Thermodynamics of Biochemical Reaction Networks: Information, Accuracy and Speed

Massimiliano Esposito

BIRS, July 28, 2020 Motivation

Thermodynamics of Classical thermodynamics Stochastic thermodynamics Chemical Reaction Networks

…

2 Outline

I) Deterministic description of Open CNRs - First and Second Law - Role of Topology - Role of Information II) Dissipative Self-Assembly III) Stochastic description and Accuracy IV) Conclusions and Perspectives

3 I) Deterministic description of CRNs

Environment Chemical Network open k+1 A + E E* k-1

Ae k+4 k-2

k-4 k+2 open k-3 Mass action kinetics E** E + B k+3 Be

Closed CRN:

Open CRN: Stoichiometric matrix (topology) Internal

Chemostatted

in autonomous CRNs

Chemical Potential Local Detailed Balance

4 Closed CRN relax to equilibrium First and Second Law

total CRN Enthalpy: CRN Entropy: concentration

Chemical Work

1st law Enthalpy Balance

Heat Flow

2nd law Entropy Balance

Entropy change in (thermal & chemical) reservoirs

Entropy production: (total entropy change)

5 [Rao & Esposito, Phys. Rev. X 6, 041064 (2016)] Topology: Conservation Laws & Cycles

Environment Chemical Network

k+1 A + E E* k-1

Ae k+4 k-2

k-4 k+2

k-3 E** E + B k+3 Be

Closed CRN: Open CRN: Conservation Laws: Conservation Laws:

Broken conservation law!

Cycles: Cycles:

Emergent cycle!

0 = 0 + 0 1 = 1 + 0 2 = 1 + 1 6 [Polettini & Esposito, J. Chem. Phys. 141, 024117 (2014)] Topology shapes Entropy Production

0 = 0 + 0 Broken conservation laws Emergent cycles 1 = 1 + 0 2 = 2 + 0 2 = 1 + 1 Chemostats 3 = 3 + 0 3 = 2 + 1 3 = 1 + 2 Nonconservative Work

Cycle Affinities Cycle Currents Detailed Balanced CRN

Driving Work NonEq semigrand Gibbs free energy

7 [ao & Esposito. New J. Phys. 20, 023007 (2018)] [Falasco, ao & Esposito, Phys. Rev. Lett. 121, 108301 (2018)] Information and the Work Principle

Equilibrium of open CRN “Relative entropy”

- Min work to generate a NonEq distrib - Max work that can be extracted from a NonEq distrib

8 [Falasco, ao & Esposito, Phys. Rev. Lett. 121, 108301 (2018)] … in Reaction-Diffusion

Mass-action kinetics

Diffusion: Fick’s Law

Diffusion Reactions Exchange Diffusion coefficients

Spacial structuring takes work:

9 [Falasco, ao & Esposito, Phys. Rev. Lett. 121, 108301 (2018)] Cost of Chemical Waves

Fisher waves Brusselator

Murray, Mathematical Auchmuty & Nicolis, Bull. Biology I. (Springer 2002) Math. Biol. 38, 325 (1976)

X 1(r,t)

X 2(r,t)

0.3 x T — 0 L f L/ 4 L/ 2 3L /4 0.2 @r J r

@tf 0.1 23 0.0 20 - 0.1 w—nc T — - 0.2 17

- 0.3 f 1 @r J - 20 - 15 - 10 - 5 0 5 10 15 20 @tf ”r 0 Amplitude - 1 Speed 0 L/4 L/2 3L/4 L 10 r” [Avanzini, Falasco & Esposito, J. Chem. Phys. 151, 234103 (2019)] Chemical Cloaking and its Cost

Pristine concentration gradient of :

Impermeable object distorting the gradient:

Preventing the object from distorting the gradient using the CRN:

Chemostats

Significant part of the energy comes from the gradient! 11 Avanzini, Falasco, Esposito, PRE 101, 060102(R) (2020) II) Dissipative Self-Assembly

fuel waste Boekhoven et al (2010) Angew. Chem. Int. Ed. 49, 4825

Ragazzon G. & Prins L. (2018) Nature Nanotech. 13, 882

12 [Penocchio, ao & Esposito, Nature Com. 10, 3865 (2019)] Energy Storage

Analyzing open chemical systems as thermodynamic machines

13 [Penocchio, ao & Esposito, Nature Com. 10, 3865 (2019)] Dissipative Synthesis

Max

linear regime 14 [Penocchio, ao & Esposito, Nature Com. 10, 3865 (2019)] III) Stochastic formulation

● Dynamics: Chemical Master Equation

- Infinite space of species abundances ( ) instead of ( )

● Thermodynamics: Stochastic Thermodynamics in Infinite Spaces

- The structure of thermodynamics is exactly the same

- Entropy is now the Shannon entropy of the probability of species abundances

- Entropy production satisfies a fluctuation relation

[ao & Esposito, J. Chem. Phys. 149, 245101 (2018)]

● From stochastic to deterministic description:

- Linear CRN: full equivalence [Polettini, Wachtel & Esposito, - Deficient CRN: equivalence at steady state J. Chem. Phys. 143, 184103 (2015)]

- In general no equivalence, in particular in presence of phase transitions

[Lazarescu, Cossetto, Falasco & Esposito, J. Chem. Phys. 151, 064117 (2019)] 15 Accuracy in Dissipative Self-Assembly Steady-state (long time limit of energy storage)

Stochasticity of species

Stochasticity of currents

Thermodynamic Uncertainty Relation

Higher accuracy away from equilibrium

16 [Falasco, Cossetto, Penocchio, & Esposito, NJP 21, 073005 (2019)] IV) Conclusions and Perspectives

● Fundamental findings:

- Topology of a network shapes its thermodynamics

- Thermo. and Info. are fundamentally related even at deterministic level

● Framework to asses the cost, accuracy and speed of various cellular operations:

- Energy transduction from molecular motors to metabolism

- Cost of cellular information processing and computation

● Perspectives:

- How do energy and information constrain biology at higher levels?

- Keeping track of energetics at higher levels is a major challenge

17 Supplementary Material

18 Thermodynamic Consistent Coarse graining

Correct dynamical coarse grainings can give rise to wrong thermodynamics !

One Emergent cycle

Only if one Two

Exact at steady-state

EP in the part to coarse-grained 19 [Wachtel, ao & Esposito, New J. Phys. 20 042002 (2018)] Stochastic Dynamics of Open CRNs

Internal: population State Chemostatted: concentrations

Probability reactions

Chemical Master Equation

Stochastic Reaction Rates

Local Detailed Balance

0th Law: Closed CN are Detailed-balanced 20 [ao & Esposito, J. Chem. Phys. 149, 245101 (2018)] Stochastic Thermodynamics of CRNs

Stochastic Trajectory: for given protocol

Enthalpy: Entropy:

reminder

Chemical Work Entropy Flow Enthalpy Balance

Heat Flow Entropy exchanged with the chemostats Entropy Balance Entropy Entropy change Entropy change in the reservoirs production 21 [ao & Esposito, J. Chem. Phys. 149, 245101 (2018)] Stochastic Thermodynamics I

Relative Entropy

22 [ao & Esposito, J. Chem. Phys. 149, 245101 (2018)] Stochastic Thermodynamics II

Relative Entropy

23 [ao & Esposito, J. Chem. Phys. 149, 245101 (2018)] Detailed Fluctuation Theorem

Initial state

24 [ao & Esposito, J. Chem. Phys. 149, 245101 (2018)] Deficiency and Complex-Balanced CRNs

Deficiency open Example: nondeficient

Complex-Balanced CN

Complex-Balanced Steady State

Multi-Poisson SS distribution

Example: deficient

25 [Horn & Jackson, 1972], [Feinberg, 1972], [Anderson, Craciun, Kurtz, 2010] Thermo of Complex-Balanced CRNs

Average Stochastic Entropy Production = Deterministic Entropy Production

26 [Polettini, Wachtel & Esposito, J. Chem. Phys. 143, 184103 (2015)] Thermo of Complex-Balanced CRNs

Adiabatic—Nonadiabatic decomposition of the deterministic entropy production

Adiabatic Nonadiabatic Relaxation Driving

Landauer Principle III

27 [Rao & Esposito, Phys. Rev. X 6, 041064 (2016)]