Chemical Analog Computers for Clock Frequency Control Based on P - - PowerPoint PPT Presentation

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Chemical Analog Computers for Clock Frequency Control Based on P Modules

Thomas Hinze Christian Bodenstein Benedict Schau Ines Heiland Stefan Schuster

Friedrich Schiller University Jena Department of Bioinformatics at School of Biology and Pharmacy Modelling Oscillatory Information Processing Group

{thomas.hinze}@uni-jena.de

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Human Daily Rhythm: Trigger and Control System

www.wikipedia.org Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Continuous or Fine-grained Real-valued Signals

force flow power current/voltage position concentration size velocity temperature brightness time pressure weight pH

endocontrol.de fritz-spieker.de rundumschule.ch gstatic.com

= ⇒ measurable system’s input and output on the fly

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Module as a Processing Unit for Computational Tasks

input signals

• utput signals

system providing input-output mapping on the fly

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster
• metabolic P system (mP system) M
• P system for cell signalling modules ΠCSM
• P system for cell signalling networks ΠCSN
• ordinary differential equations (ODEs) in

conjunction with numerical solver

• transfer function (input-output mapping)
• n its own, given explicitly or implicitly
• characteristic curve, given by numeric

values along with approximation/interpolation algorithm

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Module as a Processing Unit for Computational Tasks

input signals

• utput signals

system providing input-output mapping on the fly

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster
• metabolic P system (mP system) M
• P system for cell signalling modules ΠCSM
• P system for cell signalling networks ΠCSN
• ordinary differential equations (ODEs) in

conjunction with numerical solver

• transfer function (input-output mapping)
• n its own, given explicitly or implicitly
• characteristic curve, given by numeric

values along with approximation/interpolation algorithm

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Module as a Processing Unit for Computational Tasks

input signals

• utput signals

system providing input-output mapping on the fly

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster
• metabolic P system (mP system) M
• P system for cell signalling modules ΠCSM
• P system for cell signalling networks ΠCSN
• ordinary differential equations (ODEs) in

conjunction with numerical solver

• transfer function (input-output mapping)
• n its own, given explicitly or implicitly
• characteristic curve, given by numeric

values along with approximation/interpolation algorithm

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Module as a Processing Unit for Computational Tasks

input signals

• utput signals

system providing input-output mapping on the fly

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster
• metabolic P system (mP system) M
• P system for cell signalling modules ΠCSM
• P system for cell signalling networks ΠCSN
• ordinary differential equations (ODEs) in

conjunction with numerical solver

• transfer function (input-output mapping)
• n its own, given explicitly or implicitly
• characteristic curve, given by numeric

values along with approximation/interpolation algorithm

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Module as a Processing Unit for Computational Tasks

input signals

• utput signals

system providing input-output mapping on the fly

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster
• metabolic P system (mP system) M
• P system for cell signalling modules ΠCSM
• P system for cell signalling networks ΠCSN
• ordinary differential equations (ODEs) in

conjunction with numerical solver

• transfer function (input-output mapping)
• n its own, given explicitly or implicitly
• characteristic curve, given by numeric

values along with approximation/interpolation algorithm

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Module as a Processing Unit for Computational Tasks

input signals

• utput signals

system providing input-output mapping on the fly

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster
• metabolic P system (mP system) M
• P system for cell signalling modules ΠCSM
• P system for cell signalling networks ΠCSN
• ordinary differential equations (ODEs) in

conjunction with numerical solver

• transfer function (input-output mapping)
• n its own, given explicitly or implicitly
• characteristic curve, given by numeric

values along with approximation/interpolation algorithm

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Module as a Processing Unit for Computational Tasks

input signals

• utput signals

system providing input-output mapping on the fly

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster
• metabolic P system (mP system) M
• P system for cell signalling modules ΠCSM
• P system for cell signalling networks ΠCSN
• ordinary differential equations (ODEs) in

conjunction with numerical solver

• transfer function (input-output mapping)
• n its own, given explicitly or implicitly
• characteristic curve, given by numeric

values along with approximation/interpolation algorithm

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

P Module

• is able to fulfill an elementary computational task on the fly
• building block of an analog computer or in a control loop
• represents a container encapsulating a formal description
• f its dynamical behaviour
• specifies the interface of a general real-valued system or

its approximation

• aims to bridge building blocks in systems theory and

membrane systems More formally, a P module is a triple (↓, ↑, ) where ↓= (I1, . . . , Ii) . . . . . . . . . . indicates a list of input signal identifiers ↑= (O1, . . . , Oo) . . . . . . indicates a list of output signal identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . underlying system specification with or without inherent auxiliary signals Each signal is a real-valued function over time.

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

P Module

• is able to fulfill an elementary computational task on the fly
• building block of an analog computer or in a control loop
• represents a container encapsulating a formal description
• f its dynamical behaviour
• specifies the interface of a general real-valued system or

its approximation

• aims to bridge building blocks in systems theory and

membrane systems More formally, a P module is a triple (↓, ↑, ) where ↓= (I1, . . . , Ii) . . . . . . . . . . indicates a list of input signal identifiers ↑= (O1, . . . , Oo) . . . . . . indicates a list of output signal identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . underlying system specification with or without inherent auxiliary signals Each signal is a real-valued function over time.

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

P Module

• is able to fulfill an elementary computational task on the fly
• building block of an analog computer or in a control loop
• represents a container encapsulating a formal description
• f its dynamical behaviour
• specifies the interface of a general real-valued system or

its approximation

• aims to bridge building blocks in systems theory and

membrane systems More formally, a P module is a triple (↓, ↑, ) where ↓= (I1, . . . , Ii) . . . . . . . . . . indicates a list of input signal identifiers ↑= (O1, . . . , Oo) . . . . . . indicates a list of output signal identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . underlying system specification with or without inherent auxiliary signals Each signal is a real-valued function over time.

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

P Module

• is able to fulfill an elementary computational task on the fly
• building block of an analog computer or in a control loop
• represents a container encapsulating a formal description
• f its dynamical behaviour
• specifies the interface of a general real-valued system or

its approximation

• aims to bridge building blocks in systems theory and

membrane systems More formally, a P module is a triple (↓, ↑, ) where ↓= (I1, . . . , Ii) . . . . . . . . . . indicates a list of input signal identifiers ↑= (O1, . . . , Oo) . . . . . . indicates a list of output signal identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . underlying system specification with or without inherent auxiliary signals Each signal is a real-valued function over time.

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

P Module

• is able to fulfill an elementary computational task on the fly
• building block of an analog computer or in a control loop
• represents a container encapsulating a formal description
• f its dynamical behaviour
• specifies the interface of a general real-valued system or

its approximation

• aims to bridge building blocks in systems theory and

membrane systems More formally, a P module is a triple (↓, ↑, ) where ↓= (I1, . . . , Ii) . . . . . . . . . . indicates a list of input signal identifiers ↑= (O1, . . . , Oo) . . . . . . indicates a list of output signal identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . underlying system specification with or without inherent auxiliary signals Each signal is a real-valued function over time.

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

P Module

• is able to fulfill an elementary computational task on the fly
• building block of an analog computer or in a control loop
• represents a container encapsulating a formal description
• f its dynamical behaviour
• specifies the interface of a general real-valued system or

its approximation

• aims to bridge building blocks in systems theory and

membrane systems More formally, a P module is a triple (↓, ↑, ) where ↓= (I1, . . . , Ii) . . . . . . . . . . indicates a list of input signal identifiers ↑= (O1, . . . , Oo) . . . . . . indicates a list of output signal identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . underlying system specification with or without inherent auxiliary signals Each signal is a real-valued function over time.

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

• 1. Motivation and Concept of P Modules

2. Processing Units: Components of Chemical Control Loops

• Arithmetic Functions (add, sub, mul, div, sqrt)
• Low-pass Filter
• Controllable Goodwin-type Core Oscillator
• 3. Phase-locked Loop (PLL):

Continuous Frequency Control

• 4. Simulation Studies for

Circadian Clock Systems

• 5. Prospectives

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Addition

1 2 3 4 5 6 10 20 30 40 50 60 70 80 90 100 substrate concentration time X1 X2 Y

X1 k 1 k 2 k 3 X2 Y

˙ [X1] = ˙ [X2] = ˙ [Y] = k1[X1] + k2[X2] − k3[Y] ODE solution for asymptotic steady state in case of k1 = k2 = k3: [Y](∞) = lim

t→∞

• 1 − e−k1t

· ([X1](t) + [X2](t)) = [X1](0) + [X2](0) Input-output mapping: [Y] = [X1] + [X2]

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Non-negative Subtraction

1 2 3 4 5 6 10 20 30 40 50 60 70 80 90 100 substrate concentration time X1 X2 Y

k 1 Y Z k 1 k 2 X2 k 1 X1

˙ [X1] = ˙ [X2] = ˙ [Y] = −k2[Y][Z] − k1[Y] + k1[X1] ˙ [Z] = k1[X2] − k2[Y][Z] ODE solution for asymptotic steady state in case of k1 = k2 > 0: [Y](∞) = [X1](0) − [X2](0) iff [X1](0) > [X2](0) 0 otherwise Input-output mapping: [Y] = [X1] −(≥0) [X2]

