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Chew WX, Henkin G, Nédélec F, Surrey T. Effects of microtubule length and crowding on active microtubule network organization. iScience 2023; 26:106063. [PMID: 36852161 PMCID: PMC9958361 DOI: 10.1016/j.isci.2023.106063] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Revised: 12/12/2022] [Accepted: 01/20/2023] [Indexed: 01/28/2023] Open
Abstract
Active filament networks can organize into various dynamic architectures driven by cross-linking motors. Densities and kinetic properties of motors and microtubules have been shown previously to determine active microtubule network self-organization, but the effects of other control parameters are less understood. Using computer simulations, we study here how microtubule lengths and crowding effects determine active network architecture and dynamics. We find that attractive interactions mimicking crowding effects or long microtubules both promote the formation of extensile nematic networks instead of asters. When microtubules are very long and the network is highly connected, a new isotropically motile network state resembling a "gliding mesh" is predicted. Using in vitro reconstitutions, we confirm the existence of this gliding mesh experimentally. These results provide a better understanding of how active microtubule network organization can be controlled, with implications for cell biology and active materials in general.
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Affiliation(s)
- Wei-Xiang Chew
- Centre for Genomic Regulation (CRG), Barcelona Institute of Science and Technology (BIST), Dr Aiguader 88, 08003 Barcelona, Spain
| | - Gil Henkin
- Centre for Genomic Regulation (CRG), Barcelona Institute of Science and Technology (BIST), Dr Aiguader 88, 08003 Barcelona, Spain
| | - François Nédélec
- Sainsbury Laboratory, University of Cambridge, 47 Bateman Street, Cambridge CB2 1LR, UK,Corresponding author
| | - Thomas Surrey
- Centre for Genomic Regulation (CRG), Barcelona Institute of Science and Technology (BIST), Dr Aiguader 88, 08003 Barcelona, Spain,ICREA, Passeig de Lluis Companys 23, 08010 Barcelona, Spain,Corresponding author
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2
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Li L, Liu P, Chen K, Zheng N, Yang M. Active depletion torque between two passive rods. SOFT MATTER 2022; 18:4265-4272. [PMID: 35609282 DOI: 10.1039/d2sm00469k] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The active depletion torque experienced by two anisotropic objects in an active bath is a conceptional generalization of the equilibrium entropic torque. Using Brownian dynamics simulations, we compute the active depletion torque suffered by two passive rods immersed in an ensemble of active Brownian particles. Our results demonstrate that the active depletion torque is qualitatively different from its passive counterpart. Interestingly, we find that the active depletion torque can be greatly affected by the external constraint applied on the rotational degree of freedom of the rods, and even the direction may be changed with the orientational constraint, which is in contrast to the equilibrium depletion torque. The main reason for the remarkable features of the active depletion torque is that the active particles can significantly accumulate in the vicinity of the rods due to persistent self-propulsion, which is sensitively dependent on the constraint strength and the rod configurations. Our findings could be relevant for understanding the self-assembly and dynamics of anisotropic macromolecules in living environments.
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Affiliation(s)
- Longfei Li
- School of Physics, Beijing Institute of Technology, Beijing 100081, China.
- Beijing National Laboratory for Condensed Matter Physics and Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
| | - Peng Liu
- Beijing National Laboratory for Condensed Matter Physics and Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325001, China
| | - Ke Chen
- Beijing National Laboratory for Condensed Matter Physics and Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Ning Zheng
- School of Physics, Beijing Institute of Technology, Beijing 100081, China.
| | - Mingcheng Yang
- Beijing National Laboratory for Condensed Matter Physics and Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
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3
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Handle PH, Zaccarelli E, Gnan N. Effective potentials induced by mixtures of patchy and hard co-solutes. J Chem Phys 2021; 155:064901. [PMID: 34391347 DOI: 10.1063/5.0059304] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The addition of co-solutes to colloidal suspensions is often employed to induce tunable depletion interactions. In this work, we investigate effective colloidal interactions arising from binary co-solute mixtures of hard spheres and patchy particles. By changing the relative concentration of the two species, we show that the resulting effective potential Veff continuously changes from the one obtained for a single-component hard sphere co-solute to that mediated by the single-component patchy particle co-solute. Interestingly, we find that, independent of the relative concentration of the two components, the resulting Veff is additive, i.e., it is well-described by the linear combination of the effective interactions mediated by respective pure co-solutes. However, a breakdown of the additivity occurs when the co-solute mixture is close to the onset of a demixing transition. These results represent a step forward in understanding and predicting colloidal behavior in complex and crowded environments and for exploiting this knowledge to design targeted colloidal superstructures.
