1
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Lemma B, Lemma LM, Ems-McClung SC, Walczak CE, Dogic Z, Needleman DJ. Structure and dynamics of motor-driven microtubule bundles. SOFT MATTER 2024. [PMID: 38872426 DOI: 10.1039/d3sm01336g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2024]
Abstract
Connecting the large-scale emergent behaviors of active cytoskeletal materials to the microscopic properties of their constituents is a challenge due to a lack of data on the multiscale dynamics and structure of such systems. We approach this problem by studying the impact of depletion attraction on bundles of microtubules and kinesin-14 molecular motors. For all depletant concentrations, kinesin-14 bundles generate comparable extensile dynamics. However, this invariable mesoscopic behavior masks the transition in the microscopic motion of microtubules. Specifically, with increasing attraction, we observe a transition from bi-directional sliding with extension to pure extension with no sliding. Small-angle X-ray scattering shows that the transition in microtubule dynamics is concurrent with a structural rearrangement of microtubules from an open hexagonal to a compressed rectangular lattice. These results demonstrate that bundles of microtubules and molecular motors can display the same mesoscopic extensile behaviors despite having different internal structures and microscopic dynamics. They provide essential information for developing multiscale models of active matter.
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Affiliation(s)
- Bezia Lemma
- Physics Department, Harvard University, Cambridge, MA 02138, USA
- Physics Department, Brandeis University, Waltham, MA 02453, USA.
- Physics Department, University of California, Santa Barbara, CA 93106, USA
| | - Linnea M Lemma
- Physics Department, Brandeis University, Waltham, MA 02453, USA.
- Physics Department, University of California, Santa Barbara, CA 93106, USA
| | | | - Claire E Walczak
- Medical Sciences, Indiana University School of Medicine, Bloomington, IN 47405, USA
| | - Zvonimir Dogic
- Physics Department, Brandeis University, Waltham, MA 02453, USA.
- Physics Department, University of California, Santa Barbara, CA 93106, USA
- Biomolecular Science & Engineering Department, University of California, Santa Barbara, CA 93106, USA
| | - Daniel J Needleman
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
- Molecular & Cellular Biology Department, Harvard University, Cambridge, MA 02138, USA
- Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA
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2
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Li Y, Zarei Z, Tran PN, Wang Y, Baskaran A, Fraden S, Hagan MF, Hong P. A machine learning approach to robustly determine director fields and analyze defects in active nematics. SOFT MATTER 2024; 20:1869-1883. [PMID: 38318759 DOI: 10.1039/d3sm01253k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/07/2024]
Abstract
Active nematics are dense systems of rodlike particles that consume energy to drive motion at the level of the individual particles. They exist in natural systems like biological tissues and artificial materials such as suspensions of self-propelled colloidal particles or synthetic microswimmers. Active nematics have attracted significant attention in recent years due to their spectacular nonequilibrium collective spatiotemporal dynamics, which may enable applications in fields such as robotics, drug delivery, and materials science. The director field, which measures the direction and degree of alignment of the local nematic orientation, is a crucial characteristic of active nematics and is essential for studying topological defects. However, determining the director field is a significant challenge in many experimental systems. Although director fields can be derived from images of active nematics using traditional imaging processing methods, the accuracy of such methods is highly sensitive to the settings of the algorithms. These settings must be tuned from image to image due to experimental noise, intrinsic noise of the imaging technology, and perturbations caused by changes in experimental conditions. This sensitivity currently limits automatic analysis of active nematics. To address this, we developed a machine learning model for extracting reliable director fields from raw experimental images, which enables accurate analysis of topological defects. Application of the algorithm to experimental data demonstrates that the approach is robust and highly generalizable to experimental settings that are different from those in the training data. It could be a promising tool for investigating active nematics and may be generalized to other active matter systems.
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Affiliation(s)
- Yunrui Li
- Computer Science Department, Brandeis University, USA.
| | - Zahra Zarei
- Physics Department, Brandeis University, USA
| | - Phu N Tran
- Physics Department, Brandeis University, USA
| | - Yifei Wang
- Computer Science Department, Brandeis University, USA.
| | | | - Seth Fraden
- Physics Department, Brandeis University, USA
| | | | - Pengyu Hong
- Computer Science Department, Brandeis University, USA.
