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Martínez-Calvo A, Wingreen NS, Datta SS. Pattern formation by bacteria-phage interactions. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.09.19.558479. [PMID: 37786699 PMCID: PMC10541591 DOI: 10.1101/2023.09.19.558479] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/04/2023]
Abstract
The interactions between bacteria and phages-viruses that infect bacteria-play critical roles in agriculture, ecology, and medicine; however, how these interactions influence the spatial organization of both bacteria and phages remain largely unexplored. Here, we address this gap in knowledge by developing a theoretical model of motile, proliferating bacteria that aggregate via motility-induced phase separation (MIPS) and encounter phage that infect and lyse the cells. We find that the non-reciprocal predator-prey interactions between phage and bacteria strongly alter spatial organization, in some cases giving rise to a rich array of finite-scale stationary and dynamic patterns in which bacteria and phage coexist. We establish principles describing the onset and characteristics of these diverse behaviors, thereby helping to provide a biophysical basis for understanding pattern formation in bacteria-phage systems, as well as in a broader range of active and living systems with similar predator-prey or other non-reciprocal interactions.
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Staddon MF, Munro EM, Banerjee S. Pulsatile contractions and pattern formation in excitable actomyosin cortex. PLoS Comput Biol 2022; 18:e1009981. [PMID: 35353813 PMCID: PMC9000090 DOI: 10.1371/journal.pcbi.1009981] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Revised: 04/11/2022] [Accepted: 03/01/2022] [Indexed: 11/23/2022] Open
Abstract
The actin cortex is an active adaptive material, embedded with complex regulatory networks that can sense, generate, and transmit mechanical forces. The cortex exhibits a wide range of dynamic behaviours, from generating pulsatory contractions and travelling waves to forming organised structures. Despite the progress in characterising the biochemical and mechanical components of the actin cortex, the emergent dynamics of this mechanochemical system is poorly understood. Here we develop a reaction-diffusion model for the RhoA signalling network, the upstream regulator for actomyosin assembly and contractility, coupled to an active actomyosin gel, to investigate how the interplay between chemical signalling and mechanical forces regulates stresses and patterns in the cortex. We demonstrate that mechanochemical feedback in the cortex acts to destabilise homogeneous states and robustly generate pulsatile contractions. By tuning active stress in the system, we show that the cortex can generate propagating contraction pulses, form network structures, or exhibit topological turbulence. The cellular actin cortex is a dynamic sub-membranous network of filamentous actin, myosin motors, and other accessory proteins that regulates the ability of cells to maintain or change shapes. While the key molecular components and mechanical properties of the actin cortex have been characterized, the ways in which biochemical signalling and mechanical forces interact to regulate cortex behaviours remain poorly understood. In this article, we develop a mathematical model for the actomyosin cortex that combines the reaction-diffusion dynamics of signalling proteins with active force generation by actomyosin networks. Using this model, we investigate how the feedback between mechanics and biochemical signalling regulates the propagation of actomyosin flows, mechanical stresses, and pattern formation in the cortex. Our work reveals a variety of ways in which the cortex can tune the dynamic coupling between biochemical activity, force production, and advective transport to control mechanical behaviours.
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Affiliation(s)
- Michael F. Staddon
- Center for Systems Biology Dresden, Dresden, Germany
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
- Max Planck Institute for Molecular Cell Biology and Genetics, Dresden, Germany
| | - Edwin M. Munro
- Department of Molecular Genetics and Cell Biology, University of Chicago, Chicago, Illinois, United States of America
- Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois, United States of America
| | - Shiladitya Banerjee
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
- * E-mail:
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Maddu S, Sturm D, Müller CL, Sbalzarini IF. Inverse Dirichlet weighting enables reliable training of physics informed neural networks. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2022. [DOI: 10.1088/2632-2153/ac3712] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Abstract
We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as physics informed neural networks (PINNs). PINNs are popular machine-learning templates that allow for seamless integration of physical equation models with data. Their training amounts to solving an optimization problem over a weighted sum of data-fidelity and equation-fidelity objectives. Conflicts between objectives can arise from scale imbalances, heteroscedasticity in the data, stiffness of the physical equation, or from catastrophic interference during sequential training. We explain the training pathology arising from this and propose a simple yet effective inverse Dirichlet weighting strategy to alleviate the issue. We compare with Sobolev training of neural networks, providing the baseline of analytically ε-optimal training. We demonstrate the effectiveness of inverse Dirichlet weighting in various applications, including a multi-scale model of active turbulence, where we show orders of magnitude improvement in accuracy and convergence over conventional PINN training. For inverse modeling using sequential training, we find that inverse Dirichlet weighting protects a PINN against catastrophic forgetting.