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Multiplication

1 2 3 4 5 6 7 10 20 30 40 50 60 70 80 90 100 substrate concentration time X1 X2 Y

X1 k 2 k 1 X2 Y

˙ [X1] = ˙ [X2] = ˙ [Y] = k1[X1][X2] − k2[Y] ODE solution for asymptotic steady state in case of k1 = k2 > 0: [Y](∞) = lim

t→∞

• 1 − e−k1t

· ([X1](t) · [X2](t)) = [X1](0) · [X2](0) Input-output mapping: [Y] = [X1] · [X2]

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Division

1 2 3 4 5 6 7 10 20 30 40 50 60 70 80 90 100 substrate concentration time X1 X2 Y

X1 k 1 k 2 X2 Y

˙ [X1] = ˙ [X2] = ˙ [Y] = k2[X2] − k1[X1][Y] ODE solution for asymptotic steady state in case of k1 = k2 > 0: [Y](∞) =    lim

t→∞

• 1 − e−k1t

· [X2](t)

[X1](t)

• iff [X1](t) > 0

lim

t→∞

• k2[X2](t) dt
• therwise

Input-output mapping: [Y] = [X2]/[X1] iff [X1] > 0

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Square Root

1 2 10 20 30 40 50 60 70 80 90 100 substrate concentration time X Y

k 2 X Y k 1

˙ [X] = ˙ [Y] = k1[X] − 2k2[Y]2 ODE solution for asymptotic steady state in case of k1 = 2k2 > 0: [Y](∞) = lim

t→∞

• [X](t) · tanh(k1t
• [X](t))
• Input-output mapping: [Y] =
• [X](0)

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Low-pass Filter

X2 X3 k n Y k n−1 k 3 X1 k 2 k 1 Xn−1 X k n+1

time (days) substrate concentration [Y] time (days) substrate concentration [X]

˙ [X1] = k1[X] − k2[X1] ˙ [X2] = k2[X1] − k3[X2] . . . ˙ [X n−1] = kn−1[Xn−2] − kn[Xn−1] ˙ [Y] = kn[Xn−1] − kn+1[Y]

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Low-pass Filter: Bode Plot as Characteristic Curve

frequency in 1/s cutoff frequency slope magnitude in dB

Magnitude dB = 10 · lg

• amplitude of output signal

amplitude of input signal

• Signals affected by smoothing delay throughout cascade
• Oscillation waveform harmonisation into sinusoidal shape
• Global filter parameters:

passband damping, cutoff frequency, slope

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Controllable Goodwin-type Core Oscillator

a, A, translation transportation transcriptional inhibition Z X k 5 k 4,K 4 k 6,K 6 Y k 3 K1 k 2,K 2

time (days) substrate concentration X Y Z k6 (nM/h) period length after transient phase (h) k4 (nM/h) period length after transient phase (h) k2 (nM/h) period length after transient phase (h)

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Core Oscillator: Dynamical Behaviour

˙ [X] = a A + K1[Z]2 − k2[X] K2 + [X] ˙ [Y] = k3[X] − k5[Y] − k4[Y] K4 + [Y] ˙ [Z] = k5[Y] − k6[Z] K6 + [Z]

• B. Schau. Reverse-Engineering circadianer Oszillationssysteme als Frequenzregelkreise mit
• Nachlaufsynchronisation. Diploma thesis, 2011

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Core Oscillator: Dynamical Behaviour

k6

p e r i

• d

l e n g t h ( h )

• Velocity parameter k6 of Z degradation notably influences
• scillation frequency
• Period control coefficients assigned to each reaction

quantify influence on frequency

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

• 1. Motivation and Concept of P Modules
• 2. Processing Units:

Components of Chemical Control Loops 3. Phase-locked Loop (PLL): Continuous Frequency Control

• Chronobiology
• Circadian Clocks and Entrainment
• General Scheme of a Control Loop
• Scheme of a Phase-locked Loop
• Model of a Chemical Frequency Control

Based on PLL

• 4. Simulation Studies for

Circadian Clock Systems

• 5. Prospectives

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Chronobiology

science of biological rhythms and clock systems

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Circadian Clock

• Undamped biochemical oscillation
• Free-running period close to but typically not exactly 24

hours persisting under constant environmental conditions (e.g. permanent darkness DD or permanent light LL)

• Entrainment – adaptation to external stimuli

(e.g. light-dark cycles induced by sunlight)

