Membrane Computing Meets Temperature: A Thermoreceptor Model as - - PowerPoint PPT Presentation

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Membrane Computing Meets Temperature: A Thermoreceptor Model as Molecular Slide Rule with Evolutionary Potential

Thomas Hinze1,2 Korcan Kirkici3 Patricia Sauer1 Peter Sauer1 Jörn Behre4

1Brandenburg University of Technology Cottbus–Senftenberg 2Friedrich Schiller University Jena 3Dresden University of Technology 4Norwich Institute of Food Research, Theoretical Systems Biology

thomas.hinze@b-tu.de

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Archaea: Evolutionary Success for 2.5 Billion Years

www.studyblue.com www.noaa.gov www.berkeley.edu www.boundless.com

How could these organisms persist so long populating most regions worldwide?

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Archaea – Domain of Early Organisms

in Phylogenetic Tree of Life

www.ck12.org

• Archaea: unicellular

microorganisms, microbes, prokaryotes

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Archaea – Domain of Early Organisms

in Phylogenetic Tree of Life

www.ck12.org

• Archaea: unicellular

microorganisms, microbes, prokaryotes

• Cell length: 0.2 . . . 3µm,

asexual reproduction by binary fission, budding, or fragmentation

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Archaea – Domain of Early Organisms

in Phylogenetic Tree of Life

www.ck12.org

• Archaea: unicellular

microorganisms, microbes, prokaryotes

• Cell length: 0.2 . . . 3µm,

asexual reproduction by binary fission, budding, or fragmentation

• Today widespread: for

instance in human body and in oceanic picoplankton (up to ≈ 40%

• f microbial biomass)

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Major Part of Picoplankton and Origin of Food Chain

www.wikipedia.org lower medium higher highest archaea concentration

Archaea found in large oceanic surface regions from the equator towards the poles following sea currents

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Archaea: Fascinating Extremophilic Organisms

• Archaea seen as anchestor of subsequent

biological domains like bacteria and eukaryotes

• Combine a minimalistic molecular equipment

with astonishing flexibility in coping with environmental conditions

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Archaea: Fascinating Extremophilic Organisms

• Archaea seen as anchestor of subsequent

biological domains like bacteria and eukaryotes

• Combine a minimalistic molecular equipment

with astonishing flexibility in coping with environmental conditions

• Exhibit an outstanding robustness against

abrupt and drastic environmental changes in aqueous surroundings

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Archaea: Fascinating Extremophilic Organisms

• Archaea seen as anchestor of subsequent

biological domains like bacteria and eukaryotes

• Combine a minimalistic molecular equipment

with astonishing flexibility in coping with environmental conditions

• Exhibit an outstanding robustness against

abrupt and drastic environmental changes in aqueous surroundings

• Thermophilic exemplars grow at 130◦C

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre carleton.edu Fumaroles and geysers in Iceland www.study.com Hydro- thermal vent of black smoker

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Archaea: Fascinating Extremophilic Organisms

• Archaea seen as anchestor of subsequent

biological domains like bacteria and eukaryotes

• Combine a minimalistic molecular equipment

with astonishing flexibility in coping with environmental conditions

• Exhibit an outstanding robustness against

abrupt and drastic environmental changes in aqueous surroundings

• Thermophilic exemplars grow at 130◦C
• Alkaliphilic forms resist pH up to ≈ 10

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre carleton.edu Fumaroles and geysers in Iceland www.study.com Hydro- thermal vent of black smoker

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Archaea: Fascinating Extremophilic Organisms

• Archaea seen as anchestor of subsequent

biological domains like bacteria and eukaryotes

• Combine a minimalistic molecular equipment

with astonishing flexibility in coping with environmental conditions

• Exhibit an outstanding robustness against

abrupt and drastic environmental changes in aqueous surroundings

• Thermophilic exemplars grow at 130◦C
• Alkaliphilic forms resist pH up to ≈ 10
• Acidophilic ones prefer pH up to ≈ 0

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre carleton.edu Fumaroles and geysers in Iceland www.study.com Hydro- thermal vent of black smoker

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Archaea: Fascinating Extremophilic Organisms

