thermodynamics of open chemical reaction networksdynamics of open crns chemical network environment...
TRANSCRIPT
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Thermodynamics of Open Chemical Reaction Networks
Massimiliano Esposito
Riccardo Rao (PhD),Gianmaria Falasco (postdoc), Matteo Polettini (researcher)
Harvard, November 13, 2019
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Motivation
Cell Metabolism
Thermodynamics ofChemical Reaction Networks
“[Thermodynamics] is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts.” A. Einstein
Stochastic thermodynamicsClassical thermodynamics
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Outline
● Deterministic Dynamics of Open CNRs
● Thermodynamics of Open CRNs
- First and Second Law
- Role of Topology
● Reaction-Diffusion
● Concluding Remarks
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Dynamics of Closed CRNs
Chemical Network
Environment
k+1
k-1A + E E*
E + B
k+2
k-2
k-3
k+3
k-4
k+4
E**
Stoichiometric matrix
Rate equations
Reactions
Ideal Dilute Solution + Elementary Reactions = Mass action kinetics
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Dynamics of Open CRNs
Chemical Network
Environment
Ae
Be
k+1
k-1A + E E*
E + B
k+2
k-2
k-3
k+3
k-4
k+4
E**
Rate equations
Internal
Reactions Exchange
Autonomous CRNs
Chemostatted
Stoichiometric matrix
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Thermodynamics of CRNs
Ideal Dilute Solutions
Local equilibrium
Local Detailed Balance
“0th law of Thermodynamics”: Closed CRN relax to equilibrium
Standard-state chemical potential
Entropy of formationEnthalpy of formation
detailed-balance
Elementary Reactions
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Entropy production:(total entropy change)
Entropy change in (thermal & chemical) reservoirs
CRN Enthalpy: CRN Entropy:
[Rao & Esposito, Phys. Rev. X 6, 041064 (2016)]
Heat Flow
First and Second Lawtotal
concentration
1st lawEnthalpy Balance
2nd lawEntropy Balance
Chemical Work
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Work principle: Equilibrium of Closed CRN
Non-Eq. Gibbs free energy
“Relative entropy”Equilibrium of closed CRN
[Rao & Esposito, Phys. Rev. X 6, 041064 (2016)]
In a closed CRN, , is minimized by the dynamics until the CRN reaches equilibrium
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Conservation Laws & Cycles in Closed CRNs
Chemical Network
Environment
k+1
k-1A + E E*
E + B
k+2
k-2
k-3
k+3
k-4
k+4
E**
Conservation Laws: Cycles:
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Conservation Laws & Cycles in Open CRNsChemical Network
Environment
Ae
Be
k+1
k-1A + E E*
E + B
k+2
k-2
k-3
k+3
k-4
k+4
E**
Opening may break some conservation laws
Opening may create emergent cycles
[Polettini & Esposito, J. Chem. Phys. 141, 024117 (2014)]
broken:
emergent:
unbroken:
1 = 1 + 0 2 = 1 + 12 = 2 + 0
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Entropy Production shaped by Topology
NonEq semigrand Gibbs free energy
Nonconservative Work
Emergent Cycle Affinities
Driving Work
Fundamental Forces
[Falasco, ao & Esposito, Phys. Rev. Lett. 121, 108301 (2018)]
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Non-Eq. Steady State:(autonomous)
DB & autonomous:
[Falasco, ao & Esposito, Phys. Rev. Lett. 121, 108301 (2018)]
Equilibrium of open CRN
minimized by dynamics
Force-Flux pairs
Relaxation to Eq.:
Detailed Balanced CRNs:
Minimal work to generate a Non-Eq distribution
Some special class of CRNs
Work principle
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Example
Driving WorkNoneq. semigrand Gibbs free energyNonconservative Work
Chemical Network
Environment
Ae
Be
A + E E*
E + BE**
μAWd
Wnc
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Reaction—Diffusion Equations
Reactions ExchangeDiffusion
Diffusion: Fick’s Law
Diffusion coefficients
Adding DiffusionMass-action kinetics
[Falasco, ao & Esposito, Phys. Rev. Lett. 121, 108301 (2018)]
eq. driving
none
q. dri
ving
Spacial structuring takes work:
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Final remarks
[Wachtel, ao & Esposito, New J. Phys. 20 042002 (2018)]
[ao & Esposito, J. Chem. Phys. 149, 245101 (2018)]
[Polettini, Wachtel & Esposito, J. Chem. Phys. 143, 184103 (2015)]
Stochasticity?
Ex: Coarse-graining Biocatalysts
[Lazarescu, Cossetto, Falasco & Esposito, J. Chem. Phys. 151, 064117 (2019)]
[Penocchio, ao & Esposito, Nature Communications, 10 3865 (2019)]- Performance of energy storage and energy conversion (from molecular motors to metabolic networks)
[Avanzini, Falasco & Esposito, arXiv:1904.08874][Falasco, ao & Esposito, Phys. Rev. Lett. 121, 108301 (2018)] Ex: Turing patterns
Phase transitions
- Cost of Chemical Information Processing
Chemical waves
Useful?
Non-Eq. thermodynamics needs to describe all the degrees of freedom that are out-of-equilibrium must be described. We need coarse graining strategies which preserves thermodynamic consistency.
Thermo at stochastic vs deterministic level: yes at steady state for complex balanced CRNs
Stochastic Thermodynamics of CRNs (nonlinear)
Ex: Driven synthesis
The big issue of coarse graining
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