1
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Boffi NM, Vanden-Eijnden E. Deep learning probability flows and entropy production rates in active matter. Proc Natl Acad Sci U S A 2024; 121:e2318106121. [PMID: 38861599 PMCID: PMC11194503 DOI: 10.1073/pnas.2318106121] [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: 10/18/2023] [Accepted: 05/01/2024] [Indexed: 06/13/2024] Open
Abstract
Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. They involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework to estimate the score of this density. We show that the score, together with the microscopic equations of motion, gives access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles. To represent the score, we introduce a spatially local transformer network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of active particles undergoing motility-induced phase separation (MIPS). We show that a single network trained on a system of 4,096 particles at one packing fraction can generalize to other regions of the phase diagram, including to systems with as many as 32,768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.
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Affiliation(s)
- Nicholas M. Boffi
- Courant Institute of Mathematical Sciences, New York University, New York, NY10012
| | - Eric Vanden-Eijnden
- Courant Institute of Mathematical Sciences, New York University, New York, NY10012
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2
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Paoluzzi M, Puglisi A, Angelani L. Entropy Production of Run-and-Tumble Particles. ENTROPY (BASEL, SWITZERLAND) 2024; 26:443. [PMID: 38920452 DOI: 10.3390/e26060443] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2024] [Revised: 05/21/2024] [Accepted: 05/22/2024] [Indexed: 06/27/2024]
Abstract
We analyze the entropy production in run-and-tumble models. After presenting the general formalism in the framework of the Fokker-Planck equations in one space dimension, we derive some known exact results in simple physical situations (free run-and-tumble particles and harmonic confinement). We then extend the calculation to the case of anisotropic motion (different speeds and tumbling rates for right- and left-oriented particles), obtaining exact expressions of the entropy production rate. We conclude by discussing the general case of heterogeneous run-and-tumble motion described by space-dependent parameters and extending the analysis to the case of d-dimensional motions.
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Affiliation(s)
- Matteo Paoluzzi
- Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Via Pietro Castellino 111, I-80131 Napoli, Italy
| | - Andrea Puglisi
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Piazzale A. Moro 2, I-00185 Roma, Italy
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 2, I-00185 Roma, Italy
| | - Luca Angelani
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Piazzale A. Moro 2, I-00185 Roma, Italy
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 2, I-00185 Roma, Italy
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3
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Di Terlizzi I, Gironella M, Herraez-Aguilar D, Betz T, Monroy F, Baiesi M, Ritort F. Variance sum rule for entropy production. Science 2024; 383:971-976. [PMID: 38422150 DOI: 10.1126/science.adh1823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 01/09/2024] [Indexed: 03/02/2024]
Abstract
Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule (VSR) for displacement and force variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. We then apply the VSR to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements. The VSR paves the way to derive σ using force spectroscopy and time-resolved imaging in living and active matter.
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Affiliation(s)
- I Di Terlizzi
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - M Gironella
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
- Department of Medical Biochemistry and Cell Biology, Institute of Biomedicine, The Sahlgrenska Academy, University of Gothenburg, 40530 Gothenburg, Sweden
| | - D Herraez-Aguilar
- Facultad de Ciencias Experimentales, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1,800, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - T Betz
- Third Institute of Physics, Georg August Universität Göttingen, Göttingen, Germany
- Cluster of Excellence "Multiscale Bioimaging: from Molecular Machines to Networks of Excitable Cells" (MBExC), University of Göttingen, Göttingen, Germany
| | - F Monroy
- Departamento de Química Física, Facultad de Química, Universidad Complutense, 28040 Madrid, Spain
- Translational Biophysics, Instituto de Investigación Sanitaria Hospital Doce de Octubre (IMAS12), Av. Andalucía, 28041 Madrid, Spain
| | - M Baiesi
- Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - F Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
- Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028 Barcelona, Spain
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4
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Papo D, Buldú JM. Does the brain behave like a (complex) network? I. Dynamics. Phys Life Rev 2024; 48:47-98. [PMID: 38145591 DOI: 10.1016/j.plrev.2023.12.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Accepted: 12/10/2023] [Indexed: 12/27/2023]
Abstract
Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.
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Affiliation(s)
- D Papo
- Department of Neuroscience and Rehabilitation, Section of Physiology, University of Ferrara, Ferrara, Italy; Center for Translational Neurophysiology, Fondazione Istituto Italiano di Tecnologia, Ferrara, Italy.
| | - J M Buldú
- Complex Systems Group & G.I.S.C., Universidad Rey Juan Carlos, Madrid, Spain
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5
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Laeverenz-Schlogelhofer H, Wan KY. Bioelectric control of locomotor gaits in the walking ciliate Euplotes. Curr Biol 2024; 34:697-709.e6. [PMID: 38237598 DOI: 10.1016/j.cub.2023.12.051] [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: 09/01/2023] [Revised: 11/20/2023] [Accepted: 12/18/2023] [Indexed: 02/29/2024]
Abstract
Diverse animal species exhibit highly stereotyped behavioral actions and locomotor sequences as they explore their natural environments. In many such cases, the neural basis of behavior is well established, where dedicated neural circuitry contributes to the initiation and regulation of certain response sequences. At the microscopic scale, single-celled eukaryotes (protists) also exhibit remarkably complex behaviors and yet are completely devoid of nervous systems. Here, to address the question of how single cells control behavior, we study locomotor patterning in the exemplary hypotrich ciliate Euplotes, a highly polarized cell, which actuates a large number of leg-like appendages called cirri (each a bundle of ∼25-50 cilia) to swim in fluids or walk on surfaces. As it navigates its surroundings, a walking Euplotes cell is routinely observed to perform side-stepping reactions, one of the most sophisticated maneuvers ever observed in a single-celled organism. These are spontaneous and stereotyped reorientation events involving a transient and fast backward motion followed by a turn. Combining high-speed imaging with simultaneous time-resolved electrophysiological recordings, we show that this complex coordinated motion sequence is tightly regulated by rapid membrane depolarization events, which orchestrate the activity of different cirri on the cell. Using machine learning and computer vision methods, we map detailed measurements of cirri dynamics to the cell's membrane bioelectrical activity, revealing a differential response in the front and back cirri. We integrate these measurements with a minimal model to understand how Euplotes-a unicellular organism-manipulates its membrane potential to achieve real-time control over its motor apparatus.
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Affiliation(s)
| | - Kirsty Y Wan
- Living Systems Institute, University of Exeter, Stocker Road, Exeter EX4 4QD, UK.
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6
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Spera G, Duclut C, Durand M, Tailleur J. Nematic Torques in Scalar Active Matter: When Fluctuations Favor Polar Order and Persistence. PHYSICAL REVIEW LETTERS 2024; 132:078301. [PMID: 38427854 DOI: 10.1103/physrevlett.132.078301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Revised: 07/12/2023] [Accepted: 01/08/2024] [Indexed: 03/03/2024]
Abstract
We study the impact of nematic alignment on scalar active matter in the disordered phase. We show that nematic torques control the emergent physics of particles interacting via pairwise forces and can either induce or prevent phase separation. The underlying mechanism is a fluctuation-induced renormalization of the mass of the polar field that generically arises from nematic torques. The correlations between the fluctuations of the polar and nematic fields indeed conspire to increase the particle persistence length, contrary to what phenomenological computations predict. This effect is generic and our theory also quantitatively accounts for how nematic torques enhance particle accumulation along confining boundaries and opposes demixing in mixtures of active and passive particles.
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Affiliation(s)
- Gianmarco Spera
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
| | - Charlie Duclut
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
- Laboratoire Physique des Cellules et Cancer (PCC), CNRS UMR 168, Institut Curie, Université PSL, Sorbonne Université, 75005 Paris, France
| | - Marc Durand
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
| | - Julien Tailleur
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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7
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Copperman J, Mclean IC, Gross SM, Chang YH, Zuckerman DM, Heiser LM. Single-cell morphodynamical trajectories enable prediction of gene expression accompanying cell state change. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.01.18.576248. [PMID: 38293173 PMCID: PMC10827140 DOI: 10.1101/2024.01.18.576248] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/01/2024]
Abstract
Extracellular signals induce changes to molecular programs that modulate multiple cellular phenotypes, including proliferation, motility, and differentiation status. The connection between dynamically adapting phenotypic states and the molecular programs that define them is not well understood. Here we develop data-driven models of single-cell phenotypic responses to extracellular stimuli by linking gene transcription levels to "morphodynamics" - changes in cell morphology and motility observable in time-lapse image data. We adopt a dynamics-first view of cell state by grouping single-cell trajectories into states with shared morphodynamic responses. The single-cell trajectories enable development of a first-of-its-kind computational approach to map live-cell dynamics to snapshot gene transcript levels, which we term MMIST, Molecular and Morphodynamics-Integrated Single-cell Trajectories. The key conceptual advance of MMIST is that cell behavior can be quantified based on dynamically defined states and that extracellular signals alter the overall distribution of cell states by altering rates of switching between states. We find a cell state landscape that is bound by epithelial and mesenchymal endpoints, with distinct sequences of epithelial to mesenchymal transition (EMT) and mesenchymal to epithelial transition (MET) intermediates. The analysis yields predictions for gene expression changes consistent with curated EMT gene sets and provides a prediction of thousands of RNA transcripts through extracellular signal-induced EMT and MET with near-continuous time resolution. The MMIST framework leverages true single-cell dynamical behavior to generate molecular-level omics inferences and is broadly applicable to other biological domains, time-lapse imaging approaches and molecular snapshot data.
