1
|
Degünther J, van der Meer J, Seifert U. General theory for localizing the where and when of entropy production meets single-molecule experiments. Proc Natl Acad Sci U S A 2024; 121:e2405371121. [PMID: 39121164 PMCID: PMC11331124 DOI: 10.1073/pnas.2405371121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Accepted: 07/11/2024] [Indexed: 08/11/2024] Open
Abstract
The laws of thermodynamics apply to biophysical systems on the nanoscale as described by the framework of stochastic thermodynamics. This theory provides universal, exact relations for quantities like work, which have been verified in experiments where a fully resolved description allows direct access to such quantities. Complementary studies consider partially hidden, coarse-grained descriptions, in which the mean entropy production typically is not directly accessible but can be bounded in terms of observable quantities. Going beyond the mean, we introduce a fluctuating entropy production that applies to individual trajectories in a coarse-grained description under time-dependent driving. Thus, this concept is applicable to the broad and experimentally significant class of driven systems in which not all relevant states can be resolved. We provide a paradigmatic example by studying an experimentally verified protein unfolding process. As a consequence, the entire distribution of the coarse-grained entropy production rather than merely its mean retains spatial and temporal information about the microscopic process. In particular, we obtain a bound on the distribution of the physical entropy production of individual unfolding events.
Collapse
Affiliation(s)
- Julius Degünther
- II. Institut für Theoretische Physik, Universität Stuttgart, Stuttgart70550, Germany
| | - Jann van der Meer
- II. Institut für Theoretische Physik, Universität Stuttgart, Stuttgart70550, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, Stuttgart70550, Germany
| |
Collapse
|
2
|
Pietzonka P, Coghi F. Thermodynamic cost for precision of general counting observables. Phys Rev E 2024; 109:064128. [PMID: 39020906 DOI: 10.1103/physreve.109.064128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 05/13/2024] [Indexed: 07/20/2024]
Abstract
We analytically derive universal bounds that describe the tradeoff between thermodynamic cost and precision in a sequence of events related to some internal changes of an otherwise hidden physical system. The precision is quantified by the fluctuations in either the number of events counted over time or the waiting times between successive events. Our results are valid for the same broad class of nonequilibrium driven systems considered by the thermodynamic uncertainty relation, but they extend to both time-symmetric and asymmetric observables. We show how optimal precision saturating the bounds can be achieved. For waiting-time fluctuations of asymmetric observables, a phase transition in the optimal configuration arises, where higher precision can be achieved by combining several signals.
Collapse
|
3
|
Ertel B, Seifert U. Estimator of entropy production for partially accessible Markov networks based on the observation of blurred transitions. Phys Rev E 2024; 109:054109. [PMID: 38907510 DOI: 10.1103/physreve.109.054109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Accepted: 03/25/2024] [Indexed: 06/24/2024]
Abstract
A central task in stochastic thermodynamics is the estimation of entropy production for partially accessible Markov networks. We establish an effective transition-based description for such networks with transitions that are not distinguishable and therefore blurred for an external observer. We demonstrate that, in contrast to a description based on fully resolved transitions, this effective description is typically non-Markovian at any point in time. Starting from an information-theoretic bound, we derive an operationally accessible entropy estimator for this observation scenario. We illustrate the operational relevance and the quality of this entropy estimator with a numerical analysis of various representative examples.
Collapse
Affiliation(s)
- Benjamin Ertel
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| |
Collapse
|
4
|
Karbowski J. Bounds on the rates of statistical divergences and mutual information via stochastic thermodynamics. Phys Rev E 2024; 109:054126. [PMID: 38907417 DOI: 10.1103/physreve.109.054126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Accepted: 04/18/2024] [Indexed: 06/24/2024]
Abstract
Statistical divergences are important tools in data analysis, information theory, and statistical physics, and there exist well-known inequalities on their bounds. However, in many circumstances involving temporal evolution, one needs limitations on the rates of such quantities instead. Here, several general upper bounds on the rates of some f-divergences are derived, valid for any type of stochastic dynamics (both Markovian and non-Markovian), in terms of information-like and/or thermodynamic observables. As special cases, the analytical bounds on the rate of mutual information are obtained. The major role in all those limitations is played by temporal Fisher information, characterizing the speed of global system dynamics, and some of them contain entropy production, suggesting a link with stochastic thermodynamics. Indeed, the derived inequalities can be used for estimation of minimal dissipation and global speed in thermodynamic stochastic systems. Specific applications of these inequalities in physics and neuroscience are given, which include the bounds on the rates of free energy and work in nonequilibrium systems, limits on the speed of information gain in learning synapses, as well as the bounds on the speed of predictive inference and learning rate. Overall, the derived bounds can be applied to any complex network of interacting elements, where predictability and thermodynamics of network dynamics are of prime concern.
