations at very 1) Basic BiCMOS current-mode analog circuits exploit the tion at low current levels. tion at low current levels. low copy numbers and at relatively high noise levels. ital processors and computers. ital processors and computers. measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. 2) The ability to model cooperative binding is enabled by tun- 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our Off-chip digital processors synergistically interact with our log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- able Hill-function building-block circuits. namics of fundamental mass-action molecular kinetics able Hill-function building-block circuits. chips to carry out various functions: reading digital data from tomatically maps biological noise to electronic noise at chips to carry out various functions: reading digital data from The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at 3) An “ITD” block built by a composition of above cur- such as association, dissociation, and degradation. These 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital high copy numbers and relatively low noise levels [13]. the chips; decoding the data; performing high-speed digital such as association, dissociation, and degradation. These high copy numbers and relatively low noise levels [13]. portant categories: rent-mode circuits enables mapping of the exact differen- tuations in mRNA and protein concentrations at very rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time signal processing as necessary (e.g., scaling, diffusion, time fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling tial equations of inducer-transcription-factor binding effects such as loading, fan-out, feedback, and substrate de- tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or highly stochastic and relatively low signal-to-noise-ratios delay, and error correction); encoding the data to create or effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. and transcription-factor-DNA binding including for- pletion through the use of a few explicit connections and and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; in biological cells. modify molecular data packets via address and data strings; pletion through the use of a few explicit connections and in biological cells. ward and reverse reactions, degradation, protection from ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene storing the programmable address connectivity amongst gene Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- degradation of transcription factors bound to DNA, and tion and low power consumption are achieved through the degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips digital bits to enable our chips to communicate with each and protein circuits; and communicating data to other chips tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each the change in DNA binding affinity of transcription factors the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were or to a computer. For simplicity, the data in this paper were use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at when bound by an inducer. tion at low current levels. when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that ital processors and computers. collected with a data-acquisition board (NI PXI-6541) that tion at low current levels. ital processors and computers. 4) An “analogic” current-mode circuit determines the tran- 2) The ability to model cooperative binding is enabled by tun- 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A Off-chip digital processors synergistically interact with our interacted with our chip and with MATLAB on a computer. A such as association, dissociation, and degradation. These high copy numbers and relatively low noise levels [13]. 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our scription rate of genes based on the probability of mul- scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) high-performance FPGA (e.g., from the Xilinx Spartan family) able Hill-function building-block circuits. chips to carry out various functions: reading digital data from able Hill-function building-block circuits. chips to carry out various functions: reading digital data from fundamental circuits are general enough to capture subtle 3) An “ITD” block built by a composition of above cur- tiple transcription-factor DNA binding sites being occu- Thus, these circuits are most useful for reliably modeling tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift the chips; decoding the data; performing high-speed digital could perform all of these functions in the future as well. Shift 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital INTRODUCTION pied or unoccupied in a combinatorial fashion with the rel- rent-mode circuits enables mapping of the exact differen- pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable signal processing as necessary (e.g., scaling, diffusion, time registers, SRAM blocks, and switches on the chip enable rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time effects such as loading, fan-out, feedback, and substrate de- ative mRNA production rate of each such combinatorial highly stochastic and relatively low signal-to-noise-ratios ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- programmability of parameters (e.g., reaction rates, dissocia- tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or state programmable by the user. This strategy enables us and transcription-factor-DNA binding including for- state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as modify molecular data packets via address and data strings; tion constants, Hill coefficients, and time constants) as well as and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; pletion through the use of a few explicit connections and in biological cells. to implement any arbitrary “analogic promoter function” to implement any arbitrary “analogic promoter function” connectivity. connectivity. ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene that is capable of complex saturating digital logic or prob- degradation of transcription factors bound to DNA, and that is capable of complex saturating digital logic or prob- and protein circuits; and communicating data to other chips The organization of this paper is as follows: Section II de- The organization of this paper is as follows: Section II de- degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and abilistic analog behavior depending on the molecular con- the change in DNA binding affinity of transcription factors abilistic analog behavior depending on the molecular con- or to a computer. For simplicity, the data in this paper were scribes the core building-block circuits of the chip along with scribes the core building-block circuits of the chip along with the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were centration. centration. chip measurement data. Fig. 2 shows a die micrograph of the chip measurement data. Fig. 2 shows a die micrograph of the when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each 5) A current-mode low pass filter (LPF) circuit enables the 4) An “analogic” current-mode circuit determines the tran- 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- interacted with our chip and with MATLAB on a computer. A chip that reveals the various building blocks. Section III dis- 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A gain and dynamics of mRNA and protein production scription rate of genes based on the probability of mul- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- high-performance FPGA (e.g., from the Xilinx Spartan family) cusses design considerations that are important in BiCMOS cy- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) and degradation to be represented. and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic tomorphic chip design. Section IV discusses how cytomorphic tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift tion at low current levels. pied or unoccupied in a combinatorial fashion with the rel- ital processors and computers. registers, SRAM blocks, and switches on the chip enable pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as to implement any arbitrary “analogic promoter function” connectivity. to implement any arbitrary “analogic promoter function” connectivity. able Hill-function building-block circuits. chips to carry out various functions: reading digital data from that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital centration. chip measurement data. Fig. 2 shows a die micrograph of the centration. chip measurement data. Fig. 2 shows a die micrograph of the 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as to implement any arbitrary “analogic promoter function” connectivity. that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with centration. chip measurement data. Fig. 2 shows a die micrograph of the 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic
� 13 automatically compose complex algebraic building blocks automatically reason about operating ranges + circuit noise 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 x ′ � ′ � + c 1 x ′ � + c 2 x ′ � ′ � = 0 528 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 L ⋅ I ′ � ′ � + R ⋅ I ′ � + C − 1 ⋅ I = 0 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 Fig. 1. Poisson chemical reaction flux and Poisson electron flow in Fig. 1. Poisson chemical reaction flux and Poisson electron flow in sub-threshold transistors obey the same Boltzmann exponential laws of sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy thermodynamics, and are therefore mathematically similar [13]. Electron copy number is analogous to molecular copy number and temperature represents number is analogous to molecular copy number and temperature represents · Fig. 1. Poisson chemical reaction flux and Poisson electron flow in itself. itself. sub-threshold transistors obey the same Boltzmann exponential laws of ES = k f ⋅ E ⋅ S − k r ⋅ ES thermodynamics, and are therefore mathematically similar [13]. Electron copy single cell on a few chips and speedup multi-cell simulations single cell on a few chips and speedup multi-cell simulations number is analogous to molecular copy number and temperature represents on multi-chip electronic boards [13]. Therefore, we were moti- on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could vated to create a few fundamental molecular circuits that could itself. be composed and scaled to model large biochemical reaction be composed and scaled to model large biochemical reaction Fig. 2. Die micrograph of the Fig. 2. Die micrograph of the cytomorphic chip fabricated cytomorphic chip fabricated in an AMS BiCMOS process. The left inset is a layout screen capture in an AMS BiCMOS process. The left inset is a layout screen capture networks in the future. This paper describes these fundamental Fig. 1. Poisson chemical reaction flux and Poisson electron flow in networks in the future. This paper describes these fundamental Fig. 1. Poisson chemical reaction flux and Poisson electron flow in of one gene block (2x magnification). of one gene block (2x magnification). sub-threshold transistors obey the same Boltzmann exponential laws of building-block cytomorphic circuits. The paper focuses on building-block cytomorphic circuits. The paper focuses on sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy thermodynamics, and are therefore mathematically similar [13]. Electron copy establishing quantitative agreement of the cytomorphic chip establishing quantitative agreement of the cytomorphic chip number is analogous to molecular copy number and temperature represents number is analogous to molecular copy number and temperature represents measurements with prior biological measurements and models. itself. measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog 6) A stochastics circuit intentionally amplifies analog itself. single cell on a few chips and speedup multi-cell simulations x ′ � ′ � + ax ′ � + x + ax 2 = c 3 The building-block circuits may be classified into seven im- The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- Poisson noise in transistors to represent biological fluc- portant categories: portant categories: tuations in mRNA and protein concentrations at very tuations in mRNA and protein concentrations at very on multi-chip electronic boards [13]. Therefore, we were moti- single cell on a few chips and speedup multi-cell simulations 1) Basic BiCMOS current-mode analog circuits exploit the 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. low copy numbers and at relatively high noise levels. single cell on a few chips and speedup multi-cell simulations log-domain cytomorphic mapping to capture the exact dy- log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- The Poisson nature of biochemical reaction fluxes au- on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could namics of fundamental mass-action molecular kinetics namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at tomatically maps biological noise to electronic noise at vated to create a few fundamental molecular circuits that could be composed and scaled to model large biochemical reaction such as association, dissociation, and degradation. These Fig. 2. Die micrograph of the such as association, dissociation, and degradation. These Fig. 2. Die micrograph of the high copy numbers and relatively low noise levels [13]. cytomorphic chip fabricated high copy numbers and relatively low noise levels [13]. cytomorphic chip fabricated be composed and scaled to model large biochemical reaction be composed and scaled to model large biochemical reaction Fig. 2. Die micrograph of the cytomorphic chip fabricated Programmable in an AMS BiCMOS process. The left inset is a layout screen capture networks in the future. This paper describes these fundamental fundamental circuits are general enough to capture subtle fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling in an AMS Thus, these circuits are most useful for reliably modeling BiCMOS process. The left inset is a layout screen capture in an AMS networks in the future. This paper describes these fundamental BiCMOS process. The left inset is a layout screen capture of one gene block (2x magnification). networks in the future. This paper describes these fundamental of one gene block (2x magnification). building-block cytomorphic circuits. The paper focuses on effects such as loading, fan-out, feedback, and substrate de- effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios highly stochastic and relatively low signal-to-noise-ratios building-block cytomorphic circuits. The paper focuses on of one gene block (2x magnification). pletion through the use of a few explicit connections and pletion through the use of a few explicit connections and in biological cells. in biological cells. establishing quantitative agreement of the cytomorphic chip establishing quantitative agreement of the cytomorphic chip building-block cytomorphic circuits. The paper focuses on measurements with prior biological measurements and models. Kirchhoff’s current law. A wide dynamic range of opera- Kirchhoff’s current law. A wide dynamic range of opera- 6) A stochastics circuit intentionally amplifies analog 7) ADCs and DACs convert between analog currents and 7) ADCs and DACs convert between analog currents and Dynamical Systems measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog The building-block circuits may be classified into seven im- tion and low power consumption are achieved through the tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each Poisson noise in transistors to represent biological fluc- digital bits to enable our chips to communicate with each The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- establishing quantitative agreement of the cytomorphic chip Analog Devices use of bipolar and subthreshold MOS transistors that func- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- other via digital input/output (I/O), and with off-chip dig- portant categories: tuations in mRNA and protein concentrations at very portant categories: tuations in mRNA and protein concentrations at very 1) Basic BiCMOS current-mode analog circuits exploit the tion at low current levels. tion at low current levels. ital processors and computers. low copy numbers and at relatively high noise levels. ital processors and computers. measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. 2) The ability to model cooperative binding is enabled by tun- 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our Off-chip digital processors synergistically interact with our log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- able Hill-function building-block circuits. namics of fundamental mass-action molecular kinetics able Hill-function building-block circuits. chips to carry out various functions: reading digital data from tomatically maps biological noise to electronic noise at chips to carry out various functions: reading digital data from The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at 3) An “ITD” block built by a composition of above cur- such as association, dissociation, and degradation. These 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital high copy numbers and relatively low noise levels [13]. the chips; decoding the data; performing high-speed digital such as association, dissociation, and degradation. These high copy numbers and relatively low noise levels [13]. portant categories: rent-mode circuits enables mapping of the exact differen- tuations in mRNA and protein concentrations at very rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time signal processing as necessary (e.g., scaling, diffusion, time fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling tial equations of inducer-transcription-factor binding effects such as loading, fan-out, feedback, and substrate de- tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or highly stochastic and relatively low signal-to-noise-ratios delay, and error correction); encoding the data to create or effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. and transcription-factor-DNA binding including for- pletion through the use of a few explicit connections and and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; in biological cells. modify molecular data packets via address and data strings; pletion through the use of a few explicit connections and in biological cells. ward and reverse reactions, degradation, protection from ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene storing the programmable address connectivity amongst gene Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- degradation of transcription factors bound to DNA, and tion and low power consumption are achieved through the degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips digital bits to enable our chips to communicate with each and protein circuits; and communicating data to other chips tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each the change in DNA binding affinity of transcription factors the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were or to a computer. For simplicity, the data in this paper were use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at when bound by an inducer. tion at low current levels. when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that ital processors and computers. collected with a data-acquisition board (NI PXI-6541) that tion at low current levels. ital processors and computers. 4) An “analogic” current-mode circuit determines the tran- 2) The ability to model cooperative binding is enabled by tun- 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A Off-chip digital processors synergistically interact with our interacted with our chip and with MATLAB on a computer. A such as association, dissociation, and degradation. These high copy numbers and relatively low noise levels [13]. 