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Affiliation(s)
- Jeremy Copperman
- Cancer Early Detection Advanced Research Center, Oregon Health and Science University, Portland OR 97239, U.S.A
| | - Ian C. Mclean
- Department of Biomedical Engineering, Oregon Health and Science University, Portland OR 97239, U.S.A
| | | | - Young Hwan Chang
- Department of Biomedical Engineering, Oregon Health and Science University, Portland OR 97239, U.S.A
- Knight Cancer Institute, Oregon Health and Science University, Portland OR 97239, U.S.A
| | - Daniel M. Zuckerman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland OR 97239, U.S.A
- Knight Cancer Institute, Oregon Health and Science University, Portland OR 97239, U.S.A
| | - Laura M. Heiser
- Department of Biomedical Engineering, Oregon Health and Science University, Portland OR 97239, U.S.A
- Knight Cancer Institute, Oregon Health and Science University, Portland OR 97239, U.S.A
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8
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Schmitt MS, Colen J, Sala S, Devany J, Seetharaman S, Caillier A, Gardel ML, Oakes PW, Vitelli V. Machine learning interpretable models of cell mechanics from protein images. Cell 2024; 187:481-494.e24. [PMID: 38194965 DOI: 10.1016/j.cell.2023.11.041] [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: 03/21/2023] [Revised: 09/20/2023] [Accepted: 11/29/2023] [Indexed: 01/11/2024]
Abstract
Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. Currently, no systematic strategy exists to infer large-scale physical properties of a cell from its molecular components. This is an obstacle to understanding processes such as cell adhesion and migration. Here, we develop a data-driven modeling pipeline to learn the mechanical behavior of adherent cells. We first train neural networks to predict cellular forces from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion (FA) protein, such as zyxin, are sufficient to predict forces and can generalize to unseen biological regimes. Using this observation, we develop two approaches-one constrained by physics and the other agnostic-to construct data-driven continuum models of cellular forces. Both reveal how cellular forces are encoded by two distinct length scales. Beyond adherent cell mechanics, our work serves as a case study for integrating neural networks into predictive models for cell biology.
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Affiliation(s)
- Matthew S Schmitt
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA; Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637, USA
| | - Jonathan Colen
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA; Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637, USA
| | - Stefano Sala
- Department of Cell & Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL 60153, USA
| | - John Devany
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA
| | - Shailaja Seetharaman
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA
| | - Alexia Caillier
- Department of Cell & Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL 60153, USA
| | - Margaret L Gardel
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA.
| | - Patrick W Oakes
- Department of Cell & Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL 60153, USA.
| | - Vincenzo Vitelli
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA; Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637, USA.
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9
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Kwon E, Baek Y. α-divergence improves the entropy production estimation via machine learning. Phys Rev E 2024; 109:014143. [PMID: 38366477 DOI: 10.1103/physreve.109.014143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2023] [Accepted: 01/05/2024] [Indexed: 02/18/2024]
Abstract
Recent years have seen a surge of interest in the algorithmic estimation of stochastic entropy production (EP) from trajectory data via machine learning. A crucial element of such algorithms is the identification of a loss function whose minimization guarantees the accurate EP estimation. In this study we show that there exists a host of loss functions, namely, those implementing a variational representation of the α-divergence, which can be used for the EP estimation. By fixing α to a value between -1 and 0, the α-NEEP (Neural Estimator for Entropy Production) exhibits a much more robust performance against strong nonequilibrium driving or slow dynamics, which adversely affects the existing method based on the Kullback-Leibler divergence (α=0). In particular, the choice of α=-0.5 tends to yield the optimal results. To corroborate our findings, we present an exactly solvable simplification of the EP estimation problem, whose loss function landscape and stochastic properties give deeper intuition into the robustness of the α-NEEP.
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Affiliation(s)
- Euijoon Kwon
- Department of Physics and Astronomy & Center for Theoretical Physics, Seoul National University, Seoul 08826, Republic of Korea
| | - Yongjoo Baek
- Department of Physics and Astronomy & Center for Theoretical Physics, Seoul National University, Seoul 08826, Republic of Korea
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10
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Bondoc-Naumovitz KG, Laeverenz-Schlogelhofer H, Poon RN, Boggon AK, Bentley SA, Cortese D, Wan KY. Methods and Measures for Investigating Microscale Motility. Integr Comp Biol 2023; 63:1485-1508. [PMID: 37336589 PMCID: PMC10755196 DOI: 10.1093/icb/icad075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Revised: 05/31/2023] [Accepted: 06/06/2023] [Indexed: 06/21/2023] Open
Abstract
Motility is an essential factor for an organism's survival and diversification. With the advent of novel single-cell technologies, analytical frameworks, and theoretical methods, we can begin to probe the complex lives of microscopic motile organisms and answer the intertwining biological and physical questions of how these diverse lifeforms navigate their surroundings. Herein, we summarize the main mechanisms of microscale motility and give an overview of different experimental, analytical, and mathematical methods used to study them across different scales encompassing the molecular-, individual-, to population-level. We identify transferable techniques, pressing challenges, and future directions in the field. This review can serve as a starting point for researchers who are interested in exploring and quantifying the movements of organisms in the microscale world.
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Affiliation(s)
| | | | - Rebecca N Poon
- Living Systems Institute, University of Exeter, Stocker Road, EX4 4QD, Exeter, UK
| | - Alexander K Boggon
- Living Systems Institute, University of Exeter, Stocker Road, EX4 4QD, Exeter, UK
| | - Samuel A Bentley
- Living Systems Institute, University of Exeter, Stocker Road, EX4 4QD, Exeter, UK
| | - Dario Cortese
- Living Systems Institute, University of Exeter, Stocker Road, EX4 4QD, Exeter, UK
| | - Kirsty Y Wan
- Living Systems Institute, University of Exeter, Stocker Road, EX4 4QD, Exeter, UK
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11
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Suchanek T, Kroy K, Loos SAM. Irreversible Mesoscale Fluctuations Herald the Emergence of Dynamical Phases. PHYSICAL REVIEW LETTERS 2023; 131:258302. [PMID: 38181332 DOI: 10.1103/physrevlett.131.258302] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 10/30/2023] [Indexed: 01/07/2024]
Abstract
We study fluctuating field models with spontaneously emerging dynamical phases. We consider two typical transition scenarios associated with parity-time symmetry breaking: oscillatory instabilities and critical exceptional points. An analytical investigation of the low-noise regime reveals a drastic increase of the mesoscopic entropy production toward the transitions. For an illustrative model of two nonreciprocally coupled Cahn-Hilliard fields, we find physical interpretations in terms of actively propelled interfaces and a coupling of eigenmodes of the linearized dynamics near the critical exceptional point.
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Affiliation(s)
- Thomas Suchanek
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
| | - Klaus Kroy
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
| | - Sarah A M Loos
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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12
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Wenger J, Brigante A, Fernández Casafuz AB, Bruno L, Monastra A. Inference of the force pattern acting on a semiflexible filament from shape analysis. Phys Rev E 2023; 108:064402. [PMID: 38243502 DOI: 10.1103/physreve.108.064402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Accepted: 11/06/2023] [Indexed: 01/21/2024]
Abstract
The study of the active forces acting on semiflexible filaments networks such as the cytoskeleton requires noninvasive tools able to explore the deformation of single filaments in their natural environment. We propose here a practical method based on the solution of the hydrodynamic beam equation in the presence of transverse forces. We found that the derivative of the local curvature presents discontinuities that match the location of the applied forces, in contrast to the smooth curvature function obtained for the case of compressing longitudinal forces. These patterns can be easily appreciated in a kymograph of the curvature, which also reflects the temporal behavior of the forces. We assessed the method performance with numerical simulations describing the deformation of single microtubules provoked by the action of intracellular active forces.
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Affiliation(s)
- Julieta Wenger
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, C1428EGA Buenos Aires, Argentina
| | - Azul Brigante
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, C1428EGA Buenos Aires, Argentina
| | - Agustina B Fernández Casafuz
- Universidad de Buenos Aires, Instituto de Cálculo (IC), C1428EGA Buenos Aires, Argentina and Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), C1425FQD Buenos Aires, Argentina
| | - Luciana Bruno
- Universidad de Buenos Aires, Instituto de Cálculo (IC), C1428EGA Buenos Aires, Argentina and Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), C1425FQD Buenos Aires, Argentina
| | - Alejandro Monastra
- Universidad Nacional de General Sarmiento, Instituto de Ciencias, B1613 Los Polvorines, Buenos Aires, Argentina and Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), C1425FQD Buenos Aires, Argentina
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13
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Reboucas RB, Miksis MJ, Vlahovska PM. Stationary shapes of axisymmetric vesicles beyond lowest-energy configurations. ARXIV 2023:arXiv:2311.14193v1. [PMID: 38045475 PMCID: PMC10690299] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Subscribe] [Scholar Register] [Indexed: 12/05/2023]
Abstract
We conduct a systematic exploration of the energy landscape of vesicle morphologies within the framework of the Helfrich model. Vesicle shapes are determined by minimizing the elastic energy subject to constraints of constant area and volume. The results show that pressurized vesicles can adopt higher-energy spindle-like configurations that require the action of point forces at the poles. If the internal pressure is lower than the external one, multilobed shapes are predicted. We utilize our results to rationalize the experimentally observed spindle shapes of giant vesicles in a uniform AC field.
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Affiliation(s)
| | - Michael J. Miksis
- Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
| | - Petia M. Vlahovska
- Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
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14
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Jerez MJY, Rangaig NA, Confesor MNP. Effective temperature for an intermittent bistable potential. J Chem Phys 2023; 159:154903. [PMID: 37851394 DOI: 10.1063/5.0165670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2023] [Accepted: 09/19/2023] [Indexed: 10/19/2023] Open
Abstract
Thermodynamics of far-from-equilibrium systems often require measurement of effective parameters such as temperature. Whether such approach is valid for the general case of resetting protocols, active systems, or of confined systems under time-varying fields is still under investigation. We report on the effect of switching ON-OFF of an asymmetric bistable potential to the mean first passage time (MFPT) of a probed particle to go from one potential minima to the other. Experimental results coupled with numerical simulations shows the potential becoming more symmetric at slow switching. Moreover, the MFPT deviates from equilibrium condition with an effective temperature, Teff < T, at slow switching but approaches room temperature, T, at fast switching. For each switching rate, we quantify how far the system is from equilibrium by measuring deviation from a detailed balance like relation and the net circulation of flux present in phase-space. Both analysis suggest equilibrium condition are met at high switching.