Collapse
Affiliation(s)
- Jan Karbowski
- Institute of Applied Mathematics and Mechanics, Department of Mathematics, Informatics, and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland
| |
Collapse
|
5
|
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
|
6
|
Jo H, Hong H, Hwang HJ, Chang W, Kim JK. Density physics-informed neural networks reveal sources of cell heterogeneity in signal transduction. PATTERNS (NEW YORK, N.Y.) 2024; 5:100899. [PMID: 38370126 PMCID: PMC10873160 DOI: 10.1016/j.patter.2023.100899] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/08/2023] [Revised: 11/05/2023] [Accepted: 11/24/2023] [Indexed: 02/20/2024]
Abstract
The transduction time between signal initiation and final response provides valuable information on the underlying signaling pathway, including its speed and precision. Furthermore, multi-modality in a transduction-time distribution indicates that the response is regulated by multiple pathways with different transduction speeds. Here, we developed a method called density physics-informed neural networks (Density-PINNs) to infer the transduction-time distribution from measurable final stress response time traces. We applied Density-PINNs to single-cell gene expression data from sixteen promoters regulated by unknown pathways in response to antibiotic stresses. We found that promoters with slower signaling initiation and transduction exhibit larger cell-to-cell heterogeneity in response intensity. However, this heterogeneity was greatly reduced when the response was regulated by slow and fast pathways together. This suggests a strategy for identifying effective signaling pathways for consistent cellular responses to disease treatments. Density-PINNs can also be applied to understand other time delay systems, including infectious diseases.
Collapse
Affiliation(s)
- Hyeontae Jo
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Republic of Korea
| | - Hyukpyo Hong
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Republic of Korea
- Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of Korea
| | - Hyung Ju Hwang
- Department of Mathematics, Pohang University of Science and Technology, Pohang 37673, Republic of Korea
| | - Won Chang
- Division of Statistics and Data Science, University of Cincinnati, Cincinnati, OH 45221, USA
| | - Jae Kyoung Kim
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Republic of Korea
- Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of Korea
| |
Collapse
|
7
|
Gerry M, Segal D. Random walks on modular chains: Detecting structure through statistics. Phys Rev E 2023; 108:024135. [PMID: 37723810 DOI: 10.1103/physreve.108.024135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Accepted: 08/04/2023] [Indexed: 09/20/2023]
Abstract
We study kinetic transport through one-dimensional modular networks consisting of alternating domains using both analytical and numerical methods. We demonstrate that the mean velocity is insensitive to the local structure of the network, and it depends only on global, structural-averaged properties. However, by examining high-order cumulants characterizing the kinetics, we reveal information on the degree of inhomogeneity of blocks and the size of repeating units in the network. Specifically, in unbiased diffusion, the kurtosis is the first transport coefficient that exposes structural information, whereas in biased chains, the diffusion coefficient already reveals structural motifs. Nevertheless, this latter dependence is weak, and it disappears at both low and high biasing. Our study demonstrates that high-order moments of the population distribution over sites provide information about the network structure that is not captured by the first moment (mean velocity) alone. These results are useful towards deciphering mechanisms and determining architectures underlying long-range charge transport in biomolecules and biological and chemical reaction networks.