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3
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Najma B, Wei WS, Baskaran A, Foster PJ, Duclos G. Microscopic interactions control a structural transition in active mixtures of microtubules and molecular motors. Proc Natl Acad Sci U S A 2024; 121:e2300174121. [PMID: 38175870 PMCID: PMC10786313 DOI: 10.1073/pnas.2300174121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2023] [Accepted: 10/07/2023] [Indexed: 01/06/2024] Open
Abstract
Microtubules and molecular motors are essential components of the cellular cytoskeleton, driving fundamental processes in vivo, including chromosome segregation and cargo transport. When reconstituted in vitro, these cytoskeletal proteins serve as energy-consuming building blocks to study the self-organization of active matter. Cytoskeletal active gels display rich emergent dynamics, including extensile flows, locally contractile asters, and bulk contraction. However, it is unclear how the protein-protein interaction kinetics set their contractile or extensile nature. Here, we explore the origin of the transition from extensile bundles to contractile asters in a minimal reconstituted system composed of stabilized microtubules, depletant, adenosine 5'-triphosphate (ATP), and clusters of kinesin-1 motors. We show that the microtubule-binding and unbinding kinetics of highly processive motor clusters set their ability to end-accumulate, which can drive polarity sorting of the microtubules and aster formation. We further demonstrate that the microscopic time scale of end-accumulation sets the emergent time scale of aster formation. Finally, we show that biochemical regulation is insufficient to fully explain the transition as generic aligning interactions through depletion, cross-linking, or excluded volume interactions can drive bundle formation despite end-accumulating motors. The extensile-to-contractile transition is well captured by a simple self-assembly model where nematic and polar aligning interactions compete to form either bundles or asters. Starting from a five-dimensional organization phase space, we identify a single control parameter given by the ratio of the different component concentrations that dictates the material-scale organization. Overall, this work shows that the interplay of biochemical and mechanical tuning at the microscopic level controls the robust self-organization of active cytoskeletal materials.
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Affiliation(s)
- Bibi Najma
- Department of Physics, Brandeis University, Waltham, MA02453
| | - Wei-Shao Wei
- Department of Physics, Brandeis University, Waltham, MA02453
| | - Aparna Baskaran
- Department of Physics, Brandeis University, Waltham, MA02453
| | - Peter J. Foster
- Department of Physics, Brandeis University, Waltham, MA02453
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4
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Gergely ZR, Jones MH, Zhou B, Cash C, McIntosh JR, Betterton MD. Distinct regions of the kinesin-5 C-terminal tail are essential for mitotic spindle midzone localization and sliding force. Proc Natl Acad Sci U S A 2023; 120:e2306480120. [PMID: 37725645 PMCID: PMC10523502 DOI: 10.1073/pnas.2306480120] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2023] [Accepted: 07/05/2023] [Indexed: 09/21/2023] Open
Abstract
Kinesin-5 motor proteins play essential roles during mitosis in most organisms. Their tetrameric structure and plus-end-directed motility allow them to bind to and move along antiparallel microtubules, thereby pushing spindle poles apart to assemble a bipolar spindle. Recent work has shown that the C-terminal tail is particularly important to kinesin-5 function: The tail affects motor domain structure, ATP hydrolysis, motility, clustering, and sliding force measured for purified motors, as well as motility, clustering, and spindle assembly in cells. Because previous work has focused on presence or absence of the entire tail, the functionally important regions of the tail remain to be identified. We have therefore characterized a series of kinesin-5/Cut7 tail truncation alleles in fission yeast. Partial truncation causes mitotic defects and temperature-sensitive growth, while further truncation that removes the conserved BimC motif is lethal. We compared the sliding force generated by cut7 mutants using a kinesin-14 mutant background in which some microtubules detach from the spindle poles and are pushed into the nuclear envelope. These Cut7-driven protrusions decreased as more of the tail was truncated, and the most severe truncations produced no observable protrusions. Our observations suggest that the C-terminal tail of Cut7p contributes to both sliding force and midzone localization. In the context of sequential tail truncation, the BimC motif and adjacent C-terminal amino acids are particularly important for sliding force. In addition, moderate tail truncation increases midzone localization, but further truncation of residues N-terminal to the BimC motif decreases midzone localization.