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Romeo N, Hastewell A, Mietke A, Dunkel J. Learning developmental mode dynamics from single-cell trajectories. eLife 2021; 10:68679. [PMID: 34964437 PMCID: PMC8871385 DOI: 10.7554/elife.68679] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Accepted: 12/24/2021] [Indexed: 11/22/2022] Open
Abstract
Embryogenesis is a multiscale process during which developmental symmetry breaking transitions give rise to complex multicellular organisms. Recent advances in high-resolution live-cell microscopy provide unprecedented insights into the collective cell dynamics at various stages of embryonic development. This rapid experimental progress poses the theoretical challenge of translating high-dimensional imaging data into predictive low-dimensional models that capture the essential ordering principles governing developmental cell migration in complex geometries. Here, we combine mode decomposition ideas that have proved successful in condensed matter physics and turbulence theory with recent advances in sparse dynamical systems inference to realize a computational framework for learning quantitative continuum models from single-cell imaging data. Considering pan-embryo cell migration during early gastrulation in zebrafish as a widely studied example, we show how cell trajectory data on a curved surface can be coarse-grained and compressed with suitable harmonic basis functions. The resulting low-dimensional representation of the collective cell dynamics enables a compact characterization of developmental symmetry breaking and the direct inference of an interpretable hydrodynamic model, which reveals similarities between pan-embryo cell migration and active Brownian particle dynamics on curved surfaces. Due to its generic conceptual foundation, we expect that mode-based model learning can help advance the quantitative biophysical understanding of a wide range of developmental structure formation processes.
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Affiliation(s)
- Nicolas Romeo
- Department of Physics, Massachusetts Institute of Technology, Cambridge, United States
| | - Alasdair Hastewell
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, United States
| | - Alexander Mietke
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, United States
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, United States
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Bächer C, Gekle S. Computational modeling of active deformable membranes embedded in three-dimensional flows. Phys Rev E 2019; 99:062418. [PMID: 31330647 DOI: 10.1103/physreve.99.062418] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2019] [Indexed: 06/10/2023]
Abstract
Active gel theory has recently been very successful in describing biologically active materials such as actin filaments or moving bacteria in temporally fixed and simple geometries such as cubes or spheres. Here we develop a computational algorithm to compute the dynamic evolution of an arbitrarily shaped, deformable thin membrane of active material embedded in a three-dimensional flowing liquid. For this, our algorithm combines active gel theory with the classical theory of thin elastic shells. To compute the actual forces resulting from active stresses, we apply a parabolic fitting procedure to the triangulated membrane surface. Active forces are then dynamically coupled via an immersed-boundary method to the surrounding fluid whose dynamics can be solved by any standard, e.g., Lattice-Boltzmann, flow solver. We validate our algorithm using the Green's functions of Berthoumieux et al. [New J. Phys. 16, 065005 (2014)10.1088/1367-2630/16/6/065005] for an active cylindrical membrane subjected (i) to a locally increased active stress and (ii) to a homogeneous active stress. For the latter scenario, we predict in addition a nonaxisymmetric instability. We highlight the versatility of our method by analyzing the flow field inside an actively deforming cell embedded in external shear flow. Further applications may be cytoplasmic streaming or active membranes in blood flows.
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Affiliation(s)
- Christian Bächer
- Biofluid Simulation and Modeling, Theoretische Physik VI, Universität Bayreuth, Universitätsstrasse 30, Bayreuth, Germany
| | - Stephan Gekle
- Biofluid Simulation and Modeling, Theoretische Physik VI, Universität Bayreuth, Universitätsstrasse 30, Bayreuth, Germany
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Abstract
We investigate the self-propulsive motion of a drop containing an active polar field. The drop demonstrates spontaneous symmetry breaking from a uniform orientational order into a splay or bend instability depending on the types of active stress, namely, contractile or extensile, respectively. We develop an analytical theory of the mechanism of this instability, which has been observed only in numerical simulations. We show that both contractile and extensile active stresses result in the instability and self-propulsive motion. We also discuss asymmetry between contractile and extensile stresses and show that extensile active stress generates chaotic motion even under a simple model of the polarity field coupled with motion and deformation of the drop.
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Affiliation(s)
- Natsuhiko Yoshinaga
- WPI-Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan and MathAM-OIL, AIST, Sendai 980-8577, Japan
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Jülicher F, Grill SW, Salbreux G. Hydrodynamic theory of active matter. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:076601. [PMID: 29542442 DOI: 10.1088/1361-6633/aab6bb] [Citation(s) in RCA: 98] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/11/2024]
Abstract
We review the general hydrodynamic theory of active soft materials that is motivated in particular by biological matter. We present basic concepts of irreversible thermodynamics of spatially extended multicomponent active systems. Starting from the rate of entropy production, we identify conjugate thermodynamic fluxes and forces and present generic constitutive equations of polar active fluids and active gels. We also discuss angular momentum conservation which plays a role in the the physics of active chiral gels. The irreversible thermodynamics of active gels provides a general framework to discuss the physics that underlies a wide variety of biological processes in cells and in multicellular tissues.
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Affiliation(s)
- Frank Jülicher
- Max-Planck-Institute for the Physics of Complex Systems, Nöthnitzerstr. 38, 01187 Dresden, Germany
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Blanch-Mercader C, Yashunsky V, Garcia S, Duclos G, Giomi L, Silberzan P. Turbulent Dynamics of Epithelial Cell Cultures. PHYSICAL REVIEW LETTERS 2018; 120:208101. [PMID: 29864293 DOI: 10.1103/physrevlett.120.208101] [Citation(s) in RCA: 67] [Impact Index Per Article: 11.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2017] [Revised: 02/12/2018] [Indexed: 05/23/2023]
Abstract
We investigate the large length and long time scales collective flows and structural rearrangements within in vitro human bronchial epithelial cell (HBEC) cultures. Activity-driven collective flows result in ensembles of vortices randomly positioned in space. By analyzing a large population of vortices, we show that their area follows an exponential law with a constant mean value and their rotational frequency is size independent, both being characteristic features of the chaotic dynamics of active nematic suspensions. Indeed, we find that HBECs self-organize in nematic domains of several cell lengths. Nematic defects are found at the interface between domains with a total number that remains constant due to the dynamical balance of nucleation and annihilation events. The mean velocity fields in the vicinity of defects are well described by a hydrodynamic theory of extensile active nematics.
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Affiliation(s)
- C Blanch-Mercader
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - V Yashunsky
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - S Garcia
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - G Duclos
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - L Giomi
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
| | - P Silberzan
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
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Abstract
Epithelial cell monolayers exhibit traveling mechanical waves. We rationalize this observation thanks to a hydrodynamic description of the monolayer as a compressible, active and polar material. We show that propagating waves of the cell density, polarity, velocity and stress fields may be due to a Hopf bifurcation occurring above threshold values of active coupling coefficients.
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Affiliation(s)
- Shunsuke Yabunaka
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto, Japan.
