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Eshghi I, Zidovska A, Grosberg AY. Activity-Driven Phase Transition Causes Coherent Flows of Chromatin. PHYSICAL REVIEW LETTERS 2023; 131:048401. [PMID: 37566839 DOI: 10.1103/physrevlett.131.048401] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Accepted: 06/23/2023] [Indexed: 08/13/2023]
Abstract
We discover a new type of nonequilibrium phase transition in a model of chromatin dynamics, which accounts for the coherent motions that have been observed in experiment. The coherent motion is due to the long-range cooperation of molecular motors tethered to chromatin. Cooperation occurs if each motor acts simultaneously on the polymer and the surrounding solvent, exerting on them equal and opposite forces. This drives the flow of solvent past the polymer, which in turn affects the orientation of nearby motors and, if the drive is strong enough, an active polar ("ferromagnetic") phase of motors can spontaneously form. Depending on boundary conditions, either transverse flows or sustained longitudinal oscillations and waves are possible. Predicted length scales are consistent with experiments. We now have in hand a coarse-grained description of chromatin dynamics which reproduces the directed coherent flows of chromatin seen in experiments. This field-theoretic description can be analytically coupled to other features of the nuclear environment such as fluctuating or porous boundaries, local heterogeneities in the distribution of chromatin or its activity, leading to insights on the effects of activity on the cell nucleus and its contents.
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Affiliation(s)
- Iraj Eshghi
- Center for Soft Matter Research, Department of Physics, New York University, New York, New York 10003, USA
| | - Alexandra Zidovska
- Center for Soft Matter Research, Department of Physics, New York University, New York, New York 10003, USA
| | - Alexander Y Grosberg
- Center for Soft Matter Research, Department of Physics, New York University, New York, New York 10003, USA
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2
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Dynamic self-assembly of active particles in liquid crystals. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.118692] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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3
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Lavrentovich OD. Design of nematic liquid crystals to control microscale dynamics. LIQUID CRYSTALS REVIEWS 2021; 8:59-129. [PMID: 34956738 PMCID: PMC8698256 DOI: 10.1080/21680396.2021.1919576] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2020] [Accepted: 04/11/2021] [Indexed: 05/25/2023]
Abstract
The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.
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Affiliation(s)
- Oleg D Lavrentovich
- Advanced Materials and Liquid Crystal Institute, Department of Physics, Materials Science Graduate Program, Kent State University, Kent, OH 44242, USA
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4
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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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5
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Abstract
The emergence of macroscopic order and patterns is a central paradigm in systems of (self-)propelled agents and a key component in the structuring of many biological systems. The relationships between the ordering process and the underlying microscopic interactions have been extensively explored both experimentally and theoretically. While emerging patterns often show one specific symmetry (e.g., nematic lane patterns or polarized traveling flocks), depending on the symmetry of the alignment interactions patterns with different symmetries can apparently coexist. Indeed, recent experiments with an actomysin motility assay suggest that polar and nematic patterns of actin filaments can interact and dynamically transform into each other. However, theoretical understanding of the mechanism responsible remains elusive. Here, we present a kinetic approach complemented by a hydrodynamic theory for agents with mixed alignment symmetries, which captures the experimentally observed phenomenology and provides a theoretical explanation for the coexistence and interaction of patterns with different symmetries. We show that local, pattern-induced symmetry breaking can account for dynamically coexisting patterns with different symmetries. Specifically, in a regime with moderate densities and a weak polar bias in the alignment interaction, nematic bands show a local symmetry-breaking instability within their high-density core region, which induces the formation of polar waves along the bands. These instabilities eventually result in a self-organized system of nematic bands and polar waves that dynamically transform into each other. Our study reveals a mutual feedback mechanism between pattern formation and local symmetry breaking in active matter that has interesting consequences for structure formation in biological systems.