• Temperature compensation within a physiological range
• Reaction systems with at least one feedback loop

= ⇒ Biological counterpart of frequency control system

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Circadian Clock

• Undamped biochemical oscillation
• Free-running period close to but typically not exactly 24

hours persisting under constant environmental conditions (e.g. permanent darkness DD or permanent light LL)

• Entrainment – adaptation to external stimuli

(e.g. light-dark cycles induced by sunlight)

• Temperature compensation within a physiological range
• Reaction systems with at least one feedback loop

= ⇒ Biological counterpart of frequency control system

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

General Scheme of a Simple Control Loop

u(t) = C(D(w(t),y(t)))

controller actuator plant sensor

x(t) = P(v(t)) y(t) = F(x(t)) v(t) = A(u(t)) stimulus external system output v(t) u(t) y(t) w(t) x(t)

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Scheme of a Phase-locked Loop

external reference

• scillator reference

e(t) pd(t) x(t) with period (p), e(t) affects pl Phase detector e.g. Multiplier pd(t)=f(t)*x(t) f(t) Loop- filter Oscillator error signal: phase difference

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Scheme of a Phase-locked Loop

+ e(t) pd(t) x(t) f(t) Goodwin- Oscillator +

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Model of a Chemical Frequency Control Based on PLL

low−pass filter core oscillator

characteristic curve Bode plot

comparator

[Y] = [E][Z]

signal

core

• scillator

filter low−pass plant actuator controller [F](t) [Z](t) external stimulus [E](t)

a, A, transfer function scaled tuning signal [D] = [U]+[F]*ae ae = Y k 3 X k 5 k 4,K 4 k 6,K 6 X2 X3 l 5 E m1 K1 k 8 k 8 k 7 k 7 k 7 U F l 4 l 3 X1 l 2 l 1 X4 Z D F Z X Y k 2,K 2

magnitude (dB) frequency (1/s) k6 (nM/h)

period length after transient phase (h)

length of 0.61 days) cutoff frequency: 0.000019 1/s (corresponds to period

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

• 1. Motivation and Concept of P Modules
• 2. Processing Units:

Components of Chemical Control Loops

• 3. Phase-locked Loop (PLL):

Continuous Frequency Control 4. Simulation Studies for Circadian Clock Systems

• Period Lengths subject to Constant Ext. Stimulus
• Time to Entrainment to Different Period Lengths
• Time to Entrainment to Different Initial Phase Shift
• Best Case and Worst Case Entrainment
• 5. Prospectives

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Period Lengths subject to Constant External Stimulus

constant external stimulus [E] period length (h) of signal [Z]

Increase of external stimulus’ species concentration [E] decreases period (accelerates oscillation)

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Time to Entrainment to Different Period Lengths

period length (h) of external stimulus [E] time to entrainment (days) of signal [Z]

Natural period of core oscillator: 24.2h Fast adaptation to slightly shorter periods Slow (gradual) adaptation to longer periods

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Time to Entrainment to Different Initial Phase Shifts

initial phase shift (°) between external stimulus [E] and core oscillator output [Z] time to entrainment (days) of signal [Z] external stimulus' period length 24h 26' 24h worst case best case

Entrainment reached within convergence interval 1min

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Best Case and Worst Case Entrainment

time (days) period length (h) of signal [Z] external stimulus' period length and initial phase shift 24h and 325° 24h and 245°

Entrainment reached within convergence interval 1min

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

• 1. Motivation and Concept of P Modules
• 2. Processing Units:

Components of Chemical Control Loops

• 3. Phase-locked Loop (PLL):

Continuous Frequency Control

• 4. Simulation Studies for

Circadian Clock Systems 5. Prospectives

• Conclusions and Open Questions
• Acknowledgements

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Conclusions

• Chemical frequency control can utilise PLL
• Prototypic modelling example for

entrainment of circadian clockworks

• Chemical processing units in minimalistic manner
• Variety of chemical implementations
• Modularisation in (bio)chemical reaction systems

Some open questions

• Identification of in-vivo counterparts
• Replacement of individual processing units

(like different core oscillators)

• Balancing advantages and limitations of the PLL approach
• Inclusion of temperature entrainment (by Arrhenius terms)
• Alternative concepts of frequency control

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Conclusions

• Chemical frequency control can utilise PLL
• Prototypic modelling example for

entrainment of circadian clockworks

• Chemical processing units in minimalistic manner
• Variety of chemical implementations
• Modularisation in (bio)chemical reaction systems

Some open questions

• Identification of in-vivo counterparts
• Replacement of individual processing units

(like different core oscillators)

• Balancing advantages and limitations of the PLL approach
• Inclusion of temperature entrainment (by Arrhenius terms)
• Alternative concepts of frequency control

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Conclusions

• Chemical frequency control can utilise PLL
• Prototypic modelling example for

entrainment of circadian clockworks

• Chemical processing units in minimalistic manner
• Variety of chemical implementations
• Modularisation in (bio)chemical reaction systems

Some open questions

• Identification of in-vivo counterparts
• Replacement of individual processing units

(like different core oscillators)

• Balancing advantages and limitations of the PLL approach
• Inclusion of temperature entrainment (by Arrhenius terms)
• Alternative concepts of frequency control

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Conclusions

• Chemical frequency control can utilise PLL
• Prototypic modelling example for

entrainment of circadian clockworks

• Chemical processing units in minimalistic manner
• Variety of chemical implementations
• Modularisation in (bio)chemical reaction systems

Some open questions

• Identification of in-vivo counterparts
• Replacement of individual processing units

(like different core oscillators)

• Balancing advantages and limitations of the PLL approach
• Inclusion of temperature entrainment (by Arrhenius terms)
• Alternative concepts of frequency control

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Conclusions

• Chemical frequency control can utilise PLL
• Prototypic modelling example for

entrainment of circadian clockworks

• Chemical processing units in minimalistic manner
• Variety of chemical implementations
• Modularisation in (bio)chemical reaction systems

Some open questions

• Identification of in-vivo counterparts
• Replacement of individual processing units

(like different core oscillators)

• Balancing advantages and limitations of the PLL approach
• Inclusion of temperature entrainment (by Arrhenius terms)
• Alternative concepts of frequency control

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Conclusions

• Chemical frequency control can utilise PLL
• Prototypic modelling example for

entrainment of circadian clockworks

• Chemical processing units in minimalistic manner
• Variety of chemical implementations
• Modularisation in (bio)chemical reaction systems

Some open questions

• Identification of in-vivo counterparts
• Replacement of individual processing units

(like different core oscillators)

• Balancing advantages and limitations of the PLL approach
• Inclusion of temperature entrainment (by Arrhenius terms)
• Alternative concepts of frequency control

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Conclusions

• Chemical frequency control can utilise PLL
• Prototypic modelling example for

entrainment of circadian clockworks

• Chemical processing units in minimalistic manner
• Variety of chemical implementations
• Modularisation in (bio)chemical reaction systems

Some open questions

• Identification of in-vivo counterparts
• Replacement of individual processing units

(like different core oscillators)

• Balancing advantages and limitations of the PLL approach
• Inclusion of temperature entrainment (by Arrhenius terms)
• Alternative concepts of frequency control

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Conclusions

• Chemical frequency control can utilise PLL
• Prototypic modelling example for

entrainment of circadian clockworks

• Chemical processing units in minimalistic manner
• Variety of chemical implementations
• Modularisation in (bio)chemical reaction systems

Some open questions

• Identification of in-vivo counterparts
• Replacement of individual processing units

(like different core oscillators)

• Balancing advantages and limitations of the PLL approach
• Inclusion of temperature entrainment (by Arrhenius terms)
• Alternative concepts of frequency control

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Conclusions

• Chemical frequency control can utilise PLL
• Prototypic modelling example for

entrainment of circadian clockworks

• Chemical processing units in minimalistic manner
• Variety of chemical implementations
• Modularisation in (bio)chemical reaction systems

Some open questions

• Identification of in-vivo counterparts
• Replacement of individual processing units

(like different core oscillators)

• Balancing advantages and limitations of the PLL approach
• Inclusion of temperature entrainment (by Arrhenius terms)
• Alternative concepts of frequency control

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Conclusions

• Chemical frequency control can utilise PLL
• Prototypic modelling example for

entrainment of circadian clockworks

• Chemical processing units in minimalistic manner
• Variety of chemical implementations
• Modularisation in (bio)chemical reaction systems

Some open questions

• Identification of in-vivo counterparts
• Replacement of individual processing units

(like different core oscillators)

• Balancing advantages and limitations of the PLL approach
• Inclusion of temperature entrainment (by Arrhenius terms)
• Alternative concepts of frequency control

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster

P Modules Processing Units Phase-locked Loop Simulation Studies Prospectives

Acknowledgements

Department of Bioinformatics at School of Biology and Pharmacy Friedrich Schiller University Jena Jena Centre for Bioinformatics Research Initiative in Systems Biology German Federal Ministry of Education and Research, project no. 0315260A

Chemical Clock Frequency Control Based on P Modules

• T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster