1
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Bone RA, Sharpe DJ, Wales DJ, Green JR. Stochastic paths controlling speed and dissipation. Phys Rev E 2022; 106:054151. [PMID: 36559408 DOI: 10.1103/physreve.106.054151] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2021] [Accepted: 10/28/2022] [Indexed: 11/24/2022]
Abstract
Natural processes occur in a finite amount of time and dissipate energy, entropy, and matter. Near equilibrium, thermodynamic intuition suggests that fast irreversible processes will dissipate more energy and entropy than slow quasistatic processes connecting the same initial and final states. For small systems, recently discovered thermodynamic speed limits suggest that faster processes will dissipate more than slower processes. Here, we test the hypothesis that this relationship between speed and dissipation holds for stochastic paths far from equilibrium. To analyze stochastic paths on finite timescales, we derive an exact expression for the path probabilities of continuous-time Markov chains from the path summation solution to the master equation. We present a minimal model for a driven system in which relative energies of the initial and target states control the speed, and the nonequilibrium currents of a cycle control the dissipation. Although the hypothesis holds near equilibrium, we find that faster processes can dissipate less under far-from-equilibrium conditions because of strong currents. This model serves as a minimal prototype for designing kinetics to sculpt the nonequilibrium path space so that faster paths produce less dissipation.
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Affiliation(s)
- Rebecca A Bone
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Daniel J Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, Cambridge, United Kingdom
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, Cambridge, United Kingdom
| | - Jason R Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA.,Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
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2
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Fiorenza SA, Steckhahn DG, Betterton MD. Modeling spatiotemporally varying protein-protein interactions in CyLaKS, the Cytoskeleton Lattice-based Kinetic Simulator. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:105. [PMID: 34406510 PMCID: PMC10202044 DOI: 10.1140/epje/s10189-021-00097-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Accepted: 06/21/2021] [Indexed: 05/24/2023]
Abstract
Interaction of cytoskeletal filaments, motor proteins, and crosslinking proteins drives important cellular processes such as cell division and cell movement. Cytoskeletal networks also exhibit nonequilibrium self-assembly in reconstituted systems. An emerging problem in cytoskeletal modeling and simulation is spatiotemporal alteration of the dynamics of filaments, motors, and associated proteins. This can occur due to motor crowding, obstacles along the filament, motor interactions and direction switching, and changes, defects, or heterogeneity in the filament binding lattice. How such spatiotemporally varying cytoskeletal filaments and motor interactions affect their collective properties is not fully understood. We developed the Cytoskeleton Lattice-based Kinetic Simulator (CyLaKS) to investigate such problems. The simulation model builds on previous work by incorporating motor mechanochemistry into a simulation with many interacting motors and/or associated proteins on a discretized lattice. CyLaKS also includes detailed balance in binding kinetics, movement, and lattice heterogeneity. The simulation framework is flexible and extensible for future modeling work and is available on GitHub for others to freely use or build upon. Here we illustrate the use of CyLaKS to study long-range motor interactions, microtubule lattice heterogeneity, motion of a heterodimeric motor, and how changing crosslinker number affects filament separation.
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Affiliation(s)
- Shane A Fiorenza
- Department of Physics, University of Colorado Boulder, Boulder, USA
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3
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Lamson AR, Moore JM, Fang F, Glaser MA, Shelley MJ, Betterton MD. Comparison of explicit and mean-field models of cytoskeletal filaments with crosslinking motors. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:45. [PMID: 33779863 PMCID: PMC8220871 DOI: 10.1140/epje/s10189-021-00042-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Accepted: 02/20/2021] [Indexed: 05/17/2023]
Abstract
In cells, cytoskeletal filament networks are responsible for cell movement, growth, and division. Filaments in the cytoskeleton are driven and organized by crosslinking molecular motors. In reconstituted cytoskeletal systems, motor activity is responsible for far-from-equilibrium phenomena such as active stress, self-organized flow, and spontaneous nematic defect generation. How microscopic interactions between motors and filaments lead to larger-scale dynamics remains incompletely understood. To build from motor-filament interactions to predict bulk behavior of cytoskeletal systems, more computationally efficient techniques for modeling motor-filament interactions are needed. Here, we derive a coarse-graining hierarchy of explicit and continuum models for crosslinking motors that bind to and walk on filament pairs. We compare the steady-state motor distribution and motor-induced filament motion for the different models and analyze their computational cost. All three models agree well in the limit of fast motor binding kinetics. Evolving a truncated moment expansion of motor density speeds the computation by [Formula: see text]-[Formula: see text] compared to the explicit or continuous-density simulations, suggesting an approach for more efficient simulation of large networks. These tools facilitate further study of motor-filament networks on micrometer to millimeter length scales.
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Affiliation(s)
- Adam R Lamson
- Department of Physics, University of Colorado Boulder, Boulder, USA.
| | - Jeffrey M Moore
- Department of Physics, University of Colorado Boulder, Boulder, USA
| | - Fang Fang
- Courant Institute, New York University, New York, USA
| | - Matthew A Glaser
- Department of Physics, University of Colorado Boulder, Boulder, USA
| | - Michael J Shelley
- Courant Institute, New York University, New York, USA
- Center for Computational Biology, Flatiron Institute, New York, USA
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4
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Arango-Restrepo A, Barragán D, Rubi JM. A Criterion for the Formation of Nonequilibrium Self-Assembled Structures. J Phys Chem B 2021; 125:1838-1845. [PMID: 33566612 DOI: 10.1021/acs.jpcb.0c07824] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Is there a criterion able to determine the type of structures formed in a nonequilibrium self-assembly process? This important question has a clear answer when the process takes place under equilibrium conditions: structures emerge at minimum values of the free energy. Experiments, however, have shown that when self-assembly takes place outside equilibrium, they do not appear at those free energy minima but rather at optimal values of structural parameters. On the basis of these observations, we propose a selection criterion for which structures come up at the minima of a nonequilibrium free energy that takes into account the energy needed to change their configuration. The criterion is able to predict the formation and configuration of structures such as Liesegang rings and patterns in magnetic colloids and could constitute a powerful tool to understand the synthesis of advanced materials, enantiomers, and nanoparticles.
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Affiliation(s)
- Andrés Arango-Restrepo
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, Spain.,Institut de Nanociencia i Nanotecnologia, Universitat de Barcelona, Barcelona, Spain
| | - Daniel Barragán
- Escuela de Química, Universidad Nacional de Colombia, Medellin, Colombia
| | - J Miguel Rubi
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, Spain.,Institut de Nanociencia i Nanotecnologia, Universitat de Barcelona, Barcelona, Spain.,PoreLab, Department of Physics, Norwegian University of Science and Technology, Trondheim, Norway
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5
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Arango-Restrepo A, Rubi JM, Barragán D. The Role of Energy and Matter Dissipation in Determining the Architecture of Self-Assembled Structures. J Phys Chem B 2019; 123:5902-5908. [DOI: 10.1021/acs.jpcb.9b02928] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Andrés Arango-Restrepo
- Departament de Física de la Matéria Condensada, Facultat de Física, Universitat de Barcelona, Avinguda Diagonal 647, 08028 Barcelona, Spain
- Institut de Nanociencia i Nanotecnologia, Universitat de Barcelona, 08028 Barcelona, Spain
| | - J. Miguel Rubi
- Departament de Física de la Matéria Condensada, Facultat de Física, Universitat de Barcelona, Avinguda Diagonal 647, 08028 Barcelona, Spain
| | - Daniel Barragán
- Escuela de Química, Facultad de Ciencias, Universidad Nacional de Colombia, Carrera 65 No 59A-110, Bloque 16, Núcleo
El Volador, Medellín, Colombia
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6
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Rickman J, Nédélec F, Surrey T. Effects of spatial dimensionality and steric interactions on microtubule-motor self-organization. Phys Biol 2019; 16:046004. [PMID: 31013252 PMCID: PMC7655122 DOI: 10.1088/1478-3975/ab0fb1] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Active networks composed of filaments and motor proteins can self-organize into a
variety of architectures. Computer simulations in two or three spatial
dimensions and including or omitting steric interactions between filaments can
be used to model active networks. Here we examine how these modelling choices
affect the state space of network self-organization. We compare the networks
generated by different models of a system of dynamic microtubules and
microtubule-crosslinking motors. We find that a thin 3D model that includes
steric interactions between filaments is the most versatile, capturing a variety
of network states observed in recent experiments. In contrast, 2D models either
with or without steric interactions which prohibit microtubule crossings can
produce some, but not all, observed network states. Our results provide
guidelines for the most appropriate choice of model for the study of different
network types and elucidate mechanisms of active network organization.
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Affiliation(s)
- Jamie Rickman
- The Francis Crick Institute, 1 Midland Road, London NW1 1AT, United Kingdom. Centre for Mathematics and Physics in the Life Sciences and Experimental Biology, University College London, London WC1 6BT, United Kingdom
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7
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Ravichandran A, Duman Ö, Hoore M, Saggiorato G, Vliegenthart GA, Auth T, Gompper G. Chronology of motor-mediated microtubule streaming. eLife 2019; 8:e39694. [PMID: 30601119 PMCID: PMC6338466 DOI: 10.7554/elife.39694] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2018] [Accepted: 12/28/2018] [Indexed: 12/19/2022] Open
Abstract
We introduce a filament-based simulation model for coarse-grained, effective motor-mediated interaction between microtubule pairs to study the time-scales that compose cytoplasmic streaming. We characterise microtubule dynamics in two-dimensional systems by chronologically arranging five distinct processes of varying duration that make up streaming, from microtubule pairs to collective dynamics. The structures found were polarity sorted due to the propulsion of antialigned microtubules. This also gave rise to the formation of large polar-aligned domains, and streaming at the domain boundaries. Correlation functions, mean squared displacements, and velocity distributions reveal a cascade of processes ultimately leading to microtubule streaming and advection, spanning multiple microtubule lengths. The characteristic times for the processes extend over three orders of magnitude from fast single-microtubule processes to slow collective processes. Our approach can be used to directly test the importance of molecular components, such as motors and crosslinking proteins between microtubules, on the collective dynamics at cellular scale.
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Affiliation(s)
- Arvind Ravichandran
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced SimulationForschungszentrum JülichJülichGermany
| | - Özer Duman
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced SimulationForschungszentrum JülichJülichGermany
| | - Masoud Hoore
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced SimulationForschungszentrum JülichJülichGermany
| | - Guglielmo Saggiorato
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced SimulationForschungszentrum JülichJülichGermany
| | - Gerard A Vliegenthart
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced SimulationForschungszentrum JülichJülichGermany
| | - Thorsten Auth
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced SimulationForschungszentrum JülichJülichGermany
| | - Gerhard Gompper
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced SimulationForschungszentrum JülichJülichGermany
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8
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Arango-Restrepo A, Barragán D, Rubi JM. Self-assembling outside equilibrium: emergence of structures mediated by dissipation. Phys Chem Chem Phys 2019; 21:17475-17493. [DOI: 10.1039/c9cp01088b] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Self-assembly under non-equilibrium conditions may give rise to the formation of structures not available at equilibrium.
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Affiliation(s)
- A. Arango-Restrepo
- Departament de Física de la Matéria Condensada
- Facultat de Física
- Universitat de Barcelona
- 08028 Barcelona
- Spain
| | - D. Barragán
- Escuela de Química
- Facultad de Ciencias
- Universidad Nacional de Colombia
- Medellín
- Colombia
| | - J. M. Rubi
- Departament de Física de la Matéria Condensada
- Facultat de Física
- Universitat de Barcelona
- 08028 Barcelona
- Spain
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9
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Roostalu J, Rickman J, Thomas C, Nédélec F, Surrey T. Determinants of Polar versus Nematic Organization in Networks of Dynamic Microtubules and Mitotic Motors. Cell 2018; 175:796-808.e14. [PMID: 30340043 PMCID: PMC6198040 DOI: 10.1016/j.cell.2018.09.029] [Citation(s) in RCA: 60] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2018] [Revised: 06/25/2018] [Accepted: 09/13/2018] [Indexed: 11/03/2022]
Abstract
During cell division, mitotic motors organize microtubules in the bipolar spindle into either polar arrays at the spindle poles or a "nematic" network of aligned microtubules at the spindle center. The reasons for the distinct self-organizing capacities of dynamic microtubules and different motors are not understood. Using in vitro reconstitution experiments and computer simulations, we show that the human mitotic motors kinesin-5 KIF11 and kinesin-14 HSET, despite opposite directionalities, can both organize dynamic microtubules into either polar or nematic networks. We show that in addition to the motor properties the natural asymmetry between microtubule plus- and minus-end growth critically contributes to the organizational potential of the motors. We identify two control parameters that capture system composition and kinetic properties and predict the outcome of microtubule network organization. These results elucidate a fundamental design principle of spindle bipolarity and establish general rules for active filament network organization.
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Affiliation(s)
| | - Jamie Rickman
- The Francis Crick Institute, 1 Midland Road, London NW1 1AT, UK
| | - Claire Thomas
- The Francis Crick Institute, 1 Midland Road, London NW1 1AT, UK
| | - François Nédélec
- European Molecular Biology Laboratory, Meyerhofstrasse 1, 69117 Heidelberg, Germany.
| | - Thomas Surrey
- The Francis Crick Institute, 1 Midland Road, London NW1 1AT, UK.
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10
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Ravichandran A, Vliegenthart GA, Saggiorato G, Auth T, Gompper G. Enhanced Dynamics of Confined Cytoskeletal Filaments Driven by Asymmetric Motors. Biophys J 2017; 113:1121-1132. [PMID: 28877494 DOI: 10.1016/j.bpj.2017.07.016] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2017] [Revised: 07/10/2017] [Accepted: 07/27/2017] [Indexed: 12/27/2022] Open
Abstract
Cytoskeletal filaments and molecular motors facilitate the micron-scale force generation necessary for the distribution of organelles and the restructuring of the cytoskeleton within eukaryotic cells. Although the mesoscopic structure and the dynamics of such filaments have been studied in vitro and in vivo, their connection with filament polarity-dependent motor-mediated force generation is not well understood. Using 2D Brownian dynamics simulations, we study a dense, confined mixture of rigid microtubules (MTs) and active springs that have arms that cross-link neighboring MT pairs and move unidirectionally on the attached MT. We simulate depletion interactions between MTs using an attractive potential. We show that dimeric motors, with a motile arm on only one of the two MTs, produce large polarity-sorted MT clusters, whereas tetrameric motors, with motile arms on both microtubules, produce bundles. Furthermore, dimeric motors induce, on average, higher velocities between antialigned MTs than tetrameric motors. Our results, where MTs move faster near the confining wall, are consistent with experimental observations in Drosophila oocytes where enhanced microtubule activity is found close to the confining plasma membrane.
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Affiliation(s)
- Arvind Ravichandran
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich, Germany
| | - Gerrit A Vliegenthart
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich, Germany
| | - Guglielmo Saggiorato
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich, Germany; LPTMS, CNRS, University Paris-Sud, Université Paris-Saclay, Orsay, France
| | - Thorsten Auth
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich, Germany.
| | - Gerhard Gompper
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich, Germany
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11
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Head DA, Tronci G, Russell SJ, Wood DJ. In Silico Modeling of the Rheological Properties of Covalently Cross-Linked Collagen Triple Helices. ACS Biomater Sci Eng 2016; 2:1224-1233. [DOI: 10.1021/acsbiomaterials.6b00115] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- David A. Head
- School
of Computing, University of Leeds, Leeds LS2 9JT, U.K
| | - Giuseppe Tronci
- Nonwovens
Research Group, School of Design, University of Leeds, Leeds LS2 9JT, U.K
- Biomaterials
and Tissue Engineering Research Group, School of Dentistry, St. James’s
University Hospital, University of Leeds, Leeds LS9 7TF, U.K
| | - Stephen J. Russell
- Nonwovens
Research Group, School of Design, University of Leeds, Leeds LS2 9JT, U.K
| | - David J. Wood
- Biomaterials
and Tissue Engineering Research Group, School of Dentistry, St. James’s
University Hospital, University of Leeds, Leeds LS9 7TF, U.K
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12
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Abstract
Networks of biofilaments are essential for the formation of cellular structures that support various biological functions. For the most part, previous studies have investigated the collective dynamics of rodlike biofilaments; however, the shapes of the actual subcellular components are often more elaborate. In this study, we considered an active object composed of two active filaments, which represents the progression from rodlike biofilaments to complex-shaped biofilaments. Specifically, we numerically assessed the collective behaviors of these active objects in two dimensions and observed several types of dynamics, depending on the density and the angle of the two filaments as shape parameters of the object. Among the observed collective dynamics, a moving density band that we named a "moving smectic" is introduced here for the first time. By analyzing the trajectories of individual objects and the interactions among them, this study demonstrated how interactions among active biofilaments with complex shapes could produce collective dynamics in a nontrivial manner.
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Affiliation(s)
- Hironobu Nogucci
- Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, Japan
| | - Shuji Ishihara
- Department of Physics, School of Science and Technology, Meiji University, 1-1-1 Higashi-Mita, Tama, Kawasaki, Kanagawa, Japan
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13
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Blackwell R, Sweezy-Schindler O, Baldwin C, Hough LE, Glaser MA, Betterton MD. Microscopic origins of anisotropic active stress in motor-driven nematic liquid crystals. SOFT MATTER 2016; 12:2676-87. [PMID: 26742483 PMCID: PMC4861323 DOI: 10.1039/c5sm02506k] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
The cytoskeleton, despite comprising relatively few building blocks, drives an impressive variety of cellular phenomena ranging from cell division to motility. These building blocks include filaments, motor proteins, and static crosslinkers. Outside of cells, these same components can form novel materials exhibiting active flows and nonequilibrium contraction or extension. While dipolar extensile or contractile active stresses are common in nematic motor-filament systems, their microscopic origin remains unclear. Here we study a minimal physical model of filaments, crosslinking motors, and static crosslinkers to dissect the microscopic mechanisms of stress generation in a two-dimensional system of orientationally aligned rods. We demonstrate the essential role of filament steric interactions which have not previously been considered to significantly contribute to active stresses. With this insight, we are able to tune contractile or extensile behavior through the control of motor-driven filament sliding and crosslinking. This work provides a roadmap for engineering stresses in active liquid crystals. The mechanisms we study may help explain why flowing nematic motor-filament mixtures are extensile while gelled systems are contractile.
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Affiliation(s)
- Robert Blackwell
- Department of Physics, University of Colorado, Boulder, CO 80309, USA.
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14
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Gao T, Blackwell R, Glaser MA, Betterton MD, Shelley MJ. Multiscale modeling and simulation of microtubule-motor-protein assemblies. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062709. [PMID: 26764729 PMCID: PMC5082993 DOI: 10.1103/physreve.92.062709] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2015] [Indexed: 05/10/2023]
Abstract
Microtubules and motor proteins self-organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven out of equilibrium by adenosine triphosphate-consuming motor proteins. Microscopic motor activity causes polarity-dependent interactions between motor proteins and microtubules, but how these interactions yield larger-scale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubule-motor systems in which Brownian dynamics simulations of polar microtubules driven by motors are used to study microscopic organization and stresses created by motor-mediated microtubule interactions. We identify polarity-sorting and crosslink tether relaxation as two polar-specific sources of active destabilizing stress. We then develop a continuum Doi-Onsager model that captures polarity sorting and the hydrodynamic flows generated by these polar-specific active stresses. In simulations of active nematic flows on immersed surfaces, the active stresses drive turbulent flow dynamics and continuous generation and annihilation of disclination defects. The dynamics follow from two instabilities, and accounting for the immersed nature of the experiment yields unambiguous characteristic length and time scales. When turning off the hydrodynamics in the Doi-Onsager model, we capture formation of polar lanes as observed in the Brownian dynamics simulation.
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Affiliation(s)
- Tong Gao
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| | - Robert Blackwell
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Matthew A Glaser
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - M D Betterton
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Michael J Shelley
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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15
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Elgeti J, Winkler RG, Gompper G. Physics of microswimmers--single particle motion and collective behavior: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:056601. [PMID: 25919479 DOI: 10.1088/0034-4885/78/5/056601] [Citation(s) in RCA: 644] [Impact Index Per Article: 71.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.
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Affiliation(s)
- J Elgeti
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
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16
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Gao T, Blackwell R, Glaser MA, Betterton MD, Shelley MJ. Multiscale polar theory of microtubule and motor-protein assemblies. PHYSICAL REVIEW LETTERS 2015; 114:048101. [PMID: 25679909 PMCID: PMC4425281 DOI: 10.1103/physrevlett.114.048101] [Citation(s) in RCA: 79] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2014] [Indexed: 05/20/2023]
Abstract
Microtubules and motor proteins are building blocks of self-organized subcellular biological structures such as the mitotic spindle and the centrosomal microtubule array. These same ingredients can form new "bioactive" liquid-crystalline fluids that are intrinsically out of equilibrium and which display complex flows and defect dynamics. It is not yet well understood how microscopic activity, which involves polarity-dependent interactions between motor proteins and microtubules, yields such larger-scale dynamical structures. In our multiscale theory, Brownian dynamics simulations of polar microtubule ensembles driven by cross-linking motors allow us to study microscopic organization and stresses. Polarity sorting and cross-link relaxation emerge as two polar-specific sources of active destabilizing stress. On larger length scales, our continuum Doi-Onsager theory captures the hydrodynamic flows generated by polarity-dependent active stresses. The results connect local polar structure to flow structures and defect dynamics.
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Affiliation(s)
- Tong Gao
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| | - Robert Blackwell
- Department of Physics and Liquid Crystal Materials Research Center and Biofrontiers Institute, University of Colorado, Boulder, Colorado 80309, USA
| | - Matthew A. Glaser
- Department of Physics and Liquid Crystal Materials Research Center and Biofrontiers Institute, University of Colorado, Boulder, Colorado 80309, USA
| | - M. D. Betterton
- Department of Physics and Liquid Crystal Materials Research Center and Biofrontiers Institute, University of Colorado, Boulder, Colorado 80309, USA
| | - Michael J. Shelley
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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Córdoba A, Schieber JD, Indei T. The role of filament length, finite-extensibility and motor force dispersity in stress relaxation and buckling mechanisms in non-sarcomeric active gels. SOFT MATTER 2015; 11:38-57. [PMID: 25375087 DOI: 10.1039/c4sm01944j] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
After relaxing some assumptions we apply a single-chain mean-field mathematical model recently introduced [RSC Adv. (2014)] to describe the role of molecular motors in the mechanical properties of active gels. The model allows physics that are not available in models postulated on coarser levels of description. Moreover it proposes a level of description that allows the prediction of observables at time scales too difficult to achieve in multi-chain simulations for realistic filament lengths and densities. We model the semiflexible filaments that compose the active gel as bead-spring chains; molecular motors are accounted for by using a mean-field approach, in which filaments undergo transitions of one motor attachment state depending on the state of the probe filament. The level of description includes the end-to-end distance and attachment state of the filaments, and the motor-generated forces, as stochastic state variables which evolve according to a proposed differential Chapman-Kolmogorov equation. The motor-generated forces are drawn from a stationary distribution of motor stall forces. We consider bead-spring chains with multiple beads, explore the effect of finite-extensibility of the strands and incorporate into the model motor force distributions that have been measured experimentally. The model can no longer be solved analytically but is amenable to numerical simulation. This version of the model allows a more quantitative description of buckling dynamics [Lenz et. al. PRL, 2012, 108, 238107] and the dynamic modulus of active gels. The effect of finite extensibility of the filament strands on the dynamic modulus was also found to be in agreement with the microrheology experiments of Mizuno et. al., [Science, 2007, 315, 370-373].
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Affiliation(s)
- Andrés Córdoba
- Department of Chemical and Biological Engineering and Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 3440 S. Dearborn St, Chicago, Illinois 60616, USA.
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