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6
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Chatterjee P, Goldenfeld N. Three-body interactions drive the transition to polar order in a simple flocking model. Phys Rev E 2019; 100:040602. [PMID: 31770962 DOI: 10.1103/physreve.100.040602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2018] [Indexed: 11/07/2022]
Abstract
A large class of mesoscopic or macroscopic flocking theories are coarse-grained from microscopic models that feature binary interactions as the chief aligning mechanism. However, while such theories seemingly predict the existence of polar order with just binary interactions, actomyosin motility assay experiments show that binary interactions are insufficient to obtain polar order, especially at high densities. To resolve this paradox, here we introduce a solvable one-dimensional flocking model and derive its stochastic hydrodynamics. We show that two-body interactions are insufficient to generate polar order unless the noise is non-Gaussian. We show that noisy three-body interactions in the microscopic theory allow us to capture all essential dynamical features of the flocking transition, in systems that achieve orientational order above a critical density.
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Affiliation(s)
- Purba Chatterjee
- Department of Physics, University of Illinois at Urbana-Champaign, Loomis Laboratory of Physics, 1110 West Green Street, Urbana, Illinois 61801-3080, USA
| | - Nigel Goldenfeld
- Department of Physics, University of Illinois at Urbana-Champaign, Loomis Laboratory of Physics, 1110 West Green Street, Urbana, Illinois 61801-3080, USA
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7
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Reinken H, Klapp SHL, Bär M, Heidenreich S. Derivation of a hydrodynamic theory for mesoscale dynamics in microswimmer suspensions. Phys Rev E 2018; 97:022613. [PMID: 29548118 DOI: 10.1103/physreve.97.022613] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2017] [Indexed: 06/08/2023]
Abstract
In this paper, we systematically derive a fourth-order continuum theory capable of reproducing mesoscale turbulence in a three-dimensional suspension of microswimmers. We start from overdamped Langevin equations for a generic microscopic model (pushers or pullers), which include hydrodynamic interactions on both small length scales (polar alignment of neighboring swimmers) and large length scales, where the solvent flow interacts with the order parameter field. The flow field is determined via the Stokes equation supplemented by an ansatz for the stress tensor. In addition to hydrodynamic interactions, we allow for nematic pair interactions stemming from excluded-volume effects. The results here substantially extend and generalize earlier findings [S. Heidenreich et al., Phys. Rev. E 94, 020601 (2016)2470-004510.1103/PhysRevE.94.020601], in which we derived a two-dimensional hydrodynamic theory. From the corresponding mean-field Fokker-Planck equation combined with a self-consistent closure scheme, we derive nonlinear field equations for the polar and the nematic order parameter, involving gradient terms of up to fourth order. We find that the effective microswimmer dynamics depends on the coupling between solvent flow and orientational order. For very weak coupling corresponding to a high viscosity of the suspension, the dynamics of mesoscale turbulence can be described by a simplified model containing only an effective microswimmer velocity.
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Affiliation(s)
- Henning Reinken
- Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Sabine H L Klapp
- Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Markus Bär
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Abbestr. 2-12, 10587 Berlin, Germany
| | - Sebastian Heidenreich
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Abbestr. 2-12, 10587 Berlin, Germany
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8
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Heidenreich S, Dunkel J, Klapp SHL, Bär M. Hydrodynamic length-scale selection in microswimmer suspensions. Phys Rev E 2016; 94:020601. [PMID: 27627229 DOI: 10.1103/physreve.94.020601] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2015] [Indexed: 11/07/2022]
Abstract
A universal characteristic of mesoscale turbulence in active suspensions is the emergence of a typical vortex length scale, distinctly different from the scale invariance of turbulent high-Reynolds number flows. Collective length-scale selection has been observed in bacterial fluids, endothelial tissue, and active colloids, yet the physical origins of this phenomenon remain elusive. Here, we systematically derive an effective fourth-order field theory from a generic microscopic model that allows us to predict the typical vortex size in microswimmer suspensions. Building on a self-consistent closure condition, the derivation shows that the vortex length scale is determined by the competition between local alignment forces, rotational diffusion, and intermediate-range hydrodynamic interactions. Vortex structures found in simulations of the theory agree with recent measurements in Bacillus subtilis suspensions. Moreover, our approach yields an effective viscosity enhancement (reduction), as reported experimentally for puller (pusher) microorganisms.