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Affiliation(s)
- Zachary R Gergely
- Department of Physics, University of Colorado, Boulder, CO 80309
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, CO 80309
| | - Michele H Jones
- Department of Physics, University of Colorado, Boulder, CO 80309
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, CO 80309
| | - Bojun Zhou
- Department of Physics, University of Colorado, Boulder, CO 80309
| | - Cai Cash
- Department of Physics, University of Colorado, Boulder, CO 80309
| | - J Richard McIntosh
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, CO 80309
| | - Meredith D Betterton
- Department of Physics, University of Colorado, Boulder, CO 80309
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, CO 80309
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5
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Gergely Z, Jones MH, Zhou B, Cash C, McIntosh R, Betterton M. Distinct regions of the kinesin-5 C-terminal tail are essential for mitotic spindle midzone localization and sliding force. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.05.01.538972. [PMID: 37205432 PMCID: PMC10187184 DOI: 10.1101/2023.05.01.538972] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
Kinesin-5 motor proteins play essential roles during mitosis in most organisms. Their tetrameric structure and plus-end-directed motility allow them to bind to and move along antiparallel microtubules, thereby pushing spindle poles apart to assemble a bipolar spindle. Recent work has shown that the C-terminal tail is particularly important to kinesin-5 function: the tail affects motor domain structure, ATP hydrolysis, motility, clustering, and sliding force measured for purified motors, as well as motility, clustering, and spindle assembly in cells. Because previous work has focused on presence or absence of the entire tail, the functionally important regions of the tail remain to be identified. We have therefore characterized a series of kinesin-5/Cut7 tail truncation alleles in fission yeast. Partial truncation causes mitotic defects and temperature-sensitive growth, while further truncation that removes the conserved BimC motif is lethal. We compared the sliding force generated by cut7 mutants using a kinesin-14 mutant background in which some microtubules detach from the spindle poles and are pushed into the nuclear envelope. These Cut7-driven protrusions decreased as more of the tail was truncated, and the most severe truncations produced no observable protrusions. Our observations suggest that the C-terminal tail of Cut7p contributes to both sliding force and midzone localization. In the context of sequential tail truncation, the BimC motif and adjacent C-terminal amino acids are particularly important for sliding force. In addition, moderate tail truncation increases midzone localization, but further truncation of residues N terminal to the BimC motif decreases midzone localization.
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6
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Stam S, Gardel ML, Weirich KL. Direct detection of deformation modes on varying length scales in active biopolymer networks. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.05.15.540780. [PMID: 37292666 PMCID: PMC10245561 DOI: 10.1101/2023.05.15.540780] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Correlated flows and forces that emerge from active matter orchestrate complex processes such as shape regulation and deformations in biological cells and tissues. The active materials central to cellular mechanics are cytoskeletal networks, where molecular motor activity drives deformations and remodeling. Here, we investigate deformation modes in actin networks driven by the molecular motor myosin II through quantitative fluorescence microscopy. We examine the deformation anisotropy at different length scales in networks of entangled, cross-linked, and bundled actin. In sparsely cross-linked networks, we find myosin-dependent biaxial buckling modes across length scales. In cross-linked bundled networks, uniaxial contraction is predominate on long length scales, while the uniaxial or biaxial nature of the deformation depends on bundle microstructure at shorter length scales. The anisotropy of deformations may provide insight to regulation of collective behavior in a variety of active materials.
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Affiliation(s)
- Samantha Stam
- Biophysical Sciences Graduate Program, University of Chicago, Chicago, IL 60637
- Institute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637
- Department of Oncological Sciences, University of Utah, Salt Lake City, UT 84112
- Huntsman Cancer Institute, University of Utah, Salt Lake City, UT 84112
| | - Margaret L Gardel
- Institute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637
- James Franck Institute, University of Chicago, Chicago, IL 60637
- Department of Physics, University of Chicago, Chicago, IL 60637
| | - Kimberly L Weirich
- James Franck Institute, University of Chicago, Chicago, IL 60637
- Department of Materials Science & Engineering, Clemson University, Clemson, SC 29634
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7
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Gergely ZR, Ansari S, Jones MH, Zhou B, Cash C, McIntosh R, Betterton MD. The kinesin-5 protein Cut7 moves bidirectionally on fission yeast spindles with activity that increases in anaphase. J Cell Sci 2023; 136:jcs260474. [PMID: 36655493 PMCID: PMC10112985 DOI: 10.1242/jcs.260474] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2022] [Accepted: 01/10/2023] [Indexed: 01/20/2023] Open
Abstract
Kinesin-5 motors are essential to separate mitotic spindle poles and assemble a bipolar spindle in many organisms. These motors crosslink and slide apart antiparallel microtubules via microtubule plus-end-directed motility. However, kinesin-5 localization is enhanced away from antiparallel overlaps. Increasing evidence suggests this localization occurs due to bidirectional motility or trafficking. The purified fission-yeast kinesin-5 protein Cut7 moves bidirectionally, but bidirectionality has not been shown in cells, and the function of the minus-end-directed movement is unknown. Here, we characterized the motility of Cut7 on bipolar and monopolar spindles and observed movement toward both plus- and minus-ends of microtubules. Notably, the activity of the motor increased at anaphase B onset. Perturbations to microtubule dynamics only modestly changed Cut7 movement, whereas Cut7 mutation reduced movement. These results suggest that the directed motility of Cut7 contributes to the movement of the motor. Comparison of the Cut7 mutant and human Eg5 (also known as KIF11) localization suggest a new hypothesis for the function of minus-end-directed motility and spindle-pole localization of kinesin-5s.
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Affiliation(s)
- Zachary R. Gergely
- Department of Physics, University of Colorado Boulder, Boulder, CO 80305, USA
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado Boulder, Boulder, CO 80305, USA
| | - Saad Ansari
- Department of Physics, University of Colorado Boulder, Boulder, CO 80305, USA
| | - Michele H. Jones
- Department of Physics, University of Colorado Boulder, Boulder, CO 80305, USA
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado Boulder, Boulder, CO 80305, USA
| | - Bojun Zhou
- Department of Physics, University of Colorado Boulder, Boulder, CO 80305, USA
| | - Cai Cash
- Department of Physics, University of Colorado Boulder, Boulder, CO 80305, USA
| | - Richard McIntosh
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado Boulder, Boulder, CO 80305, USA
| | - Meredith D. Betterton
- Department of Physics, University of Colorado Boulder, Boulder, CO 80305, USA
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado Boulder, Boulder, CO 80305, USA
- Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA
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8
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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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9
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Lemma B, Mitchell NP, Subramanian R, Needleman DJ, Dogic Z. Active Microphase Separation in Mixtures of Microtubules and Tip-Accumulating Molecular Motors. PHYSICAL REVIEW. X 2022; 12:031006. [PMID: 36643940 PMCID: PMC9835929 DOI: 10.1103/physrevx.12.031006] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Mixtures of filaments and molecular motors form active materials with diverse dynamical behaviors that vary based on their constituents' molecular properties. To develop a multiscale of these materials, we map the nonequilibrium phase diagram of microtubules and tip-accumulating kinesin-4 molecular motors. We find that kinesin-4 can drive either global contractions or turbulentlike extensile dynamics, depending on the concentrations of both microtubules and a bundling agent. We also observe a range of spatially heterogeneous nonequilibrium phases, including finite-sized radial asters, 1D wormlike chains, extended 2D bilayers, and system-spanning 3D active foams. Finally, we describe intricate kinetic pathways that yield microphase separated structures and arise from the inherent frustration between the orientational order of filamentous microtubules and the positional order of tip-accumulating molecular motors. Our work reveals a range of novel active states. It also shows that the form of active stresses is not solely dictated by the properties of individual motors and filaments, but is also contingent on the constituent concentrations and spatial arrangement of motors on the filaments.