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our scription rate of genes based on the probability of mul- scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) high-performance FPGA (e.g., from the Xilinx Spartan family) able Hill-function building-block circuits. chips to carry out various functions: reading digital data from able Hill-function building-block circuits. chips to carry out various functions: reading digital data from fundamental circuits are general enough to capture subtle 3) An “ITD” block built by a composition of above cur- tiple transcription-factor DNA binding sites being occu- Thus, these circuits are most useful for reliably modeling tiple transcription-factor DNA binding sites being occu- the chips; decoding the data; performing high-speed digital could perform all of these functions in the future as well. Shift could perform all of these functions in the future as well. Shift 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital INTRODUCTION pied or unoccupied in a combinatorial fashion with the rel- rent-mode circuits enables mapping of the exact differen- pied or unoccupied in a combinatorial fashion with the rel- signal processing as necessary (e.g., scaling, diffusion, time registers, SRAM blocks, and switches on the chip enable registers, SRAM blocks, and switches on the chip enable rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time effects such as loading, fan-out, feedback, and substrate de- ative mRNA production rate of each such combinatorial highly stochastic and relatively low signal-to-noise-ratios ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- programmability of parameters (e.g., reaction rates, dissocia- tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or state programmable by the user. This strategy enables us and transcription-factor-DNA binding including for- state programmable by the user. This strategy enables us modify molecular data packets via address and data strings; tion constants, Hill coefficients, and time constants) as well as tion constants, Hill coefficients, and time constants) as well as and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; pletion through the use of a few explicit connections and in biological cells. to implement any arbitrary “analogic promoter function” to implement any arbitrary “analogic promoter function” connectivity. connectivity. ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene that is capable of complex saturating digital logic or prob- degradation of transcription factors bound to DNA, and that is capable of complex saturating digital logic or prob- and protein circuits; and communicating data to other chips The organization of this paper is as follows: Section II de- The organization of this paper is as follows: Section II de- degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and abilistic analog behavior depending on the molecular con- the change in DNA binding affinity of transcription factors abilistic analog behavior depending on the molecular con- or to a computer. For simplicity, the data in this paper were scribes the core building-block circuits of the chip along with scribes the core building-block circuits of the chip along with the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were centration. centration. chip measurement data. Fig. 2 shows a die micrograph of the chip measurement data. Fig. 2 shows a die micrograph of the when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each 5) A current-mode low pass filter (LPF) circuit enables the 4) An “analogic” current-mode circuit determines the tran- 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- interacted with our chip and with MATLAB on a computer. A chip that reveals the various building blocks. Section III dis- 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A gain and dynamics of mRNA and protein production scription rate of genes based on the probability of mul- gain and dynamics of mRNA and protein production high-performance FPGA (e.g., from the Xilinx Spartan family) cusses design considerations that are important in BiCMOS cy- cusses design considerations that are important in BiCMOS cy- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) and degradation to be represented. and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic tomorphic chip design. Section IV discusses how cytomorphic tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift tion at low current levels. pied or unoccupied in a combinatorial fashion with the rel- ital processors and computers. registers, SRAM blocks, and switches on the chip enable pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as to implement any arbitrary “analogic promoter function” connectivity. to implement any arbitrary “analogic promoter function” connectivity. able Hill-function building-block circuits. chips to carry out various functions: reading digital data from that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital centration. chip measurement data. Fig. 2 shows a die micrograph of the centration. chip measurement data. Fig. 2 shows a die micrograph of the 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as to implement any arbitrary “analogic promoter function” connectivity. that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with centration. chip measurement data. Fig. 2 shows a die micrograph of the 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic
� 14 automatically compose complex algebraic building blocks automatically reason about operating ranges + circuit noise 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 x ′ � ′ � + c 1 x ′ � + c 2 x ′ � ′ � = 0 528 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 L ⋅ I ′ � ′ � + R ⋅ I ′ � + C − 1 ⋅ I = 0 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 Fig. 1. Poisson chemical reaction flux and Poisson electron flow in Fig. 1. Poisson chemical reaction flux and Poisson electron flow in sub-threshold transistors obey the same Boltzmann exponential laws of sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy thermodynamics, and are therefore mathematically similar [13]. Electron copy number is analogous to molecular copy number and temperature represents number is analogous to molecular copy number and temperature represents · Fig. 1. Poisson chemical reaction flux and Poisson electron flow in itself. itself. sub-threshold transistors obey the same Boltzmann exponential laws of ES = k f ⋅ E ⋅ S − k r ⋅ ES thermodynamics, and are therefore mathematically similar [13]. Electron copy single cell on a few chips and speedup multi-cell simulations single cell on a few chips and speedup multi-cell simulations number is analogous to molecular copy number and temperature represents on multi-chip electronic boards [13]. Therefore, we were moti- on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could vated to create a few fundamental molecular circuits that could itself. be composed and scaled to model large biochemical reaction be composed and scaled to model large biochemical reaction Fig. 2. Die micrograph of the Fig. 2. Die micrograph of the cytomorphic chip fabricated cytomorphic chip fabricated in an AMS BiCMOS process. The left inset is a layout screen capture in an AMS BiCMOS process. The left inset is a layout screen capture networks in the future. This paper describes these fundamental Fig. 1. Poisson chemical reaction flux and Poisson electron flow in networks in the future. This paper describes these fundamental Fig. 1. Poisson chemical reaction flux and Poisson electron flow in of one gene block (2x magnification). of one gene block (2x magnification). sub-threshold transistors obey the same Boltzmann exponential laws of building-block cytomorphic circuits. The paper focuses on building-block cytomorphic circuits. The paper focuses on sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy thermodynamics, and are therefore mathematically similar [13]. Electron copy establishing quantitative agreement of the cytomorphic chip establishing quantitative agreement of the cytomorphic chip number is analogous to molecular copy number and temperature represents number is analogous to molecular copy number and temperature represents measurements with prior biological measurements and models. itself. measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog 6) A stochastics circuit intentionally amplifies analog itself. single cell on a few chips and speedup multi-cell simulations x ′ � ′ � + ax ′ � + x + ax 2 = c 3 The building-block circuits may be classified into seven im- The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- Poisson noise in transistors to represent biological fluc- portant categories: portant categories: tuations in mRNA and protein concentrations at very tuations in mRNA and protein concentrations at very on multi-chip electronic boards [13]. Therefore, we were moti- single cell on a few chips and speedup multi-cell simulations 1) Basic BiCMOS current-mode analog circuits exploit the 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. low copy numbers and at relatively high noise levels. single cell on a few chips and speedup multi-cell simulations log-domain cytomorphic mapping to capture the exact dy- log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- The Poisson nature of biochemical reaction fluxes au- on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could namics of fundamental mass-action molecular kinetics namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at tomatically maps biological noise to electronic noise at vated to create a few fundamental molecular circuits that could be composed and scaled to model large biochemical reaction such as association, dissociation, and degradation. These Fig. 2. Die micrograph of the such as association, dissociation, and degradation. These Fig. 2. Die micrograph of the high copy numbers and relatively low noise levels [13]. cytomorphic chip fabricated high copy numbers and relatively low noise levels [13]. cytomorphic chip fabricated be composed and scaled to model large biochemical reaction be composed and scaled to model large biochemical reaction Fig. 2. Die micrograph of the cytomorphic chip fabricated Programmable in an AMS BiCMOS process. The left inset is a layout screen capture networks in the future. This paper describes these fundamental fundamental