Collapse
Affiliation(s)
- Matthew Gerry
- Department of Physics, University of Toronto, 60 Saint George St., Toronto, Ontario M5S 1A7, Canada
| | - Dvira Segal
- Department of Physics, University of Toronto, 60 Saint George St., Toronto, Ontario M5S 1A7, Canada
- Chemical Physics Theory Group, Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
| |
Collapse
|
8
|
Harvey SE, Lahiri S, Ganguli S. Universal energy-accuracy tradeoffs in nonequilibrium cellular sensing. Phys Rev E 2023; 108:014403. [PMID: 37583173 DOI: 10.1103/physreve.108.014403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Accepted: 04/07/2023] [Indexed: 08/17/2023]
Abstract
We combine stochastic thermodynamics, large deviation theory, and information theory to derive fundamental limits on the accuracy with which single cell receptors can estimate external concentrations. As expected, if the estimation is performed by an ideal observer of the entire trajectory of receptor states, then no energy consuming nonequilibrium receptor that can be divided into bound and unbound states can outperform an equilibrium two-state receptor. However, when the estimation is performed by a simple observer that measures the fraction of time the receptor is bound, we derive a fundamental limit on the accuracy of general nonequilibrium receptors as a function of energy consumption. We further derive and exploit explicit formulas to numerically estimate a Pareto-optimal tradeoff between accuracy and energy. We find this tradeoff can be achieved by nonuniform ring receptors with a number of states that necessarily increases with energy. Our results yield a thermodynamic uncertainty relation for the time a physical system spends in a pool of states and generalize the classic Berg-Purcell limit [H. C. Berg and E. M. Purcell, Biophys. J. 20, 193 (1977)0006-349510.1016/S0006-3495(77)85544-6] on cellular sensing along multiple dimensions.
Collapse
Affiliation(s)
- Sarah E Harvey
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Subhaneil Lahiri
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Surya Ganguli
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| |
Collapse
|
9
|
van der Meer J, Degünther J, Seifert U. Time-Resolved Statistics of Snippets as General Framework for Model-Free Entropy Estimators. PHYSICAL REVIEW LETTERS 2023; 130:257101. [PMID: 37418719 DOI: 10.1103/physrevlett.130.257101] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Revised: 02/20/2023] [Accepted: 06/07/2023] [Indexed: 07/09/2023]
Abstract
Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time reversal like a current. We introduce a general framework that allows us to infer a lower bound on entropy production through measuring the time-resolved statistics of events with any symmetry under time reversal, in particular, time-symmetric instantaneous events. We emphasize Markovianity as a property of certain events rather than of the full system and introduce an operationally accessible criterion for this weakened Markov property. Conceptually, the approach is based on snippets as particular sections of trajectories between two Markovian events, for which a generalized detailed balance relation is discussed.
Collapse
Affiliation(s)
- Jann van der Meer
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Julius Degünther
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| |
Collapse
|
10
|
Semaan MT, Crutchfield JP. First and second laws of information processing by nonequilibrium dynamical states. Phys Rev E 2023; 107:054132. [PMID: 37329111 DOI: 10.1103/physreve.107.054132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2023] [Accepted: 05/04/2023] [Indexed: 06/18/2023]
Abstract
The averaged steady-state surprisal links a driven stochastic system's information processing to its nonequilibrium thermodynamic response. By explicitly accounting for the effects of nonequilibrium steady states, a decomposition of the surprisal results in an information processing first law that extends and tightens-to strict equalities-various information processing second laws. Applying stochastic thermodynamics' integral fluctuation theorems then shows that the decomposition reduces to the second laws under appropriate limits. In unifying them, the first law paves the way to identifying the mechanisms by which nonequilibrium steady-state systems leverage information-bearing degrees of freedom to extract heat. To illustrate, we analyze an autonomous Maxwellian information ratchet that tunably violates detailed balance in its effective dynamics. This demonstrates how the presence of nonequilibrium steady states qualitatively alters an information engine's allowed functionality.
Collapse
Affiliation(s)
- Mikhael T Semaan
- Complexity Sciences Center and Department of Physics and Astronomy, University of California, Davis, One Shields Avenue, Davis, California 95616, USA
- Science Research Initiative, College of Science, University of Utah, Salt Lake City, Utah 84112, USA
| | - James P Crutchfield
- Complexity Sciences Center and Department of Physics and Astronomy, University of California, Davis, One Shields Avenue, Davis, California 95616, USA
| |
Collapse
|
11
|
Padmanabha P, Busiello DM, Maritan A, Gupta D. Fluctuations of entropy production of a run-and-tumble particle. Phys Rev E 2023; 107:014129. [PMID: 36797901 DOI: 10.1103/physreve.107.014129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Accepted: 12/22/2022] [Indexed: 06/18/2023]
Abstract
Out-of-equilibrium systems continuously generate entropy, with its rate of production being a fingerprint of nonequilibrium conditions. In small-scale dissipative systems subject to thermal noise, fluctuations of entropy production are significant. Hitherto, mean and variance have been abundantly studied, even if higher moments might be important to fully characterize the system of interest. Here, we introduce a graphical method to compute any moment of entropy production for a generic discrete-state system. Then, we focus on a paradigmatic model of active particles, i.e., run-and-tumble dynamics, which resembles the motion observed in several micro-organisms. Employing our framework, we compute the first three cumulants of the entropy production for a discrete version of this model. We also compare our analytical results with numerical simulations. We find that as the number of states increases, the distribution of entropy production deviates from a Gaussian. Finally, we extend our framework to a continuous state-space run-and-tumble model, using an appropriate scaling of the transition rates. The approach presented here might help uncover the features of nonequilibrium fluctuations of any current in biological systems operating out-of-equilibrium.
Collapse
Affiliation(s)
- Prajwal Padmanabha
- Department of Physics and Astronomy "G. Galilei," University of Padova, Padova 35131, Italy
| | | | - Amos Maritan
- Department of Physics and Astronomy "G. Galilei," University of Padova, Padova 35131, Italy
| | - Deepak Gupta
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
- Institute for Theoretical Physics, Technical University of Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
| |
Collapse
|
12
|
Koyuk T, Seifert U. Thermodynamic Uncertainty Relation in Interacting Many-Body Systems. PHYSICAL REVIEW LETTERS 2022; 129:210603. [PMID: 36461951 DOI: 10.1103/physrevlett.129.210603] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Revised: 06/01/2022] [Accepted: 10/06/2022] [Indexed: 06/17/2023]
Abstract
The thermodynamic uncertainty relation (TUR) has been well studied for systems with few degrees of freedom. While, in principle, the TUR holds for more complex systems with many interacting degrees of freedom as well, little is known so far about its behavior in such systems. We analyze the TUR in the thermodynamic limit for mixtures of driven particles with short-range interactions. Our main result is an explicit expression for the optimal estimate of the total entropy production in terms of single-particle currents and correlations between two-particle currents. Quantitative results for various versions of a driven lattice gas demonstrate the practical implementation of this approach.
Collapse
Affiliation(s)
- Timur Koyuk
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| |
Collapse
|
13
|
Mori F, Majumdar SN, Schehr G. Time to reach the maximum for a stationary stochastic process. Phys Rev E 2022; 106:054110. [PMID: 36559509 DOI: 10.1103/physreve.106.054110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 10/11/2022] [Indexed: 11/06/2022]
Abstract
We consider a one-dimensional stationary time series of fixed duration T. We investigate the time t_{m} at which the process reaches the global maximum within the time interval [0,T]. By using a path-decomposition technique, we compute the probability density function P(t_{m}|T) of t_{m} for several processes, that are either at equilibrium (such as the Ornstein-Uhlenbeck process) or out of equilibrium (such as Brownian motion with stochastic resetting). We show that for equilibrium processes the distribution of P(t_{m}|T) is always symmetric around the midpoint t_{m}=T/2, as a consequence of the time-reversal symmetry. This property can be used to detect nonequilibrium fluctuations in stationary time series. Moreover, for a diffusive particle in a confining potential, we show that the scaled distribution P(t_{m}|T) becomes universal, i.e., independent of the details of the potential, at late times. This distribution P(t_{m}|T) becomes uniform in the "bulk" 1≪t_{m}≪T and has a nontrivial universal shape in the "edge regimes" t_{m}→0 and t_{m}→T. Some of these results have been announced in a recent letter [Europhys. Lett. 135, 30003 (2021)0295-507510.1209/0295-5075/ac19ee].
Collapse
Affiliation(s)
- Francesco Mori
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Satya N Majumdar
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Grégory Schehr
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS, UMR 7589 4 Place Jussieu, 75252 Paris Cedex 05, France
| |
Collapse
|
14
|
Bone RA, Sharpe DJ, Wales DJ, Green JR. Stochastic paths controlling speed and dissipation. Phys Rev E 2022; 106:054151. [PMID: 36559408 DOI: 10.1103/physreve.106.054151] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2021] [Accepted: 10/28/2022] [Indexed: 11/24/2022]
Abstract
Natural processes occur in a finite amount of time and dissipate energy, entropy, and matter. Near equilibrium, thermodynamic intuition suggests that fast irreversible processes will dissipate more energy and entropy than slow quasistatic processes connecting the same initial and final states. For small systems, recently discovered thermodynamic speed limits suggest that faster processes will dissipate more than slower processes. Here, we test the hypothesis that this relationship between speed and dissipation holds for stochastic paths far from equilibrium. To analyze stochastic paths on finite timescales, we derive an exact expression for the path probabilities of continuous-time Markov chains from the path summation solution to the master equation. We present a minimal model for a driven system in which relative energies of the initial and target states control the speed, and the nonequilibrium currents of a cycle control the dissipation. Although the hypothesis holds near equilibrium, we find that faster processes can dissipate less under far-from-equilibrium conditions because of strong currents. This model serves as a minimal prototype for designing kinetics to sculpt the nonequilibrium path space so that faster paths produce less dissipation.
Collapse
Affiliation(s)
- Rebecca A Bone
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Daniel J Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, Cambridge, United Kingdom
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, Cambridge, United Kingdom
| | - Jason R Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA.,Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| |
Collapse
|
15
|
Lynn CW, Holmes CM, Bialek W, Schwab DJ. Decomposing the Local Arrow of Time in Interacting Systems. PHYSICAL REVIEW LETTERS 2022; 129:118101. [PMID: 36154397 PMCID: PMC9751844 DOI: 10.1103/physrevlett.129.118101] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2022] [Revised: 06/03/2022] [Accepted: 06/24/2022] [Indexed: 05/30/2023]
Abstract
We show that the evidence for a local arrow of time, which is equivalent to the entropy production in thermodynamic systems, can be decomposed. In a system with many degrees of freedom, there is a term that arises from the irreversible dynamics of the individual variables, and then a series of non-negative terms contributed by correlations among pairs, triplets, and higher-order combinations of variables. We illustrate this decomposition on simple models of noisy logical computations, and then apply it to the analysis of patterns of neural activity in the retina as it responds to complex dynamic visual scenes. We find that neural activity breaks detailed balance even when the visual inputs do not, and that this irreversibility arises primarily from interactions between pairs of neurons.
Collapse
Affiliation(s)
- Christopher W Lynn
- Initiative for the Theoretical Sciences, The Graduate Center, City University of New York, New York, New York 10016, USA
- Joseph Henry Laboratories of Physics and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA
| | - Caroline M Holmes
- Joseph Henry Laboratories of Physics and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA
| | - William Bialek
- Initiative for the Theoretical Sciences, The Graduate Center, City University of New York, New York, New York 10016, USA
- Joseph Henry Laboratories of Physics and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA
| | - David J Schwab
- Initiative for the Theoretical Sciences, The Graduate Center, City University of New York, New York, New York 10016, USA
| |
Collapse
|
16
|
Ghosal A, Bisker G. Inferring entropy production rate from partially observed Langevin dynamics under coarse-graining. Phys Chem Chem Phys 2022; 24:24021-24031. [PMID: 36065766 PMCID: PMC7613705 DOI: 10.1039/d2cp03064k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The entropy production rate (EPR) measures time-irreversibility in systems operating far from equilibrium. The challenge in estimating the EPR for a continuous variable system is the finite spatiotemporal resolution and the limited accessibility to all of the nonequilibrium degrees of freedom. Here, we estimate the irreversibility in partially observed systems following oscillatory dynamics governed by coupled overdamped Langevin equations. We coarse-grain an observed variable of a nonequilibrium driven system into a few discrete states and estimate a lower bound on the total EPR. As a model system, we use hair-cell bundle oscillations driven by molecular motors, such that the bundle tip position is observed, but the positions of the motors are hidden. In the observed variable space, the underlying driven process exhibits second-order semi-Markov statistics. The waiting time distributions (WTD), associated with transitions among the coarse-grained states, are non-exponential and convey the information on the broken time-reversal symmetry. By invoking the underlying time-irreversibility, we calculate a lower bound on the total EPR from the Kullback-Leibler divergence (KLD) between WTD. We show that the mean dwell-time asymmetry factor - the ratio between the mean dwell-times along the forward direction and the backward direction, can qualitatively measure the degree of broken time reversal symmetry and increases with finer spatial resolution. Finally, we apply our methodology to a continuous-time discrete Markov chain model, coarse-grained into a linear system exhibiting second-order semi-Markovian statistics, and demonstrate the estimation of a lower bound on the total EPR from irreversibility manifested only in the WTD.
Collapse
Affiliation(s)
- Aishani Ghosal
- Department of Biomedical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel.
| | - Gili Bisker
- Department of Biomedical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel. .,Center for Physics and Chemistry of Living Systems, Tel-Aviv University, Tel Aviv 6997801, Israel.,Center for Nanoscience and Nanotechnology, Tel-Aviv University, Tel Aviv 6997801, Israel.,Center for Light-Matter Interaction, Tel-Aviv University, Tel Aviv 6997801, Israel
| |
Collapse
|
17
|
Zoller B, Gregor T, Tkačik G. Eukaryotic gene regulation at equilibrium, or non? CURRENT OPINION IN SYSTEMS BIOLOGY 2022; 31:100435. [PMID: 36590072 PMCID: PMC9802646 DOI: 10.1016/j.coisb.2022.100435] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Models of transcriptional regulation that assume equilibrium binding of transcription factors have been less successful at predicting gene expression from sequence in eukaryotes than in bacteria. This could be due to the non-equilibrium nature of eukaryotic regulation. Unfortunately, the space of possible non-equilibrium mechanisms is vast and predominantly uninteresting. The key question is therefore how this space can be navigated efficiently, to focus on mechanisms and models that are biologically relevant. In this review, we advocate for the normative role of theory-theory that prescribes rather than just describes-in providing such a focus. Theory should expand its remit beyond inferring mechanistic models from data, towards identifying non-equilibrium gene regulatory schemes that may have been evolutionarily selected, despite their energy consumption, because they are precise, reliable, fast, or otherwise outperform regulation at equilibrium. We illustrate our reasoning by toy examples for which we provide simulation code.
Collapse
Affiliation(s)
- Benjamin Zoller
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
- Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ, USA
- Department of Developmental and Stem Cell Biology UMR3738, Institut Pasteur, Paris, France
| | - Thomas Gregor
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
- Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ, USA
- Department of Developmental and Stem Cell Biology UMR3738, Institut Pasteur, Paris, France
| | - Gašper Tkačik
- Institute of Science and Technology Austria, Klosterneuburg, Austria
| |
Collapse
|
18
|
Tucci G, Roldán É, Gambassi A, Belousov R, Berger F, Alonso RG, Hudspeth AJ. Modeling Active Non-Markovian Oscillations. PHYSICAL REVIEW LETTERS 2022; 129:030603. [PMID: 35905355 DOI: 10.1103/physrevlett.129.030603] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Accepted: 06/10/2022] [Indexed: 06/15/2023]
Abstract
Modeling noisy oscillations of active systems is one of the current challenges in physics and biology. Because the physical mechanisms of such processes are often difficult to identify, we propose a linear stochastic model driven by a non-Markovian bistable noise that is capable of generating self-sustained periodic oscillation. We derive analytical predictions for most relevant dynamical and thermodynamic properties of the model. This minimal model turns out to describe accurately bistablelike oscillatory motion of hair bundles in bullfrog sacculus, extracted from experimental data. Based on and in agreement with these data, we estimate the power required to sustain such active oscillations to be of the order of 100 k_{B}T per oscillation cycle.