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Affiliation(s)
- Bezia Lemma
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
- Physics Department, University of California, Santa Barbara, California 93106, USA
| | - Noah P. Mitchell
- Physics Department, University of California, Santa Barbara, California 93106, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Radhika Subramanian
- Molecular Biology Department, Massachusetts General Hospital Boston, Massachusetts 02114, USA
- Genetics Department, Harvard Medical School, Boston, Massachusetts 02115, USA
| | - Daniel J. Needleman
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
- Molecular and Cellular Biology Department, Harvard University, Cambridge, Massachusetts 02138, USA
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
| | - Zvonimir Dogic
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
- Physics Department, University of California, Santa Barbara, California 93106, USA
- Biomolecular Science and Engineering Department, University of California, Santa Barbara, California 93106, USA
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10
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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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11
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Lemma LM, Norton MM, Tayar AM, DeCamp SJ, Aghvami SA, Fraden S, Hagan MF, Dogic Z. Multiscale Microtubule Dynamics in Active Nematics. PHYSICAL REVIEW LETTERS 2021; 127:148001. [PMID: 34652175 DOI: 10.1103/physrevlett.127.148001] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2020] [Revised: 06/14/2021] [Accepted: 08/12/2021] [Indexed: 05/12/2023]
Abstract
In microtubule-based active nematics, motor-driven extensile motion of microtubule bundles powers chaotic large-scale dynamics. We quantify the interfilament sliding motion both in isolated bundles and in a dense active nematic. The extension speed of an isolated microtubule pair is comparable to the molecular motor stepping speed. In contrast, the net extension in dense 2D active nematics is significantly slower; the interfilament sliding speeds are widely distributed about the average and the filaments exhibit both contractile and extensile relative motion. These measurements highlight the challenge of connecting the extension rate of isolated bundles to the multimotor and multifilament interactions present in a dense 2D active nematic. They also provide quantitative data that is essential for building multiscale models.
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Affiliation(s)
- Linnea M Lemma
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Michael M Norton
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Alexandra M Tayar
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Stephen J DeCamp
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - S Ali Aghvami
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Seth Fraden
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Michael F Hagan
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Zvonimir Dogic
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
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12
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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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13
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Wagner RJ, Such K, Hobbs E, Vernerey FJ. Treadmilling and dynamic protrusions in fire ant rafts. J R Soc Interface 2021; 18:20210213. [PMID: 34186017 PMCID: PMC8241487 DOI: 10.1098/rsif.2021.0213] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Accepted: 06/09/2021] [Indexed: 11/18/2022] Open
Abstract
Fire ants (Solenopsis invicta) are exemplary for their formation of cohered, buoyant and dynamic structures composed entirely of their own bodies when exposed to flooded environments. Here, we observe tether-like protrusions that emerge from aggregated fire ant rafts when docked to stationary, vertical rods. Ant rafts comprise a floating, structural network of interconnected ants on which a layer of freely active ants walk. We show here that sustained shape evolution is permitted by the competing mechanisms of perpetual raft contraction aided by the transition of bulk structural ants to the free active layer and outward raft expansion owing to the deposition of free ants into the structural network at the edges, culminating in global treadmilling. Furthermore, we see that protrusions emerge as a result of asymmetries in the edge deposition rate of free ants. Employing both experimental characterization and a model for self-propelled particles in strong confinement, we interpret that these asymmetries are likely to occur stochastically owing to wall accumulation effects and directional motion of active ants when strongly confined by the protrusions' relatively narrow boundaries. Together, these effects may realize the cooperative, yet spontaneous formation of protrusions that fire ants sometimes use for functional exploration and to escape flooded environments.
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Affiliation(s)
- Robert J. Wagner
- Mechanical Engineering Department, Material Science and Engineering Program, University of Colorado, Boulder, CO 80309 USA
| | - Kristen Such
- Mechanical Engineering Department, University of Colorado, Boulder, CO 80309 USA
| | - Ethan Hobbs
- Computer Science Department, Interdisciplinary Quantitative Biology Program, University of Colorado, Boulder, CO 80309 USA
| | - Franck J. Vernerey
- Mechanical Engineering Department, Material Science and Engineering Program, University of Colorado, Boulder, CO 80309 USA
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14
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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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15
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Tabatabai AP, Seara DS, Tibbs J, Yadav V, Linsmeier I, Murrell MP. Detailed Balance Broken by Catch Bond Kinetics Enables Mechanical-Adaptation in Active Materials. ADVANCED FUNCTIONAL MATERIALS 2021; 31:2006745. [PMID: 34393691 PMCID: PMC8357268 DOI: 10.1002/adfm.202006745] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2020] [Indexed: 05/04/2023]
Abstract
Unlike nearly all engineered materials which contain bonds that weaken under load, biological materials contain "catch" bonds which are reinforced under load. Consequently, materials, such as the cell cytoskeleton, can adapt their mechanical properties in response to their state of internal, non-equilibrium (active) stress. However, how large-scale material properties vary with the distance from equilibrium is unknown, as are the relative roles of active stress and binding kinetics in establishing this distance. Through course-grained molecular dynamics simulations, the effect of breaking of detailed balance by catch bonds on the accumulation and dissipation of energy within a model of the actomyosin cytoskeleton is explored. It is found that the extent to which detailed balance is broken uniquely determines a large-scale fluid-solid transition with characteristic time-reversal symmetries. The transition depends critically on the strength of the catch bond, suggesting that active stress is necessary but insufficient to mount an adaptive mechanical response.