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Affiliation(s)
- Philip H Handle
- Institute of Physical Chemistry, University of Innsbruck, Innrain 52c, A-6020, Innsbruck, Austria
| | - Emanuela Zaccarelli
- Institute of Physical Chemistry, University of Innsbruck, Innrain 52c, A-6020, Innsbruck, Austria
| | - Nicoletta Gnan
- Institute of Physical Chemistry, University of Innsbruck, Innrain 52c, A-6020, Innsbruck, Austria
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Rupprecht N, Vural DC. Depletion force between disordered linear macromolecules. Phys Rev E 2020; 101:022607. [PMID: 32168718 DOI: 10.1103/physreve.101.022607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2019] [Accepted: 01/29/2020] [Indexed: 06/10/2023]
Abstract
When two macromolecules come very near in a fluid, the surrounding molecules, having finite volume, are less likely to get in between. This leads to a pressure difference manifesting as an entropic attraction, called depletion force. Here we calculate the density profile of liquid molecules surrounding a disordered rigid macromolecules modeled as a random arrangement of hard spheres on a linear backbone. We analytically determine the position dependence of the depletion force between two such disordered molecules by calculating the free energy of the system. We then use molecular dynamics simulations to obtain the depletion force between stiff disordered polymers as well as flexible ones and compare the two against each other. We also show how the disorder averaging can be handled starting from the inhomogenous reference interaction site model equations.
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Affiliation(s)
- Nathaniel Rupprecht
- Department of Physics, University of Notre Dame, South Bend, Indiana 46556, USA
| | - Dervis Can Vural
- Department of Physics, University of Notre Dame, South Bend, Indiana 46556, USA
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Schnauß J, Händler T, Käs JA. Semiflexible Biopolymers in Bundled Arrangements. Polymers (Basel) 2016; 8:polym8080274. [PMID: 30974551 PMCID: PMC6432226 DOI: 10.3390/polym8080274] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2016] [Revised: 07/18/2016] [Accepted: 07/19/2016] [Indexed: 12/15/2022] Open
Abstract
Bundles and networks of semiflexible biopolymers are key elements in cells, lending them mechanical integrity while also enabling dynamic functions. Networks have been the subject of many studies, revealing a variety of fundamental characteristics often determined via bulk measurements. Although bundles are equally important in biological systems, they have garnered much less scientific attention since they have to be probed on the mesoscopic scale. Here, we review theoretical as well as experimental approaches, which mainly employ the naturally occurring biopolymer actin, to highlight the principles behind these structures on the single bundle level.
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Affiliation(s)
- Jörg Schnauß
- Institute for Experimental Physics I, Universität Leipzig, Linnéstraße 5, Leipzig 04103, Germany.
- Fraunhofer Institute for Cell Therapy and Immunology, Perlickstraße 1, Leipzig 04103, Germany.
| | - Tina Händler
- Institute for Experimental Physics I, Universität Leipzig, Linnéstraße 5, Leipzig 04103, Germany.
- Fraunhofer Institute for Cell Therapy and Immunology, Perlickstraße 1, Leipzig 04103, Germany.
| | - Josef A Käs
- Institute for Experimental Physics I, Universität Leipzig, Linnéstraße 5, Leipzig 04103, Germany.
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Schnauß J, Golde T, Schuldt C, Schmidt BUS, Glaser M, Strehle D, Händler T, Heussinger C, Käs JA. Transition from a Linear to a Harmonic Potential in Collective Dynamics of a Multifilament Actin Bundle. PHYSICAL REVIEW LETTERS 2016; 116:108102. [PMID: 27015510 DOI: 10.1103/physrevlett.116.108102] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2015] [Indexed: 05/22/2023]
Abstract
Attractive depletion forces between rodlike particles in highly crowded environments have been shown through recent modeling and experimental approaches to induce different structural and dynamic signatures depending on relative orientation between rods. For example, it has been demonstrated that the axial attraction between two parallel rods yields a linear energy potential corresponding to a constant contractile force of 0.1 pN. Here, we extend pairwise, depletion-induced interactions to a multifilament level with actin bundles, and find contractile forces up to 3 pN. Forces generated due to bundle relaxation were not constant, but displayed a harmonic potential and decayed exponentially with a mean decay time of 3.4 s. Through an analytical model, we explain these different fundamental dynamics as an emergent, collective phenomenon stemming from the additive, pairwise interactions of filaments within a bundle.
