1
|
Ingrosso A, Panizon E. Machine learning at the mesoscale: A computation-dissipation bottleneck. Phys Rev E 2024; 109:014132. [PMID: 38366483 DOI: 10.1103/physreve.109.014132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Accepted: 12/05/2023] [Indexed: 02/18/2024]
Abstract
The cost of information processing in physical systems calls for a trade-off between performance and energetic expenditure. Here we formulate and study a computation-dissipation bottleneck in mesoscopic systems used as input-output devices. Using both real data sets and synthetic tasks, we show how nonequilibrium leads to enhanced performance. Our framework sheds light on a crucial compromise between information compression, input-output computation and dynamic irreversibility induced by nonreciprocal interactions.
Collapse
Affiliation(s)
- Alessandro Ingrosso
- Quantitative Life Sciences, Abdus Salam International Centre for Theoretical Physics, 34151 Trieste, Italy
| | - Emanuele Panizon
- Quantitative Life Sciences, Abdus Salam International Centre for Theoretical Physics, 34151 Trieste, Italy
| |
Collapse
|
2
|
Ohga N, Ito S, Kolchinsky A. Thermodynamic Bound on the Asymmetry of Cross-Correlations. PHYSICAL REVIEW LETTERS 2023; 131:077101. [PMID: 37656850 DOI: 10.1103/physrevlett.131.077101] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 06/08/2023] [Indexed: 09/03/2023]
Abstract
The principle of microscopic reversibility says that, in equilibrium, two-time cross-correlations are symmetric under the exchange of observables. Thus, the asymmetry of cross-correlations is a fundamental, measurable, and often-used statistical signature of deviation from equilibrium. Here we find a simple and universal inequality that bounds the magnitude of asymmetry by the cycle affinity, i.e., the strength of thermodynamic driving. Our result applies to a large class of systems and all state observables, and it suggests a fundamental thermodynamic cost for various nonequilibrium functions quantified by the asymmetry. It also provides a powerful tool to infer affinity from measured cross-correlations, in a different and complementary way to the thermodynamic uncertainty relations. As an application, we prove a thermodynamic bound on the coherence of noisy oscillations, which was previously conjectured by Barato and Seifert [Phys. Rev. E 95, 062409 (2017)PRESCM2470-004510.1103/PhysRevE.95.062409]. We also derive a thermodynamic bound on directed information flow in a biochemical signal transduction model.
Collapse
Affiliation(s)
- Naruo Ohga
- Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Sosuke Ito
- Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- Universal Biology Institute, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Artemy Kolchinsky
- Universal Biology Institute, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| |
Collapse
|
3
|
Bryant SJ, Machta BB. Physical Constraints in Intracellular Signaling: The Cost of Sending a Bit. PHYSICAL REVIEW LETTERS 2023; 131:068401. [PMID: 37625074 PMCID: PMC11146629 DOI: 10.1103/physrevlett.131.068401] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Revised: 03/20/2023] [Accepted: 06/09/2023] [Indexed: 08/27/2023]
Abstract
Many biological processes require timely communication between molecular components. Cells employ diverse physical channels to this end, transmitting information through diffusion, electrical depolarization, and mechanical waves among other strategies. Here we bound the energetic cost of transmitting information through these physical channels, in k_{B}T/bit, as a function of the size of the sender and receiver, their spatial separation, and the communication latency. These calculations provide an estimate for the energy costs associated with information processing arising from the physical constraints of the cellular environment, which we find to be many orders of magnitude larger than unity in natural units. From these calculations, we construct a phase diagram indicating where each strategy is most efficient. Our results suggest that intracellular information transfer may constitute a substantial energetic cost. This provides a new tool for understanding tradeoffs in cellular network function.
Collapse
Affiliation(s)
- Samuel J. Bryant
- Department of Physics, Yale University, New Haven, Connecticut 06511, USA
| | - Benjamin B. Machta
- Department of Physics, Yale University and Quantitative Biology Institute, Yale University, New Haven, Connecticut 06511, USA
| |
Collapse
|
4
|
Tian Y, Tan Z, Hou H, Li G, Cheng A, Qiu Y, Weng K, Chen C, Sun P. Theoretical foundations of studying criticality in the brain. Netw Neurosci 2022; 6:1148-1185. [PMID: 38800464 PMCID: PMC11117095 DOI: 10.1162/netn_a_00269] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2022] [Accepted: 07/12/2022] [Indexed: 05/29/2024] Open
Abstract
Criticality is hypothesized as a physical mechanism underlying efficient transitions between cortical states and remarkable information-processing capacities in the brain. While considerable evidence generally supports this hypothesis, nonnegligible controversies persist regarding the ubiquity of criticality in neural dynamics and its role in information processing. Validity issues frequently arise during identifying potential brain criticality from empirical data. Moreover, the functional benefits implied by brain criticality are frequently misconceived or unduly generalized. These problems stem from the nontriviality and immaturity of the physical theories that analytically derive brain criticality and the statistic techniques that estimate brain criticality from empirical data. To help solve these problems, we present a systematic review and reformulate the foundations of studying brain criticality, that is, ordinary criticality (OC), quasi-criticality (qC), self-organized criticality (SOC), and self-organized quasi-criticality (SOqC), using the terminology of neuroscience. We offer accessible explanations of the physical theories and statistical techniques of brain criticality, providing step-by-step derivations to characterize neural dynamics as a physical system with avalanches. We summarize error-prone details and existing limitations in brain criticality analysis and suggest possible solutions. Moreover, we present a forward-looking perspective on how optimizing the foundations of studying brain criticality can deepen our understanding of various neuroscience questions.
Collapse
Affiliation(s)
- Yang Tian
- Department of Psychology & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China
- Laboratory of Advanced Computing and Storage, Central Research Institute, 2012 Laboratories, Huawei Technologies Co. Ltd., Beijing, China
| | - Zeren Tan
- Institute for Interdisciplinary Information Science, Tsinghua University, Beijing, China
| | - Hedong Hou
- UFR de Mathématiques, Université de Paris, Paris, France
| | - Guoqi Li
- Institute of Automation, Chinese Academy of Science, Beijing, China
- University of Chinese Academy of Science, Beijing, China
| | - Aohua Cheng
- Tsien Excellence in Engineering Program, School of Aerospace Engineering, Tsinghua University, Beijing, China
| | - Yike Qiu
- Tsien Excellence in Engineering Program, School of Aerospace Engineering, Tsinghua University, Beijing, China
| | - Kangyu Weng
- Tsien Excellence in Engineering Program, School of Aerospace Engineering, Tsinghua University, Beijing, China
| | - Chun Chen
- Department of Psychology & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China
| | - Pei Sun
- Department of Psychology & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China
| |
Collapse
|
5
|
Tian Y, Sun P. Percolation may explain efficiency, robustness, and economy of the brain. Netw Neurosci 2022; 6:765-790. [PMID: 36605416 PMCID: PMC9810365 DOI: 10.1162/netn_a_00246] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2021] [Accepted: 03/11/2022] [Indexed: 01/09/2023] Open
Abstract
The brain consists of billions of neurons connected by ultra-dense synapses, showing remarkable efficiency, robust flexibility, and economy in information processing. It is generally believed that these advantageous properties are rooted in brain connectivity; however, direct evidence remains absent owing to technical limitations or theoretical vacancy. This research explores the origins of these properties in the largest yet brain connectome of the fruit fly. We reveal that functional connectivity formation in the brain can be explained by a percolation process controlled by synaptic excitation-inhibition (E/I) balance. By increasing the E/I balance gradually, we discover the emergence of these properties as byproducts of percolation transition when the E/I balance arrives at 3:7. As the E/I balance keeps increase, an optimal E/I balance 1:1 is unveiled to ensure these three properties simultaneously, consistent with previous in vitro experimental predictions. Once the E/I balance reaches over 3:2, an intrinsic limitation of these properties determined by static (anatomical) brain connectivity can be observed. Our work demonstrates that percolation, a universal characterization of critical phenomena and phase transitions, may serve as a window toward understanding the emergence of various brain properties.