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Affiliation(s)
- Sebastian Heidenreich
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Abbestrasse 2-12, D-10587 Berlin, Germany
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue E17-412, Cambridge, Massachusetts 02139-4307, USA
| | - Sabine H L Klapp
- Institute for Theoretical Physics, Technical University Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
| | - Markus Bär
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Abbestrasse 2-12, D-10587 Berlin, Germany
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9
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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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10
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Head DA, Briels WJ, Gompper G. Nonequilibrium structure and dynamics in a microscopic model of thin-film active gels. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032705. [PMID: 24730872 DOI: 10.1103/physreve.89.032705] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2013] [Indexed: 06/03/2023]
Abstract
In the presence of adenosine triphosphate, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic modeling can help to quantify the relationship between individual motors plus filaments to organization and dynamics on molecular and supramolecular length scales. Here, we present results of extensive numerical simulations of active gels where the motors and filaments are confined between two infinite parallel plates. Thermal fluctuations and excluded-volume interactions between filaments are included. A systematic variation of rates for motor motion, attachment, and detachment, including a differential detachment rate from filament ends, reveals a range of nonequilibrium behavior. Strong motor binding produces structured filament aggregates that we refer to as asters, bundles, or layers, whose stability depends on motor speed and differential end detachment. The gross features of the dependence of the observed structures on the motor rate and the filament concentration can be captured by a simple one-filament model. Loosely bound aggregates exhibit superdiffusive mass transport, where filament translocation scales with lag time with nonunique exponents that depend on motor kinetics. An empirical data collapse of filament speed as a function of motor speed and end detachment is found, suggesting a dimensional reduction of the relevant parameter space. We conclude by discussing the perspectives of microscopic modeling in the field of active gels.
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Affiliation(s)
- D A Head
- School of Computing, Leeds University, Leeds LS2 9JT, United Kingdom
| | - W J Briels
- Computational Biophysics, University of Twente, 7500 AE Enschede, The Netherlands
| | - Gerhard Gompper
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
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11
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Cates ME. Diffusive transport without detailed balance in motile bacteria: does microbiology need statistical physics? REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:042601. [PMID: 22790505 DOI: 10.1088/0034-4885/75/4/042601] [Citation(s) in RCA: 273] [Impact Index Per Article: 22.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Microbiology is the science of microbes, particularly bacteria. Many bacteria are motile: they are capable of self-propulsion. Among these, a significant class execute so-called run-and-tumble motion: they follow a fairly straight path for a certain distance, then abruptly change direction before repeating the process. This dynamics has something in common with Brownian motion (it is diffusive at large scales), and also something in contrast. Specifically, motility parameters such as the run speed and tumble rate depend on the local environment and hence can vary in space. When they do so, even if a steady state is reached, this is not generally invariant under time reversal: the principle of detailed balance, which restores the microscopic time-reversal symmetry of systems in thermal equilibrium, is mesoscopically absent in motile bacteria. This lack of detailed balance (allowed by the flux of chemical energy that drives motility) creates pitfalls for the unwary modeller. Here I review some statistical-mechanical models for bacterial motility, presenting them as a paradigm for exploring diffusion without detailed balance. I also discuss the extent to which statistical physics is useful in understanding real or potential microbiological experiments.
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Affiliation(s)
- M E Cates
- SUPA, School of Physics and Astronomy, University of Edinburgh, JCMB, Kings Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK
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12
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Heidenreich S, Hess S, Klapp SHL. Nonlinear rheology of active particle suspensions: insights from an analytical approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:011907. [PMID: 21405713 DOI: 10.1103/physreve.83.011907] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2010] [Indexed: 05/30/2023]
Abstract
We consider active suspensions in the isotropic phase subjected to a shear flow. Using a set of extended hydrodynamic equations we derive a variety of analytical expressions for rheological quantities such as shear viscosity and normal stress differences. In agreement to full-blown numerical calculations and experiments we find a shear-thickening or -thinning behavior depending on whether the particles are contractile or extensile. Moreover, our analytical approach predicts that the normal stress differences can change their sign in contrast to passive suspensions.
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Affiliation(s)
- Sebastian Heidenreich
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, United Kingdom.
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13
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Rühle V, Ziebert F, Peter R, Zimmermann W. Instabilities in a two-dimensional polar-filament--motor system. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2008; 27:243-251. [PMID: 18972145 DOI: 10.1140/epje/i2007-10377-x] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2007] [Accepted: 09/18/2008] [Indexed: 05/27/2023]
Abstract
The dynamical interaction between filaments and motor proteins is known for their propensity to self-organize into spatio-temporal patterns. Since the filaments are polar in the sense that motors define a direction of motion on them, the system can display a spatially homogeneous polar-filament orientation. We show that the latter anisotropic state itself may become unstable with respect to inhomogeneous fluctuations. This scenario shares similarities with instabilities in planarly aligned nematic liquid crystals: in both cases the wave vector of the instability may be oriented either parallel or oblique to the polarity axis. However, the encountered instabilities here are long-wave instead of short-wave and the destabilizing modes are drifting ones due to the polar symmetry. Additionally a nonpropagating transverse instability is possible. The stability diagrams related to the various wave vector orientations relative to the polarity axis are determined and discussed for a specific model of motor-filament interactions.
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Affiliation(s)
- V Rühle
- Theoretische Physik, Universität Bayreuth, D-95440 Bayreuth, Germany
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14
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Basu A, Joanny JF, Jülicher F, Prost J. Thermal and non-thermal fluctuations in active polar gels. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2008; 27:149-160. [PMID: 18791871 DOI: 10.1140/epje/i2008-10364-9] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2008] [Accepted: 07/28/2008] [Indexed: 05/26/2023]
Abstract
We discuss general features of noise and fluctuations in active polar gels close to and away from equilibrium. We use the single-component hydrodynamic theory of active polar gels built by Kruse and coworkers to describe the cytoskeleton in cells. Close to equilibrium, we calculate the response function of the gel to external fields and introduce Langevin forces in the constitutive equations with correlation functions respecting the fluctuation-dissipation theorem. We then discuss the breakage of the fluctuation-dissipation theorem due to an external field such as the activity of the motors. Active gels away from equilibrium are considered at the scaling level. As an example of application of the theory, we calculate the density correlation function (the dynamic structure factor) of a compressible active polar gel and discuss possible instabilities.
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Affiliation(s)
- A Basu
- Theoretical Condensed Matter Physics Division and Centre for Advanced Research and Education, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, 700 064, Kolkata (Calcutta), India
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15
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Abstract
Mathematical modeling has become increasingly important in many areas of biology during the past two decades, and the area of cell migration and motility has seen significant contributions from a wide range of modeling approaches. In this chapter, we cover examples from the broad range of work in this area, emphasizing the models' biological significance and the relationships between them. We focus on three specific areas: cell protrusion, cell adhesion, and retraction/whole-cell models. At the end of this chapter, we provide our perspective on issues that future models and experiments should consider in order to advance the boundaries of this field.
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Affiliation(s)
- Anders E Carlsson
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
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16
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Zumdieck A, Voituriez R, Prost J, Joanny JF. Spontaneous flow of active polar gels in undulated channels. Faraday Discuss 2008; 139:369-75; discussion 399-417, 419-20. [DOI: 10.1039/b716934e] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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17
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Aranson IS, Sokolov A, Kessler JO, Goldstein RE. Model for dynamical coherence in thin films of self-propelled microorganisms. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:040901. [PMID: 17500857 DOI: 10.1103/physreve.75.040901] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2006] [Indexed: 05/15/2023]
Abstract
Concentrated bacterial suspensions spontaneously develop transient spatiotemporal patterns of coherent locomotion whose correlation lengths greatly exceed the size of individual organisms. Continuum models have indicated that a state of uniform swimming order is linearly unstable at finite wavelengths, but have not addressed the nonlinear dynamics of the coherent state, with its biological implications for mixing, transport, and intercellular communication. We investigate a specific model incorporating hydrodynamic interactions in thin-film geometries and show by numerical studies that it displays large scale persistently recurring vortices, as actually observed.
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Affiliation(s)
- Igor S Aranson
- Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USA
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18
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Liverpool TB, Marchetti MC. Rheology of active filament solutions. PHYSICAL REVIEW LETTERS 2006; 97:268101. [PMID: 17280467 DOI: 10.1103/physrevlett.97.268101] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2006] [Indexed: 05/13/2023]
Abstract
We study the viscoelasticity of an active solution of polar biofilaments and motor proteins. Using a molecular model, we derive the constitutive equations for the stress tensor in the isotropic phase and in phases with liquid crystalline order. The stress relaxation in the various phases is discussed. Contractile activity is responsible for a spectacular difference in the viscoelastic properties on opposite sides of the order-disorder transition.
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Affiliation(s)
- T B Liverpool
- Department of Applied Mathematics, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, United Kingdom
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19
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Liverpool TB. Active gels: where polymer physics meets cytoskeletal dynamics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2006; 364:3335-55. [PMID: 17090463 DOI: 10.1098/rsta.2006.1897] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
The cytoskeleton provides eukaryotic cells with mechanical support and helps them to perform their biological functions. It is predominantly composed of a network of semiflexible polar protein filaments. In addition, there are many accessory proteins that bind to these filaments, regulate their assembly, link them to organelles and provide the motors that either move the organelles along the filaments or move the filaments themselves. A natural approach to such a multiple particle system is the study of its collective excitations. I review some recent work on the theoretical description of the emergence of a number of particular collective motile behaviours from the interactions between different elements of the cytoskeleton. In order to do this, close analogies have been made to the study of driven soft condensed matter systems. However, it emerges naturally that a description of these soft active motile systems gives rise to new types of collective phenomena not seen in conventional soft systems. I discuss the implications of these results and perspectives for the future.
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20
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Abstract
The cellular cytoskeleton is well studied in terms of its biological and physical properties, making it an attractive subject for systems approaches. Here, we describe the experimental and theoretical strategies used to study the collective behaviour of microtubules and motors. We illustrate how this led to the beginning of an understanding of dynamic cellular patterns that have precise functions.
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Affiliation(s)
- Eric Karsenti
- European Molecular Systems Biology Laboratory, Meyerhofstrasse 1, 69117 Heidelberg, Germany.
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21
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Ahmadi A, Marchetti MC, Liverpool TB. Hydrodynamics of isotropic and liquid crystalline active polymer solutions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:061913. [PMID: 17280102 DOI: 10.1103/physreve.74.061913] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2006] [Indexed: 05/13/2023]
Abstract
We describe the large-scale collective behavior of solutions of polar biofilaments and stationary and mobile crosslinkers. Both mobile and stationary crosslinkers induce filament alignment promoting either polar or nematic order. In addition, mobile crosslinkers, such as clusters of motor proteins, exchange forces and torques among the filaments and render the homogeneous states unstable via filament bundling. We start from a Smoluchowski equation for rigid filaments in solutions, where pairwise crosslink-mediated interactions among the filaments yield translational and rotational currents. The large-scale properties of the system are described in terms of continuum equations for filament and motor densities, polarization, and alignment tensor obtained by coarse-graining the Smoluchovski equation. The possible homogeneous and inhomogeneous states of the systems are obtained as stable solutions of the dynamical equations and are characterized in terms of experimentally accessible parameters. We make contact with work by other authors and show that our model allows for an estimate of the various parameters in the hydrodynamic equations in terms of physical properties of the crosslinkers.