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Affiliation(s)
- Michael Jade Y Jerez
- Department of Physics and Complex Systems Research Center-PRISM, Mindanao State University-Iligan Institute of Technology, 9200 Iligan City, Philippines
| | - Norodin A Rangaig
- Department of Physics, Mindanao State University-Marawi Campus, 9700 Marawi City, Philippines
| | - Mark Nolan P Confesor
- Department of Physics and Complex Systems Research Center-PRISM, Mindanao State University-Iligan Institute of Technology, 9200 Iligan City, Philippines
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15
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Faluweki MK, Cammann J, Mazza MG, Goehring L. Active Spaghetti: Collective Organization in Cyanobacteria. PHYSICAL REVIEW LETTERS 2023; 131:158303. [PMID: 37897773 DOI: 10.1103/physrevlett.131.158303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2023] [Accepted: 08/30/2023] [Indexed: 10/30/2023]
Abstract
Filamentous cyanobacteria can show fascinating examples of nonequilibrium self-organization, which, however, are not well understood from a physical perspective. We investigate the motility and collective organization of colonies of these simple multicellular lifeforms. As their area density increases, linear chains of cells gliding on a substrate show a transition from an isotropic distribution to bundles of filaments arranged in a reticulate pattern. Based on our experimental observations of individual behavior and pairwise interactions, we introduce a nonreciprocal model accounting for the filaments' large aspect ratio, fluctuations in curvature, motility, and nematic interactions. This minimal model of active filaments recapitulates the observations, and rationalizes the appearance of a characteristic length scale in the system, based on the Péclet number of the cyanobacteria filaments.
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Affiliation(s)
- Mixon K Faluweki
- School of Science and Technology, Nottingham Trent University, Nottingham NG11 8NS, United Kingdom
- Malawi Institute of Technology, Malawi University of Science and Technology, S150 Road, Thyolo 310105, Malawi
| | - Jan Cammann
- Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom
| | - Marco G Mazza
- Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Faßberg 17, 37077 Göttingen, Germany
| | - Lucas Goehring
- School of Science and Technology, Nottingham Trent University, Nottingham NG11 8NS, United Kingdom
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16
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du Buisson J, Mnyulwa TDP, Touchette H. Large deviations of the stochastic area for linear diffusions. Phys Rev E 2023; 108:044136. [PMID: 37978634 DOI: 10.1103/physreve.108.044136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Accepted: 09/07/2023] [Indexed: 11/19/2023]
Abstract
The area enclosed by the two-dimensional Brownian motion in the plane was studied by Lévy, who found the characteristic function and probability density of this random variable. For other planar processes, in particular ergodic diffusions described by linear stochastic differential equations (SDEs), only the expected value of the stochastic area is known. Here we calculate the generating function of the stochastic area for linear SDEs, which can be related to the integral of the angular momentum, and extract from the result the large deviation functions characterizing the dominant part of its probability density in the long-time limit, as well as the effective SDE describing how large deviations arise in that limit. In addition, we obtain the asymptotic mean of the stochastic area, which is known to be related to the probability current, and the asymptotic variance, which is important for determining from observed trajectories whether or not a diffusion is reversible. Examples of reversible and irreversible linear SDEs are studied to illustrate our results.
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Affiliation(s)
- Johan du Buisson
- Institute of Theoretical Physics, Department of Physics, Stellenbosch University, Stellenbosch 7600, South Africa
| | - Thamu D P Mnyulwa
- Department of Mathematical Sciences, Stellenbosch University, Stellenbosch 7600, South Africa
| | - Hugo Touchette
- Department of Mathematical Sciences, Stellenbosch University, Stellenbosch 7600, South Africa
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17
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Chen S, Markovich T, MacKintosh FC. Motor-free contractility of active biopolymer networks. Phys Rev E 2023; 108:044405. [PMID: 37978629 DOI: 10.1103/physreve.108.044405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Accepted: 09/19/2023] [Indexed: 11/19/2023]
Abstract
Contractility in animal cells is often generated by molecular motors such as myosin, which require polar substrates for their function. Motivated by recent experimental evidence of motor-independent contractility, we propose a robust motor-free mechanism that can generate contraction in biopolymer networks without the need for substrate polarity. We show that contractility is a natural consequence of active binding-unbinding of crosslinkers that breaks the principle of detailed balance, together with the asymmetric force-extension response of semiflexible biopolymers. We have extended our earlier work to discuss the motor-free contraction of viscoelastic biopolymer networks. We calculate the resulting contractile velocity using a microscopic model and show that it can be reduced to a simple coarse-grained model under certain limits. Our model may provide an explanation of recent reports of motor-independent contractility in cells. Our results also suggest a mechanism for generating contractile forces in synthetic active materials.
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Affiliation(s)
- Sihan Chen
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Tomer Markovich
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- School of Mechanical Engineering, Tel Aviv University, Tel Aviv 69978, Israel
- Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 69978, Israel
| | - Fred C MacKintosh
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
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18
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Papo D, Bucolo M, Dimitriadis SI, Onton JA, Philippu A, Shannahoff-Khalsa D. Editorial: Advances in brain dynamics in the healthy and psychiatric disorders. Front Psychiatry 2023; 14:1284670. [PMID: 37779613 PMCID: PMC10539585 DOI: 10.3389/fpsyt.2023.1284670] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/28/2023] [Accepted: 08/31/2023] [Indexed: 10/03/2023] Open
Affiliation(s)
- David Papo
- Center for Translational Neurophysiology of Speech and Communication, Fondazione Istituto Italiano di Tecnologia, Ferrara, Italy
- Department of Neuroscience and Rehabilitation, Section of Physiology, University of Ferrara, Ferrara, Italy
| | - Maide Bucolo
- Department of Electrical, Electronic and Informatics, University of Catania, Catania, Italy
| | - Stavros I. Dimitriadis
- Department of Clinical Psychology and Psychobiology, Faculty of Psychology, University of Barcelona, Barcelona, Spain
| | - Julie A. Onton
- Institute of Neural Computation, University of California, San Diego, La Jolla, CA, United States
| | - Athineos Philippu
- Department of Pharmacology and Toxicology, University of Innsbruck, Innsbruck, Austria
| | - David Shannahoff-Khalsa
- BioCircuits Institute, University of California San Diego, La Jolla, CA, United States
- Center for Integrative Medicine, University of California San Diego, La Jolla, CA, United States
- The Khalsa Foundation for Medical Science, Del Mar, CA, United States
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19
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Ohga N, Ito S, Kolchinsky A. Thermodynamic Bound on the Asymmetry of Cross-Correlations. PHYSICAL REVIEW LETTERS 2023; 131:077101. [PMID: 37656850 DOI: 10.1103/physrevlett.131.077101] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 06/08/2023] [Indexed: 09/03/2023]
Abstract
The principle of microscopic reversibility says that, in equilibrium, two-time cross-correlations are symmetric under the exchange of observables. Thus, the asymmetry of cross-correlations is a fundamental, measurable, and often-used statistical signature of deviation from equilibrium. Here we find a simple and universal inequality that bounds the magnitude of asymmetry by the cycle affinity, i.e., the strength of thermodynamic driving. Our result applies to a large class of systems and all state observables, and it suggests a fundamental thermodynamic cost for various nonequilibrium functions quantified by the asymmetry. It also provides a powerful tool to infer affinity from measured cross-correlations, in a different and complementary way to the thermodynamic uncertainty relations. As an application, we prove a thermodynamic bound on the coherence of noisy oscillations, which was previously conjectured by Barato and Seifert [Phys. Rev. E 95, 062409 (2017)PRESCM2470-004510.1103/PhysRevE.95.062409]. We also derive a thermodynamic bound on directed information flow in a biochemical signal transduction model.
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Affiliation(s)
- Naruo Ohga
- Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Sosuke Ito
- Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- Universal Biology Institute, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Artemy Kolchinsky
- Universal Biology Institute, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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20
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Gupta D, Klapp SHL, Sivak DA. Efficient control protocols for an active Ornstein-Uhlenbeck particle. Phys Rev E 2023; 108:024117. [PMID: 37723713 DOI: 10.1103/physreve.108.024117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2023] [Accepted: 07/11/2023] [Indexed: 09/20/2023]
Abstract
Designing a protocol to efficiently drive a stochastic system is an active field of research. Here we extend such control theory to an active Ornstein-Uhlenbeck particle (AOUP) in a bistable potential, driven by a harmonic trap. We find that protocols designed to minimize the excess work (up to linear response) perform better than naive protocols with constant velocity for a wide range of protocol durations.
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Affiliation(s)
- Deepak Gupta
- Nordita, Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
- Institut für Theoretische Physik, Hardenbergstr. 36, Technische Universität Berlin, D-10623 Berlin, Germany
| | - Sabine H L Klapp
- Institut für Theoretische Physik, Hardenbergstr. 36, Technische Universität Berlin, D-10623 Berlin, Germany
| | - David A Sivak
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
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21
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Bacanu A, Pelletier JF, Jung Y, Fakhri N. Inferring scale-dependent non-equilibrium activity using carbon nanotubes. NATURE NANOTECHNOLOGY 2023; 18:905-911. [PMID: 37157022 DOI: 10.1038/s41565-023-01395-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2021] [Accepted: 04/04/2023] [Indexed: 05/10/2023]
Abstract
In living systems, irreversible, yet stochastic, molecular interactions form multiscale structures (such as cytoskeletal networks), which mediate processes (such as cytokinesis and cellular motility) in a close relationship between the structure and function. However, owing to a lack of methods to quantify non-equilibrium activity, their dynamics remain poorly characterized. Here, by measuring the time-reversal asymmetry encoded in the conformational dynamics of filamentous single-walled carbon nanotubes embedded in the actomyosin network of Xenopus egg extract, we characterize the multiscale dynamics of non-equilibrium activity encoded in bending-mode amplitudes. Our method is sensitive to distinct perturbations to the actomyosin network and the concentration ratio of adenosine triphosphate to adenosine diphosphate. Thus, our method can dissect the functional coupling of microscopic dynamics to the emergence of larger scale non-equilibrium activity. We relate the spatiotemporal scales of non-equilibrium activity to the key physical parameters of a semiflexible filament embedded in a non-equilibrium viscoelastic environment. Our analysis provides a general tool to characterize steady-state non-equilibrium activity in high-dimensional spaces.