circuits are general enough to capture subtle fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling in an AMS Thus, these circuits are most useful for reliably modeling BiCMOS process. The left inset is a layout screen capture in an AMS networks in the future. This paper describes these fundamental BiCMOS process. The left inset is a layout screen capture of one gene block (2x magnification). networks in the future. This paper describes these fundamental of one gene block (2x magnification). building-block cytomorphic circuits. The paper focuses on effects such as loading, fan-out, feedback, and substrate de- effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios highly stochastic and relatively low signal-to-noise-ratios building-block cytomorphic circuits. The paper focuses on of one gene block (2x magnification). pletion through the use of a few explicit connections and pletion through the use of a few explicit connections and in biological cells. in biological cells. establishing quantitative agreement of the cytomorphic chip establishing quantitative agreement of the cytomorphic chip building-block cytomorphic circuits. The paper focuses on measurements with prior biological measurements and models. Kirchhoff’s current law. A wide dynamic range of opera- Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and 6) A stochastics circuit intentionally amplifies analog 7) ADCs and DACs convert between analog currents and Dynamical Systems measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog The building-block circuits may be classified into seven im- tion and low power consumption are achieved through the tion and low power consumption are achieved through the Poisson noise in transistors to represent biological fluc- digital bits to enable our chips to communicate with each digital bits to enable our chips to communicate with each The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- establishing quantitative agreement of the cytomorphic chip Analog Devices use of bipolar and subthreshold MOS transistors that func- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- other via digital input/output (I/O), and with off-chip dig- portant categories: tuations in mRNA and protein concentrations at very portant categories: tuations in mRNA and protein concentrations at very 1) Basic BiCMOS current-mode analog circuits exploit the tion at low current levels. tion at low current levels. low copy numbers and at relatively high noise levels. ital processors and computers. ital processors and computers. measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. 2) The ability to model cooperative binding is enabled by tun- 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our Off-chip digital processors synergistically interact with our log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- able Hill-function building-block circuits. namics of fundamental mass-action molecular kinetics able Hill-function building-block circuits. chips to carry out various functions: reading digital data from tomatically maps biological noise to electronic noise at chips to carry out various functions: reading digital data from The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at 3) An “ITD” block built by a composition of above cur- such as association, dissociation, and degradation. These 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital high copy numbers and relatively low noise levels [13]. the chips; decoding the data; performing high-speed digital such as association, dissociation, and degradation. These high copy numbers and relatively low noise levels [13]. portant categories: rent-mode circuits enables mapping of the exact differen- tuations in mRNA and protein concentrations at very rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time signal processing as necessary (e.g., scaling, diffusion, time fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling tial equations of inducer-transcription-factor binding effects such as loading, fan-out, feedback, and substrate de- tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or highly stochastic and relatively low signal-to-noise-ratios delay, and error correction); encoding the data to create or effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. and transcription-factor-DNA binding including for- pletion through the use of a few explicit connections and and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; in biological cells. modify molecular data packets via address and data strings; pletion through the use of a few explicit connections and in biological cells. ward and reverse reactions, degradation, protection from ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene storing the programmable address connectivity amongst gene Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and FUNDAMENTALLY NEW COMPILATION TECHNIQUES Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- degradation of transcription factors bound to DNA, and tion and low power consumption are achieved through the degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips digital bits to enable our chips to communicate with each and protein circuits; and communicating data to other chips tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each the change in DNA binding affinity of transcription factors the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were or to a computer. For simplicity, the data in this paper were use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at when bound by an inducer. tion at low current levels. when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that ital processors and computers. collected with a data-acquisition board (NI PXI-6541) that tion at low current levels. ital processors and computers. 4) An “analogic” current-mode circuit determines the tran- 2) The ability to model cooperative binding is enabled by tun- 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A Off-chip digital processors synergistically interact with our interacted with our chip and with MATLAB on a computer. A such as association, dissociation, and degradation. These high copy numbers and relatively low noise levels [13]. 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our scription rate of genes based on the probability of mul- scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) high-performance FPGA (e.g., from the Xilinx Spartan family) able Hill-function building-block circuits. chips to carry out various functions: reading digital data from able Hill-function building-block circuits. chips to carry out various functions: reading digital data from fundamental circuits are general enough to capture subtle 3) An “ITD” block built by a composition of above cur- tiple transcription-factor DNA binding sites being occu- Thus, these circuits are most useful for reliably modeling tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift the chips; decoding the data; performing high-speed digital could perform all of these functions in the future as well. Shift 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital INTRODUCTION pied or unoccupied in a combinatorial fashion with the rel- rent-mode circuits enables mapping of the exact differen- pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable signal processing as necessary (e.g., scaling, diffusion, time registers, SRAM blocks, and switches on the chip enable rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time effects such as loading, fan-out, feedback, and substrate de- ative mRNA production rate of each such combinatorial highly stochastic and relatively low signal-to-noise-ratios ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- programmability of parameters (e.g., reaction rates, dissocia- tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or state programmable by the user. This strategy enables us and transcription-factor-DNA binding including for- state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as modify molecular data packets via address and data strings; tion constants, Hill coefficients, and time constants) as well as and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; pletion through the use of a few explicit connections and in biological cells. to implement any arbitrary “analogic promoter function” to implement any arbitrary “analogic promoter function” connectivity. connectivity. ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene that is capable of complex saturating digital logic or prob- degradation of transcription factors bound to DNA, and that is capable of complex saturating digital logic or prob- and protein circuits; and communicating data to other chips The organization of this paper is as follows: Section II de- The organization of this paper is as follows: Section II de- degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and abilistic analog behavior depending on the molecular con- the change in DNA binding affinity of transcription factors abilistic analog behavior depending on the molecular con- or to a computer. For simplicity, the data in this paper were scribes the core building-block circuits of the chip along with scribes the core building-block circuits of the chip along with the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were centration. centration. chip measurement data. Fig. 2 shows a die micrograph of the chip measurement data. Fig. 2 shows a die micrograph of the when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each 5) A current-mode low pass filter (LPF) circuit enables the 4) An “analogic” current-mode circuit determines the tran- 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- interacted with our chip and with MATLAB on a computer. A chip that reveals the various building blocks. Section III dis- 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A gain and dynamics of mRNA and protein production scription rate of genes based on the probability of mul- gain and dynamics of mRNA and protein production high-performance FPGA (e.g., from the Xilinx Spartan family) cusses design considerations that are important in BiCMOS cy- cusses design considerations that are important in BiCMOS cy- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) and degradation to be represented. and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic tomorphic chip design. Section IV discusses how cytomorphic tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift tion at low current levels. pied or unoccupied in a combinatorial fashion with the rel- ital processors and computers. registers, SRAM blocks, and switches on the chip enable pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as to implement any arbitrary “analogic promoter function” connectivity. to implement any arbitrary “analogic promoter function” connectivity. able Hill-function building-block circuits. chips to carry out various functions: reading digital data from that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital centration. chip measurement data. Fig. 2 shows a die micrograph of the centration. chip measurement data. Fig. 2 shows a die micrograph of the 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as to implement any arbitrary “analogic promoter function” connectivity. that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with centration. chip measurement data. Fig. 2 shows a die micrograph of the 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic
� 15 TALK OUTLINE ‣ Background: overview of compilation problem ‣ Arco Compiler 1 : automatically configure analog devices to simulate dynamical systems. ‣ Jaunt Solver 2 : automatically scales dynamical systems to execute analog hardware with operating range constraints. ‣ Closing Remarks 1. Configuration Synthesis for Programmable Analog Devices with Arco. Sara Achour, Rahul Sarpeshkar and Martin Rinard. June 2016. PLDI 2016. 2. Time Dilation and Contraction for Programmable Analog Devices with Jaunt. Sara Achour and Martin Rinard. December 2017. ASPLOS 2018. OUTLINE
BACKGROUND
528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 528 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 � 17 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 528 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 9, NO. 4, AUGUST 2015 Fig. 1. Poisson chemical reaction flux and Poisson electron flow in Fig. 1. Poisson chemical reaction flux and Poisson electron flow in sub-threshold transistors obey the same Boltzmann exponential laws of sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy thermodynamics, and are therefore mathematically similar [13]. Electron copy number is analogous to molecular copy number and temperature represents number is analogous to molecular copy number and temperature represents Fig. 1. Poisson chemical reaction flux and Poisson electron flow in itself. itself. sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy single cell on a few chips and speedup multi-cell simulations single cell on a few chips and speedup multi-cell simulations number is analogous to molecular copy number and temperature represents on multi-chip electronic boards [13]. Therefore, we were moti- on multi-chip electronic boards [13]. Therefore, we were moti- itself. vated to create a few fundamental molecular circuits that could vated to create a few fundamental molecular circuits that could Fig. 2. Die micrograph of the Fig. 2. Die micrograph of the cytomorphic chip fabricated cytomorphic chip fabricated be composed and scaled to model large biochemical reaction be composed and scaled to model large biochemical reaction in an AMS BiCMOS process. The left inset is a layout screen capture in an AMS BiCMOS process. The left inset is a layout screen capture networks in the future. This paper describes these fundamental networks in the future. This paper describes these fundamental Fig. 1. Poisson chemical reaction flux and Poisson electron flow in Fig. 1. Poisson chemical reaction flux and Poisson electron flow in of one gene block (2x magnification). of one gene block (2x magnification). sub-threshold transistors obey the same Boltzmann exponential laws of building-block cytomorphic circuits. The paper focuses on building-block cytomorphic circuits. The paper focuses on sub-threshold transistors obey the same Boltzmann exponential laws of thermodynamics, and are therefore mathematically similar [13]. Electron copy thermodynamics, and are therefore mathematically similar [13]. Electron copy establishing quantitative agreement of the cytomorphic chip establishing quantitative agreement of the cytomorphic chip number is analogous to molecular copy number and temperature represents number is analogous to molecular copy number and temperature represents measurements with prior biological measurements and models. itself. measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog 6) A stochastics circuit intentionally amplifies analog itself. single cell on a few chips and speedup multi-cell simulations The building-block circuits may be classified into seven im- The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- Poisson noise in transistors to represent biological fluc- portant categories: portant categories: tuations in mRNA and protein concentrations at very tuations in mRNA and protein concentrations at very on multi-chip electronic boards [13]. Therefore, we were moti- 1) Basic BiCMOS current-mode analog circuits exploit the 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. low copy numbers and at relatively high noise levels. single cell on a few chips and speedup multi-cell simulations single cell on a few chips and speedup multi-cell simulations on multi-chip electronic boards [13]. Therefore, we were moti- log-domain cytomorphic mapping to capture the exact dy- log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- The Poisson nature of biochemical reaction fluxes au- vated to create a few fundamental molecular circuits that could on multi-chip electronic boards [13]. Therefore, we were moti- vated to create a few fundamental molecular circuits that could namics of fundamental mass-action molecular kinetics namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at tomatically maps biological noise to electronic noise at vated to create a few fundamental molecular circuits that could Fig. 2. Die micrograph of the cytomorphic chip fabricated be composed and scaled to model large biochemical reaction be composed and scaled to model large biochemical reaction such as association, dissociation, and degradation. These such as association, dissociation, and degradation. These Fig. 2. Die micrograph of the high copy numbers and relatively low noise levels [13]. high copy numbers and relatively low noise levels [13]. cytomorphic chip fabricated be composed and scaled to model large biochemical reaction Fig. 2. Die micrograph of the cytomorphic chip fabricated in an AMS BiCMOS process. The left inset is a layout screen capture fundamental circuits are general enough to capture subtle fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling in an AMS Thus, these circuits are most useful for reliably modeling BiCMOS process. The left inset is a layout screen capture networks in the future. This paper describes these fundamental in an AMS networks in the future. This paper describes these fundamental BiCMOS process. The left inset is a layout screen capture of one gene block (2x magnification). of one gene block (2x magnification). networks in the future. This paper describes these fundamental effects such as loading, fan-out, feedback, and substrate de- effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios highly stochastic and relatively low signal-to-noise-ratios building-block cytomorphic circuits. The paper focuses on building-block cytomorphic circuits. The paper focuses on of one gene block (2x magnification). Analog Device establishing quantitative agreement of the cytomorphic chip pletion through the use of a few explicit connections and pletion through the use of a few explicit connections and in biological cells. in biological cells. establishing quantitative agreement of the cytomorphic chip building-block cytomorphic circuits. The paper focuses on measurements with prior biological measurements and models. Kirchhoff’s current law. A wide dynamic range of opera- Kirchhoff’s current law. A wide dynamic range of opera- 6) A stochastics circuit intentionally amplifies analog 7) ADCs and DACs convert between analog currents and 7) ADCs and DACs convert between analog currents and measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog The building-block circuits may be classified into seven im- tion and low power consumption are achieved through the tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each Poisson noise in transistors to represent biological fluc- digital bits to enable our chips to communicate with each The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- establishing quantitative agreement of the cytomorphic chip portant categories: use of bipolar and subthreshold MOS transistors that func- use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- tuations in mRNA and protein concentrations at very other via digital input/output (I/O), and with off-chip dig- portant categories: tuations in mRNA and protein concentrations at very tion at low current levels. tion at low current levels. ital processors and computers. ital processors and computers. 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. measurements with prior biological measurements and models. 6) A stochastics circuit intentionally amplifies analog 2) The ability to model cooperative binding is enabled by tun- log-domain cytomorphic mapping to capture the exact dy- 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our The Poisson nature of biochemical reaction fluxes au- Off-chip digital processors synergistically interact with our log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- able Hill-function building-block circuits. namics of fundamental mass-action molecular kinetics able Hill-function building-block circuits. chips to carry out various functions: reading digital data from tomatically maps biological noise to electronic noise at chips to carry out various functions: reading digital data from The building-block circuits may be classified into seven im- Poisson noise in transistors to represent biological fluc- namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at 3) An “ITD” block built by a composition of above cur- such as association, dissociation, and degradation. These 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital high copy numbers and relatively low noise levels [13]. the chips; decoding the data; performing high-speed digital such as association, dissociation, and degradation. These high copy numbers and relatively low noise levels [13]. portant categories: tuations in mRNA and protein concentrations at very rent-mode circuits enables mapping of the exact differen- fundamental circuits are general enough to capture subtle rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time Thus, these circuits are most useful for reliably modeling signal processing as necessary (e.g., scaling, diffusion, time fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling tial equations of inducer-transcription-factor binding tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or delay, and error correction); encoding the data to create or effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios 1) Basic BiCMOS current-mode analog circuits exploit the low copy numbers and at relatively high noise levels. and transcription-factor-DNA binding including for- and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; modify molecular data packets via address and data strings; pletion through the use of a few explicit connections and in biological cells. pletion through the use of a few explicit connections and in biological cells. ward and reverse reactions, degradation, protection from Kirchhoff’s current law. A wide dynamic range of opera- ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene 7) ADCs and DACs convert between analog currents and storing the programmable address connectivity amongst gene Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and log-domain cytomorphic mapping to capture the exact dy- The Poisson nature of biochemical reaction fluxes au- degradation of transcription factors bound to DNA, and tion and low power consumption are achieved through the degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips digital bits to enable our chips to communicate with each and protein circuits; and communicating data to other chips tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each the change in DNA binding affinity of transcription factors use of bipolar and subthreshold MOS transistors that func- the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were other via digital input/output (I/O), and with off-chip dig- or to a computer. For simplicity, the data in this paper were use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- namics of fundamental mass-action molecular kinetics tomatically maps biological noise to electronic noise at when bound by an inducer. when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that collected with a data-acquisition board (NI PXI-6541) that tion at low current levels. ital processors and computers. tion at low current levels. ital processors and computers. 4) An “analogic” current-mode circuit determines the tran- 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A interacted with our chip and with MATLAB on a computer. A 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our such as association, dissociation, and degradation. These high copy numbers and relatively low noise levels [13]. 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our scription rate of genes based on the probability of mul- able Hill-function building-block circuits. scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) chips to carry out various functions: reading digital data from high-performance FPGA (e.g., from the Xilinx Spartan family) able Hill-function building-block circuits. chips to carry out various functions: reading digital data from 3) An “ITD” block built by a composition of above cur- tiple transcription-factor DNA binding sites being occu- tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift the chips; decoding the data; performing high-speed digital could perform all of these functions in the future as well. Shift fundamental circuits are general enough to capture subtle Thus, these circuits are most useful for reliably modeling 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital pied or unoccupied in a combinatorial fashion with the rel- rent-mode circuits enables mapping of the exact differen- pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable signal processing as necessary (e.g., scaling, diffusion, time registers, SRAM blocks, and switches on the chip enable rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time effects such as loading, fan-out, feedback, and substrate de- highly stochastic and relatively low signal-to-noise-ratios ative mRNA production rate of each such combinatorial tial equations of inducer-transcription-factor binding ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- delay, and error correction); encoding the data to create or programmability of parameters (e.g., reaction rates, dissocia- tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or state programmable by the user. This strategy enables us state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as tion constants, Hill coefficients, and time constants) as well as and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; pletion through the use of a few explicit connections and in biological cells. to implement any arbitrary “analogic promoter function” ward and reverse reactions, degradation, protection from to implement any arbitrary “analogic promoter function” connectivity. storing the programmable address connectivity amongst gene connectivity. ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene that is capable of complex saturating digital logic or prob- degradation of transcription factors bound to DNA, and that is capable of complex saturating digital logic or prob- and protein circuits; and communicating data to other chips The organization of this paper is as follows: Section II de- The organization of this paper is as follows: Section II de- degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips Kirchhoff’s current law. A wide dynamic range of opera- 7) ADCs and DACs convert between analog currents and Compiler abilistic analog behavior depending on the molecular con- the change in DNA binding affinity of transcription factors abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with or to a computer. For simplicity, the data in this paper were scribes the core building-block circuits of the chip along with the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were centration. when bound by an inducer. centration. chip measurement data. Fig. 2 shows a die micrograph of the collected with a data-acquisition board (NI PXI-6541) that chip measurement data. Fig. 2 shows a die micrograph of the when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that tion and low power consumption are achieved through the digital bits to enable our chips to communicate with each 5) A current-mode low pass filter (LPF) circuit enables the 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- chip that reveals the various building blocks. Section III dis- 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A gain and dynamics of mRNA and protein production gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- cusses design considerations that are important in BiCMOS cy- scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) use of bipolar and subthreshold MOS transistors that func- other via digital input/output (I/O), and with off-chip dig- scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) and degradation to be represented. tiple transcription-factor DNA binding sites being occu- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic could perform all of these functions in the future as well. Shift tomorphic chip design. Section IV discusses how cytomorphic tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift tion at low current levels. pied or unoccupied in a combinatorial fashion with the rel- ital processors and computers. registers, SRAM blocks, and switches on the chip enable pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- 2) The ability to model cooperative binding is enabled by tun- Off-chip digital processors synergistically interact with our state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as to implement any arbitrary “analogic promoter function” connectivity. to implement any arbitrary “analogic promoter function” connectivity. able Hill-function building-block circuits. chips to carry out various functions: reading digital data from that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with 3) An “ITD” block built by a composition of above cur- the chips; decoding the data; performing high-speed digital centration. chip measurement data. Fig. 2 shows a die micrograph of the centration. chip measurement data. Fig. 2 shows a die micrograph of the Dynamical 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- rent-mode circuits enables mapping of the exact differen- signal processing as necessary (e.g., scaling, diffusion, time 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic tial equations of inducer-transcription-factor binding delay, and error correction); encoding the data to create or and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic and transcription-factor-DNA binding including for- modify molecular data packets via address and data strings; System ward and reverse reactions, degradation, protection from storing the programmable address connectivity amongst gene degradation of transcription factors bound to DNA, and and protein circuits; and communicating data to other chips the change in DNA binding affinity of transcription factors or to a computer. For simplicity, the data in this paper were when bound by an inducer. collected with a data-acquisition board (NI PXI-6541) that 4) An “analogic” current-mode circuit determines the tran- interacted with our chip and with MATLAB on a computer. A scription rate of genes based on the probability of mul- high-performance FPGA (e.g., from the Xilinx Spartan family) tiple transcription-factor DNA binding sites being occu- could perform all of these functions in the future as well. Shift pied or unoccupied in a combinatorial fashion with the rel- registers, SRAM blocks, and switches on the chip enable ative mRNA production rate of each such combinatorial programmability of parameters (e.g., reaction rates, dissocia- BACKGROUND state programmable by the user. This strategy enables us tion constants, Hill coefficients, and time constants) as well as to implement any arbitrary “analogic promoter function” connectivity. that is capable of complex saturating digital logic or prob- The organization of this paper is as follows: Section II de- abilistic analog behavior depending on the molecular con- scribes the core building-block circuits of the chip along with centration. chip measurement data. Fig. 2 shows a die micrograph of the 5) A current-mode low pass filter (LPF) circuit enables the chip that reveals the various building blocks. Section III dis- gain and dynamics of mRNA and protein production cusses design considerations that are important in BiCMOS cy- and degradation to be represented. tomorphic chip design. Section IV discusses how cytomorphic
� 18 Analog Device Specification Compiler Dynamical System BACKGROUND
� 19 Analog Device Specification Compiler Dynamical Analog Device System Configuration BACKGROUND
� 20 Analog Device Specification Compiler Dynamical Analog Device System Configuration BACKGROUND
� 21 DYNAMICAL SYSTEM SPECIFICATION E = 6800 − ES S = 4400 − ES · ES = 10 − 4 ⋅ E ⋅ S − 10 − 2 ⋅ ES ES (0) = 0 BACKGROUND
� 22 Analog Device Specification Compiler Dynamical Analog Device System Configuration BACKGROUND
� 23 ANALOG DEVICE SPECIFICATION x 3 x 5 MM DAC x 3 x 5 IADD ADC BACKGROUND
� 24 ANALOG DEVICE SPECIFICATION x 3 MM inp X0, Y0, Z0 inp A, B Input and Output Ports out X, Y, Z BACKGROUND
� 25 ANALOG DEVICE SPECIFICATION x 3 MM inp X0, Y0, Z0 inp A, B out X, Y, Z rel X.I = X0.I - Z.I rel Y.I = Y0.I - Z.I Block Dynamics rel Z.I’ = A.V X.I Y.I - B.V Z.I and Z.I(0) = Z0 BACKGROUND
� 26 ANALOG DEVICE SPECIFICATION x 5 x 5 DAC ADC inp X digital inp X out Z out Z digital rel Z.I = X rel Z = X.I BACKGROUND
� 27 ANALOG DEVICE SPECIFICATION x 3 x 5 MM DAC x 3 x 5 IADD ADC conn MM[*].Z and ADC[*].X Available Connections conn DAC[*].Z and MM[*].A conn MM[1].Z and MM[2].X BACKGROUND
� 28 Analog Device Specification Compiler Dynamical Analog Device System Configuration BACKGROUND
� 29 ANALOG DEVICE CONFIGURATION DAC DAC DAC DAC DAC 2 3 4 5 1 A X0 Z0 Y0 B mm.1 X Z Y A B C A B C A B C iadd.1 iadd.2 iadd.3 D D D ADC ADC ADC ADC ADC 1 5 2 3 4 BACKGROUND
� 30 ANALOG DEVICE CONFIGURATION 0 4400 0.01 0.0001 6800 DAC DAC DAC DAC DAC 2 3 4 5 1 A X0 Z0 Y0 B mm.1 X Z Y A B C A B C A B C iadd.1 iadd.2 iadd.3 D D D ADC ADC ADC ADC ADC 1 5 2 3 4 BACKGROUND
� 31 ANALOG DEVICE CONFIGURATION 0 4400 0.01 0.0001 6800 DAC DAC DAC DAC DAC 2 3 4 5 1 A X0 Z0 Y0 B mm.1 X Z Y A B C A B C A B C iadd.1 iadd.2 iadd.3 D D D ADC ADC ADC ADC ADC 1 5 2 3 4 BACKGROUND
� 32 ANALOG DEVICE CONFIGURATION 0 4400 0.01 0.0001 6800 DAC DAC DAC DAC DAC 2 3 4 5 1 A X0 Z0 Y0 B mm.1 X Z Y A B C A B C A B C iadd.1 iadd.2 iadd.3 D D D ADC ADC ADC ADC ADC 1 5 2 3 4 E ES S BACKGROUND
� 33 ANALOG DEVICE CONFIGURATION 0.0001 6800 0 4400 0.01 DAC DAC DAC DAC DAC 2 3 4 5 1 A X0 Z0 Y0 B mm X Z Y ADC ADC ADC 1 2 3 E ES S BACKGROUND
� 34 ANALOG DEVICE CONFIGURATION set DAC[0].X = 0.003 DAC Values … set DAC[5].X = 0.006 BACKGROUND
� 35 ANALOG DEVICE CONFIGURATION set DAC[0].X = 0.003 … set DAC[5].X = 0.006 lbl ADC[0].Z = “E” lbl ADC[1].Z = “S” ADC Values lbl ADC[2].Z = “ES” BACKGROUND
� 36 ANALOG DEVICE CONFIGURATION set DAC[0].X = 0.003 … set DAC[5].X = 0.006 lbl ADC[0].Z = “E” lbl ADC[1].Z = “S” lbl ADC[2].Z = “ES” conn DAC[0].Z to MM[0].X0 … Connections conn MM[0].Y to ADC[2].X conn MM[0].Z to ADC[3].X BACKGROUND
� 37 Analog Device Specification Compiler Dynamical Analog Device System Configuration BACKGROUND
� 38 TALK OUTLINE ‣ Background: overview of compilation problem ‣ Arco Compiler 1 : automatically configure analog devices to simulate dynamical systems. ‣ Jaunt Solver 2 : automatically scales dynamical systems to execute analog hardware with operating range constraints. ‣ Closing Remarks 1. Configuration Synthesis for Programmable Analog Devices with Arco. Sara Achour, Rahul Sarpeshkar and Martin Rinard. June 2016. PLDI 2016. 2. Time Dilation and Contraction for Programmable Analog Devices with Jaunt. Sara Achour and Martin Rinard. December 2017. ASPLOS 2018. OUTLINE
ARCO COMPILER
� 40 ARCO COMPILER OVERVIEW Arco performs a search over tableaus ARCO COMPILER
� 41 ARCO COMPILER tableau : search state { } Goals Blocks Wires Used Blocks Config ARCO COMPILER
� 42 ARCO COMPILER OVERVIEW Arco starts with an initial tableau ARCO COMPILER
� 43 ARCO COMPILER initial tableau : the initial state of the search { } Goals Blocks Wires Used Blocks Config ARCO COMPILER
� 44 ARCO COMPILER initial tableau : the initial state of the search { } Goals Blocks Wires Used Blocks Config E = 6800 − ES S = 4400 − ES · ES = 10 − 4 E ⋅ S − 10 − 2 ES ES (0) = 0 ARCO COMPILER
� 45 ARCO COMPILER initial tableau : the initial state of the search { } Goals Blocks Wires Used Blocks Config DAC [0] . O DAC[0] E = 6800 − ES MM [0] . A DAC [0] . O S = 4400 − ES ADC[0] MM [0] . X 0 · ES = 10 − 4 E ⋅ S − 10 − 2 ES MM [0] . Z MM[0] ADC [0] . X ES (0) = 0 MM [0] . X DAC[1] ADC [0] . X ARCO COMPILER
� 46 ARCO COMPILER initial tableau : the initial state of the search analog hardware is not configured yet { } Goals Blocks Wires Used Blocks Config DAC [0] . O ∅ ∅ DAC[0] E = 6800 − ES MM [0] . A DAC [0] . O S = 4400 − ES ADC[0] MM [0] . X 0 · ES = 10 − 4 E ⋅ S − 10 − 2 ES MM [0] . Z MM[0] ADC [0] . X ES (0) = 0 MM [0] . X DAC[1] ADC [0] . X ARCO COMPILER
� 47 ARCO COMPILER OVERVIEW new tableaus derived using transition rules ARCO COMPILER
� 48 ARCO COMPILER OVERVIEW Arco searches until a solved tableau is found ARCO COMPILER
� 49 ARCO COMPILER solved tableau : the final state of the search { } Goals Blocks Wires Used Blocks Config ARCO COMPILER
� 50 ARCO COMPILER solved tableau : the final state of the search no goals left { } Goals Blocks Wires Used Blocks Config ∅ ARCO COMPILER
� 51 ARCO COMPILER solved tableau : the final state of the search remaining blocks, wires { } Goals Blocks Wires Used Blocks Config ∅ DAC [0] . O ADC[3] MM [0] . X 0 MM [0] . X ADC[4] ADC [0] . X ARCO COMPILER
� 52 ARCO COMPILER solved tableau : the final state of the search blocks in use { } Goals Blocks Wires Used Blocks Config ∅ DAC [0] . O MM[0] ADC[3] MM [0] . X 0 MM [0] . X ADC[0] ADC[4] ADC [0] . X DAC[0] ADC[1] ARCO COMPILER
� 53 ARCO COMPILER solved tableau : the final state of the search analog device configuration { } Goals Blocks Wires Used Blocks Config ∅ DAC [0] . O conn DAC[0].Z MM[0] ADC[3] MM [0] . X 0 to MM[0].A MM [0] . X ADC[0] ADC[4] conn MM[0].Z ADC [0] . X to ADC[0].X DAC[0] set DAC[0].X = 10 -4 lbl ADC[2].O = “ES” ADC[1] ARCO COMPILER
� 54 ARCO COMPILER OVERVIEW Arco derives new tableaus using transition rules Unify Connect Variable Map ARCO COMPILER
� 55 ARCO COMPILER OVERVIEW Arco derives new tableaus using transition rules Unify Connect Variable Map ARCO COMPILER
� 56 UNIFICATION TRANSITION E = 6800 − ES { } Goals Blocks Wires Used Blocks Config S = 4400 − ES DAC [0] . O DAC[0] · MM [0] . A ES = 10 − 4 E ⋅ S − 10 − 2 ES DAC [0] . O ES (0) = 0 ADC[0] MM [0] . X 0 E = 6800 − ES MM [0] . Z MM[0] ADC [0] . X MM [0] . X DAC[1] ADC [0] . X ARCO COMPILER
� 57 UNIFICATION TRANSITION Goals Blocks S = 4400 − ES · ES = 10 − 4 E ⋅ S − 10 − 2 ES ES (0) = 0 E = 6800 − ES MM[0] ARCO COMPILER
� 58 MM[0] Goals A X0 Z0 Y0 B S = 4400 − ES · ES = 10 − 4 E ⋅ S − 10 − 2 ES mm ES (0) = 0 X Y Z E = 6800 − ES E = 6800 − ES ARCO COMPILER
� 59 MM[0] Goals A X0 Z0 Y0 B S = 4400 − ES · ES = 10 − 4 E ⋅ S − 10 − 2 ES mm ES (0) = 0 X Y Z E = 6800 − ES E = 6800 − ES X = X 0 − Z ARCO COMPILER
� 60 MM[0] 6800 Goals A X0 Z0 Y0 B S = 4400 − ES · ES = 10 − 4 E ⋅ S − 10 − 2 ES mm ES (0) = 0 X Y Z E = 6800 − ES E ES MM [0] . X 0 = 6800 MM [0] . X = E E = 6800 − ES MM [0] . Z = ES X = X 0 − Z ARCO COMPILER
� 61 MM[0] 6800 Goals A X0 Z0 Y0 B S = 4400 − ES · ES = 10 − 4 E ⋅ S − 10 − 2 ES mm ES (0) = 0 X Y Z E = 6800 − ES E ES MM [0] . X 0 = 6800 MM [0] . X = E · ES = 10 − 4 E ⋅ S − 10 − 2 ES MM [0] . Z = ES ES (0) = 0 · Z = A ⋅ X ⋅ Y − B ⋅ Z Z (0) = Z 0 ARCO COMPILER
� 62 MM[0] 6800 Goals A X0 Z0 Y0 B S = 4400 − ES · ES = 10 − 4 E ⋅ S − 10 − 2 ES mm ES (0) = 0 X Y Z E = 6800 − ES E ES MM [0] . X 0 = 6800 MM [0] . X = E · ES = 10 − 4 E ⋅ S − 10 − 2 ES MM [0] . Z = ES ES (0) = 0 · ES E ES ES = A ⋅ E ⋅ Y − B ⋅ ES ES (0) = Z 0 ES ARCO COMPILER
� 63 MM[0] 6800 0 10 − 4 10 − 2 Goals A X0 Z0 Y0 B S = 4400 − ES · ES = 10 − 4 E ⋅ S − 10 − 2 ES mm ES (0) = 0 X Y Z E = 6800 − ES E ES S MM [0] . X 0 = 6800 MM [0] . X = E · ES = 10 − 4 E ⋅ S − 10 − 2 ES MM [0] . Z = ES MM [0] . A = 10 − 4 ES (0) = 0 MM [0] . B = 10 − 2 MM [0] . Y = S · ES E ES ES = A ⋅ E ⋅ Y − B ⋅ ES MM [0] . Z 0 = 0 ES (0) = Z 0 ES ARCO COMPILER
� 64 MM[0] 6800 0 10 − 4 10 − 2 Goals A X0 Z0 Y0 B S = 4400 − ES · ES = 10 − 4 E ⋅ S − 10 − 2 ES mm ES (0) = 0 X Y Z E = 6800 − ES E ES S MM [0] . X 0 = 6800 MM [0] . X = E S = 4400 − ES MM [0] . Z = ES MM [0] . A = 10 − 4 MM [0] . B = 10 − 2 MM [0] . Y = S S = Y 0 − ES S ES MM [0] . Z 0 = 0 ARCO COMPILER
� 65 MM[0] 6800 0 4400 10 − 4 10 − 2 Goals A X0 Z0 Y0 B S = 4400 − ES · ES = 10 − 4 E ⋅ S − 10 − 2 ES mm ES (0) = 0 X Y Z E = 6800 − ES E ES S MM [0] . X 0 = 6800 MM [0] . X = E S = 4400 − ES MM [0] . Z = ES MM [0] . A = 10 − 4 MM [0] . B = 10 − 2 MM [0] . Y = S S = Y 0 − ES S ES MM [0] . Z 0 = 0 MM [0] . Y 0 = 4400 ARCO COMPILER
� 66 MM[0] 6800 0 4400 10 − 4 10 − 2 Goals A X0 Z0 Y0 B S = 4400 − ES · ES = 10 − 4 E ⋅ S − 10 − 2 ES mm ES (0) = 0 X Y Z E = 6800 − ES E ES S MM [0] . X 0 = 6800 MM [0] . X = E S = 4400 − ES MM [0] . Z = ES MM [0] . A = 10 − 4 MM [0] . B = 10 − 2 MM [0] . Y = S S = Y 0 − ES S ES MM [0] . Z 0 = 0 MM [0] . Y 0 = 4400 ARCO COMPILER
� 67 UNIFICATION TRANSITION { } Goals Blocks Wires Used Blocks Config S = 4400 − ES DAC [0] . O DAC[0] · MM [0] . A ES = 10 − 4 E ⋅ S − 10 − 2 ES DAC [0] . O ES (0) = 0 ADC[0] MM [0] . X 0 E = 6800 − ES MM [0] . Z MM[0] ADC [0] . X MM [0] . X DAC[1] ADC [0] . X ARCO COMPILER
� 68 UNIFICATION TRANSITION ′ � { } Goals Blocks Wires Used Blocks Config S = 4400 − ES DAC [0] . O DAC[0] MM[0] · MM [0] . A ES = 10 − 4 E ⋅ S − 10 − 2 ES DAC [0] . O ES (0) = 0 ADC[0] MM [0] . X 0 E = 6800 − ES MM [0] . Z MM[0] MM [0] . X 0 = 6800 ADC [0] . X MM [0] . X = E MM [0] . X DAC[1] ADC [0] . X MM [0] . Z = ES ARCO COMPILER
� 69 ARCO COMPILER OVERVIEW Arco derives new tableaus using transition rules Unify Connect Variable Map ARCO COMPILER
� 70 CONNECTION TRANSITION { } Goals Blocks Wires Used Blocks Config DAC [0] . O MM [0] . A = DAC [0] . O MM[1] MM[0] MM [0] . A DAC [0] . X = 10 − 4 DAC [0] . O MM[2] DAC[0] ADC [0] . X = MM [0] . Z MM [0] . X 0 ADC [0] . O = ES MM [0] . Z DAC[1] ADC[3] MM [0] . B = DAC [0] . O ADC [0] . X DAC [0] . X = 10 − 2 ADC[0] MM [0] . X ADC[4] ADC [1] . X = MM [0] . X ADC [0] . X ADC[1] ADC [1] . O = E ARCO COMPILER
� 71 CONNECTION TRANSITION { } Goals Blocks Wires Used Blocks Config DAC [0] . O MM [0] . A = DAC [0] . O MM[1] MM[0] MM [0] . A DAC [0] . X = 10 − 4 DAC [0] . O MM[2] DAC[0] ADC [0] . X = MM [0] . Z MM [0] . X 0 ADC [0] . O = ES MM [0] . Z DAC[1] ADC[3] MM [0] . B = DAC [0] . O ADC [0] . X DAC [0] . X = 10 − 2 ADC[0] MM [0] . X ADC[4] ADC [1] . X = MM [0] . X ADC [0] . X ADC[1] ADC [1] . O = E ARCO COMPILER
� 72 CONNECTION TRANSITION ′ � { } Goals Blocks Wires Used Blocks Config DAC [0] . O MM [0] . A = DAC [0] . O conn DAC[0].Z MM[1] MM[0] MM [0] . A to MM[0].A DAC [0] . X = 10 − 4 DAC [0] . O MM[2] DAC[0] ADC [0] . X = MM [0] . Z MM [0] . X 0 ADC [0] . O = ES MM [0] . Z DAC[1] ADC[3] MM [0] . B = DAC [0] . O ADC [0] . X DAC [0] . X = 10 − 2 ADC[0] MM [0] . X ADC[4] ADC [1] . X = MM [0] . X ADC [0] . X ADC[1] ADC [1] . O = E ARCO COMPILER
� 73 ARCO COMPILER OVERVIEW Arco derives new tableaus using transition rules Unify Connect Variable Map ARCO COMPILER
� 74 VARIABLE/VALUE MAPPING TRANSITION { } Goals Blocks Wires Used Blocks Config DAC [0] . O MM [0] . A = DAC [0] . O conn DAC[0].Z MM[1] MM[0] MM [0] . X 0 to MM[0].A DAC [0] . X = 10 − 4 MM [0] . Z MM[2] DAC[0] ADC [0] . X = MM [0] . Z ADC [0] . X ADC [0] . O = ES MM [0] . X DAC[1] ADC[3] MM [0] . B = DAC [0] . O ADC [0] . X DAC [0] . X = 10 − 2 ADC[0] MM [0] . Y ADC[4] ADC [1] . X = MM [0] . X ADC [0] . X ADC[1] ADC [1] . O = E ARCO COMPILER
� 75 VARIABLE/VALUE MAPPING TRANSITION ′ � { } Goals Blocks Wires Used Blocks Config DAC [0] . O MM [0] . A = DAC [0] . O conn DAC[0].Z MM[1] MM[0] MM [0] . X 0 to MM[0].A DAC [0] . X = 10 − 4 MM [0] . Z MM[2] DAC[0] ADC [0] . X = MM [0] . Z set DAC[0].X = 10 -4 ADC [0] . X ADC [0] . O = ES MM [0] . X DAC[1] ADC[3] MM [0] . B = DAC [0] . O ADC [0] . X DAC [0] . X = 10 − 2 ADC[0] MM [0] . Y ADC[4] ADC [1] . X = MM [0] . X ADC [0] . X ADC[1] ADC [1] . O = E ARCO COMPILER
� 76 VARIABLE/VALUE MAPPING TRANSITION { } Goals Blocks Wires Used Blocks Config DAC [0] . O MM [0] . A = DAC [0] . O conn DAC[0].Z MM[1] MM[0] MM [0] . X 0 to MM[0].A DAC [0] . X = 10 − 4 MM [0] . Z MM[2] DAC[0] ADC [0] . X = MM [0] . Z set DAC[0].X = 10 -4 ADC [0] . X ADC [0] . O = ES MM [0] . X DAC[1] ADC[3] MM [0] . B = DAC [0] . O ADC [0] . X DAC [0] . X = 10 − 2 ADC[0] MM [0] . Y ADC[4] ADC [1] . X = MM [0] . X ADC [0] . X ADC[1] ADC [1] . O = E ARCO COMPILER
� 77 VARIABLE/VALUE MAPPING TRANSITION ′ � { } Goals Blocks Wires Used Blocks Config DAC [0] . O MM [0] . A = DAC [0] . O conn DAC[0].Z MM[1] MM[0] MM [0] . X 0 to MM[0].A DAC [0] . X = 10 − 4 MM [0] . Z MM[2] DAC[0] ADC [0] . X = MM [0] . Z set DAC[0].X = 10 -4 ADC [0] . X ADC [0] . O = ES MM [0] . X lbl ADC[0].O = ES DAC[1] ADC[3] MM [0] . B = DAC [0] . O ADC [0] . X DAC [0] . X = 10 − 2 ADC[0] MM [0] . Y ADC[4] ADC [1] . X = MM [0] . X ADC [0] . X ADC[1] ADC [1] . O = E ARCO COMPILER
� 78 ARCO COMPILER RECAP Arco starts with an initial tableau ARCO COMPILER
� 79 ARCO COMPILER RECAP derives new tableaus using transition rules Unify Connect Variable Map ARCO COMPILER
� 80 ARCO COMPILER RECAP until a solved tableau is found ARCO COMPILER
� 81 ARCO COMPILER RECAP analog device configuration in solved tableau ARCO COMPILER
� 82 ARCO COMPILER RECAP analog device configuration in solved tableau ALGEBRAICALLY EQUIVALENT TO DYNAMICAL SYSTEM creative use of available analog blocks to model dynamics respects connectivity, block instance constraints ARCO COMPILER
� 83 CASE STUDY 1: PERK -4 Task: model PERK -4 using analog hardware that does not directly support exponentiation. PERK -1 0 B C A M O = (( A + B + C ) ⋅ K − 1 + 1) n O = A + B + C O iadd 1 O = 4 1 1 (( PERK + ( − 1) + 0) ⋅ 1 − 1 + 1) 4 n S K M M O = ( S ⋅ K − 1 + 1) n PERK -4 O switch PERK -4 TEXT
� 84 ARCO COMPILER RECAP analog device configuration in solved tableau doesn’t take into consideration PHYSICAL LIMITATIONS OF HARDWARE ARCO COMPILER
� 85 ARCO COMPILER RECAP analog device configuration in solved tableau doesn’t take into consideration PHYSICAL LIMITATIONS OF HARDWARE OPERATING RANGE CONSTRAINTS SAMPLING RATES OF ADCS/DACS ARCO COMPILER
� 86 ANALOG DEVICE CONFIGURATION REVISITED 0.0001 6800 0 4400 0.01 DAC1 DAC2 DAC3 DAC4 DAC5 A B X0 Z0 Y0 mm X Z Y ADC1 ADC2 ADC3 E ES S BACKGROUND
� 87 ANALOG DEVICE CONFIGURATION REVISITED 0.0001 6800 0 4400 0.01 Expected Simulation Dynamics DAC1 DAC2 DAC3 DAC4 DAC5 6000 molecules 4000 A B X0 Z0 Y0 2000 mm 0 0 2 4 6 8 10 time (su) X Z Y ADC1 ADC2 ADC3 E ES S BACKGROUND
� 88 ANALOG DEVICE CONFIGURATION REVISITED 0.0001 6800 0 4400 0.01 DAC1 DAC2 DAC3 DAC4 DAC5 [ 0,3300 ] [ 0,3300 ] [0,3300 ] [ 0,10 ] [ 0,10 ] A B X0 Z0 Y0 [10 -5 ,10 -3 ] [10 -4 ,1 ] [0,1000 ] [0,1000 ] [0,1000 ] mm [0,1600 ] [0,1600 ] [0,1600 ] X Z Y ADC1 ADC2 ADC3 [ 0,3300 ] [ 0,3300 ] [ 0,3300 ] E ES S BACKGROUND
� 89 ANALOG DEVICE CONFIGURATION REVISITED 0.0001 6800 0 4400 0.01 DAC1 DAC2 DAC3 DAC4 DAC5 [ 0,3300 ] [ 0,3300 ] [0,3300 ] [ 0,10 ] [ 0,10 ] A B X0 Z0 Y0 [10 -5 ,10 -3 ] [10 -4 ,1 ] [0,1000 ] [0,1000 ] [0,1000 ] mm [0,1600 ] [0,1600 ] [0,1600 ] X Z Y ADC1 ADC2 ADC3 [ 0,3300 ] [ 0,3300 ] [ 0,3300 ] E ES S BACKGROUND
� 90 ANALOG DEVICE CONFIGURATION REVISITED 0.0001 6800 0 4400 0.01 Actual Simulation Dynamics DAC1 DAC2 DAC3 DAC4 DAC5 [ 0,3300 ] [ 0,3300 ] [0,3300 ] [ 0,10 ] [ 0,10 ] 6000 6000 molecules molecules 4000 4000 A B X0 Z0 Y0 2000 2000 [10 -5 ,10 -3 ] [10 -4 ,1 ] [0,1000 ] [0,1000 ] [0,1000 ] mm 0 0 0 2 4 6 8 10 0 2 4 6 8 10 [0,1600 ] [0,1600 ] [0,1600 ] time (su) time (su) X Z Y ADC1 ADC2 ADC3 [ 0,3300 ] [ 0,3300 ] [ 0,3300 ] E ES S BACKGROUND
� 91 UNIFORMLY SCALED ANALOG DEVICE CONFIGURATION 0.1 • 10 -4 0.1 • 6800 0.1 • 0.1 • 4400 0.1 • 10 -2 DAC1 DAC2 DAC3 DAC4 DAC5 [ 0,3300 ] [ 0,3300 ] [0,3300 ] [ 0,10 ] [ 0,10 ] A B X0 Z0 Y0 [10 -5 ,10 -3 ] [10 -4 ,1 ] [0,1000 ] [0,1000 ] [0,1000 ] mm [0,1600 ] [0,1600 ] [0,1600 ] Y Z X ADC1 ADC2 ADC3 [ 0,3300 ] [ 0,3300 ] [ 0,3300 ] a 13 • E a 14 • ES a 15 • S BACKGROUND
� 92 UNIFORMLY SCALED ANALOG DEVICE CONFIGURATION 0.1 • 10 -4 0.1 • 6800 0.1 • 0.1 • 4400 0.1 • 10 -2 DAC1 DAC2 DAC3 DAC4 DAC5 [ 0,3300 ] [ 0,3300 ] [0,3300 ] [ 0,10 ] [ 0,10 ] A B X0 Z0 Y0 [10 -5 ,10 -3 ] [10 -4 ,1 ] [0,1000 ] [0,1000 ] [0,1000 ] DOES NOT WORK! mm [0,1600 ] [0,1600 ] [0,1600 ] Y Z X ADC1 ADC2 ADC3 [ 0,3300 ] [ 0,3300 ] [ 0,3300 ] a 13 • E a 14 • ES a 15 • S BACKGROUND
� 93 UNIFORMLY SCALED ANALOG DEVICE CONFIGURATION 0.1 • 10 -4 0.1 • 6800 0.1 • 0.1 • 4400 0.1 • 10 -2 DAC1 DAC2 DAC3 DAC4 DAC5 [ 0,3300 ] [ 0,3300 ] [0,3300 ] [ 0,10 ] [ 0,10 ] A B X0 Z0 Y0 [10 -5 ,10 -3 ] [10 -4 ,1 ] [0,1000 ] [0,1000 ] [0,1000 ] DOES NOT WORK! mm [0,1600 ] [0,1600 ] [0,1600 ] SCALED SIGNAL CHANGES SIMULATION Y Z X ORIGINAL SIMULATION NOT RECOVERABLE ADC1 ADC2 ADC3 [ 0,3300 ] [ 0,3300 ] [ 0,3300 ] a 13 • E a 14 • ES a 15 • S BACKGROUND
� 94 TALK OUTLINE ‣ Background: overview of compilation problem ‣ Arco Compiler 1 : automatically configure analog devices to simulate dynamical systems. ‣ Jaunt Solver 2 : automatically scales dynamical systems to execute analog hardware with operating range constraints. ‣ Closing Remarks 1. Configuration Synthesis for Programmable Analog Devices with Arco. Sara Achour, Rahul Sarpeshkar and Martin Rinard. June 2016. PLDI 2016. 2. Time Dilation and Contraction for Programmable Analog Devices with Jaunt. Sara Achour and Martin Rinard. December 2017. ASPLOS 2018. OUTLINE
JAUNT SOLVER
� 96 Analog Device Specification Jaunt Analog Device Scaled Analog Device Configuration Configuration BACKGROUND
� 97 physically realizable: signals within port operating ranges recoverable: recover original simulation at ADCs Analog Device Specification Jaunt Analog Device Scaled Analog Device Configuration Configuration BACKGROUND
� 98 ANALOG DEVICE CONFIGURATION 10 -4 6800 0 4400 10 -2 DAC1 DAC2 DAC3 DAC4 DAC5 [ 0,3300 ] [ 0,3300 ] [0,3300 ] [ 0,10 ] [ 0,10 ] A B X0 Z0 Y0 [10 -5 ,10 -3 ] [10 -4 ,1 ] [0,1000 ] [0,1000 ] [0,1000 ] mm [0,1600 ] [0,1600 ] [0,1600 ] X Z Y ADC1 ADC2 ADC3 [ 0,3300 ] [ 0,3300 ] [ 0,3300 ] E ES S BACKGROUND
� 99 SCALED ANALOG DEVICE CONFIGURATION a 1 • 10 -4 a 2 • 6800 a 3 • 0 a 4 • 4400 a 5 • 10 -2 DAC1 DAC2 DAC3 DAC4 DAC5 [ 0,3300 ] [ 0,3300 ] [0,3300 ] [ 0,10 ] [ 0,10 ] a 6 • A a 10 • B a 7 • X0 a 8 • Z0 a 9 • Y0 [10 -5 ,10 -3 ] [10 -4 ,1 ] [0,1000 ] [0,1000 ] [0,1000 ] mm [0,1600 ] [0,1600 ] [0,1600 ] a 13 • Y a 12 • Z a 11 • X simulation speed ADC1 ADC2 ADC3 τ [ 0,3300 ] [ 0,3300 ] [ 0,3300 ] a 14 • E a 15 • ES a 16 • S BACKGROUND
� 100 SCALED ANALOG DEVICE CONFIGURATION a 1 • 10 -4 a 2 • 6800 a 3 • 0 a 4 • 4400 a 5 • 10 -2 DAC1 DAC2 DAC3 DAC4 DAC5 [ 0,3300 ] [ 0,3300 ] [0,3300 ] [ 0,10 ] [ 0,10 ] a 6 • A a 10 • B a 7 • X0 a 8 • Z0 a 9 • Y0 [10 -5 ,10 -3 ] [10 -4 ,1 ] [0,1000 ] [0,1000 ] [0,1000 ] mm [0,1600 ] [0,1600 ] [0,1600 ] a 13 • Y a 12 • Z a 11 • X simulation speed ADC1 ADC2 ADC3 τ [ 0,3300 ] [ 0,3300 ] [ 0,3300 ] a 14 • E a 15 • ES a 16 • S BACKGROUND
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