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Affiliation(s)
- Aphrodite Ahmadi
- Physics Department, Syracuse University, Syracuse, New York 13244, USA
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Carlsson AE. Contractile stress generation by actomyosin gels. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:051912. [PMID: 17279944 DOI: 10.1103/physreve.74.051912] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2006] [Revised: 08/24/2006] [Indexed: 05/13/2023]
Abstract
The tension generated by randomly distributed myosin minifilaments in an actin gel is evaluated using a rigorous theorem relating the surface forces acting on the gel to the forces exerted by the myosins. The maximum tension generated per myosin depends strongly on the lengths of the myosin minifilaments and the actin filaments. The result is used to place an upper bound on the tension that can be generated during cytokinesis. It is found that actomyosin contraction by itself generates too little force for ring contraction during cytokinesis unless the actin filaments are tightly crosslinked into inextensible units much longer than a single actin filament.
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Affiliation(s)
- A E Carlsson
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
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23
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Aranson IS, Tsimring LS. Theory of self-assembly of microtubules and motors. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:031915. [PMID: 17025675 DOI: 10.1103/physreve.74.031915] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2005] [Revised: 08/07/2006] [Indexed: 05/12/2023]
Abstract
We derive a model describing spatiotemporal organization of an array of microtubules interacting via molecular motors. Starting from a stochastic model of inelastic polar rods with a generic anisotropic interaction kernel, we obtain a set of equations for the local rods concentration and orientation. At large enough mean density of rods and concentration of motors, the model describes an orientational instability. We demonstrate that the orientational instability leads to the formation of vortices and (for large density and/or kernel anisotropy) asters seen in recent experiments. We derive the specific form of the interaction kernel from the detailed analysis of microscopic interaction of two filaments mediated by a moving molecular motor and extend our results to include variable motor density and motor attachment to the substrate.
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Affiliation(s)
- Igor S Aranson
- Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA
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24
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Brand HR, Pleiner H, Ziebert F. Macroscopic dynamics of polar nematic liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:021713. [PMID: 17025458 DOI: 10.1103/physreve.74.021713] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2006] [Indexed: 05/12/2023]
Abstract
We present the macroscopic equations for polar nematic liquid crystals. We consider the case where one has both, the usual nematic director, n[over ] , characterizing quadrupolar order as well as the macroscopic polarization, P , representing polar order, but where their directions coincide and are rigidly coupled. In this case one has to choose P as the independent macroscopic variable. Such equations are expected to be relevant in connection with nematic phases with unusual properties found recently in compounds composed of banana-shaped molecules. Among the effects predicted, which are absent in conventional nematic liquid crystals showing only quadrupolar order, are pyro-electricity and its analogs for density and for concentration in mixtures as well as a flow alignment behavior, which is more complex than in usual low molecular weight nematics. We also discuss the formation of defect structures expected in such systems.
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Affiliation(s)
- Helmut R Brand
- Theoretische Physik III, Universität Bayreuth, 95440 Bayreuth, Germany and Max Planck Institute for Polymer Research, 55021 Mainz, Germany.
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25
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Kruse K, Jülicher F. Dynamics and mechanics of motor-filament systems. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2006; 20:459-65. [PMID: 16953342 DOI: 10.1140/epje/i2006-10036-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2006] [Accepted: 08/14/2006] [Indexed: 05/11/2023]
Abstract
Motivated by the cytoskeleton of eukaryotic cells, we develop a general framework for describing the large-scale dynamics of an active filament network. In the cytoskeleton, active cross-links are formed by motor proteins that are able to induce relative motion between filaments. Starting from pair-wise interactions of filaments via such active processes, our framework is based on momentum conservation and an analysis of the momentum flux. This allows us to calculate the stresses in the filament network generated by the action of motor proteins. We derive effective theories for the filament dynamics which can be related to continuum theories of active polar gels. As an example, we discuss the stability of homogenous isotropic filament distributions in two spatial dimensions.
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Affiliation(s)
- K Kruse
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzerstr. 38, 01187, Dresden, Germany.
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