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Blanch-Mercader C, Casademunt J. Hydrodynamic instabilities, waves and turbulence in spreading epithelia. SOFT MATTER 2017; 13:6913-6928. [PMID: 28825077 DOI: 10.1039/c7sm01128h] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
We present a hydrodynamic model of spreading epithelial monolayers described as polar viscous fluids, with active contractility and traction on a substrate. The combination of both active forces generates an instability that leads to nonlinear traveling waves, which propagate in the direction of polarity with characteristic time scales that depend on contact forces. Our viscous fluid model provides a comprehensive understanding of a variety of observations on the slow dynamics of epithelial monolayers, remarkably those that seemed to be characteristic of elastic media. The model also makes simple predictions to test the non-elastic nature of the mechanical waves, and provides new insights into collective cell dynamics, explaining plithotaxis as a result of strong flow-polarity coupling, and quantifying the non-locality of force transmission. In addition, we study the nonlinear regime of waves deriving an exact map of the model into the complex Ginzburg-Landau equation, which provides a complete classification of possible nonlinear scenarios. In particular, we predict the transition to different forms of weak turbulence, which in turn could explain the chaotic dynamics often observed in epithelia.
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Affiliation(s)
- C Blanch-Mercader
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona 08028, Spain. and Laboratoire Physico Chimie Curie, Institut Curie, PSL Research University, CNRS, 26 rue d' Ulm, 75005 Paris, France
| | - J Casademunt
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona 08028, Spain. and Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona, Spain
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Doostmohammadi A, Shendruk TN, Thijssen K, Yeomans JM. Onset of meso-scale turbulence in active nematics. Nat Commun 2017; 8:15326. [PMID: 28508858 PMCID: PMC5440851 DOI: 10.1038/ncomms15326] [Citation(s) in RCA: 70] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2016] [Accepted: 03/21/2017] [Indexed: 11/09/2022] Open
Abstract
Meso-scale turbulence is an innate phenomenon, distinct from inertial turbulence, that spontaneously occurs at low Reynolds number in fluidized biological systems. This spatiotemporal disordered flow radically changes nutrient and molecular transport in living fluids and can strongly affect the collective behaviour in prominent biological processes, including biofilm formation, morphogenesis and cancer invasion. Despite its crucial role in such physiological processes, understanding meso-scale turbulence and any relation to classical inertial turbulence remains obscure. Here we show how the motion of active matter along a micro-channel transitions to meso-scale turbulence through the evolution of locally disordered patches (active puffs) from an ordered vortex-lattice flow state. We demonstrate that the stationary critical exponents of this transition to meso-scale turbulence in a channel coincide with the directed percolation universality class. This finding bridges our understanding of the onset of low-Reynolds-number meso-scale turbulence and traditional scale-invariant turbulence in confinement.
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Affiliation(s)
- Amin Doostmohammadi
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK
| | - Tyler N Shendruk
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK.,Center for Studies in Physics and Biology, The Rockefeller University, 1230 York Avenue, New York, New York 10065, USA
| | - Kristian Thijssen
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK
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Zhong L, Li Y, Chen Y, Hong W, Hu W, Guo Q. Chaoticons described by nonlocal nonlinear Schrödinger equation. Sci Rep 2017; 7:41438. [PMID: 28134268 PMCID: PMC5278363 DOI: 10.1038/srep41438] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2016] [Accepted: 12/20/2016] [Indexed: 12/15/2022] Open
Abstract
It is shown that the unstable evolutions of the Hermite-Gauss-type stationary solutions for the nonlocal nonlinear Schrödinger equation with the exponential-decay response function can evolve into chaotic states. This new kind of entities are referred to as chaoticons because they exhibit not only chaotic properties (with positive Lyapunov exponents and spatial decoherence) but also soliton-like properties (with invariant statistic width and interaction of quasi-elastic collisions).
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Affiliation(s)
- Lanhua Zhong
- Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631, P.R. China
- Physical Science and Technology School, Lingnan Normal University, Zhanjiang 524048, P.R. China
| | - Yuqi Li
- Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, P.R. China
| | - Yong Chen
- Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, P.R. China
| | - Weiyi Hong
- Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631, P.R. China
| | - Wei Hu
- Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631, P.R. China
| | - Qi Guo
- Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631, P.R. China
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