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Affiliation(s)
- Alan Pasha Tabatabai
- Department of Biomedical Engineering, Yale University, 55 Prospect Street, New Haven, CT 06511, USA; Systems Biology Institute, Yale University, 850 West Campus Drive, West Haven, CT 06516, USA
| | - Daniel S Seara
- Systems Biology Institute, Yale University, 850 West Campus Drive, West Haven, CT 06516, USA; Department of Physics, Yale University, 217 Prospect Street, New Haven, CT 06511, USA
| | - Joseph Tibbs
- Department of Physics, University of Northern Iowa, Cedar Falls, IA 50614, USA
| | - Vikrant Yadav
- Department of Biomedical Engineering, Yale University, 55 Prospect Street, New Haven, CT 06511, USA; Systems Biology Institute, Yale University, 850 West Campus Drive, West Haven, CT 06516, USA
| | - Ian Linsmeier
- Department of Biomedical Engineering, Yale University, 55 Prospect Street, New Haven, CT 06511, USA; Systems Biology Institute, Yale University, 850 West Campus Drive, West Haven, CT 06516, USA
| | - Michael P Murrell
- Department of Biomedical Engineering, Yale University, 55 Prospect Street, New Haven, CT 06511, USA; Systems Biology Institute, Yale University, 850 West Campus Drive, West Haven, CT 06516, USA; Department of Physics, Yale University, 217 Prospect Street, New Haven, CT 06511, USA
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16
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Zhou Z, Joshi C, Liu R, Norton MM, Lemma L, Dogic Z, Hagan MF, Fraden S, Hong P. Machine learning forecasting of active nematics. SOFT MATTER 2021; 17:738-747. [PMID: 33220675 DOI: 10.1039/d0sm01316a] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Active nematics are a class of far-from-equilibrium materials characterized by local orientational order of force-generating, anisotropic constitutes. Traditional methods for predicting the dynamics of active nematics rely on hydrodynamic models, which accurately describe idealized flows and many of the steady-state properties, but do not capture certain detailed dynamics of experimental active nematics. We have developed a deep learning approach that uses a Convolutional Long-Short-Term-Memory (ConvLSTM) algorithm to automatically learn and forecast the dynamics of active nematics. We demonstrate our purely data-driven approach on experiments of 2D unconfined active nematics of extensile microtubule bundles, as well as on data from numerical simulations of active nematics.
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17
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Vliegenthart GA, Ravichandran A, Ripoll M, Auth T, Gompper G. Filamentous active matter: Band formation, bending, buckling, and defects. SCIENCE ADVANCES 2020; 6:eaaw9975. [PMID: 32832652 PMCID: PMC7439626 DOI: 10.1126/sciadv.aaw9975] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2019] [Accepted: 06/05/2020] [Indexed: 06/01/2023]
Abstract
Motor proteins drive persistent motion and self-organization of cytoskeletal filaments. However, state-of-the-art microscopy techniques and continuum modeling approaches focus on large length and time scales. Here, we perform component-based computer simulations of polar filaments and molecular motors linking microscopic interactions and activity to self-organization and dynamics from the filament level up to the mesoscopic domain level. Dynamic filament cross-linking and sliding and excluded-volume interactions promote formation of bundles at small densities and of active polar nematics at high densities. A buckling-type instability sets the size of polar domains and the density of topological defects. We predict a universal scaling of the active diffusion coefficient and the domain size with activity, and its dependence on parameters like motor concentration and filament persistence length. Our results provide a microscopic understanding of cytoplasmic streaming in cells and help to develop design strategies for novel engineered active materials.
