1
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Shelansky R, Abrahamsson S, Brown CR, Doody M, Lenstra TL, Larson DR, Boeger H. Single gene analysis in yeast suggests nonequilibrium regulatory dynamics for transcription. Nat Commun 2024; 15:6226. [PMID: 39043639 PMCID: PMC11266658 DOI: 10.1038/s41467-024-50419-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2023] [Accepted: 07/04/2024] [Indexed: 07/25/2024] Open
Abstract
Fluctuations in the initiation rate of transcription, the first step in gene expression, ensue from the stochastic behavior of the molecular process that controls transcription. In steady state, the regulatory process is often assumed to operate reversibly, i.e., in equilibrium. However, reversibility imposes fundamental limits to information processing. For instance, the assumption of equilibrium is difficult to square with the precision with which the regulatory process executes its task in eukaryotes. Here we provide evidence - from microscopic analyses of the transcription dynamics at a single gene copy of yeast - that the regulatory process for transcription is cyclic and irreversible (out of equilibrium). The necessary coupling to reservoirs of free energy occurs via sequence-specific transcriptional activators and the recruitment, in part, of ATP-dependent chromatin remodelers. Our findings may help explain how eukaryotic cells reconcile the dual but opposing requirements for fast regulatory kinetics and high regulatory specificity.
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Affiliation(s)
- Robert Shelansky
- Department of Molecular Cell and Developmental Biology, University of California, Santa Cruz, CA, USA
| | - Sara Abrahamsson
- Department of Electrical and Computer Engineering, University of California, Santa Cruz, CA, USA
| | - Christopher R Brown
- Department of Molecular Cell and Developmental Biology, University of California, Santa Cruz, CA, USA
- Korro Bio, Cambridge, MA, USA
| | - Michael Doody
- Department of Molecular Cell and Developmental Biology, University of California, Santa Cruz, CA, USA
| | - Tineke L Lenstra
- Division of Gene Regulation, The Netherlands Cancer Institute, Oncode Institute, Amsterdam, The Netherlands
| | - Daniel R Larson
- Laboratory of Receptor Biology and Gene Expression, National Cancer Institute, National Institutes of Health, Bethesda, Maryland, USA
| | - Hinrich Boeger
- Department of Molecular Cell and Developmental Biology, University of California, Santa Cruz, CA, USA.
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2
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Mondal A, Teimouri H, Kolomeisky AB. Molecular mechanisms of precise timing in cell lysis. Biophys J 2024:S0006-3495(24)00447-8. [PMID: 38971973 DOI: 10.1016/j.bpj.2024.07.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2024] [Revised: 04/03/2024] [Accepted: 07/02/2024] [Indexed: 07/08/2024] Open
Abstract
Many biological systems exhibit precise timing of events, and one of the most known examples is cell lysis, which is a process of breaking bacterial host cells in the virus infection cycle. However, the underlying microscopic picture of precise timing remains not well understood. We present a novel theoretical approach to explain the molecular mechanisms of effectively deterministic dynamics in biological systems. Our hypothesis is based on the idea of stochastic coupling between relevant underlying biophysical and biochemical processes that lead to noise cancellation. To test this hypothesis, we introduced a minimal discrete-state stochastic model to investigate how holin proteins produced by bacteriophages break the inner membranes of gram-negative bacteria. By explicitly solving this model, the dynamic properties of cell lysis are fully evaluated, and theoretical predictions quantitatively agree with available experimental data for both wild-type and holin mutants. It is found that the observed threshold-like behavior is a result of the balance between holin proteins entering the membrane and leaving the membrane during the lysis. Theoretical analysis suggests that the cell lysis achieves precise timing for wild-type species by maximizing the number of holins in the membrane and narrowing their spatial distribution. In contrast, for mutated species, these conditions are not satisfied. Our theoretical approach presents a possible molecular picture of precise dynamic regulation in intrinsically random biological processes.
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Affiliation(s)
- Anupam Mondal
- Center for Theoretical Biological Physics, Rice University, Houston, Texas; Department of Chemistry, Rice University, Houston, Texas
| | - Hamid Teimouri
- Center for Theoretical Biological Physics, Rice University, Houston, Texas; Department of Chemistry, Rice University, Houston, Texas
| | - Anatoly B Kolomeisky
- Center for Theoretical Biological Physics, Rice University, Houston, Texas; Department of Chemistry, Rice University, Houston, Texas; Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas.
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3
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Martinez-Corral R, Nam KM, DePace AH, Gunawardena J. The Hill function is the universal Hopfield barrier for sharpness of input-output responses. Proc Natl Acad Sci U S A 2024; 121:e2318329121. [PMID: 38787881 PMCID: PMC11145184 DOI: 10.1073/pnas.2318329121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 04/25/2024] [Indexed: 05/26/2024] Open
Abstract
The Hill functions, [Formula: see text], have been widely used in biology for over a century but, with the exception of [Formula: see text], they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, coregulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalizes most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, [Formula: see text], for any equilibrium model with [Formula: see text] input binding sites. [Formula: see text] exhibits a cusp which approaches, but never exceeds, the sharpness of [Formula: see text], but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers, and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, [Formula: see text], whose structure may be of mathematical interest, and suggest the importance of characterizing Hopfield barriers for other forms of cellular information processing.
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Affiliation(s)
| | - Kee-Myoung Nam
- Department of Systems Biology, Harvard Medical School, Boston, MA02115
| | - Angela H. DePace
- Department of Systems Biology, Harvard Medical School, Boston, MA02115
- HHMI, Boston, MA02115
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4
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Blom K, Song K, Vouga E, Godec A, Makarov DE. Milestoning estimators of dissipation in systems observed at a coarse resolution. Proc Natl Acad Sci U S A 2024; 121:e2318333121. [PMID: 38625949 PMCID: PMC11047069 DOI: 10.1073/pnas.2318333121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 03/14/2024] [Indexed: 04/18/2024] Open
Abstract
Many nonequilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such "lumped" observables display memory, and in many cases, the irreversible character of the underlying microscopic dynamics becomes blurred, e.g., when the projection hides dissipative cycles. As a result, the observations appear less irreversible, and it is very challenging to infer the degree of broken time-reversal symmetry. Here we show, contrary to intuition, that by ignoring parts of the already coarse-grained state space we may-via a process called milestoning-improve entropy-production estimates. We present diverse examples where milestoning systematically renders observations "closer to underlying microscopic dynamics" and thereby improves thermodynamic inference from lumped data assuming a given range of memory, and we hypothesize that this effect is quite general. Moreover, whereas the correct general physical definition of time reversal in the presence of memory remains unknown, we here show by means of physically relevant examples that at least for semi-Markov processes of first and second order, waiting-time contributions arising from adopting a naive Markovian definition of time reversal generally must be discarded.
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Affiliation(s)
- Kristian Blom
- Mathematical biophysics Group, Max Planck Institute for Multidisciplinary Sciences, Göttingen37077, Germany
| | - Kevin Song
- Department of Computer Science, University of Texas at Austin, Austin, TX78712
| | - Etienne Vouga
- Department of Computer Science, University of Texas at Austin, Austin, TX78712
| | - Aljaž Godec
- Mathematical biophysics Group, Max Planck Institute for Multidisciplinary Sciences, Göttingen37077, Germany
| | - Dmitrii E. Makarov
- Department of Chemistry and Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX78712
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5
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Zhao X, Hartich D, Godec A. Emergence of Memory in Equilibrium versus Nonequilibrium Systems. PHYSICAL REVIEW LETTERS 2024; 132:147101. [PMID: 38640391 DOI: 10.1103/physrevlett.132.147101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2023] [Accepted: 02/01/2024] [Indexed: 04/21/2024]
Abstract
Experiments often probe observables that correspond to low-dimensional projections of high-dimensional dynamics. In such situations distinct microscopic configurations become lumped into the same observable state. It is well known that correlations between the observable and the hidden degrees of freedom give rise to memory effects. However, how and under which conditions these correlations emerge remain poorly understood. Here we shed light on two fundamentally different scenarios of the emergence of memory in minimal stationary systems, where observed and hidden degrees of freedom either evolve cooperatively or are coupled by a hidden nonequilibrium current. In the reversible setting the strongest memory manifests when the timescales of hidden and observed dynamics overlap, whereas, strikingly, in the driven setting maximal memory emerges under a clear timescale separation. Our results hint at the possibility of fundamental differences in the way memory emerges in equilibrium versus driven systems that may be utilized as a "diagnostic" of the underlying hidden transport mechanism.
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Affiliation(s)
- Xizhu Zhao
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, Am Faßberg 11, 37077 Göttingen
- Max Planck School Matter to Life, Jahnstraße 29, D-69120 Heidelberg, Germany
| | - David Hartich
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, Am Faßberg 11, 37077 Göttingen
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, Am Faßberg 11, 37077 Göttingen
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6
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Martinez-Corral R, Nam KM, DePace AH, Gunawardena J. The Hill function is the universal Hopfield barrier for sharpness of input-output responses. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.03.27.587054. [PMID: 38585761 PMCID: PMC10996692 DOI: 10.1101/2024.03.27.587054] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/09/2024]
Abstract
The Hill functions, ℋ h ( x ) = x h / 1 + x h , have been widely used in biology for over a century but, with the exception of ℋ 1 , they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, co-regulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalises most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, Ω m ⊂ ℝ + 2 , for any equilibrium model with m input binding sites. Ω m exhibits a cusp which approaches, but never exceeds, the sharpness of ℋ m but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, Ω m , whose structure may be of mathematical interest, and suggest the importance of characterising Hopfield barriers for other forms of cellular information processing.