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Affiliation(s)
- Alexandru Bacanu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA, USA
- Department of Stem Cell and Regenerative Biology, Harvard University, Cambridge, MA, USA
| | - James F Pelletier
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Centro Nacional de Biotecnología (CNB), CSIC, Madrid, Spain
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain
| | - Yoon Jung
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Nikta Fakhri
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA.
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22
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Loos SAM. Measurement of scale-dependent time-reversal asymmetry in biological systems. NATURE NANOTECHNOLOGY 2023; 18:838-839. [PMID: 37202509 DOI: 10.1038/s41565-023-01400-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Affiliation(s)
- Sarah A M Loos
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge, UK.
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23
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Tewarie PKB, Hindriks R, Lai YM, Sotiropoulos SN, Kringelbach M, Deco G. Non-reversibility outperforms functional connectivity in characterisation of brain states in MEG data. Neuroimage 2023; 276:120186. [PMID: 37268096 DOI: 10.1016/j.neuroimage.2023.120186] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Revised: 04/27/2023] [Accepted: 05/22/2023] [Indexed: 06/04/2023] Open
Abstract
Characterising brain states during tasks is common practice for many neuroscientific experiments using electrophysiological modalities such as electroencephalography (EEG) and magnetoencephalography (MEG). Brain states are often described in terms of oscillatory power and correlated brain activity, i.e. functional connectivity. It is, however, not unusual to observe weak task induced functional connectivity alterations in the presence of strong task induced power modulations using classical time-frequency representation of the data. Here, we propose that non-reversibility, or the temporal asymmetry in functional interactions, may be more sensitive to characterise task induced brain states than functional connectivity. As a second step, we explore causal mechanisms of non-reversibility in MEG data using whole brain computational models. We include working memory, motor, language tasks and resting-state data from participants of the Human Connectome Project (HCP). Non-reversibility is derived from the lagged amplitude envelope correlation (LAEC), and is based on asymmetry of the forward and reversed cross-correlations of the amplitude envelopes. Using random forests, we find that non-reversibility outperforms functional connectivity in the identification of task induced brain states. Non-reversibility shows especially better sensitivity to capture bottom-up gamma induced brain states across all tasks, but also alpha band associated brain states. Using whole brain computational models we find that asymmetry in the effective connectivity and axonal conduction delays play a major role in shaping non-reversibility across the brain. Our work paves the way for better sensitivity in characterising brain states during both bottom-up as well as top-down modulation in future neuroscientific experiments.
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Affiliation(s)
- Prejaas K B Tewarie
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Spain; Clinical Neurophysiology Group, University of Twente, Enschede, The Netherlands; Department of Neurology, Amsterdam UMC, Amsterdam, the Netherlands; Sir Peter Mansfield Imaging Centre, School of Physics, University of Nottingham, Nottingham, United Kingdom.
| | - Rikkert Hindriks
- Department of Mathematics, Faculty of Science, Vrije Universiteit Amsterdam, Amsterdam, the Netherlands
| | - Yi Ming Lai
- Sir Peter Mansfield Imaging Centre, School of Medicine, University of Nottingham, United Kingdom
| | - Stamatios N Sotiropoulos
- Sir Peter Mansfield Imaging Centre, School of Medicine, University of Nottingham, United Kingdom; NIHR Biomedical Research Centre, University of Nottingham, Nottingham University Hospitals NHS Trust, Nottingham, UK
| | - Morten Kringelbach
- Centre for Eudaimonia and Human Flourishing, Linacre College, University of Oxford, Oxford, UK; Center for Music in the Brain, Department of Clinical Medicine, Aarhus University, Aarhus, Denmark; Department of Psychiatry, University of Oxford, Oxford, UK
| | - Gustavo Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Spain; Institució Catalana de la Recerca i Estudis Avançats (ICREA), Barcelona, Spain; Department of Neuropsychology, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
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24
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Alicki R, Šindelka M, Gelbwaser-Klimovsky D. Violation of Detailed Balance in Quantum Open Systems. PHYSICAL REVIEW LETTERS 2023; 131:040401. [PMID: 37566852 DOI: 10.1103/physrevlett.131.040401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2022] [Revised: 05/04/2023] [Accepted: 07/05/2023] [Indexed: 08/13/2023]
Abstract
We consider the dynamics of a quantum system immersed in a dilute gas at thermodynamic equilibrium using a quantum Markovian master equation derived by applying the low-density limit technique. It is shown that the Gibbs state at the bath temperature is always stationary while the detailed balance condition at this state can be violated beyond the Born approximation. This violation is generically related to the absence of time-reversal symmetry for the scattering T matrix, which produces a thermalization mechanism that allows the presence of persistent probability and heat currents at thermal equilibrium. This phenomenon is illustrated by a model of an electron hopping between three quantum dots in an external magnetic field.
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Affiliation(s)
- Robert Alicki
- International Centre for Theory of Quantum Technologies (ICTQT), University of Gdańsk, 80-308, Gdańsk, Poland
| | - Milan Šindelka
- Institute of Plasma Physics of the Czech Academy of Sciences, Za Slovankou 1782/3, 18200 Prague, Czech Republic
| | - David Gelbwaser-Klimovsky
- Schulich Faculty of Chemistry and Helen Diller Quantum Center, Technion-Israel Institute of Technology, Haifa 3200003, Israel
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25
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Fu Y, Wu Z, Zhan S, Yang J, Gardi G, Kishore V, Malgaretti P, Wang W. Entropy by Neighbor Distance as a New Measure for Characterizing Spatiotemporal Orders in Microscopic Collective Systems. MICROMACHINES 2023; 14:1503. [PMID: 37630039 PMCID: PMC10456758 DOI: 10.3390/mi14081503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Revised: 07/21/2023] [Accepted: 07/24/2023] [Indexed: 08/27/2023]
Abstract
Collective systems self-organize to form globally ordered spatiotemporal patterns. Finding appropriate measures to characterize the order in these patterns will contribute to our understanding of the principles of self-organization in all collective systems. Here we examine a new measure based on the entropy of the neighbor distance distributions in the characterization of collective patterns. We study three types of systems: a simulated self-propelled boid system, two active colloidal systems, and one centimeter-scale robotic swarm system. In all these systems, the new measure proves sensitive in revealing active phase transitions and in distinguishing steady states. We envision that the entropy by neighbor distance could be useful for characterizing biological swarms such as bird flocks and for designing robotic swarms.
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Affiliation(s)
- Yulei Fu
- University of Michigan—Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Zongyuan Wu
- University of Michigan—Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China
- Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213, USA
| | - Sirui Zhan
- University of Michigan—Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China
- College of Engineering, University of Michigan, Ann Arbor, MI 48109, USA
| | - Jiacheng Yang
- The Academy for Engineering and Technology, Fudan University, Shanghai 200433, China
| | - Gaurav Gardi
- Physical Intelligence Department, Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany
- Department of Physics, University of Stuttgart, 70569 Stuttgart, Germany
| | - Vimal Kishore
- Department of Physics, Banaras Hindu University, Varanasi 221005, India
| | - Paolo Malgaretti
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Wendong Wang
- University of Michigan—Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China
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26
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G-Guzmán E, Perl YS, Vohryzek J, Escrichs A, Manasova D, Türker B, Tagliazucchi E, Kringelbach M, Sitt JD, Deco G. The lack of temporal brain dynamics asymmetry as a signature of impaired consciousness states. Interface Focus 2023; 13:20220086. [PMID: 37065259 PMCID: PMC10102727 DOI: 10.1098/rsfs.2022.0086] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Accepted: 03/17/2023] [Indexed: 04/18/2023] Open
Abstract
Life is a constant battle against equilibrium. From the cellular level to the macroscopic scale, living organisms as dissipative systems require the violation of their detailed balance, i.e. metabolic enzymatic reactions, in order to survive. We present a framework based on temporal asymmetry as a measure of non-equilibrium. By means of statistical physics, it was discovered that temporal asymmetries establish an arrow of time useful for assessing the reversibility in human brain time series. Previous studies in human and non-human primates have shown that decreased consciousness states such as sleep and anaesthesia result in brain dynamics closer to the equilibrium. Furthermore, there is growing interest in the analysis of brain symmetry based on neuroimaging recordings and since it is a non-invasive technique, it can be extended to different brain imaging modalities and applied at different temporo-spatial scales. In the present study, we provide a detailed description of our methodological approach, paying special attention to the theories that motivated this work. We test, for the first time, the reversibility analysis in human functional magnetic resonance imaging data in patients suffering from disorder of consciousness. We verify that the tendency of a decrease in the asymmetry of the brain signal together with the decrease in non-stationarity are key characteristics of impaired consciousness states. We expect that this work will open the way for assessing biomarkers for patients' improvement and classification, as well as motivating further research on the mechanistic understanding underlying states of impaired consciousness.