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18
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Edelmaier C, Lamson AR, Gergely ZR, Ansari S, Blackwell R, McIntosh JR, Glaser MA, Betterton MD. Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling. eLife 2020; 9:48787. [PMID: 32053104 PMCID: PMC7311174 DOI: 10.7554/elife.48787] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2019] [Accepted: 02/12/2020] [Indexed: 01/19/2023] Open
Abstract
The essential functions required for mitotic spindle assembly and chromosome biorientation and segregation are not fully understood, despite extensive study. To illuminate the combinations of ingredients most important to align and segregate chromosomes and simultaneously assemble a bipolar spindle, we developed a computational model of fission-yeast mitosis. Robust chromosome biorientation requires progressive restriction of attachment geometry, destabilization of misaligned attachments, and attachment force dependence. Large spindle length fluctuations can occur when the kinetochore-microtubule attachment lifetime is long. The primary spindle force generators are kinesin-5 motors and crosslinkers in early mitosis, while interkinetochore stretch becomes important after biorientation. The same mechanisms that contribute to persistent biorientation lead to segregation of chromosomes to the poles after anaphase onset. This model therefore provides a framework to interrogate key requirements for robust chromosome biorientation, spindle length regulation, and force generation in the spindle. Before a cell divides, it must make a copy of its genetic material and then promptly split in two. This process, called mitosis, is coordinated by many different molecular machines. The DNA is copied, then the duplicated chromosomes line up at the middle of the cell. Next, an apparatus called the mitotic spindle latches onto the chromosomes before pulling them apart. The mitotic spindle is a bundle of long, thin filaments called microtubules. It attaches to chromosomes at the kinetochore, the point where two copied chromosomes are cinched together in their middle. Proper cell division is vital for the healthy growth of all organisms, big and small, and yet some parts of the process remain poorly understood despite extensive study. Specifically, there is more to learn about how the mitotic spindle self-assembles, and how microtubules and kinetochores work together to correctly orient and segregate chromosomes into two sister cells. These nanoscale processes are happening a hundred times a minute, so computer simulations are a good way to test what we know. Edelmaier et al. developed a computer model to simulate cell division in fission yeast, a species of yeast often used to study fundamental processes in the cell. The model simulates how the mitotic spindle assembles, how its microtubules attach to the kinetochore and the force required to pull two sister chromosomes apart. Building the simulation involved modelling interactions between the mitotic spindle and kinetochore, their movement and forces applied. To test its accuracy, model simulations were compared to recordings of the mitotic spindle – including its length, structure and position – imaged from dividing yeast cells. Running the simulation, Edelmaier et al. found that several key effects are essential for the proper movement of chromosomes in mitosis. This includes holding chromosomes in the correct orientation as the mitotic spindle assembles and controlling the relative position of microtubules as they attach to the kinetochore. Misaligned attachments must also be readily deconstructed and corrected to prevent any errors. The simulations also showed that kinetochores must begin to exert more force (to separate the chromosomes) once the mitotic spindle is attached correctly. Altogether, these findings improve the current understanding of how the mitotic spindle and its counterparts control cell division. Errors in chromosome segregation are associated with birth defects and cancer in humans, and this new simulation could potentially now be used to help make predictions about how to correct mistakes in the process.