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Affiliation(s)
| | - Kee-Myoung Nam
- Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA
| | - Angela H. DePace
- Howard Hughes Medical Institute, Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA
| | - Jeremy Gunawardena
- Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA
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7
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Sawada T, Sone K, Hamazaki R, Ashida Y, Sagawa T. Role of Topology in Relaxation of One-Dimensional Stochastic Processes. PHYSICAL REVIEW LETTERS 2024; 132:046602. [PMID: 38335331 DOI: 10.1103/physrevlett.132.046602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Revised: 10/04/2023] [Accepted: 12/11/2023] [Indexed: 02/12/2024]
Abstract
Stochastic processes are commonly used models to describe dynamics of a wide variety of nonequilibrium phenomena ranging from electrical transport to biological motion. The transition matrix describing a stochastic process can be regarded as a non-Hermitian Hamiltonian. Unlike general non-Hermitian systems, the conservation of probability imposes additional constraints on the transition matrix, which can induce unique topological phenomena. Here, we reveal the role of topology in relaxation phenomena of classical stochastic processes. Specifically, we define a winding number that is related to topology of stochastic processes and show that it predicts the existence of a spectral gap that characterizes the relaxation time. Then, we numerically confirm that the winding number corresponds to the system-size dependence of the relaxation time and the characteristic transient behavior. One can experimentally realize such topological phenomena in magnetotactic bacteria and cell adhesions.
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Affiliation(s)
- Taro Sawada
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Kazuki Sone
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Ryusuke Hamazaki
- Nonequilibrium Quantum Statistical Mechanics RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR), RIKEN iTHEMS, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
| | - Yuto Ashida
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- Institute for Physics of Intelligence, The University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
| | - Takahiro Sagawa
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Quantum-Phase Electronics Center (QPEC), The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
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8
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Hathcock D, Yu Q, Mello BA, Amin DN, Hazelbauer GL, Tu Y. A nonequilibrium allosteric model for receptor-kinase complexes: The role of energy dissipation in chemotaxis signaling. Proc Natl Acad Sci U S A 2023; 120:e2303115120. [PMID: 37824527 PMCID: PMC10589639 DOI: 10.1073/pnas.2303115120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 08/29/2023] [Indexed: 10/14/2023] Open
Abstract
The Escherichia coli chemotaxis signaling pathway has served as a model system for the adaptive sensing of environmental signals by large protein complexes. The chemoreceptors control the kinase activity of CheA in response to the extracellular ligand concentration and adapt across a wide concentration range by undergoing methylation and demethylation. Methylation shifts the kinase response curve by orders of magnitude in ligand concentration while incurring a much smaller change in the ligand binding curve. Here, we show that the disproportionate shift in binding and kinase response is inconsistent with equilibrium allosteric models. To resolve this inconsistency, we present a nonequilibrium allosteric model that explicitly includes the dissipative reaction cycles driven by adenosine triphosphate (ATP) hydrolysis. The model successfully explains all existing joint measurements of ligand binding, receptor conformation, and kinase activity for both aspartate and serine receptors. Our results suggest that the receptor complex acts as an enzyme: Receptor methylation modulates the ON-state kinetics of the kinase (e.g., phosphorylation rate), while ligand binding controls the equilibrium balance between kinase ON/OFF states. Furthermore, sufficient energy dissipation is responsible for maintaining and enhancing the sensitivity range and amplitude of the kinase response. We demonstrate that the nonequilibrium allosteric model is broadly applicable to other sensor-kinase systems by successfully fitting previously unexplained data from the DosP bacterial oxygen-sensing system. Overall, this work provides a nonequilibrium physics perspective on cooperative sensing by large protein complexes and opens up research directions for understanding their microscopic mechanisms through simultaneous measurements and modeling of ligand binding and downstream responses.
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Affiliation(s)
- David Hathcock
- IBM T. J. Watson Research Center, Yorktown Heights, NY10598
| | - Qiwei Yu
- IBM T. J. Watson Research Center, Yorktown Heights, NY10598
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ08544
| | - Bernardo A. Mello
- International Center of Physics, Physics Institute, University of Brasilia, Brasilia70919-970, Brazil
| | - Divya N. Amin
- Department of Biochemistry, University of Missouri, Columbia, MO65211
| | | | - Yuhai Tu
- IBM T. J. Watson Research Center, Yorktown Heights, NY10598
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9
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Flatt S, Busiello DM, Zamuner S, De Los Rios P. ABC transporters are billion-year-old Maxwell Demons. COMMUNICATIONS PHYSICS 2023; 6:205. [PMID: 38665399 PMCID: PMC11041718 DOI: 10.1038/s42005-023-01320-y] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Accepted: 07/26/2023] [Indexed: 04/28/2024]
Abstract
ATP-Binding Cassette (ABC) transporters are a broad family of biological machines, found in most prokaryotic and eukaryotic cells, performing the crucial import or export of substrates through both plasma and organellar membranes, and maintaining a steady concentration gradient driven by ATP hydrolysis. Building upon the present biophysical and biochemical characterization of ABC transporters, we propose here a model whose solution reveals that these machines are an exact molecular realization of the autonomous Maxwell Demon, a century-old abstract device that uses an energy source to drive systems away from thermodynamic equilibrium. In particular, the Maxwell Demon does not perform any direct mechanical work on the system, but simply selects which spontaneous processes to allow and which ones to forbid based on information that it collects and processes. In its autonomous version, the measurement device is embedded in the system itself. In the molecular model introduced here, the different operations that characterize Maxwell Demons (measurement, feedback, resetting) are features that emerge from the biochemical and structural properties of ABC transporters, revealing the crucial role of allostery to process information. Our framework allows us to develop an explicit bridge between the molecular-level description and the higher-level language of information theory for ABC transporters.
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Affiliation(s)
- Solange Flatt
- Institute of Physics, School of Basic Sciences, École Polytechnique Fédérale de Lausanne—EPFL, Lausanne, 1015 Switzerland
| | - Daniel Maria Busiello
- Institute of Physics, School of Basic Sciences, École Polytechnique Fédérale de Lausanne—EPFL, Lausanne, 1015 Switzerland
- Max Planck Institute for the Physics of Complex Systems, Dresden, 01187 Germany
| | - Stefano Zamuner
- Institute of Physics, School of Basic Sciences, École Polytechnique Fédérale de Lausanne—EPFL, Lausanne, 1015 Switzerland
| | - Paolo De Los Rios
- Institute of Physics, School of Basic Sciences, École Polytechnique Fédérale de Lausanne—EPFL, Lausanne, 1015 Switzerland
- Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne—EPFL, Lausanne, 1015 Switzerland
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10
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Harvey SE, Lahiri S, Ganguli S. Universal energy-accuracy tradeoffs in nonequilibrium cellular sensing. Phys Rev E 2023; 108:014403. [PMID: 37583173 DOI: 10.1103/physreve.108.014403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Accepted: 04/07/2023] [Indexed: 08/17/2023]
Abstract
We combine stochastic thermodynamics, large deviation theory, and information theory to derive fundamental limits on the accuracy with which single cell receptors can estimate external concentrations. As expected, if the estimation is performed by an ideal observer of the entire trajectory of receptor states, then no energy consuming nonequilibrium receptor that can be divided into bound and unbound states can outperform an equilibrium two-state receptor. However, when the estimation is performed by a simple observer that measures the fraction of time the receptor is bound, we derive a fundamental limit on the accuracy of general nonequilibrium receptors as a function of energy consumption. We further derive and exploit explicit formulas to numerically estimate a Pareto-optimal tradeoff between accuracy and energy. We find this tradeoff can be achieved by nonuniform ring receptors with a number of states that necessarily increases with energy. Our results yield a thermodynamic uncertainty relation for the time a physical system spends in a pool of states and generalize the classic Berg-Purcell limit [H. C. Berg and E. M. Purcell, Biophys. J. 20, 193 (1977)0006-349510.1016/S0006-3495(77)85544-6] on cellular sensing along multiple dimensions.
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Affiliation(s)
- Sarah E Harvey
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Subhaneil Lahiri
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Surya Ganguli
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
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11
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Bell-Davies MCR, Curran A, Liu Y, Dullens RPA. Dynamics of a colloidal particle driven by continuous time-delayed feedback. Phys Rev E 2023; 107:064601. [PMID: 37464682 DOI: 10.1103/physreve.107.064601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2023] [Accepted: 04/25/2023] [Indexed: 07/20/2023]
Abstract
We perform feedback experiments and simulations in which a colloidal dumbbell particle, acting as a particle on a ring, is followed by a repulsive optical trap controlled by a continuous-time-delayed feedback protocol. The dynamics are described by a persistent random walk similarly to that of an active Brownian particle, with a transition from predominantly diffusive to driven behavior at a critical delay time. We model the dynamics in the short and long delay regimes using stochastic delay differential equations and derive a condition for stable driven motion. We study the stochastic thermodynamic properties of the system, finding that the maximum work done by the trap coincides with a local minimum in the mutual information between the trap and the particle position at the onset of stable driven dynamics.