Collapse
Affiliation(s)
- Yang Tian
- Department of Psychology and Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China,Laboratory of Advanced Computing and Storage, Central Research Institute, 2012 Laboratories, Huawei Technologies Co. Ltd., Beijing, China,* Corresponding Author: ;
| | - Pei Sun
- Department of Psychology and Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China,* Corresponding Author: ;
| |
Collapse
|
6
|
Sadeghi A, Dervey R, Gligorovski V, Labagnara M, Rahi SJ. The optimal strategy balancing risk and speed predicts DNA damage checkpoint override times. NATURE PHYSICS 2022; 18:832-839. [PMID: 36281344 PMCID: PMC7613727 DOI: 10.1038/s41567-022-01601-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2020] [Accepted: 03/29/2022] [Indexed: 05/15/2023]
Abstract
Checkpoints arrest biological processes allowing time for error correction. The phenomenon of checkpoint override (also known as checkpoint adaptation, slippage, or leakage), during cellular self-replication is biologically critical but currently lacks a quantitative, functional, or system-level understanding. To uncover fundamental laws governing error-correction systems, we derived a general theory of optimal checkpoint strategies, balancing the trade-off between risk and self-replication speed. Mathematically, the problem maps onto the optimization of an absorbing boundary for a random walk. We applied the theory to the DNA damage checkpoint (DDC) in budding yeast, an intensively researched model checkpoint. Using novel reporters for double-strand DNA breaks (DSBs), we first quantified the probability distribution of DSB repair in time including rare events and, secondly, the survival probability after override. With these inputs, the optimal theory predicted remarkably accurately override times as a function of DSB numbers, which we measured precisely for the first time. Thus, a first-principles calculation revealed undiscovered patterns underlying highly noisy override processes. Our multi-DSB measurements revise well-known past results and show that override is more general than previously thought.
Collapse
Affiliation(s)
- Ahmad Sadeghi
- Laboratory of the Physics of Biological Systems, Institute of Physics, École polytechnique fÉdÉrale de Lausanne (EPFL), Lausanne, Switzerland
| | - Roxane Dervey
- Laboratory of the Physics of Biological Systems, Institute of Physics, École polytechnique fÉdÉrale de Lausanne (EPFL), Lausanne, Switzerland
| | - Vojislav Gligorovski
- Laboratory of the Physics of Biological Systems, Institute of Physics, École polytechnique fÉdÉrale de Lausanne (EPFL), Lausanne, Switzerland
| | - Marco Labagnara
- Laboratory of the Physics of Biological Systems, Institute of Physics, École polytechnique fÉdÉrale de Lausanne (EPFL), Lausanne, Switzerland
| | - Sahand Jamal Rahi
- Laboratory of the Physics of Biological Systems, Institute of Physics, École polytechnique fÉdÉrale de Lausanne (EPFL), Lausanne, Switzerland
| |
Collapse
|
7
|
Oberreiter L, Seifert U, Barato AC. Universal minimal cost of coherent biochemical oscillations. Phys Rev E 2022; 106:014106. [PMID: 35974563 DOI: 10.1103/physreve.106.014106] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Accepted: 06/13/2022] [Indexed: 06/15/2023]
Abstract
Biochemical clocks are essential for virtually all living systems. A biochemical clock that is isolated from an external periodic signal and subjected to fluctuations can oscillate coherently only for a finite number of oscillations. Furthermore, such an autonomous clock can oscillate only if it consumes free energy. What is the minimum amount of free-energy consumption required for a certain number of coherent oscillations? We conjecture a universal bound that answers this question. A system that oscillates coherently for N oscillations has a minimal free-energy cost per oscillation of 4π^{2}Nk_{B}T. Our bound is valid for general finite Markov processes, is conjectured based on extensive numerical evidence, is illustrated with numerical simulations of a known model for a biochemical oscillator, and applies to existing experimental data.
Collapse
Affiliation(s)
- Lukas Oberreiter
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Andre C Barato
- Department of Physics, University of Houston, Houston, Texas 77204, USA
| |
Collapse
|
8
|
Tian Y, Sun P. Information thermodynamics of encoding and encoders. CHAOS (WOODBURY, N.Y.) 2022; 32:063109. [PMID: 35778156 DOI: 10.1063/5.0068115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Accepted: 05/09/2022] [Indexed: 06/15/2023]
Abstract
Non-isolated systems have diverse coupling relations with the external environment. These relations generate complex thermodynamics and information transmission between the system and its environment. The framework depicted in the current research attempts to glance at the critical role of the internal orders inside the non-isolated system in shaping the information thermodynamics coupling. We characterize the coupling as a generalized encoding process, where the system acts as an information thermodynamics encoder to encode the external information based on thermodynamics. We formalize the encoding process in the context of the nonequilibrium second law of thermodynamics, revealing an intrinsic difference in information thermodynamics characteristics between information thermodynamics encoders with and without internal correlations. During the information encoding process of an external source Y, specific sub-systems in an encoder X with internal correlations can exceed the information thermodynamics bound on ( X , Y ) and encode more information than system X works as a whole. We computationally verify this theoretical finding in an Ising model with a random external field and a neural data set of the human brain during visual perception and recognition. Our analysis demonstrates that the stronger internal correlation inside these systems implies a higher possibility for specific sub-systems to encode more information than the global one. These findings may suggest a new perspective in studying information thermodynamics in diverse physical and biological systems.
Collapse
Affiliation(s)
- Yang Tian
- Department of Psychology, Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing 100084, China
| | - Pei Sun
- Department of Psychology, Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing 100084, China
| |
Collapse
|
9
|
Developmental energetics: Energy expenditure, budgets and metabolism during animal embryogenesis. Semin Cell Dev Biol 2022; 138:83-93. [PMID: 35317962 DOI: 10.1016/j.semcdb.2022.03.009] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2021] [Revised: 02/07/2022] [Accepted: 03/05/2022] [Indexed: 11/22/2022]
Abstract
Developing embryos are metabolically active, open systems that constantly exchange matter and energy with their environment. They function out of thermodynamic equilibrium and continuously use metabolic pathways to obtain energy from maternal nutrients, in order to fulfill the energetic requirements of growth and development. While an increasing number of studies highlight the role of metabolism in different developmental contexts, the physicochemical basis of embryogenesis, or how cellular processes use energy and matter to act together and transform a zygote into an adult organism, remains unknown. As we obtain a better understanding of metabolism, and benefit from current technology development, it is a promising time to revisit the energetic cost of development and how energetic principles may govern embryogenesis. Here, we review recent advances in methodology to measure and infer energetic parameters in developing embryos. We highlight a potential common pattern in embryonic energy expenditure and metabolic strategy across animal embryogenesis, and discuss challenges and open questions in developmental energetics.
Collapse
|
10
|
Moffett AS, Eckford AW. Minimal informational requirements for fitness. Phys Rev E 2022; 105:014403. [PMID: 35193272 DOI: 10.1103/physreve.105.014403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2021] [Accepted: 12/02/2021] [Indexed: 11/07/2022]
Abstract
The existing concept of the "fitness value of information" provides a theoretical upper bound on the fitness advantage of using information concerning a fluctuating environment. Using concepts from rate-distortion theory, we develop a theoretical framework to answer a different pair of questions: What is the minimal amount of information needed for a population to achieve a certain growth rate? What is the minimal amount of information gain needed for one subpopulation to achieve a certain average selection coefficient over another? We introduce a correspondence between fitness and distortion and solve for the rate-distortion functions of several systems using analytical and numerical methods. Because accurate information processing is energetically costly, our approach provides a theoretical basis for understanding evolutionary "design principles" underlying information-cost trade-offs.
Collapse
Affiliation(s)
- Alexander S Moffett
- Department of Electrical Engineering and Computer Science, York University, Toronto, Ontario, Canada
| | - Andrew W Eckford
- Department of Electrical Engineering and Computer Science, York University, Toronto, Ontario, Canada
| |
Collapse
|
11
|
Abstract
Living systems maintain or increase local order by working against the second law of thermodynamics. Thermodynamic consistency is restored as they consume free energy, thereby increasing the net entropy of their environment. Recently introduced estimators for the entropy production rate have provided major insights into the efficiency of important cellular processes. In experiments, however, many degrees of freedom typically remain hidden to the observer, and, in these cases, existing methods are not optimal. Here, by reformulating the problem within an optimization framework, we are able to infer improved bounds on the rate of entropy production from partial measurements of biological systems. Our approach yields provably optimal estimates given certain measurable transition statistics. In contrast to prevailing methods, the improved estimator reveals nonzero entropy production rates even when nonequilibrium processes appear time symmetric and therefore may pretend to obey detailed balance. We demonstrate the broad applicability of this framework by providing improved bounds on the energy consumption rates in a diverse range of biological systems including bacterial flagella motors, growing microtubules, and calcium oscillations within human embryonic kidney cells.
Collapse
Affiliation(s)
- Dominic J Skinner
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139
| |
Collapse
|
12
|
Song Y, Hyeon C. Thermodynamic uncertainty relation to assess biological processes. J Chem Phys 2021; 154:130901. [PMID: 33832251 DOI: 10.1063/5.0043671] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
We review the trade-offs between speed, fluctuations, and thermodynamic cost involved with biological processes in nonequilibrium states and discuss how optimal these processes are in light of the universal bound set by the thermodynamic uncertainty relation (TUR). The values of the uncertainty product Q of TUR, which can be used as a measure of the precision of enzymatic processes realized for a given thermodynamic cost, are suboptimal when the substrate concentration is at the Michaelis constant, and some of the key biological processes are found to work around this condition. We illustrate the utility of Q in assessing how close the molecular motors and biomass producing machineries are to the TUR bound, and for the cases of biomass production (or biological copying processes), we discuss how their optimality quantified in terms of Q is balanced with the error rate in the information transfer process. We also touch upon the trade-offs in other error-minimizing processes in biology, such as gene regulation and chaperone-assisted protein folding. A spectrum of Q recapitulating the biological processes surveyed here provides glimpses into how biological systems are evolved to optimize and balance the conflicting functional requirements.
Collapse
Affiliation(s)
- Yonghyun Song
- Korea Institute for Advanced Study, Seoul 02455, South Korea
| | - Changbong Hyeon
- Korea Institute for Advanced Study, Seoul 02455, South Korea
| |
Collapse
|
13
|
Vishen AS. Optimizing energetic cost of uncertainty in a driven system with and without feedback. Phys Rev E 2020; 102:052405. [PMID: 33327083 DOI: 10.1103/physreve.102.052405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2019] [Accepted: 10/12/2020] [Indexed: 11/07/2022]
Abstract
Many biological functions require dynamics to be necessarily driven out of equilibrium. In contrast, in various contexts, a nonequilibrium dynamics at fast timescales can be described by an effective equilibrium dynamics at a slower timescale. In this work, we study two different aspects: (i) the energy-efficiency tradeoff for a specific nonequilibrium linear dynamics of two variables with feedback and (ii) the cost of effective parameters in a coarse-grained theory as given by the "hidden" dissipation and entropy production rate in the effective equilibrium limit of the dynamics. To meaningfully discuss the tradeoff between energy consumption and the efficiency of the desired function, a one-to-one mapping between function(s) and energy input is required. The function considered in this work is the variance of one of the variables. We get a one-to-one mapping by considering the minimum variance obtained for a fixed entropy production rate and vice versa. We find that this minimum achievable variance is a monotonically decreasing function of the given entropy production rate. When there is a timescale separation, in the effective equilibrium limit, the cost of the effective potential and temperature is the associated "hidden" entropy production rate.
Collapse
Affiliation(s)
- Amit Singh Vishen
- Laboratoire Physico Chimie Curie, Institut Curie, PSL Research University, CNRS UMR168, 75005 Paris, France
| |
Collapse
|
14
|
Moffett AS, Wallbridge N, Plummer C, Eckford AW. Fitness value of information with delayed phenotype switching: Optimal performance with imperfect sensing. Phys Rev E 2020; 102:052403. [PMID: 33327185 DOI: 10.1103/physreve.102.052403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2020] [Accepted: 10/12/2020] [Indexed: 11/07/2022]
Abstract
The ability of organisms to accurately sense their environment and respond accordingly is critical for evolutionary success. However, exactly how the sensory ability influences fitness is a topic of active research, while the necessity of a time delay between when unreliable environmental cues are sensed and when organisms can mount a response has yet to be explored at any length. Accounting for this delay in phenotype response in models of population growth, we find that a critical error probability can exist under certain environmental conditions: An organism with a sensory system with any error probability less than the critical value can achieve the same long-term growth rate as an organism with a perfect sensing system. We also observe a tradeoff between the evolutionary value of sensory information and robustness to error, mediated by the rate at which the phenotype distribution relaxes to steady state. The existence of the critical error probability could have several important evolutionary consequences, primarily that sensory systems operating at the nonzero critical error probability may be evolutionarily optimal.
Collapse
Affiliation(s)
- Alexander S Moffett
- Department of Electrical Engineering and Computer Science, York University, Toronto, Ontario M3J 1P3, Canada
| | | | | | - Andrew W Eckford
- Department of Electrical Engineering and Computer Science, York University, Toronto, Ontario M3J 1P3, Canada
| |
Collapse
|
15
|
Falasco G, Esposito M. Dissipation-Time Uncertainty Relation. PHYSICAL REVIEW LETTERS 2020; 125:120604. [PMID: 33016734 DOI: 10.1103/physrevlett.125.120604] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2020] [Accepted: 08/14/2020] [Indexed: 05/10/2023]
Abstract
We show that the entropy production rate bounds the rate at which physical processes can be performed in stochastic systems far from equilibrium. In particular, we prove the fundamental tradeoff ⟨S[over ˙]_{e}⟩T≥k_{B} between the entropy flow ⟨S[over ˙]_{e}⟩ into the reservoirs and the mean time T to complete any process whose time-reversed is exponentially rarer. This dissipation-time uncertainty relation is a novel form of speed limit: the smaller the dissipation, the larger the time to perform a process.
Collapse
Affiliation(s)
- Gianmaria Falasco
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| |
Collapse
|
16
|
Vinterstare J, Hulthén K, Nilsson DE, Nilsson PA, Brönmark C. More than meets the eye: Predator-induced pupil size plasticity in a teleost fish. J Anim Ecol 2020; 89:2258-2267. [PMID: 33460050 DOI: 10.1111/1365-2656.13303] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2020] [Accepted: 06/24/2020] [Indexed: 11/27/2022]
Abstract
Most animals are visually oriented, and their eyes provide their 'window to the world'. Eye size correlates positively with visual performance, because larger eyes can house larger pupils that increase photon catch and contrast discrimination, particularly under dim light, which have positive effects on behaviours that enhance fitness, including predator avoidance and foraging. Recent studies have linked predation risk to selection for larger eyes and pupils, and such changes should be of importance for the majority of teleost fishes as they have a pupil that is fixed in size (eyes lack a pupillary sphincter muscle) and, hence, do not respond to changes in light conditions. Here, we quantify eye and pupil size of individual crucian carp, a common freshwater fish, following controlled manipulations of perceived predation risk (presence/absence). We also tested if crucian carp responded to increased predation risk by shifts in diel activity patterns. We found that crucian carp show phenotypic plasticity with regards to pupil size, but not eye size, as pupil size increased when exposed to predators (pike). Predator-exposed crucian carp also shifted from diurnal to nocturnal activity. Using a modelling exercise, we moreover show that the plastically enlarged pupils significantly increase visual range, especially for small objects under dim light conditions. Overall, our results provide compelling evidence for predator-induced pupil enlargement resulting in enhanced visual capabilities in a teleost fish. Pupil size plasticity in combination with the observed shift towards nocturnal activity may allow for efficient foraging also under dark conditions when predation risk from diurnal and visually oriented predators is reduced. The data highlight the powerful role of predation risk for eye development and evolution.
Collapse
Affiliation(s)
- Jerker Vinterstare
- Department of Biology, Aquatic Ecology Unit, Ecology Building, Lund University, Lund, Sweden
| | - Kaj Hulthén
- Department of Biology, Aquatic Ecology Unit, Ecology Building, Lund University, Lund, Sweden
| | - Dan E Nilsson
- Department of Biology, Lund Vision Group, Biology Building, Lund University, Lund, Sweden
| | - Per Anders Nilsson
- Department of Biology, Aquatic Ecology Unit, Ecology Building, Lund University, Lund, Sweden.,Department of Environmental and Life Sciences, Karlstad University, Karlstad, Sweden
| | - Christer Brönmark
- Department of Biology, Aquatic Ecology Unit, Ecology Building, Lund University, Lund, Sweden
| |
Collapse
|
17
|
Design of a MAPK signalling cascade balances energetic cost versus accuracy of information transmission. Nat Commun 2020; 11:3494. [PMID: 32661402 PMCID: PMC7359329 DOI: 10.1038/s41467-020-17276-4] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2019] [Accepted: 06/22/2020] [Indexed: 01/30/2023] Open
Abstract
Cellular processes are inherently noisy, and the selection for accurate responses in presence of noise has likely shaped signalling networks. Here, we investigate the trade-off between accuracy of information transmission and its energetic cost for a mitogen-activated protein kinase (MAPK) signalling cascade. Our analysis of the pheromone response pathway of budding yeast suggests that dose-dependent induction of the negative transcriptional feedbacks in this network maximizes the information per unit energetic cost, rather than the information transmission capacity itself. We further demonstrate that futile cycling of MAPK phosphorylation and dephosphorylation has a measurable effect on growth fitness, with energy dissipation within the signalling cascade thus likely being subject to evolutionary selection. Considering optimization of accuracy versus the energetic cost of information processing, a concept well established in physics and engineering, may thus offer a general framework to understand the regulatory design of cellular signalling systems. Cellular signalling networks provide information to the cell, but the trade-off between accuracy of information transfer and energetic cost of doing so has not been assessed. Here, the authors investigate a MAPK signalling cascade in budding yeast and find that information is maximised per unit energetic cost.
Collapse
|
18
|
Guan S, Xu L, Zhang Q, Shi H. Trade-offs between effectiveness and cost in bifunctional enzyme circuit with concentration robustness. Phys Rev E 2020; 101:012409. [PMID: 32069674 DOI: 10.1103/physreve.101.012409] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Indexed: 01/01/2023]
Abstract
A fundamental trade-off in biological systems is whether they consume resources to perform biological functions or save resources. Bacteria need to reliably and rapidly respond to input signals by using limited cellular resources. However, excessive resource consumption will become a burden for bacteria growth. To investigate the relationship between functional effectiveness and resource cost, we study the ubiquitous bifunctional enzyme circuit, which is robust to fluctuations in protein concentration and responds quickly to signal changes. We show that trade-off relationships exist between functional effectiveness and protein cost. Expressing more proteins of the circuit increases concentration robustness and response speed but affects bacterial growth. In particular, our study reveals a general relationship between free-energy dissipation rate, response speed, and concentration robustness. The dissipation of free energy plays an important role in the concentration robustness and response speed. High robustness can only be achieved with a large amount of free-energy consumption and protein cost. In addition, the noise of the output increases with increasing protein cost, while the noise of the response time decreases with increasing protein cost. We also calculate the trade-off relationships in the EnvZ-OmpR system and the nitrogen assimilation system, which both have the bifunctional enzyme. Similar results indicate that these relationships are mainly derived from the specific feature of the bifunctional enzyme circuits and are not relevant to the details of the models. According to the trade-off relationships, bacteria take a compromise solution that reliably performs biological functions at a reasonable cost.
Collapse
Affiliation(s)
- Shaohua Guan
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.,School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Liufang Xu
- Department of Physics and Biophysics & Complex System Center, Jilin University, Changchun 130012, Jilin, China
| | - Qing Zhang
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hualin Shi
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.,School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| |
Collapse
|
19
|
Schneeberger K, Taborsky M. The role of sensory ecology and cognition in social decisions: Costs of acquiring information matter. Funct Ecol 2020. [DOI: 10.1111/1365-2435.13488] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Karin Schneeberger
- Behavioural Ecology Division Institute for Ecology and Evolution University of Bern Hinterkappelen/Bern Switzerland
| | - Michael Taborsky
- Behavioural Ecology Division Institute for Ecology and Evolution University of Bern Hinterkappelen/Bern Switzerland
| |
Collapse
|
20
|
Prediction and Dissipation in Nonequilibrium Molecular Sensors: Conditionally Markovian Channels Driven by Memoryful Environments. Bull Math Biol 2020; 82:25. [PMID: 31993762 DOI: 10.1007/s11538-020-00694-2] [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: 12/05/2018] [Accepted: 12/31/2019] [Indexed: 10/25/2022]
Abstract
Biological sensors must often predict their input while operating under metabolic constraints. However, determining whether or not a particular sensor is evolved or designed to be accurate and efficient is challenging. This arises partly from the functional constraints being at cross purposes and partly since quantifying the prediction performance of even in silico sensors can require prohibitively long simulations, especially when highly complex environments drive sensors out of equilibrium. To circumvent these difficulties, we develop new expressions for the prediction accuracy and thermodynamic costs of the broad class of conditionally Markovian sensors subject to complex, correlated (unifilar hidden semi-Markov) environmental inputs in nonequilibrium steady state. Predictive metrics include the instantaneous memory and the total predictable information (the mutual information between present sensor state and input future), while dissipation metrics include power extracted from the environment and the nonpredictive information rate. Success in deriving these formulae relies on identifying the environment's causal states, the input's minimal sufficient statistics for prediction. Using these formulae, we study large random channels and the simplest nontrivial biological sensor model-that of a Hill molecule, characterized by the number of ligands that bind simultaneously-the sensor's cooperativity. We find that the seemingly impoverished Hill molecule can capture an order of magnitude more predictable information than large random channels.
Collapse
|
21
|
Affiliation(s)
- Francesco Avanzini
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Gianmaria Falasco
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| |
Collapse
|
22
|
Abstract
In order to respond to environmental signals, cells often use small molecular circuits to transmit information about their surroundings. Recently, motivated by specific examples in signaling and gene regulation, a body of work has focused on the properties of circuits that function out of equilibrium and dissipate energy. We briefly review the probabilistic measures of information and dissipation and use simple models to discuss and illustrate trade-offs between information and dissipation in biological circuits. We find that circuits with non-steady state initial conditions can transmit more information at small readout delays than steady state circuits. The dissipative cost of this additional information proves marginal compared to the steady state dissipation. Feedback does not significantly increase the transmitted information for out of steady state circuits but does decrease dissipative costs. Lastly, we discuss the case of bursty gene regulatory circuits that, even in the fast switching limit, function out of equilibrium.
Collapse
|
23
|
Rupprecht N, Vural DC. Maxwell's Demons with Finite Size and Response Time. PHYSICAL REVIEW LETTERS 2019; 123:080603. [PMID: 31491195 DOI: 10.1103/physrevlett.123.080603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2019] [Revised: 06/17/2019] [Indexed: 06/10/2023]
Abstract
Nearly all theoretical analyses of Maxwell's demon focus on its energetic and entropic costs of operation. Here, we focus on its rate of operation. In our model, a demon's rate limitation stems from its finite response time and gate area. We determine the rate limits of mass and energy transfer, as well as entropic reduction for four such demons: those that select particles according to (1) direction, (2) energy, (3) number, and (4) entropy. Last, we determine the optimal gate size for a demon with small, finite response time, and compare our predictions with molecular dynamics simulations with both ideal and nonideal gasses. Also, we study the conditions under which the demons are able to move both energy and particles in the chosen direction when attempting to only move one.
Collapse
Affiliation(s)
- Nathaniel Rupprecht
- Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Dervis Can Vural
- Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
| |
Collapse
|
24
|
Ashida K, Oka K. Stochastic thermodynamic limit on E. coli adaptation by information geometric approach. Biochem Biophys Res Commun 2019; 508:690-694. [PMID: 30528391 DOI: 10.1016/j.bbrc.2018.11.115] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2018] [Accepted: 11/19/2018] [Indexed: 11/19/2022]
Abstract
Biological systems process information under noisy environment. Sensory adaptation model of E. coli is suitable for investigation because of its simplicity. To understand the adaptation processing quantitatively, stochastic thermodynamic approach has been attempted. Information processing can be assumed as state transition of a system that consists of signal transduction molecules using thermodynamic approach, and efficiency can be measured as thermodynamic cost. Recently, using information geometry and stochastic thermodynamics, a relationship between speed of the transition and the thermodynamic cost has been investigated for a chemical reaction model. Here, we introduce this approach to sensory adaptation model of E. coli, and examined a relationship between adaptation speed and the thermodynamic cost, and efficiency of the adaptation speed. For increasing external noise level in stimulation, the efficiency decreased, but the efficiency was highly robust to external stimulation strength. Moreover, we demonstrated that there is the best noise to achieve the adaptation in the aspect of thermodynamic efficiency. Our quantification method provides a framework to understand the adaptation speed and the thermodynamic cost for various biological systems.
Collapse
Affiliation(s)
- Keita Ashida
- Department of Biosciences and Informatics, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan
| | - Kotaro Oka
- Department of Biosciences and Informatics, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan; Graduate Institute of Medicine, College of Medicine, Kaohsiung Medical University, Taiwan.
| |
Collapse
|
25
|
Fernandez VI, Yawata Y, Stocker R. A Foraging Mandala for Aquatic Microorganisms. ISME JOURNAL 2018; 13:563-575. [PMID: 30446738 PMCID: PMC6461837 DOI: 10.1038/s41396-018-0309-4] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/05/2018] [Revised: 10/01/2018] [Accepted: 10/11/2018] [Indexed: 11/27/2022]
Abstract
Aquatic environments harbor a great diversity of microorganisms, which interact with the same patchy, particulate, or diffuse resources by means of a broad array of physiological and behavioral adaptations, resulting in substantially different life histories and ecological success. To date, efforts to uncover and understand this diversity have not been matched by equivalent efforts to identify unifying frameworks that can provide a degree of generality and thus serve as a stepping stone to scale up microscale dynamics to predict their ecosystem-level consequences. In particular, evaluating the ecological consequences of different resource landscapes and of different microbial adaptations has remained a major challenge in aquatic microbial ecology. Here, inspired by Ramon Margalef’s mandala for phytoplankton, we propose a foraging mandala for microorganisms in aquatic environments, which accounts for both the local environment and individual adaptations. This biophysical framework distills resource acquisition into two fundamental parameters: the search time for a new resource and the growth return obtained from encounter with a resource. We illustrate the foraging mandala by considering a broad range of microbial adaptations and environmental characteristics. The broad applicability of the foraging mandala suggests that it could be a useful framework to compare disparate microbial strategies in aquatic environments and to reduce the vast complexity of microbe-environment interactions into a minimal number of fundamental parameters.
Collapse
Affiliation(s)
- Vicente I Fernandez
- Department of Civil, Environmental and Geomatic Engineering, Institute of Environmental Engineering, ETH Zurich, Zurich, Switzerland
| | - Yutaka Yawata
- Department of Civil, Environmental and Geomatic Engineering, Institute of Environmental Engineering, ETH Zurich, Zurich, Switzerland.,Faculty of Life and Environmental Sciences, University of Tsukuba, Tsukuba, Japan
| | - Roman Stocker
- Department of Civil, Environmental and Geomatic Engineering, Institute of Environmental Engineering, ETH Zurich, Zurich, Switzerland.
| |
Collapse
|
26
|
Ito S. Stochastic Thermodynamic Interpretation of Information Geometry. PHYSICAL REVIEW LETTERS 2018; 121:030605. [PMID: 30085772 DOI: 10.1103/physrevlett.121.030605] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2018] [Indexed: 06/08/2023]
Abstract
In recent years, the unified theory of information and thermodynamics has been intensively discussed in the context of stochastic thermodynamics. The unified theory reveals that information theory would be useful to understand nonstationary dynamics of systems far from equilibrium. In this Letter, we have found a new link between stochastic thermodynamics and information theory well-known as information geometry. By applying this link, an information geometric inequality can be interpreted as a thermodynamic uncertainty relationship between speed and thermodynamic cost. We have numerically applied an information geometric inequality to a thermodynamic model of a biochemical enzyme reaction.
Collapse
Affiliation(s)
- Sosuke Ito
- RIES, Hokkaido University, N20 W10, Kita-ku, Sapporo, Hokkaido 001-0020, Japan
| |
Collapse
|
27
|
Wong F, Amir A, Gunawardena J. Energy-speed-accuracy relation in complex networks for biological discrimination. Phys Rev E 2018; 98:012420. [PMID: 30110782 DOI: 10.1103/physreve.98.012420] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2017] [Indexed: 06/08/2023]
Abstract
Discriminating between correct and incorrect substrates is a core process in biology, but how is energy apportioned between the conflicting demands of accuracy (μ), speed (σ), and total entropy production rate (P)? Previous studies have focused on biochemical networks with simple structure or relied on simplifying kinetic assumptions. Here, we use the linear framework for timescale separation to analytically examine steady-state probabilities away from thermodynamic equilibrium for networks of arbitrary complexity. We also introduce a method of scaling parameters that is inspired by Hopfield's treatment of kinetic proofreading. Scaling allows asymptotic exploration of high-dimensional parameter spaces. We identify in this way a broad class of complex networks and scalings for which the quantity σln(μ)/P remains asymptotically finite whenever accuracy improves from equilibrium, so that μ_{eq}/μ→0. Scalings exist, however, even for Hopfield's original network, for which σln(μ)/P is asymptotically infinite, illustrating the parametric complexity. Outside the asymptotic regime, numerical calculations suggest that, under more restrictive parametric assumptions, networks satisfy the bound, σln(μ/μ_{eq})/P<1, and we discuss the biological implications for discrimination by ribosomes and DNA polymerase. The methods introduced here may be more broadly useful for analyzing complex networks that implement other forms of cellular information processing.
Collapse
Affiliation(s)
- Felix Wong
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Systems Biology, Harvard Medical School, Boston, Massachusetts 02115, USA
| | - Ariel Amir
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Jeremy Gunawardena
- Department of Systems Biology, Harvard Medical School, Boston, Massachusetts 02115, USA
| |
Collapse
|
28
|
Gnesotto FS, Mura F, Gladrow J, Broedersz CP. Broken detailed balance and non-equilibrium dynamics in living systems: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:066601. [PMID: 29504517 DOI: 10.1088/1361-6633/aab3ed] [Citation(s) in RCA: 116] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.
Collapse
Affiliation(s)
- F S Gnesotto
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
| | | | | | | |
Collapse
|
29
|
Matsumoto T, Sagawa T. Role of sufficient statistics in stochastic thermodynamics and its implication to sensory adaptation. Phys Rev E 2018; 97:042103. [PMID: 29758679 DOI: 10.1103/physreve.97.042103] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2017] [Indexed: 11/07/2022]
Abstract
A sufficient statistic is a significant concept in statistics, which means a probability variable that has sufficient information required for an inference task. We investigate the roles of sufficient statistics and related quantities in stochastic thermodynamics. Specifically, we prove that for general continuous-time bipartite networks, the existence of a sufficient statistic implies that an informational quantity called the sensory capacity takes the maximum. Since the maximal sensory capacity imposes a constraint that the energetic efficiency cannot exceed one-half, our result implies that the existence of a sufficient statistic is inevitably accompanied by energetic dissipation. We also show that, in a particular parameter region of linear Langevin systems there exists the optimal noise intensity at which the sensory capacity, the information-thermodynamic efficiency, and the total entropy production are optimized at the same time. We apply our general result to a model of sensory adaptation of E. coli and find that the sensory capacity is nearly maximal with experimentally realistic parameters.
Collapse
Affiliation(s)
- Takumi Matsumoto
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Takahiro Sagawa
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| |
Collapse
|
30
|
Hasegawa Y. Multidimensional biochemical information processing of dynamical patterns. Phys Rev E 2018; 97:022401. [PMID: 29548224 DOI: 10.1103/physreve.97.022401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2017] [Indexed: 06/08/2023]
Abstract
Cells receive signaling molecules by receptors and relay information via sensory networks so that they can respond properly depending on the type of signal. Recent studies have shown that cells can extract multidimensional information from dynamical concentration patterns of signaling molecules. We herein study how biochemical systems can process multidimensional information embedded in dynamical patterns. We model the decoding networks by linear response functions, and optimize the functions with the calculus of variations to maximize the mutual information between patterns and output. We find that, when the noise intensity is lower, decoders with different linear response functions, i.e., distinct decoders, can extract much information. However, when the noise intensity is higher, distinct decoders do not provide the maximum amount of information. This indicates that, when transmitting information by dynamical patterns, embedding information in multiple patterns is not optimal when the noise intensity is very large. Furthermore, we explore the biochemical implementations of these decoders using control theory and demonstrate that these decoders can be implemented biochemically through the modification of cascade-type networks, which are prevalent in actual signaling pathways.
Collapse
Affiliation(s)
- Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| |
Collapse
|
31
|
Seoane LF, Solé RV. Information theory, predictability and the emergence of complex life. ROYAL SOCIETY OPEN SCIENCE 2018; 5:172221. [PMID: 29515907 PMCID: PMC5830796 DOI: 10.1098/rsos.172221] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Accepted: 01/24/2018] [Indexed: 05/07/2023]
Abstract
Despite the obvious advantage of simple life forms capable of fast replication, different levels of cognitive complexity have been achieved by living systems in terms of their potential to cope with environmental uncertainty. Against the inevitable cost associated with detecting environmental cues and responding to them in adaptive ways, we conjecture that the potential for predicting the environment can overcome the expenses associated with maintaining costly, complex structures. We present a minimal formal model grounded in information theory and selection, in which successive generations of agents are mapped into transmitters and receivers of a coded message. Our agents are guessing machines and their capacity to deal with environments of different complexity defines the conditions to sustain more complex agents.
Collapse
Affiliation(s)
- Luís F. Seoane
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra (GRIB), Dr Aiguader 80, 08003 Barcelona, Spain
- Institut de Biologia Evolutiva, CSIC-UPF, Pg Maritim de la Barceloneta 37, 08003 Barcelona, Spain
| | - Ricard V. Solé
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra (GRIB), Dr Aiguader 80, 08003 Barcelona, Spain
- Institut de Biologia Evolutiva, CSIC-UPF, Pg Maritim de la Barceloneta 37, 08003 Barcelona, Spain
- Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
| |
Collapse
|
32
|
Ehrich J, Engel A. Stochastic thermodynamics of interacting degrees of freedom: Fluctuation theorems for detached path probabilities. Phys Rev E 2018; 96:042129. [PMID: 29347633 DOI: 10.1103/physreve.96.042129] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2017] [Indexed: 11/07/2022]
Abstract
Systems with interacting degrees of freedom play a prominent role in stochastic thermodynamics. Our aim is to use the concept of detached path probabilities and detached entropy production for bipartite Markov processes and elaborate on a series of special cases including measurement-feedback systems, sensors, and hidden Markov models. For these special cases we show that fluctuation theorems involving the detached entropy production recover known results which have been obtained separately before. Additionally, we show that the fluctuation relation for the detached entropy production can be used in model selection for data stemming from a hidden Markov model. We discuss the relation to previous approaches including those which use information flow or learning rate to quantify the influence of one subsystem on the other. In conclusion, we present a complete framework with which to find fluctuation relations for coupled systems.
Collapse
Affiliation(s)
- Jannik Ehrich
- Universität Oldenburg, Institut für Physik, 26111 Oldenburg, Germany
| | - Andreas Engel
- Universität Oldenburg, Institut für Physik, 26111 Oldenburg, Germany
| |
Collapse
|
33
|
Marsland R, England J. Limits of predictions in thermodynamic systems: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:016601. [PMID: 28976362 DOI: 10.1088/1361-6633/aa9101] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The past twenty years have seen a resurgence of interest in nonequilibrium thermodynamics, thanks to advances in the theory of stochastic processes and in their thermodynamic interpretation. Fluctuation theorems provide fundamental constraints on the dynamics of systems arbitrarily far from thermal equilibrium. Thermodynamic uncertainty relations bound the dissipative cost of precision in a wide variety of processes. Concepts of excess work and excess heat provide the basis for a complete thermodynamics of nonequilibrium steady states, including generalized Clausius relations and thermodynamic potentials. But these general results carry their own limitations: fluctuation theorems involve exponential averages that can depend sensitively on unobservably rare trajectories; steady-state thermodynamics makes use of a dual dynamics that lacks any direct physical interpretation. This review aims to present these central results of contemporary nonequilibrium thermodynamics in such a way that the power of each claim for making physical predictions can be clearly assessed, using examples from current topics in soft matter and biophysics.
Collapse
|
34
|
Cortese-Krott MM, Koning A, Kuhnle GG, Nagy P, Bianco CL, Pasch A, Wink DA, Fukuto JM, Jackson AA, van Goor H, Olson KR, Feelisch M. The Reactive Species Interactome: Evolutionary Emergence, Biological Significance, and Opportunities for Redox Metabolomics and Personalized Medicine. Antioxid Redox Signal 2017; 27:684-712. [PMID: 28398072 PMCID: PMC5576088 DOI: 10.1089/ars.2017.7083] [Citation(s) in RCA: 228] [Impact Index Per Article: 32.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/24/2017] [Accepted: 04/10/2017] [Indexed: 12/20/2022]
Abstract
SIGNIFICANCE Oxidative stress is thought to account for aberrant redox homeostasis and contribute to aging and disease. However, more often than not, administration of antioxidants is ineffective, suggesting that our current understanding of the underlying regulatory processes is incomplete. Recent Advances: Similar to reactive oxygen species and reactive nitrogen species, reactive sulfur species are now emerging as important signaling molecules, targeting regulatory cysteine redox switches in proteins, affecting gene regulation, ion transport, intermediary metabolism, and mitochondrial function. To rationalize the complexity of chemical interactions of reactive species with themselves and their targets and help define their role in systemic metabolic control, we here introduce a novel integrative concept defined as the reactive species interactome (RSI). The RSI is a primeval multilevel redox regulatory system whose architecture, together with the physicochemical characteristics of its constituents, allows efficient sensing and rapid adaptation to environmental changes and various other stressors to enhance fitness and resilience at the local and whole-organism level. CRITICAL ISSUES To better characterize the RSI-related processes that determine fluxes through specific pathways and enable integration, it is necessary to disentangle the chemical biology and activity of reactive species (including precursors and reaction products), their targets, communication systems, and effects on cellular, organ, and whole-organism bioenergetics using system-level/network analyses. FUTURE DIRECTIONS Understanding the mechanisms through which the RSI operates will enable a better appreciation of the possibilities to modulate the entire biological system; moreover, unveiling molecular signatures that characterize specific environmental challenges or other forms of stress will provide new prevention/intervention opportunities for personalized medicine. Antioxid. Redox Signal. 00, 000-000.
Collapse
Affiliation(s)
- Miriam M. Cortese-Krott
- Cardiovascular Research Laboratory, Department of Cardiology, Pneumology and Angiology, Medical Faculty, Heinrich Heine University, Düsseldorf, Germany
| | - Anne Koning
- Department of Pathology and Medical Biology, University Medical Center Groningen, University of Groningen, Groningen, The Netherlands
| | - Gunter G.C. Kuhnle
- Department of Food and Nutritional Sciences, University of Reading, Reading, United Kingdom
| | - Peter Nagy
- Molecular Immunology and Toxicology, National Institute of Oncology, Budapest, Hungary
| | | | - Andreas Pasch
- Department of Clinical Chemistry, University of Bern and Calciscon AG, Bern, Switzerland
| | - David A. Wink
- Cancer and Inflammation Program, National Cancer Institute, National Institutes of Health, Frederick, Maryland
| | - Jon M. Fukuto
- Department of Chemistry, Sonoma State University, Rohnert Park, California
| | - Alan A. Jackson
- NIHR Southampton Biomedical Research Center, University Hospital Southampton NHS Foundation Trust, Southampton, United Kingdom
| | - Harry van Goor
- Department of Pathology and Medical Biology, University Medical Center Groningen, University of Groningen, Groningen, The Netherlands
| | - Kenneth R. Olson
- Indiana University School of Medicine-South Bend, South Bend, Indiana
| | - Martin Feelisch
- NIHR Southampton Biomedical Research Center, University Hospital Southampton NHS Foundation Trust, Southampton, United Kingdom
- Clinical and Experimental Sciences, Faculty of Medicine, Southampton General Hospital and Institute for Life Sciences, University of Southampton, Southampton, United Kingdom
| |
Collapse
|
35
|
Information-Theoretic Bound on the Entropy Production to Maintain a Classical Nonequilibrium Distribution Using Ancillary Control. ENTROPY 2017. [DOI: 10.3390/e19070333] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
There are many functional contexts where it is desirable to maintain a mesoscopic system in a nonequilibrium state. However, such control requires an inherent energy dissipation. In this article, we unify and extend a number of works on the minimum energetic cost to maintain a mesoscopic system in a prescribed nonequilibrium distribution using ancillary control. For a variety of control mechanisms, we find that the minimum amount of energy dissipation necessary can be cast as an information-theoretic measure of distinguishability between the target nonequilibrium state and the underlying equilibrium distribution. This work offers quantitative insight into the intuitive idea that more energy is needed to maintain a system farther from equilibrium.
Collapse
|
36
|
Barato AC, Seifert U. Coherence of biochemical oscillations is bounded by driving force and network topology. Phys Rev E 2017; 95:062409. [PMID: 28709274 DOI: 10.1103/physreve.95.062409] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2017] [Indexed: 12/20/2022]
Abstract
Biochemical oscillations are prevalent in living organisms. Systems with a small number of constituents cannot sustain coherent oscillations for an indefinite time because of fluctuations in the period of oscillation. We show that the number of coherent oscillations that quantifies the precision of the oscillator is universally bounded by the thermodynamic force that drives the system out of equilibrium and by the topology of the underlying biochemical network of states. Our results are valid for arbitrary Markov processes, which are commonly used to model biochemical reactions. We apply our results to a model for a single KaiC protein and to an activator-inhibitor model that consists of several molecules. From a mathematical perspective, based on strong numerical evidence, we conjecture a universal constraint relating the imaginary and real parts of the first nontrivial eigenvalue of a stochastic matrix.
Collapse
Affiliation(s)
- Andre C Barato
- Max Planck Institute for the Physics of Complex Systems, Nöthnizer Straβe 38, 01187 Dresden, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| |
Collapse
|
37
|
Yang K, Wu J, Xu G, Xie D, Peretz-Soroka H, Santos S, Alexander M, Zhu L, Zhang M, Liu Y, Lin F. A dual-docking microfluidic cell migration assay (D 2-Chip) for testing neutrophil chemotaxis and the memory effect. Integr Biol (Camb) 2017; 9:303-312. [PMID: 28367571 PMCID: PMC5511521 DOI: 10.1039/c7ib00037e] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Chemotaxis is a classic mechanism for guiding cell migration and an important topic in both fundamental cell biology and health sciences. Neutrophils are a widely used model to study eukaryotic cell migration and neutrophil chemotaxis itself can lead to protective or harmful immune actions to the body. While much has been learnt from past research about how neutrophils effectively navigate through a chemoattractant gradient, many interesting questions remain unclear. For example, while it is tempting to model neutrophil chemotaxis using the well-established biased random walk theory, the experimental proof was challenged by the cell's highly persistent migrating nature. A special experimental design is required to test the key predictions from the random walk model. Another question that has interested the cell migration community for decades concerns the existence of chemotactic memory and its underlying mechanism. Although chemotactic memory has been suggested in various studies, a clear quantitative experimental demonstration will improve our understanding of the migratory memory effect. Motivated by these questions, we developed a microfluidic cell migration assay (so-called dual-docking chip or D2-Chip) that can test both the biased random walk model and the memory effect for neutrophil chemotaxis on a single chip enabled by multi-region gradient generation and dual-region cell alignment. Our results provide experimental support for the biased random walk model and chemotactic memory for neutrophil chemotaxis. Quantitative data analyses provide new insights into neutrophil chemotaxis and memory by making connections to entropic disorder, cell morphology and oscillating migratory response.
Collapse
Affiliation(s)
- Ke Yang
- Institute of Applied Technology, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, Anhui, P.R. China
- University of Science and Technology of China, Hefei, Anhui, P.R. China
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB, Canada
| | - Jiandong Wu
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB, Canada
| | - Guoqing Xu
- Applied Computer Science, the University of Winnipeg, Winnipeg, MB, Canada
| | - Dongxue Xie
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB, Canada
- Department of Genetics, Jilin University, China
| | - Hagit Peretz-Soroka
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB, Canada
| | - Susy Santos
- Victoria General Hospital and River Heights/Fort Garry Community areas, Winnipeg, MB, Canada
- South Winnipeg Integrated Health & Social Services, Winnipeg, MB, Canada
| | - Murray Alexander
- Department of Physics, University of Winnipeg, Winnipeg, MB, Canada
| | - Ling Zhu
- Institute of Applied Technology, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, Anhui, P.R. China
| | | | - Yong Liu
- Institute of Applied Technology, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, Anhui, P.R. China
| | - Francis Lin
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB, Canada
| |
Collapse
|
38
|
Wang CH, Mehta P, Elbaum M. Thermodynamic Paradigm for Solution Demixing Inspired by Nuclear Transport in Living Cells. PHYSICAL REVIEW LETTERS 2017; 118:158101. [PMID: 28452496 PMCID: PMC5519409 DOI: 10.1103/physrevlett.118.158101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2016] [Indexed: 06/01/2023]
Abstract
Living cells display a remarkable capacity to compartmentalize their functional biochemistry. A particularly fascinating example is the cell nucleus. Exchange of macromolecules between the nucleus and the surrounding cytoplasm does not involve traversing a lipid bilayer membrane. Instead, large protein channels known as nuclear pores cross the nuclear envelope and regulate the passage of other proteins and RNA molecules. Beyond simply gating diffusion, the system of nuclear pores and associated transport receptors is able to generate substantial concentration gradients, at the energetic expense of guanosine triphosphate hydrolysis. In contrast to conventional approaches to demixing such as reverse osmosis and dialysis, the biological system operates continuously, without application of cyclic changes in pressure or solvent exchange. Abstracting the biological paradigm, we examine this transport system as a thermodynamic machine of solution demixing. Building on the construct of free energy transduction and biochemical kinetics, we find conditions for the stable operation and optimization of the concentration gradients as a function of dissipation in the form of entropy production.
Collapse
Affiliation(s)
- Ching-Hao Wang
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | - Pankaj Mehta
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | - Michael Elbaum
- Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot, 7600001 Israel
| |
Collapse
|
39
|
Loutchko D, Eisbach M, Mikhailov AS. Stochastic thermodynamics of a chemical nanomachine: The channeling enzyme tryptophan synthase. J Chem Phys 2017; 146:025101. [DOI: 10.1063/1.4973544] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
40
|
McGrath T, Jones NS, Ten Wolde PR, Ouldridge TE. Biochemical Machines for the Interconversion of Mutual Information and Work. PHYSICAL REVIEW LETTERS 2017; 118:028101. [PMID: 28128612 DOI: 10.1103/physrevlett.118.028101] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2016] [Indexed: 05/18/2023]
Abstract
We propose a physically realizable information-driven device consisting of an enzyme in a chemical bath, interacting with pairs of molecules prepared in correlated states. These correlations persist without direct interaction and thus store free energy equal to the mutual information. The enzyme can harness this free energy, and that stored in the individual molecular states, to do chemical work. Alternatively, the enzyme can use the chemical driving to create mutual information. A modified system can function without external intervention, approaching biological systems more closely.
Collapse
Affiliation(s)
- Thomas McGrath
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Nick S Jones
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| | | | - Thomas E Ouldridge
- Department of Bioengineering, Imperial College London, London SW7 2AZ, United Kingdom
| |
Collapse
|
41
|
Goldt S, Seifert U. Stochastic Thermodynamics of Learning. PHYSICAL REVIEW LETTERS 2017; 118:010601. [PMID: 28106416 DOI: 10.1103/physrevlett.118.010601] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2016] [Indexed: 06/06/2023]
Abstract
Virtually every organism gathers information about its noisy environment and builds models from those data, mostly using neural networks. Here, we use stochastic thermodynamics to analyze the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency η≤1. We discuss the conditions for optimal learning and analyze Hebbian learning in the thermodynamic limit.
Collapse
Affiliation(s)
- Sebastian Goldt
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| |
Collapse
|
42
|
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
|
43
|
Ito S. Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality. Sci Rep 2016; 6:36831. [PMID: 27833120 PMCID: PMC5104982 DOI: 10.1038/srep36831] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2016] [Accepted: 10/21/2016] [Indexed: 11/16/2022] Open
Abstract
The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to a hidden Markov model. Furthermore, we discuss physical interpretations of the backward transfer entropy in completely different settings of thermodynamics for information processing and the gambling with side information. In both settings of thermodynamics and the gambling, the backward transfer entropy characterizes a possible loss of some benefit, where the conventional transfer entropy characterizes a possible benefit. Our result implies the deep connection between thermodynamics and the gambling in the presence of information flow, and that the backward transfer entropy would be useful as a novel measure of information flow in nonequilibrium thermodynamics, biochemical sciences, economics and statistics.
Collapse
Affiliation(s)
- Sosuke Ito
- Department of Physics, Tokyo Institute of Technology, Oh-okayama 2-12-1, Meguro-ku, Tokyo 152-8551, Japan
- FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
| |
Collapse
|
44
|
Yamamoto S, Ito S, Shiraishi N, Sagawa T. Linear irreversible thermodynamics and Onsager reciprocity for information-driven engines. Phys Rev E 2016; 94:052121. [PMID: 27967007 DOI: 10.1103/physreve.94.052121] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2016] [Indexed: 06/06/2023]
Abstract
In the recent progress in nonequilibrium thermodynamics, information has been recognized as a kind of thermodynamic resource that can drive thermodynamic current without any direct energy injection. In this paper, we establish the framework of linear irreversible thermodynamics for a broad class of autonomous information processing. In particular, we prove that the Onsager reciprocity holds true with information: The linear response matrix is well-defined and is shown symmetric with both of the information affinity and the conventional thermodynamic affinity. As an application, we derive a universal bound for the efficiency at maximum power for information-driven engines in the linear regime. Our result reveals the fundamental role of information flow in linear irreversible thermodynamics.
Collapse
Affiliation(s)
- Shumpei Yamamoto
- Department of Basic Science, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
| | - Sosuke Ito
- Department of Physics, Tokyo Institute of Technology, Oh-okayama 2-12-1, Meguro-ku, Tokyo 152-8551, Japan
| | - Naoto Shiraishi
- Department of Basic Science, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
| | - Takahiro Sagawa
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| |
Collapse
|
45
|
Lan G, Tu Y. Information processing in bacteria: memory, computation, and statistical physics: a key issues review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:052601. [PMID: 27058315 PMCID: PMC4955840 DOI: 10.1088/0034-4885/79/5/052601] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Living systems have to constantly sense their external environment and adjust their internal state in order to survive and reproduce. Biological systems, from as complex as the brain to a single E. coli cell, have to process these data in order to make appropriate decisions. How do biological systems sense external signals? How do they process the information? How do they respond to signals? Through years of intense study by biologists, many key molecular players and their interactions have been identified in different biological machineries that carry out these signaling functions. However, an integrated, quantitative understanding of the whole system is still lacking for most cellular signaling pathways, not to say the more complicated neural circuits. To study signaling processes in biology, the key thing to measure is the input-output relationship. The input is the signal itself, such as chemical concentration, external temperature, light (intensity and frequency), and more complex signals such as the face of a cat. The output can be protein conformational changes and covalent modifications (phosphorylation, methylation, etc), gene expression, cell growth and motility, as well as more complex output such as neuron firing patterns and behaviors of higher animals. Due to the inherent noise in biological systems, the measured input-output dependence is often noisy. These noisy data can be analysed by using powerful tools and concepts from information theory such as mutual information, channel capacity, and the maximum entropy hypothesis. This information theory approach has been successfully used to reveal the underlying correlations between key components of biological networks, to set bounds for network performance, and to understand possible network architecture in generating observed correlations. Although the information theory approach provides a general tool in analysing noisy biological data and may be used to suggest possible network architectures in preserving information, it does not reveal the underlying mechanism that leads to the observed input-output relationship, nor does it tell us much about which information is important for the organism and how biological systems use information to carry out specific functions. To do that, we need to develop models of the biological machineries, e.g. biochemical networks and neural networks, to understand the dynamics of biological information processes. This is a much more difficult task. It requires deep knowledge of the underlying biological network-the main players (nodes) and their interactions (links)-in sufficient detail to build a model with predictive power, as well as quantitative input-output measurements of the system under different perturbations (both genetic variations and different external conditions) to test the model predictions to guide further development of the model. Due to the recent growth of biological knowledge thanks in part to high throughput methods (sequencing, gene expression microarray, etc) and development of quantitative in vivo techniques such as various florescence technology, these requirements are starting to be realized in different biological systems. The possible close interaction between quantitative experimentation and theoretical modeling has made systems biology an attractive field for physicists interested in quantitative biology. In this review, we describe some of the recent work in developing a quantitative predictive model of bacterial chemotaxis, which can be considered as the hydrogen atom of systems biology. Using statistical physics approaches, such as the Ising model and Langevin equation, we study how bacteria, such as E. coli, sense and amplify external signals, how they keep a working memory of the stimuli, and how they use these data to compute the chemical gradient. In particular, we will describe how E. coli cells avoid cross-talk in a heterogeneous receptor cluster to keep a ligand-specific memory. We will also study the thermodynamic costs of adaptation for cells to maintain an accurate memory. The statistical physics based approach described here should be useful in understanding design principles for cellular biochemical circuits in general.
Collapse
Affiliation(s)
- Ganhui Lan
- George Washington University, Washington DC 20052, USA
| | - Yuhai Tu
- IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA
| |
Collapse
|
46
|
The Free Energy Requirements of Biological Organisms; Implications for Evolution. ENTROPY 2016. [DOI: 10.3390/e18040138] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
47
|
Hartich D, Barato AC, Seifert U. Sensory capacity: An information theoretical measure of the performance of a sensor. Phys Rev E 2016; 93:022116. [PMID: 26986297 DOI: 10.1103/physreve.93.022116] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2015] [Indexed: 05/10/2023]
Abstract
For a general sensory system following an external stochastic signal, we introduce the sensory capacity. This quantity characterizes the performance of a sensor: sensory capacity is maximal if the instantaneous state of the sensor has as much information about a signal as the whole time series of the sensor. We show that adding a memory to the sensor increases the sensory capacity. This increase quantifies the improvement of the sensor with the addition of the memory. Our results are obtained with the framework of stochastic thermodynamics of bipartite systems, which allows for the definition of an efficiency that relates the rate with which the sensor learns about the signal with the energy dissipated by the sensor, which is given by the thermodynamic entropy production. We demonstrate a general trade-off between sensory capacity and efficiency: if the sensory capacity is equal to its maximum 1, then the efficiency must be less than 1/2. As a physical realization of a sensor we consider a two-component cellular network estimating a fluctuating external ligand concentration as signal. This model leads to coupled linear Langevin equations that allow us to obtain explicit analytical results.
Collapse
Affiliation(s)
- David Hartich
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Andre C Barato
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
- Max Planck Institute for the Physics of Complex Systems, Nöthnizer Straße 38, 01187 Dresden, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| |
Collapse
|
48
|
Funo K, Ueda M. Work Fluctuation-Dissipation Trade-Off in Heat Engines. PHYSICAL REVIEW LETTERS 2015; 115:260601. [PMID: 26764979 DOI: 10.1103/physrevlett.115.260601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2015] [Indexed: 06/05/2023]
Abstract
Reducing work fluctuation and dissipation in heat engines or, more generally, information heat engines that perform feedback control, is vital to maximize their efficiency. The same problem arises when we attempt to maximize the efficiency of a given thermodynamic task that undergoes nonequilibrium processes for arbitrary initial and final states. We find that the most general trade-off relation between work fluctuation and dissipation applicable to arbitrary nonequilibrium processes is bounded from below by the information distance characterizing how far the system is from thermal equilibrium. The minimum amount of dissipation is found to be given in terms of the relative entropy and the Renyi divergence, both of which quantify the information distance between the state of the system and the canonical distribution. We give an explicit protocol that achieves the fundamental lower bound of the trade-off relation.
Collapse
Affiliation(s)
- Ken Funo
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Masahito Ueda
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
| |
Collapse
|
49
|
Micali G, Endres RG. Bacterial chemotaxis: information processing, thermodynamics, and behavior. Curr Opin Microbiol 2015; 30:8-15. [PMID: 26731482 DOI: 10.1016/j.mib.2015.12.001] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2015] [Revised: 12/01/2015] [Accepted: 12/02/2015] [Indexed: 01/05/2023]
Abstract
Escherichia coli has long been used as a model organism due to the extensive experimental characterization of its pathways and molecular components. Take chemotaxis as an example, which allows bacteria to sense and swim in response to chemicals, such as nutrients and toxins. Many of the pathway's remarkable sensing and signaling properties are now concisely summarized in terms of design (or engineering) principles. More recently, new approaches from information theory and stochastic thermodynamics have begun to address how pathways process environmental stimuli and what the limiting factors are. However, to fully capitalize on these theoretical advances, a closer connection with single-cell experiments will be required.
Collapse
Affiliation(s)
- Gabriele Micali
- Department of Life Sciences, Imperial College, London, United Kingdom; Centre for Integrative Systems Biology and Bioinformatics, Imperial College, London, United Kingdom
| | - Robert G Endres
- Department of Life Sciences, Imperial College, London, United Kingdom; Centre for Integrative Systems Biology and Bioinformatics, Imperial College, London, United Kingdom.
| |
Collapse
|
50
|
Strasberg P, Cerrillo J, Schaller G, Brandes T. Thermodynamics of stochastic Turing machines. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042104. [PMID: 26565165 DOI: 10.1103/physreve.92.042104] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2015] [Indexed: 06/05/2023]
Abstract
In analogy to Brownian computers we explicitly show how to construct stochastic models which mimic the behavior of a general-purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation, which are logically reversible and have a well-defined and consistent thermodynamic interpretation. The resulting master equation, which describes a simple one-step process on an enormously large state space, allows us to thoroughly investigate the thermodynamics of computation for this situation. Especially in the stationary regime we can well approximate the master equation by a simple Fokker-Planck equation in one dimension. We then show that the entropy production rate at steady state can be made arbitrarily small, but the total (integrated) entropy production is finite and grows logarithmically with the number of computational steps.
Collapse
Affiliation(s)
- Philipp Strasberg
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Javier Cerrillo
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Gernot Schaller
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Tobias Brandes
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| |
Collapse
|