• Archaea seen as anchestor of subsequent

biological domains like bacteria and eukaryotes

• Combine a minimalistic molecular equipment

with astonishing flexibility in coping with environmental conditions

• Exhibit an outstanding robustness against

abrupt and drastic environmental changes in aqueous surroundings

• Thermophilic exemplars grow at 130◦C
• Alkaliphilic forms resist pH up to ≈ 10
• Acidophilic ones prefer pH up to ≈ 0
• Halophilic archaea prefer salt lakes,

hot springs and other extreme habitats

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre carleton.edu Fumaroles and geysers in Iceland www.study.com Hydro- thermal vent of black smoker

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Hypothetical Archaea Survival Strategy

daytime nighttime water temperature difference: approx. 3 C

• Nearly no atmospheric

protection against high-energy radiation

• n earth at primeval era
• High-energy radiation

comes with sunlight and can cause life-threatening damages of DNA

• Avoid water near surface during penetration of sunlight
• Move towards surface at night for nutrition
• Moderate movement by chemotaxis
• No light receptors found in archaea but thermoreceptors instead

= ⇒ Temperature receptors can indicate daytime and nighttime

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

It is believed that archaea are the first organisms equipped with temperature sensors. Hence, they might have initiated mechanisms of biological information processing by purposive evaluation of environmental signals.

P . Sengupta, P . Garrity. Sensing temperature. Current Biology 23(8):R304, 2012

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Temperature Reception Based on Ion Channel

+ + + + + + + + + + + + + + + + + + + + − −

cation concentration local intracellular spike cations outside cell voltage difference nearly compensated ion channel throughout outer cell membrane cations outside cell voltage difference molecular gate (closed) time (temporary open) molecular gate

Transient Receptor Potential (TRP) channels highly conserved

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Ion Channel Acting as Thermosensor

time cation concentration time cation concentration

lower temperature higher temperature

• With increasing temperature, diminished electrical forces

to open molecular gate within TRP channel

• Increasing temperature results in higher frequency of

spiking oscillation (warm sensor)

• Frequency encoding of temperature within physiological

range but non-linear mapping between temperature and

• scillation frequency

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Reaction Scheme: Ion Channel as Thermosensor

k4 k1 k3 k2

B D C W A Species identifiers A . . . . . . . . . . . . . . . . . . inositol triphosphate (IP3) B . . . . . . . . . . . . . . . . . . . calcium ions outside cell C . . . . . . . . . . . . calcium ions inside cell (output) D . . . . . . . . . . . . . . . . .permeability of ion channel expressed by spatial protein structure W . . waste (excess of open-gate D structure)

A

k1

− → D; C + 2D

k2

− → 3D; B + D

k3

− → C; D

k4

− → W

• Suppliers A (second messenger IP3) and B (Ca2+) fuel the oscillator
• Self-amplifying effect attracts more and more B to enter the cell leading

to fast increase of C (positive feedback induces spike)

• Short-time self-amplification, afterwards collapsing due to lack of B
• As soon as enough B accumulated, next spike generated
• Resembles operation principle of Brusselator

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Modelling Reaction Behaviour by Mass Action Kinetics

Considering scheme of r reactions and p involved species a1,1S1 + a2,1S2 + . . . + ap,1Sp

k1

− → b1,1S1 + b2,1S2 + . . . + bp,1Sp a1,2S1 + a2,2S2 + . . . + ap,2Sp

k2

− → b1,2S1 + b2,2S2 + . . . + bp,2Sp . . . a1,rS1 + a2,rS2 + . . . + ap,rSp

kr

− → b1,rS1 + b2,rS2 + . . . + bp,rSp, Results in system of ordinary differential equations (ODEs): ˙ [Si] = d[Si] dt =

r

• h=1

 kh · (bi,h − ai,h) ·

p

• j=1

[Sj]aj,h   with i = 1, . . . , p

(Guldberg 1867)

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Incorporation of Temperature by Arrhenius Term

Kinetic parameter k of a reaction Substrates

k

− → Products

k = A(T) · e−E(T)

R·T with reaction-specific quantities T ∈ R>0 . . . . . . . . . . . . . . . . . . . . . . . .Kelvin temperature (0◦C = 273.15K) E(T) . . . . . . activation energy (≈ 30 . . . 100 kJ

mol, guidance value 67 kJ mol)

A(T) . . sensitivity to spatial orientation of colliding molecules (calibr.) R ≈ 8.3144621

J K·mol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gas constant

e ≈ 2.7182818 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Euler’s constant Slide rule effect Q10 law: When temperature is increased by 10K, reaction runs twice up to three times faster

(Arrhenius 1889)

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Observations from Systems Biology Point of View

• Dynamical behaviour of reaction systems typically captured by ODEs
• Consideration of multiple particle systems with huge number of

molecules

• Repositories focused on ODEs including appropriate parameter settings

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Observations from Systems Biology Point of View

• Dynamical behaviour of reaction systems typically captured by ODEs
• Consideration of multiple particle systems with huge number of

molecules

• Repositories focused on ODEs including appropriate parameter settings

Exploitation for Membrane Computing Approaches

• Bring together ODE-based models for multiple particle systems with

rule-based or multiset-based models for low-concentration species or species with evaluation of inner structure and its dynamics

• T. Hinze et al. Membrane Systems and Tools Combining Dynamical Structures with Reaction Kinetics for

Applications in Chronobiology. In P . Frisco, M. Gheorghe, M.J. Perez-Jimenez (Eds.), Applications of Membrane Computing in Systems and Synthetic Biology., Series Emergence, Complexity, and Computation, Vol. 7,

• pp. 133-173, Springer Verlag, 2014

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Observations from Systems Biology Point of View

• Dynamical behaviour of reaction systems typically captured by ODEs
• Consideration of multiple particle systems with huge number of

molecules

• Repositories focused on ODEs including appropriate parameter settings

Exploitation for Membrane Computing Approaches

• Bring together ODE-based models for multiple particle systems with

rule-based or multiset-based models for low-concentration species or species with evaluation of inner structure and its dynamics

• Notice that internal numerical solution of ODEs can be mapped into
• utput of multiset of molecular counts for each point in time
• T. Hinze et al. Membrane Systems and Tools Combining Dynamical Structures with Reaction Kinetics for

Applications in Chronobiology. In P . Frisco, M. Gheorghe, M.J. Perez-Jimenez (Eds.), Applications of Membrane Computing in Systems and Synthetic Biology., Series Emergence, Complexity, and Computation, Vol. 7,

• pp. 133-173, Springer Verlag, 2014

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Observations from Systems Biology Point of View

• Dynamical behaviour of reaction systems typically captured by ODEs
• Consideration of multiple particle systems with huge number of

molecules

• Repositories focused on ODEs including appropriate parameter settings

Exploitation for Membrane Computing Approaches

• Bring together ODE-based models for multiple particle systems with

rule-based or multiset-based models for low-concentration species or species with evaluation of inner structure and its dynamics

• Notice that internal numerical solution of ODEs can be mapped into
• utput of multiset of molecular counts for each point in time
• Deterministic P module captures ODE-based system description

together with marked input and output species and provides multisets of molecular counts

• T. Hinze et al. Membrane Systems and Tools Combining Dynamical Structures with Reaction Kinetics for

Applications in Chronobiology. In P . Frisco, M. Gheorghe, M.J. Perez-Jimenez (Eds.), Applications of Membrane Computing in Systems and Synthetic Biology., Series Emergence, Complexity, and Computation, Vol. 7,

• pp. 133-173, Springer Verlag, 2014

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Deterministic P module of Thermosensor

General structure of a deterministic P module

<module name>= (list of input signal identifiers, list of output signal identifiers, )

Thermosensor module with temperature as input parameter

thermosensor = ((T), ([C]), ) with

• :

˙ [A] = −k(T)[A], ˙ [B] = −k(T)[B][D], ˙ [W] = k(T)[D], ˙ [C] = k(T)[B][D] − k(T)[C][D]2, ˙ [D] = −k(T)[B][D] + k(T)[C][D]2 + k(T)[A] − k(T)[D], k(T) = Act(T) · e− E(T)