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Affiliation(s)
| | - Adam R Lamson
- Department of Physics, University of Colorado Boulder, Boulder, United States
| | - Zachary R Gergely
- Department of Physics, University of Colorado Boulder, Boulder, United States.,Department of Molecular, Cellular, and Developmental Biology, University of Colorado Boulder, Boulder, United States
| | - Saad Ansari
- Department of Physics, University of Colorado Boulder, Boulder, United States
| | - Robert Blackwell
- Department of Physics, University of Colorado Boulder, Boulder, United States
| | - J Richard McIntosh
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado Boulder, Boulder, United States
| | - Matthew A Glaser
- Department of Physics, University of Colorado Boulder, Boulder, United States
| | - Meredith D Betterton
- Department of Physics, University of Colorado Boulder, Boulder, United States.,Department of Molecular, Cellular, and Developmental Biology, University of Colorado Boulder, Boulder, United States
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19
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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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20
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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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21
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Freedman SL, Hocky GM, Banerjee S, Dinner AR. Nonequilibrium phase diagrams for actomyosin networks. SOFT MATTER 2018; 14:7740-7747. [PMID: 30204203 PMCID: PMC6192427 DOI: 10.1039/c8sm00741a] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
Living cells dynamically modulate the local morphologies of their actin networks to perform biological functions, including force transduction, intracellular transport, and cell division. A major challenge is to understand how diverse structures of the actin cytoskeleton are assembled from a limited set of molecular building blocks. Here we study the spontaneous self-assembly of a minimal model of cytoskeletal materials, consisting of semiflexible actin filaments, crosslinkers, and molecular motors. Using coarse-grained simulations, we demonstrate that by changing concentrations and kinetics of crosslinkers and motors, as well as filament lengths, we can generate three distinct structural phases of actomyosin assemblies: bundled, polarity-sorted, and contracted. We introduce new metrics to distinguish these structural phases and demonstrate their functional roles. We find that the binding kinetics of motors and crosslinkers can be tuned to optimize contractile force generation, motor transport, and mechanical response. By quantitatively characterizing the relationships between the modes of cytoskeletal self-assembly, the resulting structures, and their functional consequences, our work suggests new principles for the design of active materials.
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Affiliation(s)
- Simon L. Freedman
- Department of Physics, The University of Chicago, 929 East 57th Street, Chicago, IL 60637, USA
| | - Glen M. Hocky
- James Franck Institute & Department of Chemistry, The University of Chicago, 929 East 57th Street, Chicago, IL 60637, USA, Chicago, IL, USA;
| | - Shiladitya Banerjee
- Department of Physics and Astronomy, University College London, Gower Street, London, WC1E-6BT
| | - Aaron R. Dinner
- James Franck Institute & Department of Chemistry, The University of Chicago, 929 East 57th Street, Chicago, IL 60637, USA, Chicago, IL, USA;
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22
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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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23
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Filament rigidity and connectivity tune the deformation modes of active biopolymer networks. Proc Natl Acad Sci U S A 2017; 114:E10037-E10045. [PMID: 29114058 DOI: 10.1073/pnas.1708625114] [Citation(s) in RCA: 53] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Molecular motors embedded within collections of actin and microtubule filaments underlie the dynamics of cytoskeletal assemblies. Understanding the physics of such motor-filament materials is critical to developing a physical model of the cytoskeleton and designing biomimetic active materials. Here, we demonstrate through experiments and simulations that the rigidity and connectivity of filaments in active biopolymer networks regulates the anisotropy and the length scale of the underlying deformations, yielding materials with variable contractility. We find that semiflexible filaments can be compressed and bent by motor stresses, yielding materials that undergo predominantly biaxial deformations. By contrast, rigid filament bundles slide without bending under motor stress, yielding materials that undergo predominantly uniaxial deformations. Networks dominated by biaxial deformations are robustly contractile over a wide range of connectivities, while networks dominated by uniaxial deformations can be tuned from extensile to contractile through cross-linking. These results identify physical parameters that control the forces generated within motor-filament arrays and provide insight into the self-organization and mechanics of cytoskeletal assemblies.
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24
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Alvarado J, Sheinman M, Sharma A, MacKintosh FC, Koenderink GH. Force percolation of contractile active gels. SOFT MATTER 2017; 13:5624-5644. [PMID: 28812094 DOI: 10.1039/c7sm00834a] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Living systems provide a paradigmatic example of active soft matter. Cells and tissues comprise viscoelastic materials that exert forces and can actively change shape. This strikingly autonomous behavior is powered by the cytoskeleton, an active gel of semiflexible filaments, crosslinks, and molecular motors inside cells. Although individual motors are only a few nm in size and exert minute forces of a few pN, cells spatially integrate the activity of an ensemble of motors to produce larger contractile forces (∼nN and greater) on cellular, tissue, and organismal length scales. