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Computation by Synthetic Cell Signaling and Oscillating Processes - - PowerPoint PPT Presentation

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Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Computation by Synthetic Cell Signaling and Oscillating Processes Modelled using Mass-Action Kinetics T.Hinze 1 R.Faler 1 G.Escuela 2 B.Ibrahim 3 S.Schuster 1

slide-1
SLIDE 1

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Computation by Synthetic Cell Signaling and Oscillating Processes Modelled using Mass-Action Kinetics

T.Hinze1 R.Faßler1 G.Escuela2 B.Ibrahim3 S.Schuster1

{thomas.hinze,gabi.escuela,stefan.schu}@uni-jena.de, raf@minet.uni-jena.de, b.ibrahim@dkfz-heidelberg.de

Friedrich Schiller University Jena

1Department Bioinformatics at

School of Biology/Pharmacy

2Bio Systems Analysis Group 3German Cancer Research Center

Mol.Biol.of Centrosomes & Cilia Computability in Europe (CiE 2009)

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
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SLIDE 2

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Outline

Computation by Synthetic Cell Signaling

  • 1. Motivation
  • 2. Chemical information processing:

Cell signaling

  • 3. Mass-action kinetics
  • 4. Deterministic register machine (RAM)
  • 5. Chemical RAM representation
  • Clock
  • Master-slave flip-flops
  • Registers
  • Program control
  • 6. Example 1: Integer addition
  • 7. Example 2: Maximum of three nat. numbers
  • 8. Outlook and acknowledgement

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

1 1 1 1 1 1 1 1 1 1 1 1 1

# time

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SLIDE 3

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Motivation

  • Chemical/Molecular computing
  • Potential high capacity and density of

molecular data storage

  • Exploring similarities to

biological information processing

  • Identification of

computational units in biological systems

  • Artificial evolution of

reaction networks towards specific tasks

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

A B = 0,02

R Stoffkonzentration Stoffkonzentration

k

time species concentration

A] [ B] [ B [ A] [ ] (0) = 24 (0) = 0

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SLIDE 4

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Biological Principles of Cell Signaling

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

genomic dna gene expression

cell membrane

phospholipid bilayer

cytosol

transformation, amplification via pathways signal transduction, cell response ADP ATP phosphorylation activation by protein kinases activation cascade GDP GTP

external signal

endocrine (dist.) paracrine (near) autocrine (same cell) ligands hormones, factors, ... inner membrane

receptors

enzyme−linked ion−channel G−protein−linked

nucleus

slide-5
SLIDE 5

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Typical Information Flow in Cell Signaling

K signal/stimulus A B P P C D P P E F P P reception activation cascades (pathways) information flow via transduction: signal amplification, transformation, combination

  • Motif: stepwise protein activation by phosphorylation
  • Cascadization of motifs for signal transduction,

amplification, transformation, combination

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
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SLIDE 6

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Typical Information Flow in Metabolic Networks

C D A2 B’ C’ C2 D’ B2 A B K3 K1 K2

  • Sequence of catalyzed reactions
  • Reactants and products usually not acting as catalysts

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-7
SLIDE 7

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Mass-Action Kinetics: Background

Modeling Temporal Behavior of Chemical Reaction Networks

Assumption: number of effective reactant collisions Z proportional to reactant concentrations (Guldberg 1867) A + B

ˆ k

− → C . . . . ZC ∼ [A] and ZC ∼ [B], so ZC ∼ [A] · [B] Production rate generating C: vprod([C]) = ˆ k · [A] · [B] Consumption rate of C: . . . . . .vcons([C]) = 0

d [C] d t

= vprod([C]) − vcons([C])

d [C] d t

= ˆ k · [A] · [B] Initial conditions: [C](0), [A](0), [B](0) to be set

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-8
SLIDE 8

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Mass-Action Kinetics: Background

Modeling Temporal Behavior of Chemical Reaction Networks

Assumption: number of effective reactant collisions Z proportional to reactant concentrations (Guldberg 1867) A + B

ˆ k

− → C . . . . ZC ∼ [A] and ZC ∼ [B], so ZC ∼ [A] · [B] Production rate generating C: vprod([C]) = ˆ k · [A] · [B] Consumption rate of C: . . . . . .vcons([C]) = 0

d [C] d t

= vprod([C]) − vcons([C])

d [C] d t

= ˆ k · [A] · [B] Initial conditions: [C](0), [A](0), [B](0) to be set

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-9
SLIDE 9

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Mass-Action Kinetics: Background

Modeling Temporal Behavior of Chemical Reaction Networks

Assumption: number of effective reactant collisions Z proportional to reactant concentrations (Guldberg 1867) A + B

ˆ k

− → C . . . . ZC ∼ [A] and ZC ∼ [B], so ZC ∼ [A] · [B] Production rate generating C: vprod([C]) = ˆ k · [A] · [B] Consumption rate of C: . . . . . .vcons([C]) = 0

d [C] d t

= vprod([C]) − vcons([C])

d [C] d t

= ˆ k · [A] · [B] Initial conditions: [C](0), [A](0), [B](0) to be set

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-10
SLIDE 10

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Mass-Action Kinetics: Background

Modeling Temporal Behavior of Chemical Reaction Networks

Assumption: number of effective reactant collisions Z proportional to reactant concentrations (Guldberg 1867) A + B

ˆ k

− → C . . . . ZC ∼ [A] and ZC ∼ [B], so ZC ∼ [A] · [B] Production rate generating C: vprod([C]) = ˆ k · [A] · [B] Consumption rate of C: . . . . . .vcons([C]) = 0

d [C] d t

= vprod([C]) − vcons([C])

d [C] d t

= ˆ k · [A] · [B] Initial conditions: [C](0), [A](0), [B](0) to be set

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-11
SLIDE 11

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Mass-Action Kinetics: Background

Modeling Temporal Behavior of Chemical Reaction Networks

Assumption: number of effective reactant collisions Z proportional to reactant concentrations (Guldberg 1867) A + B

ˆ k

− → C . . . . ZC ∼ [A] and ZC ∼ [B], so ZC ∼ [A] · [B] Production rate generating C: vprod([C]) = ˆ k · [A] · [B] Consumption rate of C: . . . . . .vcons([C]) = 0

d [C] d t

= vprod([C]) − vcons([C])

d [C] d t

= ˆ k · [A] · [B] Initial conditions: [C](0), [A](0), [B](0) to be set

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-12
SLIDE 12

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Mass-Action Kinetics: Background

Modeling Temporal Behavior of Chemical Reaction Networks

Assumption: number of effective reactant collisions Z proportional to reactant concentrations (Guldberg 1867) A + B

ˆ k

− → C . . . . ZC ∼ [A] and ZC ∼ [B], so ZC ∼ [A] · [B] Production rate generating C: vprod([C]) = ˆ k · [A] · [B] Consumption rate of C: . . . . . .vcons([C]) = 0

d [C] d t

= vprod([C]) − vcons([C])

d [C] d t

= ˆ k · [A] · [B] Initial conditions: [C](0), [A](0), [B](0) to be set

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-13
SLIDE 13

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Mass-Action Kinetics: General ODE Model

Chemical reaction system a1,1S1 + a2,1S2 + . . . + an,1Sn

ˆ k1

− → b1,1S1 + b2,1S2 + . . . + bn,1Sn a1,2S1 + a2,2S2 + . . . + an,2Sn

ˆ k2

− → b1,2S1 + b2,2S2 + . . . + bn,2Sn . . . a1,hS1 + a2,hS2 + . . . + an,hSn

ˆ kh

− → b1,hS1 + b2,hS2 + . . . + bn,hSn, results in ordinary differential equations d [Si] d t =

h

  • ν=1
  • ˆ

kν · (bi,ν − ai,ν) ·

n

  • l=1

[Sl]al,ν

  • with

i = 1, . . . , n.

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
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SLIDE 14

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Mass-Action Kinetics: A Simple Example

2A + 0B

ˆ k1

− → 0A + 1B ODE system d [A] d t = −2 · ˆ k1 · [A]2 d [B] d t = ˆ k1 · [A]2 Analytic solution [A](t) =

  • 2ˆ

k1t + 1 [A](0) −1 iff [A](0) > 0 else [A](t) = 0 [B](t) =

  • −2
  • 2ˆ

k1t + 1 [A](0) −1 + [A](0) 2 + [B](0)

  • T. Hinze, M. Sturm. Rechnen mit DNA. ISBN 978-3-486-27530-5, Oldenbourg Wissenschaftsverlag, 2004

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

A B

= 0,02

R

Stoffkonzentration Stoffkonzentration

k

time species concentration

A] [ B] [ B [ A] [ ] (0) = 24 (0) = 0

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SLIDE 15

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Register Machine (RAM)

  • Syntactical denotation of components

RAM = (R, L, P, #0)

jump label of first instruction program (finite set of instructions) finite set of jump labels L = {#0, . . . , #n} finite set of registers R = {R1, . . . , Rm}, Rk ∈ N

  • Available instructions
  • #i : INC Rk #j

increment register Rk, jump to #j

  • #i : DEC Rk #j

decrement register Rk, jump to #j

  • #i : IFZ Rk #j #p

if Rk = 0 jump to #j else jump to #p

  • #i : HALT

terminate program and output

  • Useful assumptions
  • Consecutive indexing of jump labels and registers
  • Determinism
  • Initialization of registers at start
  • Output of all m registers when HALT

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
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SLIDE 16

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Chemical RAM with Self-Reproducible Components

  • 1. Construction of chemical reaction networks for boolean

logic gates

  • 2. Introduction of a chemical clock based on oscillating

reactions

  • 3. Specification of a chemical master-slave flip-flop (MSFF)
  • 4. Utilize chemical master-slave flip-flop as 1-bit storage unit

(initial register)

  • 5. Extend registers if needed by integration of further 1-bit

storage units (self-replicable components)

  • 6. Transform register machine program into chemical

program control (INC, DEC, IFZ, HALT)

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
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SLIDE 17

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Chemical Implementation of Boolean Variables and Logic Gates

Boolean variable z represented by two correlated species Z T and Z F Chemical reaction network for NAND

x1 x2 y 1 1 1 1 1 1 1

F 2

x

F 1

x

F

y

T

y

F

y

T

y

F 1

x

F 2

x

F 1

x

F 2

x + + + +

T 2

x

T 1

x

T

y

F

y

T

y

F

y

T 1

x

T 2

x

T 1

x

T 2

x + + + +

T 2

x

F 1

x

F

y

T

y

F 2

x

T 1

x

F

y

T

y

F

y

T

y

F 1

x

T 2

x

F 1

x

T 2

x

F

y

T

y

T 1

x

F 2

x

F 2

x

T 1

x + + + + + + + +

  • T. Hinze, R. Fassler, T. Lenser, P

. Dittrich. Register Machine Computations on Binary Numbers by Oscillating and Catalytic Chemical Reactions Modelled using Mass-Action Kinetics. International Journal of Foundations of Computer Science 20(3):411-426, 2009 Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
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SLIDE 18

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

A Chemical Clock

  • Based on Belousov-Zhabotinsky reactions
  • Cascade of auxiliary reactions for fast-switching behavior
  • Two offset oscillators provide clock signals [C1] and [C2]

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
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SLIDE 19

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Master-Slave Flip-Flop (MSFF)

Reliable 1-bit storage unit, well-studied

master slave C S R M Q

M

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-20
SLIDE 20

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Chemical MSFF Implementation

Two-stage switching from FALSE to TRUE using trigger species and offset clocks C1 and C2

C 1 C 2

species MF, MT: master bit value species SF, ST: slave bit value

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-21
SLIDE 21

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Chemical MSFF Implementation

Two-stage switching from FALSE to TRUE using trigger species and offset clocks C1 and C2

C 2 C 1

species MF, MT: master bit value species SF, ST: slave bit value

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-22
SLIDE 22

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Chemical MSFF Implementation

Two-stage switching from FALSE to TRUE using trigger species and offset clocks C1 and C2

C 2 C 1

species MF, MT: master bit value species SF, ST: slave bit value

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-23
SLIDE 23

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Chemical MSFF Implementation

Two-stage switching from FALSE to TRUE using trigger species and offset clocks C1 and C2

C 2 C 1

species MF, MT: master bit value species SF, ST: slave bit value

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-24
SLIDE 24

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

From MSFF to Register

  • Four network motifs (all switching scenarios) form MSFF
  • Chaining of MSFFs to build register of arbitrary length
  • Assumption of MSFF as self-replicable modular unit

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-25
SLIDE 25

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

From MSFF to Register

  • Four network motifs (all switching scenarios) form MSFF
  • Chaining of MSFFs to build register of arbitrary length
  • Assumption of MSFF as self-replicable modular unit

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-26
SLIDE 26

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Chemical Program Control

Simple example for sequential instruction flow: #0 : IFZ R1 #2 #1 #1 : DEC R1 #0 #2 : HALT

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-27
SLIDE 27

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Chemical Program Control

Transformation scheme instruction reactions #i : INC Rh #j #i + C2

kp

− → INCj

h + C2

INCj

h + C1 kb

− → #j + C1 #i : DEC Rh #j #i + C2

kp

− → DECj

h + C2

DECj

h + C1 kb

− → #j + C1 #i : IFZ Rh #j #q #i + C2

kp

− → IFZ j,q

h + C2

IFZ j,q

h + ET h + C1 ks

− → #j + ET

h + C1

IFZ j,q

h + EF h + C1 ks

− → #q + EF

h + C1

#i : HALT #i + C2

kp

− → HALT + C2 C1, C2: Species providing offset clock signals

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-28
SLIDE 28

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Example 1: Integer Addition “2 + 1"

  • Initialization of registers R1 and R2 with summands
  • R2 := R2 + R1; R1 := 0
  • Bitwise extension of registers if needed
  • Simulation carried out using CellDesigner (SBML)

0.2 0.4 0.6 0.8 1 1.2 0 100 200 300 400 500 600 700 800 Concentration Time scale 0.2 0.4 0.6 0.8 1 1.2 0 100 200 300 400 500 600 700 800 Concentration Time scale 0.2 0.4 0.6 0.8 1 1.2 0 100 200 300 400 500 600 700 800 Concentration Time scale 01 10 10 10 01 01 01 00 00 00 00 00 00 01 01 01 10 10 10 11 11 00 0.2 0.4 0.6 0.8 1 1.2 0 100 200 300 400 500 600 700 800 Concentration Time scale 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 100 200 300 400 500 600 700 800 Concentration Time scale

C 2

M 1,1

T

[ ]

b 1 b 2

M 1,2

T

[ ] M 2,1

T

[ ]

b 1 b 2

M 2,2

T

[ ]

INC # 0 R 1 # 1 INC # 1 R 1 # 2 INC # 2 R 2 # 3 # 6 # 4 IFZ # 3 R 1 # 6 # 4 IFZ # 3 R 1 # 6 # 4 IFZ # 3 R 1 HALT # 6 INC # 5 R 2 # 3 DEC # 4 R 1 # 5 INC # 5 R 2 # 3 DEC # 4 R 1 # 5

clock register R1 register R2

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-29
SLIDE 29

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Example 2: Maximum of Three Numbers “max(2, 1, 3)"

  • R5 := max(R1, R2, R3)
  • Idea: R4 := max(R1, R2); R5 := max(R4, R3)
  • Full network: 142 species and 223 reactions in total

0.5 1 500 1000 1500 2000 0.5 1 500 1000 1500 2000 0.5 1 500 1000 1500 2000 0.5 1 500 1000 1500 2000 0.5 1 500 1000 1500 2000 0.5 1 500 1000 1500 2000 0.5 1 500 1000 1500 2000 0.5 1 500 1000 1500 2000 0.5 1 500 1000 1500 2000 0.5 1 500 1000 1500 2000 0.5 1 500 1000 1500 2000

T

[M ]

5,1 1

b

2

b

5,2 T

[M ]

T

[M ]

1,1 1

b

T

[M ]

1,2 2

b

T

[M ]

2,1 1

b

T

[M ]

2,2 2

b

T

[M ]

3,1 1

b

T

[M ]

3,2 2

b

T

[M ]

4,1 1

b

T

[M ]

4,2 2

b

register R register R register R register R clock

2

[C ]

register R

#0 #1 #2 #3 #4 #0 #1 #5 #9 #10 #11 #9 #12 #13 #14 #15 #16 #12 #13 #14 #15 #16 #12 #17 #18 #19 #20 #18 #24

5 3 2 1 4

  • R. Fassler, T. Hinze, T. Lenser, P

. Dittrich. Construction of Oscillating Chemical Register Machines on Binary Numbers using Mass-Action Kinetics. In O.H. Ibarra, P . Sosik (Eds.), Proceedings PIWMC2008 in conjunction with DNA14, ISBN 978-80-7248-468-3, pp. 11-22, Silesian University Press, 2008 Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-30
SLIDE 30

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Outlook

Take home message

  • Pure chemical computers with self-reproducible

components can reach Turing-completeness

  • Oscillatory processes as universal clock generators
  • Digital (based on two correlated species) vs. analog

(concentration-based) encoding of data

  • Chemical RAM: Framework for providing network

prototypes with dedicated functionality for comparative studies (reverse engineering) Further work

  • Parallelization of chemical RAM following CREW strategy

for memory access

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster
slide-31
SLIDE 31

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook

Special Thanks go to . . . Gabi Escuela

Bio Systems Analysis Group, FSU Jena

Raffael Faßler

Department Bioinformatics, FSU Jena

Bashar Ibrahim

German Cancer Research Center

Stefan Schuster

Department Bioinformatics, FSU Jena

... the funding organization

German Federal Ministry of Education and Research, project 0315260A within Research Initiative in Systems Biology

... you for your attention. Questions? ... my coworkers

Computation by Synthetic Cell Signaling

  • T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster