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 "utline I) Deterministic description of O"en CNRs $ First and Second &aw $ Role of Topology $ Role of Information II) Dissipati(e Self-)ssembly III) Stochastic descri"tion and Accuracy IV) Conclusions and ,ers"ectives ! I) Deterministic description of CRNs Environment Chemical Network o"en k'( A + E E* k)( Ae k'# k)2 k)# k'2 o"en k)! 0ass action kinetics E** E + B k'! Be Closed CRN2 #"en CRN2 Stoichiometric matrix (topology Internal Chemosta-ed in autonomous CRNs Chemical Potential &ocal !etailed Balance # Closed CRN relax to e1uili*rium +irst and Second Law total CRN Enthal"y2 CRN Entropy2 concentration Chemical ;ork 1st law Enthalpy Balance :eat %low 2nd law Entropy Balance 3ntropy chan'e in (thermal & chemical reser(oirs Entropy production2 (total entropy change * 5Rao & Es"osito, Phys. Rev. X 6, 067086 (2078 9 .opolo/y: &onser ation Laws & Cycles Environment Chemical Network k'( A + E E* k)( Ae k'# k)2 k)# k'2 k)! E** E + B k'! Be Closed CRN2 #"en CRN2 Conser(ation Laws2 Conser(ation Laws2 Broken conser(ation law= Cycles2 Cycles2 Emergent cycle= 0 > 0 + 0 7 > 1 + 0 2 > 1 + 1 - 5,ole-ini & Es"osito, J. Chem. Phys. 141, 02677< (2076 9 .opolo/y shapes Entropy 3roduction 0 > 0 ? 0 Broken conser(ation laws Emergent cycles 7 > 1 ? 0 2 > 2 ? 0 2 > 1 ? 1 Chemostats C > 3 ? 0 C > 2 ? 1 C > 1 ? 2 Nonconser(ative ;ork Cycle )Ainities Cycle Currents Detailed Balanced CRN !riving ;ork NonEq semigrand @ib*s free energy 1 5Bao & Es"ositoD New J. Phys. 20, 02C00< (2078 9 5%alasco, Bao & Es"osito, Phys. Rev. Lett. 121, 708C07 (2078)] Information and the 5ork Principle 31uilibrium of open CRN ERelative entropy” - 0in work to generate a NonEq distri* - 0a. work that can be extracted from a NonEq distri* 4 5Falasco, Bao & 3s"osito, Phys. Rev. Lett. 121, 108301 (2018 9 … in Reaction)%iffusion 0ass$action kinetics !iAusion: %ickGs &aw !iAusion Reactions Exchange Diffusion coeAicients Spacial structuring takes work2 6 5Falasco, Bao & 3s"osito, Phys. Rev. Lett. 121, 108301 (2018 9 Cost of &hemical Wa es Fisher waves Brusselator 0urray, Mathematical )uchmuty & Nicolis, BullD Biology I. (Springer 2002 MathD BiolD 38, 32J (1I<8 X 1(r,t) X 2(r,t) 0.3 x T — 0 L f L/ 4 L/ 2 3L /4 0.2 @r J r @tf 0.1 23 0.0 20 - 0.1 w—nc T — - 0.2 17 - 0.3 f 1 @r J - 20 - 15 - 10 - 5 0 5 10 15 20 @tf ”r 0 )m"litude - 1 Speed 0 L/4 L/2 3L/4 L (9 r” 5)(anzini, %alasco & Es"osito, J. Chem. Phys. 151, 2C670C (207I 9 &hemical Cloaking and its Cost Pristine concentration gradient of 2 Im"ermeable object distorting the 'radient: Pre(enting the object from distorting the gradient using the CRN2 Chemostats Significant "art of the energy comes from the gradient= (( K)(anzini, %alasco, Es"osito, PRE 101, 080702(R) (2020 II) Dissipati e Self-Assembly fuel waste Boekho en et al :29(9$ Angew. Chem. Int. Ed. 49, #42* Raga;;on <= & 3rins ,= :29(4$ Nature Nanotech. 13, 842 (2 5,enocchio, Bao & Es"osito, Nature Com. 10, C88J (207I 9 3nergy Storage Analy;ing open chemical systems as thermodynamic machines (! 5,enocchio, Bao & Es"osito, Nature Com. 10, 388J (207I 9 !issi"ati(e Synthesis 0a. 0a. linear re/ime (# 5,enocchio, Bao & Es"osito, Nature Com. 10, 388J (207I 9 III) Stochastic formulation ● !ynamics2 Chemical 0aster Equation $ Infinite s"ace of s"ecies a*undances ( ) instead of ( ) ● Thermodynamics2 Stochastic Thermodynamics in Infinite Spaces $ The structure of thermodynamics is exactly the same $ Entropy is now the Shannon entropy of the "roba*ility of s"ecies a*undances $ Entropy production satisfies a fluctuation relation 5Bao & Es"osito, J. Chem. Phys. 149, 26J707 (2078 9 ● %rom stochastic to deterministic description: $ Linear CRN2 full equivalence 5,ole-ini, Wachtel & Es"osito, $ Deficient CRN2 e1uivalence at steady state J. Chem. Phys. 143, 78670C (207J 9 $ In general no e1ui(alence, in "articular in presence of phase transitions 5&aHarescu, Cosse-o, Falasco & Es"osito, J. Chem. Phys. 151, 08677< (207I 9 (* )ccuracy in Dissi"ati(e Self$)ssem*ly Steady-state /long time limit of energy storage) Stochasticity of s"ecies Stochasticity of currents Thermodynamic Mncertainty Relation :igher accuracy away from equilibrium (- 5%alasco, Cosse-o, ,enocchio, & Es"osito, NJP 21, 0<C00J (207I 9 IV) Conclusions and Perspecti es ● +undamental findings: - .opology of a network shapes its thermodynamics - Thermo= and Info= are fundamentally related e en at deterministic le el ● +ramework to asses the cost, accuracy and speed of arious cellular operations: - 2nergy transduction from molecular motors to meta>olism - &ost of cellular information processing and computation ● 3erspectives: - How do energy and information constrain biology at higher le elsB - Keeping track of energetics at higher le els is a major challenge (1 Supplementary Material (4 Thermodynamic Consistent Coarse grainin/ Correct dynamical coarse grainings can give rise to wrong thermodynamics = #ne Emergent cycle #nly if one Two 3.act at steady$state 3, in the "art to coarse-grained (6 5;achtel, Bao & 3s"osito, New J. Phys. 20 042002 (2018 9 Stochastic Dynamics of Open CRNs Internal: population State &hemostaEed: concentrations ,roba*ility reactions Chemical Master Equation Stochastic Reaction Rates &ocal Detailed Balance 0th Law: Closed CN are Detailed$*alanced 29 5Bao & Es"osito, J. Chem. Phys. 149, 26J707 (2078 9 Stochastic Thermodynamics of CRNs Stochastic Trajectory: for gi(en "rotocol Enthal"y: Entropy: reminder Chemical ;ork Entropy %low Enthalpy Balance :eat %low Entropy e.changed with the chemostats Entropy Balance Entropy Entropy change Entropy change in the reser(oirs "roduction 2( 5Bao & Es"osito, J. Chem. Phys. 149, 26J707 (2078 9 Stochastic Thermodynamics I Relative 2ntropy 22 5Bao & Es"osito, J. Chem. Phys. 149, 26J707 (2078 9 Stochastic Thermodynamics II Relative Entropy 2! 5Bao & Es"osito, J. Chem. Phys. 149, 26J707 (2078 9 %etailed Fluctuation Theorem Initial state 2# 5Bao & Es"osito, J. Chem. Phys. 149, 26J707 (2078 9 %eficiency and CompleF)Balanced CRNs !eficiency open 2Fample: nondeficient Com"lex-Balanced CN Com"le.-Balanced Steady State Multi-Poisson SS distribution 2Fample: deficient 2* 5:orn & Jackson, 7I<2], [Feinberg, 7I<2], 5)nderson, Craciun, NurtH, 20709 Thermo of CompleF)Balanced CRNs A era/e Stochastic Entropy Production G %eterministic Entropy Production 2- 5,ole-ini, ;achtel & Es"osito, J. Chem. Phys. 143, 18670C (207J 9 Thermo of &omplex-Balanced CRNs Adiabatic!Nonadiabatic decom"osition of the deterministic entro"y production Adiabatic Nonadiabatic Rela ation Driving &andauer ,rinciple III 21 5Rao & Es"osito, Phys. Rev. X 6, 067086 (2078 9.