R·T ,

[A](0) = 1, [B](0) = 3, [C](0) = 0.5, [D](0) = 0.5, [W](0) = 0, Act(T) = 2.0149 · 1014, E(T) = 67 000, R = 8.31446

[A], [B], [C], [D], [W] . . . . . . . involved chemical species concentrations T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kelvin temperature [C] . . . . . . . . . . . . molecular count provided as integer output over time

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Copasi: Software Tool for Deterministic P Modules

• Copasi: Complex Pathway Simulator
• Freely available at www.copasi.org
• Very stable and reliable tool, convenient user interface
• Particle numbers (multiset of molecular counts) as output

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Estimation of Time Course using Copasi

• Numerical ODE solver based on adaptive Runge-Kutta method
• Variable time discretisation stepsize according to volatility
• High internal numerical precision
• Output rounded to obtain integer numbers for molecular counts

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Spiking Behaviour of Thermosensor

substrate concentration [C] (mmol/l) time (s)

• At 20◦C (293.15K) spiking period length of 100ms
• Higher temperature shortens period length
• Thermosensor maps temperature into period length

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Period Length subject to Environmental Temperature

period length (in seconds) of spiking oscillation by species C temperature in degrees centigrade (Kelvin = centigrade + 273.15)

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Thermoreceptor Incorporates Frequency Decoder

numerical integrator (frequency decoding) cascaded summation of oscillating signal higher temperature lowest temperature smoother subtractor (differencer) multiplicator (scaler)

time cation concentration

period length (frequency encoding) thermosensor

• Freq.-encoded temperature signal transduced through cytosol
• Freq. decoding converts period length into steady concentration

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Thermoreceptor: Entire Reaction Scheme

k k k k

subtractor integrator numerical smoothing cascade multipli− cator thermosensor B D W A k I1 k I7 k I7 k I7 k I7 k I7 L M k I7 k S1 k D3 k D4 X2 k I8 k S2 k S3 k D2 Z Y F k M

1

X k k I3 k I2

I4

k I5 K I 1 I 2 I 3 I 4 I 5 I 6 k D1 C S Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

P Meta Framework

Connects deterministic P modules in M according to program P on the fly Πthermoreceptor = (M, P) with M = {(thermosensor, 1), (integrator, 1), (smoother, 1), (subtractor, 1), (multiplicator, 1)} P = {0 : ModuleConnect(thermosensor[1] → integrator[1], {(C, C)}), 0 : ModuleConnect(integrator[1] → smoother[1], {(K, K)}), 0 : ModuleConnect(smoother[1] → subtractor[1], {(X1, X1)}), 0 : ModuleConnect(subtractor[1] → multiplicator[1], {(S, S)})}

• Providing modules: integrator, smoother, subtractor, multiplicator
• Connecting individual deterministic P modules via shared species
• Now operating on module level to cope with complex system

Concept of P Meta Framework:

• T. Hinze, B. Schell, M. Schumann, C. Bodenstein. Maintenance of Chronobiological

Information by P System Mediated Assembly of Control Units for Oscillatory Waveforms and Frequency. Lecture Notes in Computer Science 7762:208-227, 2013

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Thermoreceptor: Transfer Curve

environmental temperature T [Y] integrator[1] smoother[1] subtractor[1] multiplicator[1] thermosensor[1]

1

X C K S

substrate concentration [Y] (mmol/l) temperature (degrees centigrade) 2 4 6 8 10 20 40 60 80

• Appropriate resolution within physiological temperature range of

approximately 5 . . . 40◦C (corresponds to typical oceanic water surface temperatures)

• Composition of underlying modules can be seen as a result of

an artificial evolution on module level

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Circadian Clock – Biological Daily Rhythm

• Sustained biochemical oscillation maintained by itself

(endogenous rhythm)

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Circadian Clock – Biological Daily Rhythm

• Sustained biochemical oscillation maintained by itself

(endogenous rhythm)

• Free-running period close to but typically not exactly 24 hours

(circa – approximately, dies – day)

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Circadian Clock – Biological Daily Rhythm

• Sustained biochemical oscillation maintained by itself

(endogenous rhythm)

• Free-running period close to but typically not exactly 24 hours

(circa – approximately, dies – day)

• Oscillation persists under constant environmental conditions

(light, temperature, . . . )

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Circadian Clock – Biological Daily Rhythm

• Sustained biochemical oscillation maintained by itself

(endogenous rhythm)

• Free-running period close to but typically not exactly 24 hours

(circa – approximately, dies – day)

• Oscillation persists under constant environmental conditions

(light, temperature, . . . )

• Adaptation to external stimuli with daily rhythmicity like sunlight

(entrainment)

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Circadian Clock – Biological Daily Rhythm

• Sustained biochemical oscillation maintained by itself

(endogenous rhythm)

• Free-running period close to but typically not exactly 24 hours

(circa – approximately, dies – day)

• Oscillation persists under constant environmental conditions

(light, temperature, . . . )

• Adaptation to external stimuli with daily rhythmicity like sunlight

(entrainment)

• Ability for temperature compensation within physiological range

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Circadian Clock – Biological Daily Rhythm

• Sustained biochemical oscillation maintained by itself

(endogenous rhythm)

• Free-running period close to but typically not exactly 24 hours

(circa – approximately, dies – day)

• Oscillation persists under constant environmental conditions

(light, temperature, . . . )

• Adaptation to external stimuli with daily rhythmicity like sunlight

(entrainment)

• Ability for temperature compensation within physiological range
• Biological counterpart of a frequency control loop

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Archaea could have emerged a simple circadian clock which facilitates an anticipating behaviour with respect to daytime and nighttime activities. Up to now, cyanobacteria equipped with light sensors (photoreceptors) are presumed to be the earliest

• rganisms with circadian clock.

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Simple Circadian Clock Model (Phase Locked Loop)

core oscillator (Goodwin type) scaled tuning signal [D] = [U]+[G]*ae ae = filter low−pass [F] = [E][Z] multiplicator comparator signal adder for a, b, Y k 3 X k 5 k 4,K 4 k 6,K 6 l 5 E m1 K1 k 8 k 8 k 7 k 7 k 7 U l 4 l 3 F1 l 2 l 1 F4 D k 2,K 2 G Z F F2 F3

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

Computers for Clock Frequency Control Based on P Modules. Lecture Notes in Computer Science 7184:182-202, 2012

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Poor Entrainability (Restricted to ∆ T ≤ 0.3K)

[E](t) = 5 (const.), reactions with Arrhenius terms, temperature as external stimulus

∆ T = 0.3 K ∆ T = 3 K

environmental temperature rhythm 24 h 24.5 h 25 h persistent period length of environmental temperature rhythm pi/2 pi initial phase shift to

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

With Thermoreceptor Improved Entrainability

A simple module connection can cause an evolutionary advantage

environmental temperature T integrator[1] smoother[1] subtractor[1] thermosensor[1] multiplicator[2] lp_filter[1] adder[1] core_oscillator[1] [Z] multiplicator[1]

ratio between initial period length in [Z] and period length in [E] amplitude of oscillating course [E](t)

thermoreceptor circadian clock

This intermodular link between thermoreceptor and circadian clock provides evolutionary advantage.

Arnold tongue (significant section)

1

X C K S F Z G D Y = E

region of entrainability

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Take Home Message

We hypothesise that effective circadian clocks could have been emerged without evolution of photoreceptors and light sensors merely by exploitation of daily temperature cycles.

Conclusions

• Application of membrane computing in systems biology
• Modularisation of reaction units as a useful tool
• ”Play“ with dynamical connection of modules
• Evolutionary principle becomes visible:

small changes can have strong effects

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre

Motivation Thermosensor dP Module Thermoreceptor Circadian Clock

Acknowledgements to my Team Colleagues

Korcan Kirkici Patricia Sauer Peter Sauer Behre Cottbus Joern Dresden Norwich

Membrane Computing Meets Temperature: A Thermoreceptor Model

• T. Hinze, K. Kirkici, P

. Sauer, P . Sauer, J. Behre