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Affiliation(s)
- Miranda C R Bell-Davies
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
| | - Arran Curran
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
| | - Yanyan Liu
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Roel P A Dullens
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
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12
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Owen JA, Horowitz JM. Size limits the sensitivity of kinetic schemes. Nat Commun 2023; 14:1280. [PMID: 36890153 PMCID: PMC9995461 DOI: 10.1038/s41467-023-36705-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2022] [Accepted: 02/10/2023] [Indexed: 03/10/2023] Open
Abstract
Living things benefit from exquisite molecular sensitivity in many of their key processes, including DNA replication, transcription and translation, chemical sensing, and morphogenesis. At thermodynamic equilibrium, the basic biophysical mechanism for sensitivity is cooperative binding, for which it can be shown that the Hill coefficient, a sensitivity measure, cannot exceed the number of binding sites. Generalizing this fact, we find that for any kinetic scheme, at or away from thermodynamic equilibrium, a very simple structural quantity, the size of the support of a perturbation, always limits the effective Hill coefficient. We show how this bound sheds light on and unifies diverse sensitivity mechanisms, including kinetic proofreading and a nonequilibrium Monod-Wyman-Changeux (MWC) model proposed for the E. coli flagellar motor switch, representing in each case a simple, precise bridge between experimental observations and the models we write down. In pursuit of mechanisms that saturate the support bound, we find a nonequilibrium binding mechanism, nested hysteresis, with sensitivity exponential in the number of binding sites, with implications for our understanding of models of gene regulation and the function of biomolecular condensates.
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Affiliation(s)
- Jeremy A Owen
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
- Department of Chemistry, Princeton University, Princeton, NJ, 08540, USA.
| | - Jordan M Horowitz
- Department of Biophysics, University of Michigan, Ann Arbor, MI, 48109, USA.
- Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI, 48104, USA.
- Department of Physics, University of Michigan, Ann Arbor, MI, 48109, USA.
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13
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Godec A, Makarov DE. Challenges in Inferring the Directionality of Active Molecular Processes from Single-Molecule Fluorescence Resonance Energy Transfer Trajectories. J Phys Chem Lett 2023; 14:49-56. [PMID: 36566432 DOI: 10.1021/acs.jpclett.2c03244] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
We discuss some of the practical challenges that one faces in using stochastic thermodynamics to infer directionality of molecular machines from experimental single-molecule trajectories. Because of the limited spatiotemporal resolution of single-molecule experiments and because both forward and backward transitions between the same pairs of states cannot always be detected, differentiating between the forward and backward directions of, e.g., an ATP-consuming molecular machine that operates periodically, turns out to be a nontrivial task. Using a simple extension of a Markov-state model that is commonly employed to analyze single-molecule transition-path measurements, we illustrate how irreversibility can be hidden from such measurements but in some cases can be uncovered when non-Markov effects in low-dimensional single-molecule trajectories are considered.
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Affiliation(s)
- Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, 37077Göttingen, Germany
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14
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Wang X, Blumenfeld R, Feng XQ, Weitz DA. 'Phase transitions' in bacteria - From structural transitions in free living bacteria to phenotypic transitions in bacteria within biofilms. Phys Life Rev 2022; 43:98-138. [PMID: 36252408 DOI: 10.1016/j.plrev.2022.09.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 09/30/2022] [Indexed: 12/05/2022]
Abstract
Phase transitions are common in inanimate systems and have been studied extensively in natural sciences. Less explored are the rich transitions that take place at the micro- and nano-scales in biological systems. In conventional phase transitions, large-scale properties of the media change discontinuously in response to continuous changes in external conditions. Such changes play a significant role in the dynamic behaviours of organisms. In this review, we focus on some transitions in both free-living and biofilms of bacteria. Particular attention is paid to the transitions in the flagellar motors and filaments of free-living bacteria, in cellular gene expression during the biofilm growth, in the biofilm morphology transitions during biofilm expansion, and in the cell motion pattern transitions during the biofilm formation. We analyse the dynamic characteristics and biophysical mechanisms of these phase transition phenomena and point out the parallels between these transitions and conventional phase transitions. We also discuss the applications of some theoretical and numerical methods, established for conventional phase transitions in inanimate systems, in bacterial biofilms.
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Affiliation(s)
- Xiaoling Wang
- School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China; John A. Paulson School of Engineering and Applied Sciences, Harvard University, 9 Oxford St, Cambridge, MA, 02138, USA.
| | - Raphael Blumenfeld
- Gonville & Caius College, University of Cambridge, Trinity St., Cambridge CB2 1TA, UK
| | - Xi-Qiao Feng
- Institute of Biomechanics and Medical Engineering, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - David A Weitz
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, 9 Oxford St, Cambridge, MA, 02138, USA; Department of Physics, Harvard University, 9 Oxford St, Cambridge, MA, 02138, USA
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15
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Mori F, Majumdar SN, Schehr G. Time to reach the maximum for a stationary stochastic process. Phys Rev E 2022; 106:054110. [PMID: 36559509 DOI: 10.1103/physreve.106.054110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 10/11/2022] [Indexed: 11/06/2022]
Abstract
We consider a one-dimensional stationary time series of fixed duration T. We investigate the time t_{m} at which the process reaches the global maximum within the time interval [0,T]. By using a path-decomposition technique, we compute the probability density function P(t_{m}|T) of t_{m} for several processes, that are either at equilibrium (such as the Ornstein-Uhlenbeck process) or out of equilibrium (such as Brownian motion with stochastic resetting). We show that for equilibrium processes the distribution of P(t_{m}|T) is always symmetric around the midpoint t_{m}=T/2, as a consequence of the time-reversal symmetry. This property can be used to detect nonequilibrium fluctuations in stationary time series. Moreover, for a diffusive particle in a confining potential, we show that the scaled distribution P(t_{m}|T) becomes universal, i.e., independent of the details of the potential, at late times. This distribution P(t_{m}|T) becomes uniform in the "bulk" 1≪t_{m}≪T and has a nontrivial universal shape in the "edge regimes" t_{m}→0 and t_{m}→T. Some of these results have been announced in a recent letter [Europhys. Lett. 135, 30003 (2021)0295-507510.1209/0295-5075/ac19ee].
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Affiliation(s)
- Francesco Mori
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Satya N Majumdar
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Grégory Schehr
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS, UMR 7589 4 Place Jussieu, 75252 Paris Cedex 05, France
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16
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Ghosal A, Bisker G. Inferring entropy production rate from partially observed Langevin dynamics under coarse-graining. Phys Chem Chem Phys 2022; 24:24021-24031. [PMID: 36065766 PMCID: PMC7613705 DOI: 10.1039/d2cp03064k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The entropy production rate (EPR) measures time-irreversibility in systems operating far from equilibrium. The challenge in estimating the EPR for a continuous variable system is the finite spatiotemporal resolution and the limited accessibility to all of the nonequilibrium degrees of freedom. Here, we estimate the irreversibility in partially observed systems following oscillatory dynamics governed by coupled overdamped Langevin equations. We coarse-grain an observed variable of a nonequilibrium driven system into a few discrete states and estimate a lower bound on the total EPR. As a model system, we use hair-cell bundle oscillations driven by molecular motors, such that the bundle tip position is observed, but the positions of the motors are hidden. In the observed variable space, the underlying driven process exhibits second-order semi-Markov statistics. The waiting time distributions (WTD), associated with transitions among the coarse-grained states, are non-exponential and convey the information on the broken time-reversal symmetry. By invoking the underlying time-irreversibility, we calculate a lower bound on the total EPR from the Kullback-Leibler divergence (KLD) between WTD. We show that the mean dwell-time asymmetry factor - the ratio between the mean dwell-times along the forward direction and the backward direction, can qualitatively measure the degree of broken time reversal symmetry and increases with finer spatial resolution. Finally, we apply our methodology to a continuous-time discrete Markov chain model, coarse-grained into a linear system exhibiting second-order semi-Markovian statistics, and demonstrate the estimation of a lower bound on the total EPR from irreversibility manifested only in the WTD.
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Affiliation(s)
- Aishani Ghosal
- Department of Biomedical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel.
| | - Gili Bisker
- Department of Biomedical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel.
- Center for Physics and Chemistry of Living Systems, Tel-Aviv University, Tel Aviv 6997801, Israel
- Center for Nanoscience and Nanotechnology, Tel-Aviv University, Tel Aviv 6997801, Israel
- Center for Light-Matter Interaction, Tel-Aviv University, Tel Aviv 6997801, Israel
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17
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Zoller B, Gregor T, Tkačik G. Eukaryotic gene regulation at equilibrium, or non? CURRENT OPINION IN SYSTEMS BIOLOGY 2022; 31:100435. [PMID: 36590072 PMCID: PMC9802646 DOI: 10.1016/j.coisb.2022.100435] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Models of transcriptional regulation that assume equilibrium binding of transcription factors have been less successful at predicting gene expression from sequence in eukaryotes than in bacteria. This could be due to the non-equilibrium nature of eukaryotic regulation. Unfortunately, the space of possible non-equilibrium mechanisms is vast and predominantly uninteresting. The key question is therefore how this space can be navigated efficiently, to focus on mechanisms and models that are biologically relevant. In this review, we advocate for the normative role of theory-theory that prescribes rather than just describes-in providing such a focus. Theory should expand its remit beyond inferring mechanistic models from data, towards identifying non-equilibrium gene regulatory schemes that may have been evolutionarily selected, despite their energy consumption, because they are precise, reliable, fast, or otherwise outperform regulation at equilibrium. We illustrate our reasoning by toy examples for which we provide simulation code.
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Affiliation(s)
- Benjamin Zoller
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
- Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ, USA
- Department of Developmental and Stem Cell Biology UMR3738, Institut Pasteur, Paris, France
| | - Thomas Gregor
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
- Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ, USA
- Department of Developmental and Stem Cell Biology UMR3738, Institut Pasteur, Paris, France
| | - Gašper Tkačik
- Institute of Science and Technology Austria, Klosterneuburg, Austria
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18
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Gupta R, Yuan J, Lele PP. Bacterial Proprioception: Can a Bacterium Sense Its Movement? Front Microbiol 2022; 13:928408. [PMID: 35875555 PMCID: PMC9302961 DOI: 10.3389/fmicb.2022.928408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 06/16/2022] [Indexed: 11/13/2022] Open
Abstract
The evolution of the bacterial flagellum gave rise to motility and repurposing of a signaling network, now termed the chemotaxis network, enabled biasing of cell movements. This made it possible for the bacterium to seek out favorable chemical environments. To enable chemotaxis, the chemotaxis network sensitively detects extracellular chemical stimuli and appropriately modulates flagellar functions. Additionally, the flagellar motor itself is capable of detecting mechanical stimuli and adapts its structure and function in response, likely triggering a transition from planktonic to surface-associated lifestyles. Recent work has shown a link between the flagellar motor's response to mechanical stimuli and the chemotactic output. Here, we elaborate on this link and discuss how it likely helps the cell sense and adapt to changes in its swimming speeds in different environments. We discuss the mechanism whereby the motor precisely tunes its chemotaxis output under different mechanical loads, analogous to proprioception in higher order organisms. We speculate on the roles bacterial proprioception might play in a variety of phenomena including the transition to surface-associated lifestyles such as swarming and biofilms.
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Affiliation(s)
- Rachit Gupta
- Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX, United States
| | - Junhua Yuan
- Department of Physics, University of Science and Technology of China, Hefei, China
| | - Pushkar P Lele
- Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX, United States
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19
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Tucci G, Roldán É, Gambassi A, Belousov R, Berger F, Alonso RG, Hudspeth AJ. Modeling Active Non-Markovian Oscillations. PHYSICAL REVIEW LETTERS 2022; 129:030603. [PMID: 35905355 DOI: 10.1103/physrevlett.129.030603] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Accepted: 06/10/2022] [Indexed: 06/15/2023]
Abstract
Modeling noisy oscillations of active systems is one of the current challenges in physics and biology. Because the physical mechanisms of such processes are often difficult to identify, we propose a linear stochastic model driven by a non-Markovian bistable noise that is capable of generating self-sustained periodic oscillation. We derive analytical predictions for most relevant dynamical and thermodynamic properties of the model. This minimal model turns out to describe accurately bistablelike oscillatory motion of hair bundles in bullfrog sacculus, extracted from experimental data. Based on and in agreement with these data, we estimate the power required to sustain such active oscillations to be of the order of 100 k_{B}T per oscillation cycle.
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Affiliation(s)
- G Tucci
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, 34136 Trieste, Italy
| | - É Roldán
- ICTP-The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - A Gambassi
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, 34136 Trieste, Italy
| | - R Belousov
- ICTP-The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- EMBL-European Molecular Biology Laboratory, Meyerhofstrasse 1, 69117 Heidelberg, Germany
| | - F Berger
- Cell Biology, Neurobiology and Biophysics, Department of Biology, Faculty of Science, Utrecht University, 3584 CH Utrecht, Netherlands
| | - R G Alonso
- Howard Hughes Medical Institute and Laboratory of Sensory Neuroscience, The Rockefeller University, 1230 York Avenue, New York, New York 10065, USA
| | - A J Hudspeth
- Howard Hughes Medical Institute and Laboratory of Sensory Neuroscience, The Rockefeller University, 1230 York Avenue, New York, New York 10065, USA
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20
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Guo X, Tang T, Duan M, Zhang L, Ge H. The nonequilibrium mechanism of noise-enhanced drug synergy in HIV latency reactivation. iScience 2022; 25:104358. [PMID: 35620426 PMCID: PMC9127169 DOI: 10.1016/j.isci.2022.104358] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Revised: 03/04/2022] [Accepted: 04/29/2022] [Indexed: 11/29/2022] Open
Abstract
Noise-modulating chemicals can synergize with transcriptional activators in reactivating latent HIV to eliminate latent HIV reservoirs. To understand the underlying biomolecular mechanism, we investigate a previous two-gene-state model and identify two necessary conditions for the synergy: an assumption of the inhibition effect of transcription activators on noise enhancers; and frequent transitions to the gene non-transcription-permissive state. We then develop a loop-four-gene-state model with Tat transcription/translation and find that drug synergy is mainly determined by the magnitude and direction of energy input into the genetic regulatory kinetics of the HIV promoter. The inhibition effect of transcription activators is actually a phenomenon of energy dissipation in the nonequilibrium gene transition system. Overall, the loop-four-state model demonstrates that energy dissipation plays a crucial role in HIV latency reactivation, which might be useful for improving drug effects and identifying other synergies on lentivirus latency reactivation. The inhibition of Activator on Noise enhancer is necessary for their synergy in reactivating HIV The drug synergy is a nonequilibrium phenomenon in the gene regulatory system The magnitude and direction of energy input determine the drug synergy This nonequilibrium mechanism is general without regarding molecular details
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21
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Ma S, Zhang R, Yuan J. Observation of broken detailed balance in polymorphic transformation of bacterial flagellar filament. Biophys J 2022; 121:2345-2352. [PMID: 35596526 DOI: 10.1016/j.bpj.2022.05.022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Revised: 04/16/2022] [Accepted: 05/17/2022] [Indexed: 11/29/2022] Open
Abstract
Living systems operate far from thermodynamic equilibrium, which usually manifests as broken detailed balance at the molecular scale. At larger scales with collective function of many molecules, the presence of non-equilibrium thermodynamics may not be evident. In bacterial motility, the switching dynamics of the flagellar rotary motor was recently discovered to be operating in non-equilibrium. However, the resulting motility pattern at the mesoscale, the run-and-tumble behavior, was normally considered to be a Poisson process that can be described by a two-state equilibrium model. Here, we studied the details of the run-and-tumble behavior by following the polymorphic transformation of the flagellar filaments, observing broken detailed balance that reveals its non-equilibrium nature. Evaluation of entropy production provided a direct measure of the lack of detailed balance, and a quantification of the rate of energy dissipation for bacterial run-and-tumble regulation.
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Affiliation(s)
- Shuwen Ma
- Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rongjing Zhang
- Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
| | - Junhua Yuan
- Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
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22
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Cellular sentience as the primary source of biological order and evolution. Biosystems 2022; 218:104694. [PMID: 35595194 DOI: 10.1016/j.biosystems.2022.104694] [Citation(s) in RCA: 16] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2022] [Revised: 05/09/2022] [Accepted: 05/09/2022] [Indexed: 12/17/2022]
Abstract
All life is cellular, starting some 4 billion years ago with the emergence of the first cells. In order to survive their early evolution in the face of an extremely challenging environment, the very first cells invented cellular sentience and cognition, allowing them to make relevant decisions to survive through creative adaptations in a continuously running evolutionary narrative. We propose that the success of cellular life has crucially depended on a biological version of Maxwell's demons which permits the extraction of relevant sensory information and energy from the cellular environment, allowing cells to sustain anti-entropic actions. These sensor-effector actions allowed for the creative construction of biological order in the form of diverse organic macromolecules, including crucial polymers such as DNA, RNA, and cytoskeleton. Ordered biopolymers store analogue (structures as templates) and digital (nucleotide sequences of DNA and RNA) information that functioned as a form memory to support the development of organisms and their evolution. Crucially, all cells are formed by the division of previous cells, and their plasma membranes are physically and informationally continuous across evolution since the beginning of cellular life. It is argued that life is supported through life-specific principles which support cellular sentience, distinguishing life from non-life. Biological order, together with cellular cognition and sentience, allow the creative evolution of all living organisms as the authentic authors of evolutionary novelty.
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23
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Yu Q, Tu Y. State-space renormalization group theory of nonequilibrium reaction networks: Exact solutions for hypercubic lattices in arbitrary dimensions. Phys Rev E 2022; 105:044140. [PMID: 35590650 PMCID: PMC9223417 DOI: 10.1103/physreve.105.044140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2022] [Accepted: 04/05/2022] [Indexed: 06/15/2023]
Abstract
Nonequilibrium reaction networks (NRNs) underlie most biological functions. Despite their diverse dynamic properties, NRNs share the signature characteristics of persistent probability fluxes and continuous energy dissipation even in the steady state. Dynamics of NRNs can be described at different coarse-grained levels. Our previous work showed that the apparent energy dissipation rate at a coarse-grained level follows an inverse power-law dependence on the scale of coarse-graining. The scaling exponent is determined by the network structure and correlation of stationary probability fluxes. However, it remains unclear whether and how the (renormalized) flux correlation varies with coarse-graining. Following Kadanoff's real space renormalization group (RG) approach for critical phenomena, we address this question by developing a state-space renormalization group theory for NRNs, which leads to an iterative RG equation for the flux correlation function. In square and hypercubic lattices, we solve the RG equation exactly and find two types of fixed point solutions. There is a family of nontrivial fixed points where the correlation exhibits power-law decay, characterized by a power exponent that can take any value within a continuous range. There is also a trivial fixed point where the correlation vanishes beyond the nearest neighbors. The power-law fixed point is stable if and only if the power exponent is less than the lattice dimension n. Consequently, the correlation function converges to the power-law fixed point only when the correlation in the fine-grained network decays slower than r^{-n} and to the trivial fixed point otherwise. If the flux correlation in the fine-grained network contains multiple stable solutions with different exponents, the RG iteration dynamics select the fixed point solution with the smallest exponent. The analytical results are supported by numerical simulations. We also discuss a possible connection between the RG flows of flux correlation with those of the Kosterlitz-Thouless transition.
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Affiliation(s)
- Qiwei Yu
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA
| | - Yuhai Tu
- IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
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24
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Wang B, Niu Y, Zhang R, Yuan J. Dynamics of Switching at Stall Reveals Nonequilibrium Mechanism in the Allosteric Regulation of the Bacterial Flagellar Switch. PHYSICAL REVIEW LETTERS 2021; 127:268101. [PMID: 35029477 DOI: 10.1103/physrevlett.127.268101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Accepted: 12/02/2021] [Indexed: 06/14/2023]
Abstract
Behavior of the bacterial flagellar motor depends sensitively on the external loads it drives. Motor switching, which provides the basis for the run-and-tumble behavior of flagellated bacteria, has been studied for motors under zero to high loads, revealing a nonequilibrium effect that is proportional to the motor torque. However, behavior of the motor switching at stall (with maximum torque) remains unclear. An extrapolation from previous studies would suggest the maximum nonequilibrium effect for motor switching at stall. Here, we stalled the motor using optical tweezers and studied the motor switching with a high time resolution of about 2 ms. Surprisingly, our results showed exponentially distributed counterclockwise (CCW) and clockwise (CW) intervals, indicating that motor switching at stall is probably an equilibrium process. Combined with previous experiments at other loads, our result suggested that the nonequilibrium effect in motor switching arises from the asymmetry of the torque generation in the CCW and CW directions. By including this nonequilibrium effect in the general Ising-type conformation spread model of the flagellar switch, we consistently explained the motor switching over the whole range of load conditions. We expect to see a similar mechanism of nonequilibrium regulation in other molecular machines.
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Affiliation(s)
- Bin Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yuhui Niu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rongjing Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Junhua Yuan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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25
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Cook J, Pawar S, Endres RG. Thermodynamic constraints on the assembly and diversity of microbial ecosystems are different near to and far from equilibrium. PLoS Comput Biol 2021; 17:e1009643. [PMID: 34860834 PMCID: PMC8673627 DOI: 10.1371/journal.pcbi.1009643] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Revised: 12/15/2021] [Accepted: 11/15/2021] [Indexed: 11/30/2022] Open
Abstract
Non-equilibrium thermodynamics has long been an area of substantial interest to ecologists because most fundamental biological processes, such as protein synthesis and respiration, are inherently energy-consuming. However, most of this interest has focused on developing coarse ecosystem-level maximisation principles, providing little insight into underlying mechanisms that lead to such emergent constraints. Microbial communities are a natural system to decipher this mechanistic basis because their interactions in the form of substrate consumption, metabolite production, and cross-feeding can be described explicitly in thermodynamic terms. Previous work has considered how thermodynamic constraints impact competition between pairs of species, but restrained from analysing how this manifests in complex dynamical systems. To address this gap, we develop a thermodynamic microbial community model with fully reversible reaction kinetics, which allows direct consideration of free-energy dissipation. This also allows species to interact via products rather than just substrates, increasing the dynamical complexity, and allowing a more nuanced classification of interaction types to emerge. Using this model, we find that community diversity increases with substrate lability, because greater free-energy availability allows for faster generation of niches. Thus, more niches are generated in the time frame of community establishment, leading to higher final species diversity. We also find that allowing species to make use of near-to-equilibrium reactions increases diversity in a low free-energy regime. In such a regime, two new thermodynamic interaction types that we identify here reach comparable strengths to the conventional (competition and facilitation) types, emphasising the key role that thermodynamics plays in community dynamics. Our results suggest that accounting for realistic thermodynamic constraints is vital for understanding the dynamics of real-world microbial communities. There is a growing interest in microbial communities due to their important role in biogeochemical cycling as well as plant and animal health. Although our understanding of thermodynamic constraints on individual cells is rapidly improving, the impact of these constraints on complex microbial communities remains largely unexplored theoretically and empirically. Here, we develop a new microbial community model which allows thermodynamic efficiency and entropy production to be calculated directly. We find that availability of substrates with greater free-energy allows for a faster rate of niche generation, leading to higher final species diversity. We also show that when the free-energy availability is low, species with reactions close to thermodynamic equilibrium are favoured, leading to more diverse and efficient communities. In addition to the conventional interaction types (competition and facilitation), our model reveals the existence of two novel interaction types mediated by products rather than substrates. Though the conventional interactions are generally the strongest, the novel interaction types are significant when free-energy availability is low. Our results suggest that non-equilibrium thermodynamics need to be considered when studying microbial community dynamics.
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Affiliation(s)
- Jacob Cook
- Department of Life Sciences, Imperial College London, London, United Kingdom
- Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London, United Kingdom
- * E-mail: (JC); (RGE)
| | - Samraat Pawar
- Department of Life Sciences, Imperial College London, Silwood Park Campus, Ascot, United Kingdom
| | - Robert G. Endres
- Department of Life Sciences, Imperial College London, London, United Kingdom
- Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London, United Kingdom
- * E-mail: (JC); (RGE)
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26
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Skinner DJ, Dunkel J. Estimating Entropy Production from Waiting Time Distributions. PHYSICAL REVIEW LETTERS 2021; 127:198101. [PMID: 34797138 DOI: 10.1103/physrevlett.127.198101] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2021] [Accepted: 08/17/2021] [Indexed: 06/13/2023]
Abstract
Living systems operate far from thermal equilibrium by converting the chemical potential of ATP into mechanical work to achieve growth, replication, or locomotion. Given time series observations of intra-, inter-, or multicellular processes, a key challenge is to detect nonequilibrium behavior and quantify the rate of free energy consumption. Obtaining reliable bounds on energy consumption and entropy production directly from experimental data remains difficult in practice, as many degrees of freedom typically are hidden to the observer, so that the accessible coarse-grained dynamics may not obviously violate detailed balance. Here, we introduce a novel method for bounding the entropy production of physical and living systems which uses only the waiting time statistics of hidden Markov processes and, hence, can be directly applied to experimental data. By determining a universal limiting curve, we infer entropy production bounds from experimental data for gene regulatory networks, mammalian behavioral dynamics, and numerous other biological processes. Further considering the asymptotic limit of increasingly precise biological timers, we estimate the necessary entropic cost of heartbeat regulation in humans, dogs, and mice.
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Affiliation(s)
- Dominic J Skinner
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
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27
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A strong nonequilibrium bound for sorting of cross-linkers on growing biopolymers. Proc Natl Acad Sci U S A 2021; 118:2102881118. [PMID: 34518221 DOI: 10.1073/pnas.2102881118] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/22/2021] [Indexed: 12/18/2022] Open
Abstract
Understanding the role of nonequilibrium driving in self-organization is crucial for developing a predictive description of biological systems, yet it is impeded by their complexity. The actin cytoskeleton serves as a paradigm for how equilibrium and nonequilibrium forces combine to give rise to self-organization. Motivated by recent experiments that show that actin filament growth rates can tune the morphology of a growing actin bundle cross-linked by two competing types of actin-binding proteins [S. L. Freedman et al., Proc. Natl. Acad. Sci. U.S.A. 116, 16192-16197 (2019)], we construct a minimal model for such a system and show that the dynamics of a growing actin bundle are subject to a set of thermodynamic constraints that relate its nonequilibrium driving, morphology, and molecular fluxes. The thermodynamic constraints reveal the importance of correlations between these molecular fluxes and offer a route to estimating microscopic driving forces from microscopy experiments.
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28
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Physical bioenergetics: Energy fluxes, budgets, and constraints in cells. Proc Natl Acad Sci U S A 2021; 118:2026786118. [PMID: 34140336 DOI: 10.1073/pnas.2026786118] [Citation(s) in RCA: 33] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
Cells are the basic units of all living matter which harness the flow of energy to drive the processes of life. While the biochemical networks involved in energy transduction are well-characterized, the energetic costs and constraints for specific cellular processes remain largely unknown. In particular, what are the energy budgets of cells? What are the constraints and limits energy flows impose on cellular processes? Do cells operate near these limits, and if so how do energetic constraints impact cellular functions? Physics has provided many tools to study nonequilibrium systems and to define physical limits, but applying these tools to cell biology remains a challenge. Physical bioenergetics, which resides at the interface of nonequilibrium physics, energy metabolism, and cell biology, seeks to understand how much energy cells are using, how they partition this energy between different cellular processes, and the associated energetic constraints. Here we review recent advances and discuss open questions and challenges in physical bioenergetics.
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29
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Joseph T, V K. Efficiency estimation for an equilibrium version of the Maxwell refrigerator. Phys Rev E 2021; 103:022131. [PMID: 33735980 DOI: 10.1103/physreve.103.022131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Accepted: 01/27/2021] [Indexed: 11/07/2022]
Abstract
Maxwell refrigerator as a device that can transfer heat from a cold to hot temperature reservoir making use of information reservoir was introduced by Mandal et al. [Phys. Rev. Lett. 111, 030602 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.030602]. The model has a two-state demon and a bit stream interacting with two thermal reservoirs simultaneously. We work out a simpler version of the refrigerator where the demon and bit system interact with the reservoirs separately and for a duration long enough to establish equilibrium. The efficiency, η, of the device when working as an engine as well as the coefficient of performance (COP) when working as a refrigerator are calculated. It is shown that the maximum efficiency matches that of a Carnot engine/refrigerator working between the same temperatures, as expected. The COP, when cooling per cycle is a maximum, decreases as 1/T_{h} when T_{h}>T_{c}≫ΔE (k_{B}=1), where T_{h} and T_{c} are the temperatures of the hot and cold reservoirs, respectively, and ΔE is the level spacing of the demon. η, when work per cycle is a maximum, is found to be T_{h}/0.779+T_{h} when T_{c}≪ΔE and T_{h}≫ΔE.
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Affiliation(s)
- Toby Joseph
- Department of Physics, BITS Pilani K K Birla Goa Campus, Zuarinagar 403726, Goa, India
| | - Kiran V
- Department of Physics, BITS Pilani K K Birla Goa Campus, Zuarinagar 403726, Goa, India
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30
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Eck E, Liu J, Kazemzadeh-Atoufi M, Ghoreishi S, Blythe SA, Garcia HG. Quantitative dissection of transcription in development yields evidence for transcription-factor-driven chromatin accessibility. eLife 2020; 9:e56429. [PMID: 33074101 PMCID: PMC7738189 DOI: 10.7554/elife.56429] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2020] [Accepted: 10/16/2020] [Indexed: 12/28/2022] Open
Abstract
Thermodynamic models of gene regulation can predict transcriptional regulation in bacteria, but in eukaryotes, chromatin accessibility and energy expenditure may call for a different framework. Here, we systematically tested the predictive power of models of DNA accessibility based on the Monod-Wyman-Changeux (MWC) model of allostery, which posits that chromatin fluctuates between accessible and inaccessible states. We dissected the regulatory dynamics of hunchback by the activator Bicoid and the pioneer-like transcription factor Zelda in living Drosophila embryos and showed that no thermodynamic or non-equilibrium MWC model can recapitulate hunchback transcription. Therefore, we explored a model where DNA accessibility is not the result of thermal fluctuations but is catalyzed by Bicoid and Zelda, possibly through histone acetylation, and found that this model can predict hunchback dynamics. Thus, our theory-experiment dialogue uncovered potential molecular mechanisms of transcriptional regulatory dynamics, a key step toward reaching a predictive understanding of developmental decision-making.
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Affiliation(s)
- Elizabeth Eck
- Biophysics Graduate Group, University of California at BerkeleyBerkeleyUnited States
| | - Jonathan Liu
- Department of Physics, University of California at BerkeleyBerkeleyUnited States
| | | | - Sydney Ghoreishi
- Department of Molecular and Cell Biology, University of California at BerkeleyBerkeleyUnited States
| | - Shelby A Blythe
- Department of Molecular Biosciences, Northwestern UniversityEvanstonUnited States
| | - Hernan G Garcia
- Biophysics Graduate Group, University of California at BerkeleyBerkeleyUnited States
- Department of Physics, University of California at BerkeleyBerkeleyUnited States
- Department of Molecular and Cell Biology, University of California at BerkeleyBerkeleyUnited States
- Institute for Quantitative Biosciences-QB3, University of California at BerkeleyBerkeleyUnited States
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31
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Biddle JW, Gunawardena J. Reversal symmetries for cyclic paths away from thermodynamic equilibrium. Phys Rev E 2020; 101:062125. [PMID: 32688527 DOI: 10.1103/physreve.101.062125] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2019] [Accepted: 04/21/2020] [Indexed: 11/07/2022]
Abstract
If a system is at thermodynamic equilibrium, an observer cannot tell whether a film of it is being played forward or in reverse: any transition will occur with the same frequency in the forward as in the reverse direction. However, if expenditure of energy changes the rate of even a single transition to yield a nonequilibrium steady state, such time-reversal symmetry undergoes a widespread breakdown, far beyond the point at which the energy is expended. An explosion of interdependency also arises, with steady-state probabilities of system states depending in a complicated manner on the rate of every transition in the system. Nevertheless, in the midst of this global nonequilibrium complexity, we find that cyclic paths have reversibility properties that remain local, and which can exhibit symmetry, no matter how far the system is from thermodynamic equilibrium. Specifically, given any cycle of reversible transitions, the ratio of the frequencies with which the cycle occurs in one direction versus the other is determined, in the long-time limit, only by the thermodynamic force on the cycle itself, without requiring knowledge of transition rates elsewhere in the system. In particular, if there is no net energy expenditure on the cycle, then, over long times, the cycle occurrence frequencies are the same in either direction.
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Affiliation(s)
- John W Biddle
- Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States
| | - Jeremy Gunawardena
- Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States
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32
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Khan S. The Architectural Dynamics of the Bacterial Flagellar Motor Switch. Biomolecules 2020; 10:E833. [PMID: 32486003 PMCID: PMC7355467 DOI: 10.3390/biom10060833] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2020] [Revised: 05/23/2020] [Accepted: 05/25/2020] [Indexed: 02/06/2023] Open
Abstract
The rotary bacterial flagellar motor is remarkable in biochemistry for its highly synchronized operation and amplification during switching of rotation sense. The motor is part of the flagellar basal body, a complex multi-protein assembly. Sensory and energy transduction depends on a core of six proteins that are adapted in different species to adjust torque and produce diverse switches. Motor response to chemotactic and environmental stimuli is driven by interactions of the core with small signal proteins. The initial protein interactions are propagated across a multi-subunit cytoplasmic ring to switch torque. Torque reversal triggers structural transitions in the flagellar filament to change motile behavior. Subtle variations in the core components invert or block switch operation. The mechanics of the flagellar switch have been studied with multiple approaches, from protein dynamics to single molecule and cell biophysics. The architecture, driven by recent advances in electron cryo-microscopy, is available for several species. Computational methods have correlated structure with genetic and biochemical databases. The design principles underlying the basis of switch ultra-sensitivity and its dependence on motor torque remain elusive, but tantalizing clues have emerged. This review aims to consolidate recent knowledge into a unified platform that can inspire new research strategies.
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Affiliation(s)
- Shahid Khan
- Molecular Biology Consortium, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
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33
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Abstract
The QBIT theory is an attempt toward solving the problem of consciousness based on empirical evidence provided by various scientific disciplines including quantum mechanics, biology, information theory, and thermodynamics. This theory formulates the problem of consciousness in the following four questions, and provides preliminary answers for each question: Question 1: What is the nature of qualia? ANSWER A quale is a superdense pack of quantum information encoded in maximally entangled pure states. Question 2: How are qualia generated? ANSWER When a pack of quantum information is compressed beyond a certain threshold, a quale is generated. Question 3: Why are qualia subjective? ANSWER A quale is subjective because a pack of information encoded in maximally entangled pure states are essentially private and unshareable. Question 4: Why does a quale have a particular meaning? ANSWER A pack of information within a cognitive system gradually obtains a particular meaning as it undergoes a progressive process of interpretation performed by an internal model installed in the system. This paper introduces the QBIT theory of consciousness, and explains its basic assumptions and conjectures.
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Affiliation(s)
- Majid Beshkar
- Tehran University of Medical Sciences, Tehran, Iran.
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34
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Abstract
The reliable detection of environmental molecules in the presence of noise is an important cellular function, yet the underlying computational mechanisms are not well understood. We introduce a model of two interacting sensors which allows for the principled exploration of signal statistics, cooperation strategies and the role of energy consumption in optimal sensing, quantified through the mutual information between the signal and the sensors. Here we report that in general the optimal sensing strategy depends both on the noise level and the statistics of the signals. For joint, correlated signals, energy consuming (nonequilibrium), asymmetric couplings result in maximum information gain in the low-noise, high-signal-correlation limit. Surprisingly we also find that energy consumption is not always required for optimal sensing. We generalise our model to incorporate time integration of the sensor state by a population of readout molecules, and demonstrate that sensor interaction and energy consumption remain important for optimal sensing. Cells exhibit exceptional chemical sensitivity, yet we haven’t fully understood how they achieve it. Here the authors consider the mutual information between signals and two coupled sensors as a proxy for sensing performance and show its optimisation depending on noise level and signal statistics.
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35
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Topology, landscapes, and biomolecular energy transport. Nat Commun 2019; 10:4662. [PMID: 31604949 PMCID: PMC6789131 DOI: 10.1038/s41467-019-12700-w] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2019] [Accepted: 09/12/2019] [Indexed: 12/20/2022] Open
Abstract
While ubiquitous, energy redistribution remains a poorly understood facet of the nonequilibrium thermodynamics of biomolecules. At the molecular level, finite-size effects, pronounced nonlinearities, and ballistic processes produce behavior that diverges from the macroscale. Here, we show that transient thermal transport reflects macromolecular energy landscape architecture through the topological characteristics of molecular contacts and the nonlinear processes that mediate dynamics. While the former determines transport pathways via pairwise interactions, the latter reflects frustration within the landscape for local conformational rearrangements. Unlike transport through small-molecule systems, such as alkanes, nonlinearity dominates over coherent processes at even quite short time- and length-scales. Our exhaustive all-atom simulations and novel local-in-time and space analysis, applicable to both theory and experiment, permit dissection of energy migration in biomolecules. The approach demonstrates that vibrational energy transport can probe otherwise inaccessible aspects of macromolecular dynamics and interactions that underly biological function. Understanding vibrational energy transfer in macromolecules has been challenging to both theory and experiment. Here the authors use non-equilibrium molecular dynamics to reveal the relationship between heat transport in a model peptide, emergent nonlinearity, and the underlying free energy landscape.
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36
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Abstract
Numerous studies based on new single-cell and single-gene techniques show that individual genes can be transcribed in short bursts or pulses accompanied by changes in pulsing frequencies. Since so many examples of such discontinuous or fluctuating transcription have been found from prokaryotes to mammals, it now seems to be a common mode of gene expression. In this review we discuss the occurrence of the transcriptional fluctuations, the techniques used for their detection, their putative causes, kinetic characteristics, and probable physiological significance.
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Affiliation(s)
- Evgeny Smirnov
- a Institute of Biology and Medical Genetics , First Faculty of Medicine , Charles University and General University Hospital in Prague , Prague , Czech Republic
| | - Matúš Hornáček
- a Institute of Biology and Medical Genetics , First Faculty of Medicine , Charles University and General University Hospital in Prague , Prague , Czech Republic
| | - Tomáš Vacík
- a Institute of Biology and Medical Genetics , First Faculty of Medicine , Charles University and General University Hospital in Prague , Prague , Czech Republic
| | - Dušan Cmarko
- a Institute of Biology and Medical Genetics , First Faculty of Medicine , Charles University and General University Hospital in Prague , Prague , Czech Republic
| | - Ivan Raška
- a Institute of Biology and Medical Genetics , First Faculty of Medicine , Charles University and General University Hospital in Prague , Prague , Czech Republic
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37
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Ehrmann A, Nguyen B, Seifert U. Interlinked GTPase cascades provide a motif for both robust switches and oscillators. J R Soc Interface 2019; 16:20190198. [PMID: 31387482 DOI: 10.1098/rsif.2019.0198] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
GTPases regulate a wide range of cellular processes, such as intracellular vesicular transport, signal transduction and protein translation. These hydrolase enzymes operate as biochemical switches by toggling between an active guanosine triphosphate (GTP)-bound state and an inactive guanosine diphosphate (GDP)-bound state. We compare two network motifs, a single-species switch and an interlinked cascade that consists of two species coupled through positive and negative feedback loops. We find that interlinked cascades are closer to the ideal all-or-none switch and are more robust against fluctuating signals. While the single-species switch can only achieve bistability, interlinked cascades can be converted into oscillators by tuning the cofactor concentrations, which catalyse the activity of the cascade. These regimes can only be achieved with sufficient chemical driving provided by GTP hydrolysis. In this study, we present a thermodynamically consistent model that can achieve bistability and oscillations with the same feedback motif.
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Affiliation(s)
- Andreas Ehrmann
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Basile Nguyen
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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38
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Inferring broken detailed balance in the absence of observable currents. Nat Commun 2019; 10:3542. [PMID: 31387988 PMCID: PMC6684597 DOI: 10.1038/s41467-019-11051-w] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2019] [Accepted: 06/12/2019] [Indexed: 11/22/2022] Open
Abstract
Identifying dissipation is essential for understanding the physical mechanisms underlying nonequilibrium processes. In living systems, for example, the dissipation is directly related to the hydrolysis of fuel molecules such as adenosine triphosphate (ATP). Nevertheless, detecting broken time-reversal symmetry, which is the hallmark of dissipative processes, remains a challenge in the absence of observable directed motion, flows, or fluxes. Furthermore, quantifying the entropy production in a complex system requires detailed information about its dynamics and internal degrees of freedom. Here we introduce a novel approach to detect time irreversibility and estimate the entropy production from time-series measurements, even in the absence of observable currents. We apply our technique to two different physical systems, namely, a partially hidden network and a molecular motor. Our method does not require complete information about the system dynamics and thus provides a new tool for studying nonequilibrium phenomena. Non-equilibrium systems with hidden states are relevant for biological systems such as molecular motors. Here the authors introduce a method for quantifying irreversibility in such a system by exploiting the fluctuations in the waiting times of time series data.
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39
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Abstract
Multisubunit protein complexes are ubiquitous in biology and perform a plethora of essential functions. Most of the scientific literature treats such assemblies as static: their function is assumed to be independent of their manner of assembly, and their structure is assumed to remain intact until they are degraded. Recent observations of the bacterial flagellar motor, among others, bring these notions into question. The torque-generating stator units of the motor assemble and disassemble in response to changes in load. Here, we used electrorotation to drive tethered cells forward, which decreases motor load, and measured the resulting stator dynamics. No disassembly occurred while the torque remained high, but all of the stator units were released when the motor was spun near the zero-torque speed. When the electrorotation was turned off, so that the load was again high, stator units were recruited, increasing motor speed in a stepwise fashion. A model in which speed affects the binding rate and torque affects the free energy of bound stator units captures the observed torque-dependent stator assembly dynamics, providing a quantitative framework for the environmentally regulated self-assembly of a major macromolecular machine.
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40
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Shi H, Ma S, Zhang R, Yuan J. A hidden state in the turnover of a functioning membrane protein complex. SCIENCE ADVANCES 2019; 5:eaau6885. [PMID: 30906857 PMCID: PMC6426456 DOI: 10.1126/sciadv.aau6885] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/05/2018] [Accepted: 01/30/2019] [Indexed: 06/09/2023]
Abstract
Most membrane proteins exist in complexes that carry out critical cellular functions and exhibit rich dynamics. The bacterial flagellar motor, a large membrane-spanning ion-driven rotary motor that propels the bacteria to swim, provides a canonical example. Rotation of the motor is driven by multiple torque-generating units (stators). Turnover of the stators has been shown previously, demonstrating the exchange of stator units between the motor and a membrane pool. But the details of the turnover kinetics remain unclear. Here, we directly measured the kinetics of stator turnover in individual motors via analysis of a large dataset of long-term high-resolution recordings of motor speed at high load. We found that the dwell time distribution of the stator units exhibits a multi-exponential shape, suggesting the existence of a hidden state in the turnover of the stators.
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41
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Zhang C, He R, Zhang R, Yuan J. Motor Adaptive Remodeling Speeds Up Bacterial Chemotactic Adaptation. Biophys J 2019. [PMID: 29539407 DOI: 10.1016/j.bpj.2018.01.018] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Bacterial chemotaxis is a canonical system for the study of signal transduction. One of the hallmarks of this system is its robust adaptive behavior. However, how fast the system adapts remains controversial. The adaptation time measured at the level of the kinase activity was tens of seconds, whereas that measured at the level of the flagellar motor was <10 s. The flagellar motor was recently shown to exhibit adaptive remodeling, its main physiological function being to provide a robust match between the chemoreceptor output and the motor input, whereas its adaptation timescale was thought to be too slow to contribute much to the overall adaptation timescale of the chemotaxis system. Here, through theoretical modeling of the motor adaptive remodeling and experimental tests, we show that this motor adaptation contributes significantly to speeding up the overall chemotactic adaptation, thereby resolving the previous inconsistency.
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Affiliation(s)
- Chi Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui, China
| | - Rui He
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui, China
| | - Rongjing Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui, China.
| | - Junhua Yuan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui, China.
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42
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A Programmable Mechanical Maxwell's Demon. ENTROPY 2019; 21:e21010065. [PMID: 33266781 PMCID: PMC7514173 DOI: 10.3390/e21010065] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/21/2018] [Revised: 12/22/2018] [Accepted: 01/09/2019] [Indexed: 12/04/2022]
Abstract
We introduce and investigate a simple and explicitly mechanical model of Maxwell’s demon—a device that interacts with a memory register (a stream of bits), a thermal reservoir (an ideal gas) and a work reservoir (a mass that can be lifted or lowered). Our device is similar to one that we have briefly described elsewhere, but it has the additional feature that it can be programmed to recognize a chosen reference sequence, for instance, the binary representation of π. If the bits in the memory register match those of the reference sequence, then the device extracts heat from the thermal reservoir and converts it into work to lift a small mass. Conversely, the device can operate as a generalized Landauer’s eraser (or copier), harnessing the energy of a dropping mass to write the chosen reference sequence onto the memory register, replacing whatever information may previously have been stored there. Our model can be interpreted either as a machine that autonomously performs a conversion between information and energy, or else as a feedback-controlled device that is operated by an external agent. We derive generalized second laws of thermodynamics for both pictures. We illustrate our model with numerical simulations, as well as analytical calculations in a particular, exactly solvable limit.
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43
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Dasbiswas K, Mandadapu KK, Vaikuntanathan S. Topological localization in out-of-equilibrium dissipative systems. Proc Natl Acad Sci U S A 2018; 115:E9031-E9040. [PMID: 30206153 PMCID: PMC6166820 DOI: 10.1073/pnas.1721096115] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
In this paper, we report that notions of topological protection can be applied to stationary configurations that are driven far from equilibrium by active, dissipative processes. We consider two physically disparate systems: stochastic networks governed by microscopic single-particle dynamics, and collections of driven interacting particles described by coarse-grained hydrodynamic theory. We derive our results by mapping to well-known electronic models and exploiting the resulting correspondence between a bulk topological number and the spectrum of dissipative modes localized at the boundary. For the Markov networks, we report a general procedure to uncover the topological properties in terms of the transition rates. For the active fluid on a substrate, we introduce a topological interpretation of fluid dissipative modes at the edge. In both cases, the presence of dissipative couplings to the environment that break time-reversal symmetry are crucial to ensuring topological protection. These examples constitute proof of principle that notions of topological protection do indeed extend to dissipative processes operating out of equilibrium. Such topologically robust boundary modes have implications for both biological and synthetic systems.
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Affiliation(s)
- Kinjal Dasbiswas
- The James Franck Institute, The University of Chicago, Chicago, IL 60637
- Department of Physics, University of California, Merced, CA 95343
| | - Kranthi K Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA 94720
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720
| | - Suriyanarayanan Vaikuntanathan
- The James Franck Institute, The University of Chicago, Chicago, IL 60637;
- Department of Chemistry, The University of Chicago, Chicago, IL 60637
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44
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Wan KY, Goldstein RE. Time Irreversibility and Criticality in the Motility of a Flagellate Microorganism. PHYSICAL REVIEW LETTERS 2018; 121:058103. [PMID: 30118294 PMCID: PMC7616082 DOI: 10.1103/physrevlett.121.058103] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2017] [Revised: 03/27/2018] [Indexed: 06/08/2023]
Abstract
Active living organisms exhibit behavioral variability, partitioning between fast and slow dynamics. Such variability may be key to generating rapid responses in a heterogeneous, unpredictable environment wherein cellular activity effects continual exchanges of energy fluxes. We demonstrate a novel, noninvasive strategy for revealing nonequilibrium control of swimming-specifically, in an octoflagellate microalga. These organisms exhibit surprising features of flagellar excitability and mechanosensitivity, which characterize a novel, time-irreversible "run-stop-shock" motility comprising forward runs, knee-jerk shocks with dramatic beat reversal, and long stops during which cells are quiescent yet continue to exhibit submicron flagellar vibrations. Entropy production, associated with flux cycles arising in a reaction graph representation of the gait-switching dynamics, provides a direct measure of detailed balance violation in this primitive alga.
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Affiliation(s)
- Kirsty Y. Wan
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
- Living Systems Institute, University of Exeter, Exeter EX4 4QD, United Kingdom
| | - Raymond E. Goldstein
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
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45
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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.
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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
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46
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Waite AJ, Frankel NW, Emonet T. Behavioral Variability and Phenotypic Diversity in Bacterial Chemotaxis. Annu Rev Biophys 2018; 47:595-616. [PMID: 29618219 DOI: 10.1146/annurev-biophys-062215-010954] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Living cells detect and process external signals using signaling pathways that are affected by random fluctuations. These variations cause the behavior of individual cells to fluctuate over time (behavioral variability) and generate phenotypic differences between genetically identical individuals (phenotypic diversity). These two noise sources reduce our ability to predict biological behavior because they diversify cellular responses to identical signals. Here, we review recent experimental and theoretical advances in understanding the mechanistic origin and functional consequences of such variation in Escherichia coli chemotaxis-a well-understood model of signal transduction and behavior. After briefly summarizing the architecture and logic of the chemotaxis system, we discuss determinants of behavior and chemotactic performance of individual cells. Then, we review how cell-to-cell differences in protein abundance map onto differences in individual chemotactic abilities and how phenotypic variability affects the performance of the population. We conclude with open questions to be addressed by future research.
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Affiliation(s)
- Adam James Waite
- Department of Molecular, Cellular, and Developmental Biology, Yale University, New Haven, Connecticut 06520; .,Current affiliation: Calico Life Sciences, LLC, South San Francisco, California 94080
| | - Nicholas W Frankel
- Department of Molecular, Cellular, and Developmental Biology, Yale University, New Haven, Connecticut 06520; .,Department of Cellular and Molecular Pharmacology, University of California, San Francisco, California 94158
| | - Thierry Emonet
- Department of Molecular, Cellular, and Developmental Biology, Yale University, New Haven, Connecticut 06520; .,Department of Physics, Yale University, New Haven, Connecticut 06520
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47
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Saakian DB. Kinetics of biochemical sensing by single cells and populations of cells. Phys Rev E 2017; 96:042413. [PMID: 29347567 DOI: 10.1103/physreve.96.042413] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2017] [Indexed: 11/07/2022]
Abstract
We investigate the collective stationary sensing using N communicative cells, which involves surface receptors, diffusive signaling molecules, and cell-cell communication messengers. We restrict the scenarios to the signal-to-noise ratios (SNRs) for both strong communication and extrinsic noise only. We modified a previous model [Bialek and Setayeshgar, Proc. Natl. Acad. Sci. USA 102, 10040 (2005)PNASA60027-842410.1073/pnas.0504321102] to eliminate the singularities in the fluctuation correlations by considering a uniform receptor distribution over the surface of each cell with a finite radius a. The modified model enables a simple and rigorous mathematical treatment of the collective sensing phenomenon. We then derive the scaling of the SNR for both juxtacrine and autocrine cases in all dimensions. For the optimal locations of the cells in the autocrine case, we find identical scaling for both two and three dimensions.
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Affiliation(s)
- David B Saakian
- Theoretical Physics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam; and A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, 2 Alikhanian Brothers St., Yerevan 375036, Armenia
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48
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Deshpande A, Gopalkrishnan M, Ouldridge TE, Jones NS. Designing the optimal bit: balancing energetic cost, speed and reliability. Proc Math Phys Eng Sci 2017; 473:20170117. [PMID: 28878557 PMCID: PMC5582178 DOI: 10.1098/rspa.2017.0117] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2017] [Accepted: 07/04/2017] [Indexed: 11/12/2022] Open
Abstract
We consider the challenge of operating a reliable bit that can be rapidly erased. We find that both erasing and reliability times are non-monotonic in the underlying friction, leading to a trade-off between erasing speed and bit reliability. Fast erasure is possible at the expense of low reliability at moderate friction, and high reliability comes at the expense of slow erasure in the underdamped and overdamped limits. Within a given class of bit parameters and control strategies, we define 'optimal' designs of bits that meet the desired reliability and erasing time requirements with the lowest operational work cost. We find that optimal designs always saturate the bound on the erasing time requirement, but can exceed the required reliability time if critically damped. The non-trivial geometry of the reliability and erasing time scales allows us to exclude large regions of parameter space as suboptimal. We find that optimal designs are either critically damped or close to critical damping under the erasing procedure.
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Affiliation(s)
- Abhishek Deshpande
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK.,School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai 400005, India
| | - Manoj Gopalkrishnan
- Department of Electrical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Thomas E Ouldridge
- Department of Bioengineering, Imperial College London, London SW7 2AZ, UK
| | - Nick S Jones
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK
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Nguyen B, Hartich D, Seifert U, Rios PDL. Thermodynamic Bounds on the Ultra- and Infra-affinity of Hsp70 for Its Substrates. Biophys J 2017; 113:362-370. [PMID: 28746847 DOI: 10.1016/j.bpj.2017.06.010] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2017] [Revised: 05/31/2017] [Accepted: 06/09/2017] [Indexed: 12/16/2022] Open
Abstract
The 70 kDa heat shock protein Hsp70 has several essential functions in living systems, such as protecting cells against protein aggregation, assisting protein folding, remodeling protein complexes, and driving translocation into organelles. These functions require high affinity for nonspecific amino acid sequences that are ubiquitous in proteins. It has been recently shown that this high affinity, called ultra-affinity, depends on a process driven out of equilibrium by ATP hydrolysis. Here, we establish the thermodynamic bounds for ultra-affinity, and further show that the same reaction scheme can in principle be used both to strengthen and to weaken affinities (leading in this case to infra-affinity). We show that cofactors are essential to achieve affinity beyond the equilibrium range. Finally, biological implications are discussed.
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Affiliation(s)
- Basile Nguyen
- II. Institut für Theoretische Physik, Universität Stuttgart, Stuttgart, Germany; Laboratory of Statistical Biophysics, Institute of Physics, School of Basic Science and Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland.
| | - David Hartich
- II. Institut für Theoretische Physik, Universität Stuttgart, Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, Stuttgart, Germany
| | - Paolo De Los Rios
- Laboratory of Statistical Biophysics, Institute of Physics, School of Basic Science and Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
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Abstract
Swimming bacteria exhibit a repertoire of motility patterns, in which persistent motion is interrupted by turning events. What are the statistical properties of such random walks? If some particular instances have long been studied, the general case where turning times do not follow a Poisson process has remained unsolved. We present a generic extension of the continuous time random walks formalism relying on operators and noncommutative calculus. The approach is first applied to a unimodal model of bacterial motion. We examine the existence of a minimum in velocity correlation function and discuss the maximum of diffusivity at an optimal value of rotational diffusion. The model is then extended to bimodal patterns and includes as particular cases all swimming strategies: run-and-tumble, run-stop, run-reverse and run-reverse-flick. We characterize their velocity correlation functions and investigate how bimodality affects diffusivity. Finally, the wider applicability of the method is illustrated by considering curved trajectories and Lévy walks. Our results are relevant for intermittent motion of living beings, be they swimming micro-organisms or crawling cells.
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Affiliation(s)
- François Detcheverry
- Univ Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France
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