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Affiliation(s)
- Elvira G-Guzmán
- Department of Information and Communication Technologies, Centre for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Barcelona, Spain
| | - Yonatan Sanz Perl
- Department of Information and Communication Technologies, Centre for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Barcelona, Spain
- Sorbonne Université, Institut du Cerveau - Paris Brain Institute - ICM, Inserm Physiological Investigation of Clinically Normal and Impaired Cognition Team, CNRS, 75013, Paris, France
| | - Jakub Vohryzek
- Department of Information and Communication Technologies, Centre for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Barcelona, Spain
- Centre for Eudaimonia and Human Flourishing, Linacre College, University of Oxford, Oxford, UK
| | - Anira Escrichs
- Department of Information and Communication Technologies, Centre for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Barcelona, Spain
| | - Dragana Manasova
- Sorbonne Université, Institut du Cerveau - Paris Brain Institute - ICM, Inserm Physiological Investigation of Clinically Normal and Impaired Cognition Team, CNRS, 75013, Paris, France
- Université Paris Cité, Paris, France
| | - Başak Türker
- Sorbonne Université, Institut du Cerveau - Paris Brain Institute - ICM, Inserm Physiological Investigation of Clinically Normal and Impaired Cognition Team, CNRS, 75013, Paris, France
| | - Enzo Tagliazucchi
- Buenos Aires Physics Institute and Physics Department, University of Buenos Aires, Buenos Aires, Argentina
- Latin American Brain Health (BrainLat), Universidad Adolfo Ibáñez, Santiago, Chile
| | - Morten Kringelbach
- Centre for Eudaimonia and Human Flourishing, Linacre College, University of Oxford, Oxford, UK
- Department of Clinical Medicine, Center for Music in the Brain, Aarhus University, Jutland, Denmark
| | - Jacobo D. Sitt
- Sorbonne Université, Institut du Cerveau - Paris Brain Institute - ICM, Inserm Physiological Investigation of Clinically Normal and Impaired Cognition Team, CNRS, 75013, Paris, France
| | - Gustavo Deco
- Department of Information and Communication Technologies, Centre for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Barcelona, Spain
- Institució Catalana de la Recerca i Estudis Avançats (ICREA), Barcelona, Catalonia, Spain
- Department of Neuropsychology, Max Planck Institute for human Cognitive and Brain Sciences, Leipzig, Germany
- School of Psychological Sciences, Monash University, Melbourne, Australia
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27
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Daneshpour H, van den Bersselaar P, Chao CH, Fazzio TG, Youk H. Macroscopic quorum sensing sustains differentiating embryonic stem cells. Nat Chem Biol 2023; 19:596-606. [PMID: 36635563 PMCID: PMC10154202 DOI: 10.1038/s41589-022-01225-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2022] [Accepted: 11/14/2022] [Indexed: 01/14/2023]
Abstract
Cells can secrete molecules that help each other's replication. In cell cultures, chemical signals might diffuse only within a cell colony or between colonies. A chemical signal's interaction length-how far apart interacting cells are-is often assumed to be some value without rigorous justifications because molecules' invisible paths and complex multicellular geometries pose challenges. Here we present an approach, combining mathematical models and experiments, for determining a chemical signal's interaction length. With murine embryonic stem (ES) cells as a testbed, we found that differentiating ES cells secrete FGF4, among others, to communicate over many millimeters in cell culture dishes and, thereby, form a spatially extended, macroscopic entity that grows only if its centimeter-scale population density is above a threshold value. With this 'macroscopic quorum sensing', an isolated macroscopic, but not isolated microscopic, colony can survive differentiation. Our integrated approach can determine chemical signals' interaction lengths in generic multicellular communities.
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Affiliation(s)
- Hirad Daneshpour
- Kavli Institute of Nanoscience, Delft, The Netherlands
- Department of Systems Biology, University of Massachusetts Chan Medical School, Worcester, MA, USA
| | - Pim van den Bersselaar
- Kavli Institute of Nanoscience, Delft, The Netherlands
- Department of Systems Biology, University of Massachusetts Chan Medical School, Worcester, MA, USA
| | - Chun-Hao Chao
- Department of Molecular, Cell, and Cancer Biology, University of Massachusetts Chan Medical School, Worcester, MA, USA
| | - Thomas G Fazzio
- Department of Molecular, Cell, and Cancer Biology, University of Massachusetts Chan Medical School, Worcester, MA, USA
| | - Hyun Youk
- Department of Systems Biology, University of Massachusetts Chan Medical School, Worcester, MA, USA.
- CIFAR Azrieli Global Scholars Program, CIFAR, Toronto, ON, Canada.
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28
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O'Byrne J. Nonequilibrium currents in stochastic field theories: A geometric insight. Phys Rev E 2023; 107:054105. [PMID: 37329107 DOI: 10.1103/physreve.107.054105] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2023] [Accepted: 04/03/2023] [Indexed: 06/18/2023]
Abstract
We introduce a formalism to study nonequilibrium steady-state probability currents in stochastic field theories. We show that generalizing the exterior derivative to functional spaces allows identification of the subspaces in which the system undergoes local rotations. In turn, this allows prediction of the counterparts in the real, physical space of these abstract probability currents. The results are presented for the case of the Active Model B undergoing motility-induced phase separation, which is known to be out of equilibrium but whose steady-state currents have not yet been observed, as well as for the Kardar-Parisi-Zhang equation. We locate and measure these currents and show that they manifest in real space as propagating modes localized in regions with nonvanishing gradients of the fields.
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Affiliation(s)
- J O'Byrne
- Université Paris-Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France and DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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29
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Mayer DB, Franosch T, Mast C, Braun D. Thermophoresis beyond Local Thermodynamic Equilibrium. PHYSICAL REVIEW LETTERS 2023; 130:168202. [PMID: 37154655 DOI: 10.1103/physrevlett.130.168202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Accepted: 03/08/2023] [Indexed: 05/10/2023]
Abstract
We measure the thermophoresis of polysterene beads over a wide range of temperature gradients and find a pronounced nonlinear phoretic characteristic. The transition to the nonlinear behavior is marked by a drastic slowing down of thermophoretic motion and is characterized by a Péclet number of order unity as corroborated for different particle sizes and salt concentrations. The data follow a single master curve covering the entire nonlinear regime for all system parameters upon proper rescaling of the temperature gradients with the Péclet number. For low thermal gradients, the thermal drift velocity follows a theoretical linear model relying on the local-equilibrium assumption, while linear theoretical approaches based on hydrodynamic stresses, ignoring fluctuations, predict significantly slower thermophoretic motion for steeper thermal gradients. Our findings suggest that thermophoresis is fluctuation dominated for small gradients and crosses over to a drift-dominated regime for larger Péclet numbers in striking contrast to electrophoresis.
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Affiliation(s)
- Daniel B Mayer
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Christof Mast
- Systems Biophysics, Physics Department, Nanosystems Initiative Munich and Center for NanoScience, Ludwig-Maximilians-Universität München, Amalienstrasse 54, D-80799 München, Germany
| | - Dieter Braun
- Systems Biophysics, Physics Department, Nanosystems Initiative Munich and Center for NanoScience, Ludwig-Maximilians-Universität München, Amalienstrasse 54, D-80799 München, Germany
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30
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Foster PJ, Bae J, Lemma B, Zheng J, Ireland W, Chandrakar P, Boros R, Dogic Z, Needleman DJ, Vlassak JJ. Dissipation and energy propagation across scales in an active cytoskeletal material. Proc Natl Acad Sci U S A 2023; 120:e2207662120. [PMID: 37000847 PMCID: PMC10083585 DOI: 10.1073/pnas.2207662120] [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: 05/09/2022] [Accepted: 02/22/2023] [Indexed: 04/03/2023] Open
Abstract
Living systems are intrinsically nonequilibrium: They use metabolically derived chemical energy to power their emergent dynamics and self-organization. A crucial driver of these dynamics is the cellular cytoskeleton, a defining example of an active material where the energy injected by molecular motors cascades across length scales, allowing the material to break the constraints of thermodynamic equilibrium and display emergent nonequilibrium dynamics only possible due to the constant influx of energy. Notwithstanding recent experimental advances in the use of local probes to quantify entropy production and the breaking of detailed balance, little is known about the energetics of active materials or how energy propagates from the molecular to emergent length scales. Here, we use a recently developed picowatt calorimeter to experimentally measure the energetics of an active microtubule gel that displays emergent large-scale flows. We find that only approximately one-billionth of the system's total energy consumption contributes to these emergent flows. We develop a chemical kinetics model that quantitatively captures how the system's total thermal dissipation varies with ATP and microtubule concentrations but that breaks down at high motor concentration, signaling an interference between motors. Finally, we estimate how energy losses accumulate across scales. Taken together, these results highlight energetic efficiency as a key consideration for the engineering of active materials and are a powerful step toward developing a nonequilibrium thermodynamics of living systems.
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Affiliation(s)
- Peter J. Foster
- Physics of Living Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, MA02139
- Department of Physics, Brandeis University, Waltham, MA02454
| | - Jinhye Bae
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA02138
- Department of NanoEngineering, University of California San Diego, La Jolla, CA92093
| | - Bezia Lemma
- Department of Physics, Brandeis University, Waltham, MA02454
- Department of Physics, Harvard University, Cambridge, MA02138
- Department of Physics, University of California, Santa Barbara, CA93106
| | - Juanjuan Zheng
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA02138
| | - William Ireland
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA02138
| | - Pooja Chandrakar
- Department of Physics, Brandeis University, Waltham, MA02454
- Department of Physics, University of California, Santa Barbara, CA93106
| | - Rémi Boros
- Department of Physics, University of California, Santa Barbara, CA93106
| | - Zvonimir Dogic
- Department of Physics, Brandeis University, Waltham, MA02454
- Department of Physics, University of California, Santa Barbara, CA93106
| | - Daniel J. Needleman
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA02138
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA02138
- Center for Computational Biology, Flatiron Institute, New York, NY10010
| | - Joost J. Vlassak
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA02138
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31
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Yin M, Chen Y, Liu X, Tian S, Zhao L, Bai Y, Wang H, Lin J, Jiang D, Lei Z, Meng F, Tian D, Luo L. Targeted Computed Tomography Visualization and Healing of Inflammatory Bowel Disease by Orally Delivered Bacterial-Flagella-Inspired Polydiiododiacetylene Nanofibers. ACS NANO 2023; 17:3873-3888. [PMID: 36791326 DOI: 10.1021/acsnano.2c12154] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Accurate diagnosis and timely therapeutic intervention of inflammatory bowel disease (IBD) is essential in preventing the progression of the disease, although it still represents an insurmountable challenge. Here we report the design of bacterial-flagella-inspired polydiiododiacetylene (PIDA) nanofibers and its performance in targeted computed tomography (CT) imaging and on-demand therapeutic intervention of IBD. With a morphology mimicking bacterial flagella, PIDA nanofibers attach on the mucus layer of the gastrointestinal (GI) tract after oral administration, evenly distributing on the GI surface to portray the GI lining under CT scan within 2 h. PIDA can retain for a longer time in the damaged mucosa at the inflamed lesions than in normal GI tissues to enable the targeted CT visualization of IBD. PIDA also scavenges reactive oxygen species and ameliorates gut dysbiosis attributed to its iodine-substituted polydiacetylene structure, so that the enriched PIDA nanofibers at the targeted IBD lesions can alleviate the inflammation while maintaining the gut microbiota homeostasis, thus promoting the rebalance of GI microenvironment and the mucosal healing.