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Affiliation(s)
- Jörg Schnauß
- Institute of Experimental Physics I, Universität Leipzig, Linnéstraße 5, 04103 Leipzig, Germany
| | - Tom Golde
- Institute of Experimental Physics I, Universität Leipzig, Linnéstraße 5, 04103 Leipzig, Germany
| | - Carsten Schuldt
- Institute of Experimental Physics I, Universität Leipzig, Linnéstraße 5, 04103 Leipzig, Germany
| | - B U Sebastian Schmidt
- Institute of Experimental Physics I, Universität Leipzig, Linnéstraße 5, 04103 Leipzig, Germany
| | - Martin Glaser
- Institute of Experimental Physics I, Universität Leipzig, Linnéstraße 5, 04103 Leipzig, Germany
| | - Dan Strehle
- Institute of Experimental Physics I, Universität Leipzig, Linnéstraße 5, 04103 Leipzig, Germany
| | - Tina Händler
- Institute of Experimental Physics I, Universität Leipzig, Linnéstraße 5, 04103 Leipzig, Germany
| | - Claus Heussinger
- Institute for Theoretical Physics, Georg-August University of Göttingen, Friedrich-Hund Platz 1, 37077 Göttingen, Germany
| | - Josef A Käs
- Institute of Experimental Physics I, Universität Leipzig, Linnéstraße 5, 04103 Leipzig, Germany
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Binder K, Virnau P, Statt A. Perspective: The Asakura Oosawa model: A colloid prototype for bulk and interfacial phase behavior. J Chem Phys 2014; 141:140901. [DOI: 10.1063/1.4896943] [Citation(s) in RCA: 72] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
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Triplett DA, Fichthorn KA. Entropic forces and directed alignment of hard squares in suspensions of rods and disks. J Chem Phys 2010; 133:144910. [PMID: 20950044 DOI: 10.1063/1.3503975] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We use Monte Carlo simulations in two dimensions to study the depletion forces between two hard squares in a suspension of hard rods or disks. We determine the effects of size and concentration of rods and disks on the potential of mean force between the squares. Both rods and disks produce a short-range depletion attraction between the two squares. The depletion interaction can be strong enough to outweigh the (rotational) entropic repulsion between the squares at certain sizes and concentrations of the rods and disks. We also probe the relative orientation that two squares adopt as they approach each other and we observe rich behavior, in which the relative orientation depends on the size, concentration, and shape of the depletion agent. Simple models based on the ideas of Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)] can explain trends in the potentials of mean force obtained from the simulations.
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Affiliation(s)
- Derek A Triplett
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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Li W, Yang T, Ma HR. Depletion potentials in colloidal mixtures of hard spheres and rods. J Chem Phys 2008; 128:044910. [DOI: 10.1063/1.2820785] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Jungblut S, Tuinier R, Binder K, Schilling T. Depletion induced isotropic-isotropic phase separation in suspensions of rod-like colloids. J Chem Phys 2007; 127:244909. [DOI: 10.1063/1.2815805] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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Schilling T, Jungblut S, Miller MA. Depletion-induced percolation in networks of nanorods. PHYSICAL REVIEW LETTERS 2007; 98:108303. [PMID: 17358576 DOI: 10.1103/physrevlett.98.108303] [Citation(s) in RCA: 71] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2006] [Indexed: 05/14/2023]
Abstract
Above a certain density threshold, suspensions of rodlike colloidal particles form system-spanning networks. Using Monte Carlo simulations, we investigate how the depletion forces caused by spherical particles affect these networks in isotropic suspensions of rods. Although the depletion forces are strongly anisotropic and favor alignment of the rods, the percolation threshold of the rods decreases significantly. The relative size of the effect increases with the aspect ratio of the rods. The structural changes induced in the suspension by the depletant are characterized in detail and the system is compared to an ideal fluid of freely interpenetrable rods.
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Affiliation(s)
- T Schilling
- Institut für Physik, Johannes Gutenberg-Universität, D-55099 Mainz, Staudinger Weg 7, Germany
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König PM, Roth R, Dietrich S. Depletion forces between nonspherical objects. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:041404. [PMID: 17155054 DOI: 10.1103/physreve.74.041404] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2006] [Indexed: 05/12/2023]
Abstract
We extend the insertion approach for calculating depletion potentials to the case of nonspherical solutes. We suggest to employ the recently developed curvature expansion of density profiles close to complexly shaped walls. The approximations introduced in the calculation by the use of the curvature expansion and of weight functions for nonspherical objects can be tested independently. As an application for our approach we calculate and discuss the depletion potential between two hard oblate ellipsoids in a solvent of hard spheres. For this system we calculate the entropic force and torque acting on the objects.
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Affiliation(s)
- P-M König
- Max-Planck-Institut für Metallforschung, Heisenbergstrasse 3, D-70569 Stuttgart, Germany
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Xiao C, Guo J, Hu P. Geometrical confinements and depletion interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:061403. [PMID: 16906823 DOI: 10.1103/physreve.73.061403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2005] [Revised: 03/23/2006] [Indexed: 05/11/2023]
Abstract
In the system with two large spheres confined between two parallel plates, there are depletion interactions between the two large spheres and between one large sphere and the closely placed plate. Obviously, the depletion interactions exerted on one large sphere will be strongly affected by the presence of the closely placed plate or the other large sphere. This prediction is confirmed by the numerical results obtained through the acceptance ratio method (ARM) or density integration method (DIM), i.e., they are strengthened when two large spheres are contacted. Furthermore, it is found that the influences on the depletion forces are also sensitive to the angle of the centers' connection line between the two large spheres and the confining walls. In addition, the numerical results show that the total depletion force exerted on one large sphere from both the other large sphere and the closely placed plate can be determined through ARM or DIM from the interactions between the two large spheres or between one large sphere and the corresponding closely placed plate.
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Affiliation(s)
- Changming Xiao
- Department of Physics, Hunan Normal University, 410081 China.
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