1
|
Blom K, Song K, Vouga E, Godec A, Makarov DE. Milestoning estimators of dissipation in systems observed at a coarse resolution. Proc Natl Acad Sci U S A 2024; 121:e2318333121. [PMID: 38625949 PMCID: PMC11047069 DOI: 10.1073/pnas.2318333121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 03/14/2024] [Indexed: 04/18/2024] Open
Abstract
Many nonequilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such "lumped" observables display memory, and in many cases, the irreversible character of the underlying microscopic dynamics becomes blurred, e.g., when the projection hides dissipative cycles. As a result, the observations appear less irreversible, and it is very challenging to infer the degree of broken time-reversal symmetry. Here we show, contrary to intuition, that by ignoring parts of the already coarse-grained state space we may-via a process called milestoning-improve entropy-production estimates. We present diverse examples where milestoning systematically renders observations "closer to underlying microscopic dynamics" and thereby improves thermodynamic inference from lumped data assuming a given range of memory, and we hypothesize that this effect is quite general. Moreover, whereas the correct general physical definition of time reversal in the presence of memory remains unknown, we here show by means of physically relevant examples that at least for semi-Markov processes of first and second order, waiting-time contributions arising from adopting a naive Markovian definition of time reversal generally must be discarded.
Collapse
Affiliation(s)
- Kristian Blom
- Mathematical biophysics Group, Max Planck Institute for Multidisciplinary Sciences, Göttingen37077, Germany
| | - Kevin Song
- Department of Computer Science, University of Texas at Austin, Austin, TX78712
| | - Etienne Vouga
- Department of Computer Science, University of Texas at Austin, Austin, TX78712
| | - Aljaž Godec
- Mathematical biophysics Group, Max Planck Institute for Multidisciplinary Sciences, Göttingen37077, Germany
| | - Dmitrii E. Makarov
- Department of Chemistry and Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX78712
| |
Collapse
|
2
|
Chun HM, Horowitz JM. Trade-offs between number fluctuations and response in nonequilibrium chemical reaction networks. J Chem Phys 2023; 158:2888610. [PMID: 37144710 DOI: 10.1063/5.0148662] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 04/17/2023] [Indexed: 05/06/2023] Open
Abstract
We study the response of chemical reaction networks driven far from equilibrium to logarithmic perturbations of reaction rates. The response of the mean number of a chemical species is observed to be quantitively limited by number fluctuations and the maximum thermodynamic driving force. We prove these trade-offs for linear chemical reaction networks and a class of nonlinear chemical reaction networks with a single chemical species. Numerical results for several model systems support the conclusion that these trade-offs continue to hold for a broad class of chemical reaction networks, though their precise form appears to sensitively depend on the deficiency of the network.
Collapse
Affiliation(s)
- Hyun-Myung Chun
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, South Korea
| | - Jordan M Horowitz
- Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48104, USA
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| |
Collapse
|
3
|
Ravoni A. Long-term behaviours of Autocatalytic Sets. J Theor Biol 2021; 529:110860. [PMID: 34389361 DOI: 10.1016/j.jtbi.2021.110860] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Revised: 08/04/2021] [Accepted: 08/05/2021] [Indexed: 10/20/2022]
Abstract
Autocatalytic Sets are reaction networks theorised as networks at the basis of life. Their main feature is the ability of spontaneously emerging and self-reproducing. The Reflexively and Food-generated theory provides a formal definition of Autocatalytic Sets in terms of graphs with peculiar topological properties. This formalisation has been proved to be a powerful tool for the study of the chemical networks underlying life, and it was able to identify autocatalytic structures in real metabolic networks. However, the dynamical behaviour of such networks has not been yet complitely clarified. In this work, I present a first attempt to connect the topology of an Autocatalytic Set with its dynamics. For this purpose, I represent Autocatalytic Sets in terms of Chemical Reaction Networks, and I use the Chemical Reaction Network theory to detect motifs in the networks'structure, that allow to determine the long-term behaviour of the system.
Collapse
Affiliation(s)
- Alessandro Ravoni
- Department of Mathematics and Physics, University of Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy.
| |
Collapse
|
4
|
Gaspard P. Stochastic approach to entropy production in chemical chaos. CHAOS (WOODBURY, N.Y.) 2020; 30:113103. [PMID: 33261359 DOI: 10.1063/5.0025350] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2020] [Accepted: 10/14/2020] [Indexed: 06/12/2023]
Abstract
Methods are presented to evaluate the entropy production rate in stochastic reactive systems. These methods are shown to be consistent with known results from nonequilibrium chemical thermodynamics. Moreover, it is proved that the time average of the entropy production rate can be decomposed into the contributions of the cycles obtained from the stoichiometric matrix in both stochastic processes and deterministic systems. These methods are applied to a complex reaction network constructed on the basis of Rössler's reinjection principle and featuring chemical chaos.
Collapse
Affiliation(s)
- Pierre Gaspard
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (U.L.B.), Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
| |
Collapse
|
5
|
Pucci F, Rooman M. Deciphering noise amplification and reduction in open chemical reaction networks. J R Soc Interface 2019; 15:20180805. [PMID: 30958227 DOI: 10.1098/rsif.2018.0805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The impact of fluctuations on the dynamical behaviour of complex biological systems is a longstanding issue, whose understanding would elucidate how evolutionary pressure tends to modulate intrinsic noise. Using the Itō stochastic differential equation formalism, we performed analytic and numerical analyses of model systems containing different molecular species in contact with the environment and interacting with each other through mass-action kinetics. For networks of zero deficiency, which admit a detailed- or complex-balanced steady state, all molecular species are uncorrelated and their Fano factors are Poissonian. Systems of higher deficiency have non-equilibrium steady states and non-zero reaction fluxes flowing between the complexes. When they model homo-oligomerization, the noise on each species is reduced when the flux flows from the oligomers of lowest to highest degree, and amplified otherwise. In the case of hetero-oligomerization systems, only the noise on the highest-degree species shows this behaviour.
Collapse
Affiliation(s)
- Fabrizio Pucci
- 2 Department of BioModeling, BioInformatics and BioProcesses, Université Libre de Bruxelles , 50 Roosevelt Ave, 1050 Brussels , Belgium
| | - Marianne Rooman
- 1 Department of Theoretical Physics, BioInformatics and BioProcesses, Université Libre de Bruxelles , 50 Roosevelt Ave, 1050 Brussels , Belgium.,2 Department of BioModeling, BioInformatics and BioProcesses, Université Libre de Bruxelles , 50 Roosevelt Ave, 1050 Brussels , Belgium
| |
Collapse
|
6
|
Lazarescu A, Cossetto T, Falasco G, Esposito M. Large deviations and dynamical phase transitions in stochastic chemical networks. J Chem Phys 2019. [DOI: 10.1063/1.5111110] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Affiliation(s)
| | - Tommaso Cossetto
- Complex Systems and Statistical Mechanics, Physics and Material Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Gianmaria Falasco
- Complex Systems and Statistical Mechanics, Physics and Material Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Massimiliano Esposito
- CPHT, CNRS, École Polytechnique, IP Paris, F-91128 Palaiseau, France
- Complex Systems and Statistical Mechanics, Physics and Material Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| |
Collapse
|
7
|
Rao R, Esposito M. Conservation laws and work fluctuation relations in chemical reaction networks. J Chem Phys 2018; 149:245101. [DOI: 10.1063/1.5042253] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Affiliation(s)
- Riccardo Rao
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, G.D. Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, G.D. Luxembourg
| |
Collapse
|
8
|
Gawthrop P, Crampin EJ. Bond Graph Representation of Chemical Reaction Networks. IEEE Trans Nanobioscience 2018; 17:449-455. [DOI: 10.1109/tnb.2018.2876391] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
|
9
|
Pucci F, Rooman M. Insights into noise modulation in oligomerization systems of increasing complexity. Phys Rev E 2018; 98:012137. [PMID: 30110836 DOI: 10.1103/physreve.98.012137] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2017] [Indexed: 11/07/2022]
Abstract
Understanding under which conditions the increase of systems complexity is evolutionarily advantageous, and how this trend is related to the modulation of the intrinsic noise, are fascinating issues of utmost importance for synthetic and systems biology. To get insights into these matters, we analyzed a series of chemical reaction networks with different topologies and complexity, described by mass-action kinetics. We showed, analytically and numerically, that the global level of fluctuations at the steady state, measured by the sum over all species of the Fano factors of the number of molecules, is directly related to the network's deficiency. For zero-deficiency systems, this sum is constant and equal to the rank of the network. For higher deficiencies, additional terms appear in the Fano factor sum, which are proportional to the net reaction fluxes between the molecular complexes. We showed that the system's global intrinsic noise is reduced when all fluxes flow from lower to higher degree oligomers, or equivalently, towards the species of higher complexity, whereas it is amplified when the fluxes are directed towards lower complexity species.
Collapse
Affiliation(s)
- Fabrizio Pucci
- Department of BioModeling, BioInformatics & BioProcesses, Université Libre de Bruxelles, Roosevelt Avenue 50, B-1050 Brussels, Belgium and Department of Theoretical Physics, Université Libre de Bruxelles, Triumph Boulevard, B-1050 Brussels, Belgium
| | - Marianne Rooman
- Department of BioModeling, BioInformatics & BioProcesses, Université Libre de Bruxelles, Roosevelt Avenue 50, B-1050 Brussels, Belgium and Department of Theoretical Physics, Université Libre de Bruxelles, Triumph Boulevard, B-1050 Brussels, Belgium
| |
Collapse
|
10
|
Mozgunov P, Beccuti M, Horvath A, Jaki T, Sirovich R, Bibbona E. A review of the deterministic and diffusion approximations for stochastic chemical reaction networks. REACTION KINETICS MECHANISMS AND CATALYSIS 2018. [DOI: 10.1007/s11144-018-1351-y] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
11
|
Polettini M, Esposito M. Effective Thermodynamics for a Marginal Observer. PHYSICAL REVIEW LETTERS 2017; 119:240601. [PMID: 29286715 DOI: 10.1103/physrevlett.119.240601] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2017] [Indexed: 06/07/2023]
Abstract
Thermodynamics is usually formulated on the presumption that the observer has complete information about the system he or she deals with: no parasitic current, exact evaluation of the forces that drive the system. For example, the acclaimed fluctuation relation (FR), relating the probability of time-forward and time-reversed trajectories, assumes that the measurable transitions suffice to characterize the process as Markovian (in our case, a continuous-time jump process). However, most often the observer only measures a marginal current. We show that he or she will nonetheless produce an effective description that does not dispense with the fundamentals of thermodynamics, including the FR and the 2nd law. Our results stand on the mathematical construction of a hidden time reversal of the dynamics, and on the physical requirement that the observed current only accounts for a single transition in the configuration space of the system. We employ a simple abstract example to illustrate our results and to discuss the feasibility of generalizations.
Collapse
Affiliation(s)
- Matteo Polettini
- Physics and Materials Science Research Unit, University of Luxembourg, Campus Limpertsberg, 162a avenue de la Faïencerie, L-1511 Luxembourg, Luxembourg
| | - Massimiliano Esposito
- Physics and Materials Science Research Unit, University of Luxembourg, Campus Limpertsberg, 162a avenue de la Faïencerie, L-1511 Luxembourg, Luxembourg
| |
Collapse
|
12
|
Constantino PH, Kaznessis YN. Maximum Entropy Prediction of Non-Equilibrium Stationary Distributions for Stochastic Reaction Networks with Oscillatory Dynamics. Chem Eng Sci 2017; 171:139-148. [PMID: 30899124 DOI: 10.1016/j.ces.2017.05.029] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Abstract
Many chemical reaction networks in biological systems present complex oscillatory dynamics. In systems such as regulatory gene networks, cell cycle, and enzymatic processes, the number of molecules involved is often far from the thermodynamic limit. Although stochastic models based on the probabilistic approach of the Chemical Master Equation (CME) have been proposed, studies in the literature have been limited by the challenges of solving the CME and the lack of computational power to perform large-scale stochastic simulations. In this paper, we show that the infinite set of stationary moment equations describing the stochastic Brusselator and Schnakenberg oscillatory reactions networks can be truncated and solved using maximization of the entropy of the distributions. The results from our numerical experiments compare with the distributions obtained from well-established kinetic Monte Carlo methods and suggest that the accuracy of the prediction increases exponentially with the closure order chosen for the system. We conclude that maximum entropy models can be used as an efficient closure scheme alternative for moment equations to predict the non-equilibrium stationary distributions of stochastic chemical reactions with oscillatory dynamics. This prediction is accomplished without any prior knowledge of the system dynamics and without imposing any biased assumptions on the mathematical relations among species involved.
Collapse
Affiliation(s)
- Pedro H Constantino
- Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Ave. SE, Minneapolis, MN 55455, USA.
| | - Yiannis N Kaznessis
- Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Ave. SE, Minneapolis, MN 55455, USA.
| |
Collapse
|
13
|
Krishnamurthy S, Smith E. Solving moment hierarchies for chemical reaction networks. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL 2017; 50:425002. [PMID: 29333197 PMCID: PMC5764546 DOI: 10.1088/1751-8121/aa89d0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
The study of chemical reaction networks (CRN's) is a very active field. Earlier well-known results (Feinberg 1987 Chem. Enc. Sci. 42 2229, Anderson et al 2010 Bull. Math. Biol. 72 1947) identify a topological quantity called deficiency, for any CRN, which, when exactly equal to zero, leads to a unique factorized steady-state for these networks. No results exist however for the steady states of non-zero-deficiency networks. In this paper, we show how to write the full moment-hierarchy for any non-zero-deficiency CRN obeying mass-action kinetics, in terms of equations for the factorial moments. Using these, we can recursively predict values for lower moments from higher moments, reversing the procedure usually used to solve moment hierarchies. We show, for nontrivial examples, that in this manner we can predict any moment of interest, for CRN's with non-zero deficiency and non-factorizable steady states.
Collapse
Affiliation(s)
| | - Eric Smith
- Earth-Life Science Institute, Tokyo Institute of Technology, 2-12-1-IE-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan
- Department of Biology, Georgia Institute of Technology, 310 Ferst Drive NW, Atlanta, GA 30332, United States of America
- Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, United States of America
- Ronin Institute, 127 Haddon Place, Montclair, NJ 07043, United States of America
| |
Collapse
|
14
|
Hartich D, Seifert U. Optimal inference strategies and their implications for the linear noise approximation. Phys Rev E 2016; 94:042416. [PMID: 27841626 DOI: 10.1103/physreve.94.042416] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2016] [Indexed: 12/11/2022]
Abstract
We study the information loss of a class of inference strategies that is solely based on time averaging. For an array of independent binary sensors (e.g., receptors, single electron transistors) measuring a weak random signal (e.g., ligand concentration, gate voltage) this information loss is up to 0.5 bit per measurement irrespective of the number of sensors. We derive a condition related to the local detailed balance relation that determines whether or not such a loss of information occurs. Specifically, if the free-energy difference arising from the signal is symmetrically distributed among the forward and backward rates, time integration mechanisms will capture the full information about the signal. As an implication, for the linear noise approximation, we can identify the same loss of information, arising from its inherent simplification of the dynamics.
Collapse
Affiliation(s)
- David Hartich
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| |
Collapse
|
15
|
Polettini M, Bulnes-Cuetara G, Esposito M. Conservation laws and symmetries in stochastic thermodynamics. Phys Rev E 2016; 94:052117. [PMID: 27967081 DOI: 10.1103/physreve.94.052117] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2016] [Indexed: 06/06/2023]
Abstract
Phenomenological nonequilibrium thermodynamics describes how fluxes of conserved quantities, such as matter, energy, and charge, flow from outer reservoirs across a system and how they irreversibly degrade from one form to another. Stochastic thermodynamics is formulated in terms of probability fluxes circulating in the system's configuration space. The consistency of the two frameworks is granted by the condition of local detailed balance, which specifies the amount of physical quantities exchanged with the reservoirs during single transitions between configurations. We demonstrate that the topology of the configuration space crucially determines the number of independent thermodynamic affinities (forces) that the reservoirs generate across the system and provides a general algorithm that produces the fundamental affinities and their conjugate currents contributing to the total dissipation, based on the interplay between macroscopic conservations laws for the currents and microscopic symmetries of the affinities.
Collapse
Affiliation(s)
- Matteo Polettini
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, Campus Limpertsberg, 162a avenue de la Faïencerie, L-1511 Luxembourg (G. D. Luxembourg)
| | - Gregory Bulnes-Cuetara
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, Campus Limpertsberg, 162a avenue de la Faïencerie, L-1511 Luxembourg (G. D. Luxembourg)
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, Campus Limpertsberg, 162a avenue de la Faïencerie, L-1511 Luxembourg (G. D. Luxembourg)
| |
Collapse
|
16
|
Altaner B, Polettini M, Esposito M. Fluctuation-Dissipation Relations Far from Equilibrium. PHYSICAL REVIEW LETTERS 2016; 117:180601. [PMID: 27835007 DOI: 10.1103/physrevlett.117.180601] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2016] [Indexed: 06/06/2023]
Abstract
Near equilibrium, where all currents of a system vanish on average, the fluctuation-dissipation relation (FDR) connects a current's spontaneous fluctuations with its response to perturbations of the conjugate thermodynamic force. Out of equilibrium, fluctuation-response relations generally involve additional nondissipative contributions. Here, in the framework of stochastic thermodynamics, we show that an equilibriumlike FDR holds for internally equilibrated currents, if the perturbing conjugate force only affects the microscopic transitions that contribute to the current. We discuss the physical requirements for the validity of our result and apply it to nanosized electronic devices.
Collapse
Affiliation(s)
- Bernhard Altaner
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg 1511, Luxembourg
| | - Matteo Polettini
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg 1511, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg 1511, Luxembourg
| |
Collapse
|
17
|
Nonequilibrium thermodynamic formalism of nonlinear chemical reaction systems with Waage–Guldberg’s law of mass action. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.03.026] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
|