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Affiliation(s)
- Mingming Yin
- National Engineering Research Center for Nanomedicine, College of Life Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Yu Chen
- Department of Gastroenterology, Tongji Hospital of Tongji Medical College, Huazhong University of Science and Technology, Wuhan 430030, China
| | - Xiaoming Liu
- Department of Radiology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan 430022, China
- Hubei Province Key Laboratory of Molecular Imaging, Wuhan 430022, China
| | - Sidan Tian
- National Engineering Research Center for Nanomedicine, College of Life Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Liyuan Zhao
- National Engineering Research Center for Nanomedicine, College of Life Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Yaowei Bai
- Department of Radiology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan 430022, China
| | - Hao Wang
- Department of Nuclear Medicine, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan 430022, China
| | - Jinfeng Lin
- National Engineering Research Center for Nanomedicine, College of Life Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Dawei Jiang
- Hubei Province Key Laboratory of Molecular Imaging, Wuhan 430022, China
- Department of Nuclear Medicine, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan 430022, China
| | - Ziqiao Lei
- Department of Radiology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan 430022, China
- Hubei Province Key Laboratory of Molecular Imaging, Wuhan 430022, China
| | - Fanling Meng
- National Engineering Research Center for Nanomedicine, College of Life Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
- Key Laboratory of Molecular Biophysics of the Ministry of Education, College of Life Science and Technology, Huazhong University of Science and Technology, 430074 Wuhan, China
- Hubei Key Laboratory of Bioinorganic Chemistry and Materia Medica, School of Chemistry and Chemical Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
| | - De'an Tian
- Department of Gastroenterology, Tongji Hospital of Tongji Medical College, Huazhong University of Science and Technology, Wuhan 430030, China
| | - Liang Luo
- National Engineering Research Center for Nanomedicine, College of Life Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
- Key Laboratory of Molecular Biophysics of the Ministry of Education, College of Life Science and Technology, Huazhong University of Science and Technology, 430074 Wuhan, China
- Hubei Key Laboratory of Bioinorganic Chemistry and Materia Medica, School of Chemistry and Chemical Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
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32
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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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33
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Tewarie PKB, Beernink TMJ, Eertman-Meyer CJ, Cornet AD, Beishuizen A, van Putten MJAM, Tjepkema-Cloostermans MC. Early EEG monitoring predicts clinical outcome in patients with moderate to severe traumatic brain injury. Neuroimage Clin 2023; 37:103350. [PMID: 36801601 PMCID: PMC9984683 DOI: 10.1016/j.nicl.2023.103350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2022] [Revised: 01/23/2023] [Accepted: 02/11/2023] [Indexed: 02/16/2023]
Abstract
There is a need for reliable predictors in patients with moderate to severe traumatic brain injury to assist clinical decision making. We assess the ability of early continuous EEG monitoring at the intensive care unit (ICU) in patients with traumatic brain injury (TBI) to predict long term clinical outcome and evaluate its complementary value to current clinical standards. We performed continuous EEG measurements in patients with moderate to severe TBI during the first week of ICU admission. We assessed the Extended Glasgow Outcome Scale (GOSE) at 12 months, dichotomized into poor (GOSE 1-3) and good (GOSE 4-8) outcome. We extracted EEG spectral features, brain symmetry index, coherence, aperiodic exponent of the power spectrum, long range temporal correlations, and broken detailed balance. A random forest classifier using feature selection was trained to predict poor clinical outcome based on EEG features at 12, 24, 48, 72 and 96 h after trauma. We compared our predictor with the IMPACT score, the best available predictor, based on clinical, radiological and laboratory findings. In addition we created a combined model using EEG as well as the clinical, radiological and laboratory findings. We included hundred-seven patients. The best prediction model using EEG parameters was found at 72 h after trauma with an AUC of 0.82 (0.69-0.92), specificity of 0.83 (0.67-0.99) and sensitivity of 0.74 (0.63-0.93). The IMPACT score predicted poor outcome with an AUC of 0.81 (0.62-0.93), sensitivity of 0.86 (0.74-0.96) and specificity of 0.70 (0.43-0.83). A model using EEG and clinical, radiological and laboratory parameters resulted in a better prediction of poor outcome (p < 0.001) with an AUC of 0.89 (0.72-0.99), sensitivity of 0.83 (0.62-0.93) and specificity of 0.85 (0.75-1.00). EEG features have potential use for predicting clinical outcome and decision making in patients with moderate to severe TBI and provide complementary information to current clinical standards.
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Affiliation(s)
- Prejaas K B Tewarie
- Clinical Neurophysiology Group, University of Twente, Enschede, the Netherlands; Department of Neurology and Clinical Neurophysiology, Medisch Spectrum Twente, Enschede, the Netherlands; Department of Neurology, Amsterdam UMC/VUmc, Amsterdam, the Netherlands.
| | - Tim M J Beernink
- Department of Neurology and Clinical Neurophysiology, Medisch Spectrum Twente, Enschede, the Netherlands
| | - Carin J Eertman-Meyer
- Department of Neurology and Clinical Neurophysiology, Medisch Spectrum Twente, Enschede, the Netherlands
| | - Alexander D Cornet
- Intensive Care Center, Medisch Spectrum Twente, Enschede, the Netherlands
| | | | - Michel J A M van Putten
- Clinical Neurophysiology Group, University of Twente, Enschede, the Netherlands; Department of Neurology and Clinical Neurophysiology, Medisch Spectrum Twente, Enschede, the Netherlands
| | - Marleen C Tjepkema-Cloostermans
- Clinical Neurophysiology Group, University of Twente, Enschede, the Netherlands; Department of Neurology and Clinical Neurophysiology, Medisch Spectrum Twente, Enschede, the Netherlands
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34
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Loose M, Auer A, Brognara G, Budiman HR, Kowalski L, Matijević I. In vitro
reconstitution of small
GTPase
regulation. FEBS Lett 2022; 597:762-777. [PMID: 36448231 DOI: 10.1002/1873-3468.14540] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Revised: 10/27/2022] [Accepted: 11/07/2022] [Indexed: 12/05/2022]
Abstract
Small GTPases play essential roles in the organization of eukaryotic cells. In recent years, it has become clear that their intracellular functions result from intricate biochemical networks of the GTPase and their regulators that dynamically bind to a membrane surface. Due to the inherent complexities of their interactions, however, revealing the underlying mechanisms of action is often difficult to achieve from in vivo studies. This review summarizes in vitro reconstitution approaches developed to obtain a better mechanistic understanding of how small GTPase activities are regulated in space and time.
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Affiliation(s)
- Martin Loose
- Institute of Science and Technology Austria (ISTA) Klosterneuburg Austria
| | - Albert Auer
- Institute of Science and Technology Austria (ISTA) Klosterneuburg Austria
| | - Gabriel Brognara
- Institute of Science and Technology Austria (ISTA) Klosterneuburg Austria
| | | | - Lukasz Kowalski
- Institute of Science and Technology Austria (ISTA) Klosterneuburg Austria
| | - Ivana Matijević
- Institute of Science and Technology Austria (ISTA) Klosterneuburg Austria
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35
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Hack P, Gottwald S, Braun DA. Jarzyski's Equality and Crooks' Fluctuation Theorem for General Markov Chains with Application to Decision-Making Systems. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1731. [PMID: 36554136 PMCID: PMC9777588 DOI: 10.3390/e24121731] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Revised: 11/19/2022] [Accepted: 11/24/2022] [Indexed: 06/17/2023]
Abstract
We define common thermodynamic concepts purely within the framework of general Markov chains and derive Jarzynski's equality and Crooks' fluctuation theorem in this setup. In particular, we regard the discrete-time case, which leads to an asymmetry in the definition of work that appears in the usual formulation of Crooks' fluctuation theorem. We show how this asymmetry can be avoided with an additional condition regarding the energy protocol. The general formulation in terms of Markov chains allows transferring the results to other application areas outside of physics. Here, we discuss how this framework can be applied in the context of decision-making. This involves the definition of the relevant quantities, the assumptions that need to be made for the different fluctuation theorems to hold, as well as the consideration of discrete trajectories instead of the continuous trajectories, which are relevant in physics.
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36
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Ro S, Guo B, Shih A, Phan TV, Austin RH, Levine D, Chaikin PM, Martiniani S. Model-Free Measurement of Local Entropy Production and Extractable Work in Active Matter. PHYSICAL REVIEW LETTERS 2022; 129:220601. [PMID: 36493452 DOI: 10.1103/physrevlett.129.220601] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2022] [Accepted: 09/09/2022] [Indexed: 06/17/2023]
Abstract
Time-reversal symmetry breaking and entropy production are universal features of nonequilibrium phenomena. Despite its importance in the physics of active and living systems, the entropy production of systems with many degrees of freedom has remained of little practical significance because the high dimensionality of their state space makes it difficult to measure. Here we introduce a local measure of entropy production and a numerical protocol to estimate it. We establish a connection between the entropy production and extractability of work in a given region of the system and show how this quantity depends crucially on the degrees of freedom being tracked. We validate our approach in theory, simulation, and experiments by considering systems of active Brownian particles undergoing motility-induced phase separation, as well as active Brownian particles and E.coli in a rectifying device in which the time-reversal asymmetry of the particle dynamics couples to spatial asymmetry to reveal its effects on a macroscopic scale.
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Affiliation(s)
- Sunghan Ro
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Buming Guo
- Center for Soft Matter Research, Department of Physics, New York University, New York 10003, USA
| | - Aaron Shih
- Center for Soft Matter Research, Department of Physics, New York University, New York 10003, USA
- Courant Institute of Mathematical Sciences, New York University, New York 10003, USA
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Trung V Phan
- Department of Physics, Princeton University, Princeton 08544, New Jersey, USA
| | - Robert H Austin
- Department of Physics, Princeton University, Princeton 08544, New Jersey, USA
| | - Dov Levine
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Paul M Chaikin
- Center for Soft Matter Research, Department of Physics, New York University, New York 10003, USA
| | - Stefano Martiniani
- Center for Soft Matter Research, Department of Physics, New York University, New York 10003, USA
- Courant Institute of Mathematical Sciences, New York University, New York 10003, USA
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
- Simons Center for Computational Physical Chemistry, Department of Chemistry, New York University, New York 10003, USA
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37
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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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38
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Dieball C, Godec A. Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space. PHYSICAL REVIEW LETTERS 2022; 129:140601. [PMID: 36240401 DOI: 10.1103/physrevlett.129.140601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2021] [Revised: 07/19/2022] [Accepted: 07/28/2022] [Indexed: 06/16/2023]
Abstract
We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of Markovian diffusion in equilibrium or nonequilibrium steady states on all timescales. We unravel a deep connection between current fluctuations and generalized time-reversal symmetry, providing new insight into time-averaged observables. We highlight the essential role of coarse graining in space from mathematical, thermodynamical, and experimental points of view. Spatial coarse graining is required to uncover salient features of currents that break detailed balance, and a thermodynamically "optimal" coarse graining ensures the most precise inference of dissipation. Defined without coarse graining, the fluctuations of empirical density and current are proven to diverge on all timescales in dimensions higher than one, which has far-reaching consequences for the central-limit regime in continuous space. We apply the results to examples of irreversible diffusion. Our findings provide new intuition about time-averaged observables and allow for a more efficient analysis of single-molecule experiments.
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Affiliation(s)
- Cai Dieball
- 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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39
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Cho JH, Li ZA, Zhu L, Muegge BD, Roseman HF, Lee EY, Utterback T, Woodhams LG, Bayly PV, Hughes JW. Islet primary cilia motility controls insulin secretion. SCIENCE ADVANCES 2022; 8:eabq8486. [PMID: 36149960 PMCID: PMC9506710 DOI: 10.1126/sciadv.abq8486] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/04/2022] [Accepted: 07/13/2022] [Indexed: 06/16/2023]
Abstract
Primary cilia are specialized cell-surface organelles that mediate sensory perception and, in contrast to motile cilia and flagella, are thought to lack motility function. Here, we show that primary cilia in human and mouse pancreatic islets exhibit movement that is required for glucose-dependent insulin secretion. Islet primary cilia contain motor proteins conserved from those found in classic motile cilia, and their three-dimensional motion is dynein-driven and dependent on adenosine 5'-triphosphate and glucose metabolism. Inhibition of cilia motion blocks beta cell calcium influx and insulin secretion. Human beta cells have enriched ciliary gene expression, and motile cilia genes are altered in type 2 diabetes. Our findings redefine primary cilia as dynamic structures having both sensory and motile function and establish that pancreatic islet cilia movement plays a regulatory role in insulin secretion.
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Affiliation(s)
- Jung Hoon Cho
- Department of Medicine, Washington University School of Medicine, 660 South Euclid Ave, St. Louis, MO, USA
| | - Zipeng A. Li
- Department of Medicine, Washington University School of Medicine, 660 South Euclid Ave, St. Louis, MO, USA
| | - Lifei Zhu
- Department of Medicine, Washington University School of Medicine, 660 South Euclid Ave, St. Louis, MO, USA
| | - Brian D. Muegge
- Department of Medicine, Washington University School of Medicine, 660 South Euclid Ave, St. Louis, MO, USA
- Department of Medicine, VA Medical Center, 915 North Grand Blvd, St. Louis, MO, USA
| | - Henry F. Roseman
- Department of Medicine, Washington University School of Medicine, 660 South Euclid Ave, St. Louis, MO, USA
| | - Eun Young Lee
- Department of Medicine, Washington University School of Medicine, 660 South Euclid Ave, St. Louis, MO, USA
- Division of Endocrinology and Metabolism, Department of Internal Medicine, Seoul St. Mary’s Hospital, The Catholic University of Korea, Seoul, South Korea
| | - Toby Utterback
- Department of Mechanical Engineering and Materials Science, Washington University McKelvey School of Engineering, 1 Brookings Drive, St. Louis, MO, USA
| | - Louis G. Woodhams
- Department of Mechanical Engineering and Materials Science, Washington University McKelvey School of Engineering, 1 Brookings Drive, St. Louis, MO, USA
| | - Philip V. Bayly
- Department of Mechanical Engineering and Materials Science, Washington University McKelvey School of Engineering, 1 Brookings Drive, St. Louis, MO, USA
| | - Jing W. Hughes
- Department of Medicine, Washington University School of Medicine, 660 South Euclid Ave, St. Louis, MO, USA
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40
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Larson BT, Garbus J, Pollack JB, Marshall WF. A unicellular walker controlled by a microtubule-based finite-state machine. Curr Biol 2022; 32:3745-3757.e7. [PMID: 35963241 PMCID: PMC9474717 DOI: 10.1016/j.cub.2022.07.034] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Revised: 05/20/2022] [Accepted: 07/14/2022] [Indexed: 11/21/2022]
Abstract
Cells are complex biochemical systems whose behaviors emerge from interactions among myriad molecular components. Computation is often invoked as a general framework for navigating this cellular complexity. However, it is unclear how cells might embody computational processes such that the theories of computation, including finite-state machine models, could be productively applied. Here, we demonstrate finite-state-machine-like processing embodied in cells using the walking behavior of Euplotes eurystomus, a ciliate that walks across surfaces using fourteen motile appendages (cirri). We found that cellular walking entails regulated transitions among a discrete set of gait states. The set of observed transitions decomposes into a small group of high-probability, temporally irreversible transitions and a large group of low-probability, time-symmetric transitions, thus revealing stereotypy in the sequential patterns of state transitions. Simulations and experiments suggest that the sequential logic of the gait is functionally important. Taken together, these findings implicate a finite-state-machine-like process. Cirri are connected by microtubule bundles (fibers), and we found that the dynamics of cirri involved in different state transitions are associated with the structure of the fiber system. Perturbative experiments revealed that the fibers mediate gait coordination, suggesting a mechanical basis of gait control.
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Affiliation(s)
- Ben T Larson
- Department of Biochemistry and Biophysics, University of California, San Francisco, San Francisco, CA 94158, USA.
| | - Jack Garbus
- Computer Science Department, Brandeis University, Waltham, MA 02453, USA
| | - Jordan B Pollack
- Computer Science Department, Brandeis University, Waltham, MA 02453, USA
| | - Wallace F Marshall
- Department of Biochemistry and Biophysics, University of California, San Francisco, San Francisco, CA 94158, USA.
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41
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Lynn CW, Holmes CM, Bialek W, Schwab DJ. Decomposing the Local Arrow of Time in Interacting Systems. PHYSICAL REVIEW LETTERS 2022; 129:118101. [PMID: 36154397 PMCID: PMC9751844 DOI: 10.1103/physrevlett.129.118101] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2022] [Revised: 06/03/2022] [Accepted: 06/24/2022] [Indexed: 05/30/2023]
Abstract
We show that the evidence for a local arrow of time, which is equivalent to the entropy production in thermodynamic systems, can be decomposed. In a system with many degrees of freedom, there is a term that arises from the irreversible dynamics of the individual variables, and then a series of non-negative terms contributed by correlations among pairs, triplets, and higher-order combinations of variables. We illustrate this decomposition on simple models of noisy logical computations, and then apply it to the analysis of patterns of neural activity in the retina as it responds to complex dynamic visual scenes. We find that neural activity breaks detailed balance even when the visual inputs do not, and that this irreversibility arises primarily from interactions between pairs of neurons.
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Affiliation(s)
- Christopher W Lynn
- Initiative for the Theoretical Sciences, The Graduate Center, City University of New York, New York, New York 10016, USA
- Joseph Henry Laboratories of Physics and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA
| | - Caroline M Holmes
- Joseph Henry Laboratories of Physics and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA
| | - William Bialek
- Initiative for the Theoretical Sciences, The Graduate Center, City University of New York, New York, New York 10016, USA
- Joseph Henry Laboratories of Physics and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA
| | - David J Schwab
- Initiative for the Theoretical Sciences, The Graduate Center, City University of New York, New York, New York 10016, USA
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42
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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] [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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43
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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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44
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Ferretti F, Grosse-Holz S, Holmes C, Shivers JL, Giardina I, Mora T, Walczak AM. Signatures of irreversibility in microscopic models of flocking. Phys Rev E 2022; 106:034608. [PMID: 36266796 DOI: 10.1103/physreve.106.034608] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2022] [Accepted: 08/17/2022] [Indexed: 06/16/2023]
Abstract
Flocking in d=2 is a genuine nonequilibrium phenomenon for which irreversibility is an essential ingredient. We study a class of minimal flocking models whose only source of irreversibility is self-propulsion and use the entropy production rate (EPR) to quantify the departure from equilibrium across their phase diagrams. The EPR is maximal in the vicinity of the order-disorder transition, where reshuffling of the interaction network is fast. We show that signatures of irreversibility come in the form of asymmetries in the steady-state distribution of the flock's microstates. These asymmetries occur as consequences of the time-reversal symmetry breaking in the considered self-propelled systems, independently of the interaction details. In the case of metric pairwise forces, they reduce to local asymmetries in the distribution of pairs of particles. This study suggests a possible use of pair asymmetries both to quantify the departure from equilibrium and to learn relevant information about aligning interaction potentials from data.