Collapse
Affiliation(s)
- G Tucci
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, 34136 Trieste, Italy
| | - É Roldán
- ICTP-The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - A Gambassi
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, 34136 Trieste, Italy
| | - R Belousov
- ICTP-The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- EMBL-European Molecular Biology Laboratory, Meyerhofstrasse 1, 69117 Heidelberg, Germany
| | - F Berger
- Cell Biology, Neurobiology and Biophysics, Department of Biology, Faculty of Science, Utrecht University, 3584 CH Utrecht, Netherlands
| | - R G Alonso
- Howard Hughes Medical Institute and Laboratory of Sensory Neuroscience, The Rockefeller University, 1230 York Avenue, New York, New York 10065, USA
| | - A J Hudspeth
- Howard Hughes Medical Institute and Laboratory of Sensory Neuroscience, The Rockefeller University, 1230 York Avenue, New York, New York 10065, USA
| |
Collapse
|
19
|
Nicoletti G, Maritan A, Busiello DM. Information-driven transitions in projections of underdamped dynamics. Phys Rev E 2022; 106:014118. [PMID: 35974569 DOI: 10.1103/physreve.106.014118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2022] [Accepted: 07/05/2022] [Indexed: 06/15/2023]
Abstract
Low-dimensional representations of underdamped systems often provide useful insights and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most information on observed spatial trajectories. We show that, in paradigmatic systems, the minimization of the information loss drives the appearance of a discontinuous transition in the optimal model parameters. Our results raise serious warnings for general inference approaches, and they unravel fundamental properties of effective dynamical representations impacting several fields, from biophysics to dimensionality reduction.
Collapse
Affiliation(s)
- Giorgio Nicoletti
- Department of Physics and Astronomy "G. Galilei," University of Padova, Padova, Italy
| | - Amos Maritan
- Department of Physics and Astronomy "G. Galilei," University of Padova, Padova, Italy
| | - Daniel Maria Busiello
- Institute of Physics, École Polytechnique Fédérale de Lausanne-EPFL, 1015 Lausanne, Switzerland
| |
Collapse
|
20
|
Cao Z, Hou Z. Improved estimation for energy dissipation in biochemical oscillations. J Chem Phys 2022; 157:025102. [DOI: 10.1063/5.0092126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Biochemical oscillations, regulating the timing of life processes, need consume energy to achieve good performance on crucial functions, such as high accuracy of phase period and high sensitivity to external signals. However, it is a great challenge to precisely estimate the energy dissipation in such systems. Here, based on the stochastic normal form theory (SNFT), we calculate the Pearson correlation coefficient between the oscillatory amplitude and phase, and a trade-off relation between transport efficiency and phase sensitivity can then be derived, which serves as a tighter form than the estimator resulting from the conventional thermodynamic uncertainty relation (TUR). Our findings demonstrate that a more precise energy dissipation estimation can be obtained by enhancing the sensitivity of the biochemical oscillations. Moreover, the internal noise and amplitude power effects have also been discovered.
Collapse
Affiliation(s)
- Zhiyu Cao
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, University of Science and Technology of China Department of Chemical Physics, China
| | - Zhonghuai Hou
- Department of Chemical Physics, University of Science and Technology of China Hefei National Laboratory for Physical Sciences at the Microscale, China
| |
Collapse
|
21
|
Zanin M, Papo D. Algorithmic Approaches for Assessing Irreversibility in Time Series: Review and Comparison. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1474. [PMID: 34828172 PMCID: PMC8622570 DOI: 10.3390/e23111474] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/21/2021] [Revised: 11/04/2021] [Accepted: 11/06/2021] [Indexed: 11/25/2022]
Abstract
The assessment of time irreversibility, i.e., of the lack of invariance of the statistical properties of a system under the operation of time reversal, is a topic steadily gaining attention within the research community. Irreversible dynamics have been found in many real-world systems, with alterations being connected to, for instance, pathologies in the human brain, heart and gait, or to inefficiencies in financial markets. Assessing irreversibility in time series is not an easy task, due to its many aetiologies and to the different ways it manifests in data. It is thus not surprising that several numerical methods have been proposed in the last decades, based on different principles and with different applications in mind. In this contribution we review the most important algorithmic solutions that have been proposed to test the irreversibility of time series, their underlying hypotheses, computational and practical limitations, and their comparative performance. We further provide an open-source software library that includes all tests here considered. As a final point, we show that "one size does not fit all", as tests yield complementary, and sometimes conflicting views to the problem; and discuss some future research avenues.
Collapse
Affiliation(s)
- Massimiliano Zanin
- Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - David Papo
- Department of Neuroscience and Rehabilitation, Section of Physiology, University of Ferrara, 44121 Ferrara, Italy;
- Fondazione Istituto Italiano di Tecnologia, 44121 Ferrara, Italy
| |
Collapse
|