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Affiliation(s)
- Federica Ferretti
- Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy
- Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy
| | - Simon Grosse-Holz
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Institut Curie, Paris 75005, France
| | - Caroline Holmes
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Jordan L Shivers
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77030, USA
| | - Irene Giardina
- Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy
- Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy
- INFN, Unità di Roma 1, 00185 Rome, Italy
| | - Thierry Mora
- Laboratoire de Physique de l'École Normale Supérieure (PSL University), CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
| | - Aleksandra M Walczak
- Laboratoire de Physique de l'École Normale Supérieure (PSL University), CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
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45
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Lynn CW, Holmes CM, Bialek W, Schwab DJ. Emergence of local irreversibility in complex interacting systems. Phys Rev E 2022; 106:034102. [PMID: 36266789 PMCID: PMC9751845 DOI: 10.1103/physreve.106.034102] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2022] [Accepted: 06/24/2022] [Indexed: 04/28/2023]
Abstract
Living systems are fundamentally irreversible, breaking detailed balance and establishing an arrow of time. But how does the evident arrow of time for a whole system arise from the interactions among its multiple elements? We show that the local evidence for the arrow of time, which is the entropy production for thermodynamic systems, can be decomposed. First, it can be split into two components: an independent term reflecting the dynamics of individual elements and an interaction term driven by the dependencies among elements. Adapting tools from nonequilibrium physics, we further decompose the interaction term into contributions from pairs of elements, triplets, and higher-order terms. We illustrate our methods on models of cellular sensing and logical computations, as well as on patterns of neural activity in the retina as it responds to visual inputs. We find that neural activity can define the arrow of time even when the visual inputs do not, and that the dominant contribution to this breaking of detailed balance comes from interactions among pairs of neurons.
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Affiliation(s)
- Christopher W Lynn
- Initiative for the Theoretical Sciences, Graduate Center, City University of New York, New York, New York 10016, USA
- Joseph Henry Laboratories of Physics and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA
| | - Caroline M Holmes
- Joseph Henry Laboratories of Physics and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA
| | - William Bialek
- Initiative for the Theoretical Sciences, Graduate Center, City University of New York, New York, New York 10016, USA
- Joseph Henry Laboratories of Physics and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA
| | - David J Schwab
- Initiative for the Theoretical Sciences, Graduate Center, City University of New York, New York, New York 10016, USA
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46
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Teitsworth S, Neu JC. Stochastic line integrals and stream functions as metrics of irreversibility and heat transfer. Phys Rev E 2022; 106:024124. [PMID: 36109900 DOI: 10.1103/physreve.106.024124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Accepted: 08/09/2022] [Indexed: 06/15/2023]
Abstract
Stochastic line integrals are presented as a useful metric for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled electrical circuits. Here we provide a general framework for understanding properties of stochastic line integrals and clarify their implementation for experiments and simulations. For two-dimensional systems, stochastic line integrals can be expressed in terms of a stream function, the sign of which determines the orientation of nonequilibrium steady-state probability currents. Theoretical results are supported by numerical studies of an overdamped two-dimensional mass-spring system driven out of equilibrium. Additionally, the stream function permits analytical understanding of the scaling dependence of stochastic area growth rate on key parameters such as the noise strength for both linear and nonlinear springs.
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Affiliation(s)
- Stephen Teitsworth
- Department of Physics, Duke University, Box 90305, Durham, North Carolina 27708-0305, USA
| | - John C Neu
- Department of Mathematics, University of California, Berkeley, Berkeley, California 94720-3840, USA
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47
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Jia W, Duddu AS, Jolly MK, Levine H. Lack of Correlation between Landscape Geometry and Transition Rates. J Phys Chem B 2022; 126:5613-5618. [PMID: 35876849 DOI: 10.1021/acs.jpcb.2c02837] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
Biological cells can exist in a variety of distinct phenotypes, determined by the steady-state solutions of genetic networks governing their cell fate. A popular way of representing these states relies on the creation of landscape related to the relative occupation of these states. It is often assumed that this landscape offers direct information regarding the state-to-state transition rates, suggesting that these are related to barrier heights separating landscape minima. Here, we study a toggle triad network exhibiting multistability and directly demonstrate the lack of any direct correlation between properties of the landscape and corresponding transition rates.
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Affiliation(s)
- Wen Jia
- Center for Theoretical Biological Physics, Northeastern University, Boston, Massachusetts 02115, United States.,Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Atchuta Srinivas Duddu
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore 560012, India
| | - Mohit Kumar Jolly
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore 560012, India
| | - Herbert Levine
- Center for Theoretical Biological Physics, Northeastern University, Boston, Massachusetts 02115, United States.,Department of Bioengineering, Northeastern University, Boston, Massachusetts 02115, United States.,Department of Physics, Northeastern University, Boston, Massachusetts 02115, United States
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48
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Kumar N, Zhang R, Redford SA, de Pablo JJ, Gardel ML. Catapulting of topological defects through elasticity bands in active nematics. SOFT MATTER 2022; 18:5271-5281. [PMID: 35789364 DOI: 10.1039/d2sm00414c] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Active materials are those in which individual, uncoordinated local stresses drive the material out of equilibrium on a global scale. Examples of such assemblies can be seen across scales from schools of fish to the cellular cytoskeleton and underpin many important biological processes. Synthetic experiments that recapitulate the essential features of such active systems have been the object of study for decades as their simple rules allow us to elucidate the physical underpinnings of collective motion. One system of particular interest has been active nematic liquid crystals (LCs). Because of their well understood passive physics, LCs provide a rich platform to interrogate the effects of active stress. The flows and steady state structures that emerge in an active LCs have been understood to result from a competition between nematic elasticity and the local activity. However most investigations of such phenomena consider only the magnitude of the elastic resistance and not its peculiarities. Here we investigate a nematic liquid crystal and selectively change the ratio of the material's splay and bend elasticities. We show that increases in the nematic's bend elasticity specifically drives the material into an exotic steady state where elongated regions of acute bend distortion or "elasticity bands" dominate the structure and dynamics. We show that these bands strongly influence defect dynamics, including the rapid motion or "catapulting" along the disintegration of one of these bands thus converting bend distortion into defect transport. Thus, we report a novel dynamical state resultant from the competition between nematic elasticity and active stress.
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Affiliation(s)
- Nitin Kumar
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
- Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA
- Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, Indian Institute of Technology Bombay, Mumbai, India
| | - Rui Zhang
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Steven A Redford
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
- Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
- Graduate Program in Biophysical Sciences, The University of Chicago, Chicago, Illinois 60637, USA
| | - Juan J de Pablo
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
- Institute for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Margaret L Gardel
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
- Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA
- Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
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49
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Abstract
Active crystals are highly ordered structures that emerge from the self-organization of motile objects, and have been widely studied in synthetic1,2 and bacterial3,4 active matter. Whether persistent crystalline order can emerge in groups of autonomously developing multicellular organisms is currently unknown. Here we show that swimming starfish embryos spontaneously assemble into chiral crystals that span thousands of spinning organisms and persist for tens of hours. Combining experiments, theory and simulations, we demonstrate that the formation, dynamics and dissolution of these living crystals are controlled by the hydrodynamic properties and the natural development of embryos. Remarkably, living chiral crystals exhibit self-sustained chiral oscillations as well as various unconventional deformation response behaviours recently predicted for odd elastic materials5,6. Our results provide direct experimental evidence for how non-reciprocal interactions between autonomous multicellular components may facilitate non-equilibrium phases of chiral active matter.
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50
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Cerasoli S, Ciliberto S, Marinari E, Oshanin G, Peliti L, Rondoni L. Spectral fingerprints of nonequilibrium dynamics: The case of a Brownian gyrator. Phys Rev E 2022; 106:014137. [PMID: 35974646 DOI: 10.1103/physreve.106.014137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 06/30/2022] [Indexed: 06/15/2023]
Abstract
The same system can exhibit a completely different dynamical behavior when it evolves in equilibrium conditions or when it is driven out-of-equilibrium by, e.g., connecting some of its components to heat baths kept at different temperatures. Here we concentrate on an analytically solvable and experimentally relevant model of such a system-the so-called Brownian gyrator-a two-dimensional nanomachine that performs a systematic, on average, rotation around the origin under nonequilibrium conditions, while no net rotation takes place under equilibrium ones. On this example, we discuss a question whether it is possible to distinguish between two types of a behavior judging not upon the statistical properties of the trajectories of components but rather upon their respective spectral densities. The latter are widely used to characterize diverse dynamical systems and are routinely calculated from the data using standard built-in packages. From such a perspective, we inquire whether the power spectral densities possess some "fingerprint" properties specific to the behavior in nonequilibrium. We show that indeed one can conclusively distinguish between equilibrium and nonequilibrium dynamics by analyzing the cross-correlations between the spectral densities of both components in the short frequency limit, or from the spectral densities of both components evaluated at zero frequency. Our analytical predictions, corroborated by experimental and numerical results, open a new direction for the analysis of a nonequilibrium dynamics.
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Affiliation(s)
- Sara Cerasoli
- Department of Civil and Environmental Engineering, Princeton University, Princeton New Jersey 08544, USA
| | - Sergio Ciliberto
- Laboratoire de Physique (UMR CNRS 567246), Ecole Normale Supérieure, Allée d'Italie, 69364 Lyon, France
| | - Enzo Marinari
- Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy
- INFN, Sezione di Roma 1 and Nanotech-CNR, UOS di Roma, P.le A. Moro 2, I-00185 Roma, Italy
| | - Gleb Oshanin
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Luca Peliti
- Santa Marinella Research Institute, Santa Marinella, Italy
| | - Lamberto Rondoni
- Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
- INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
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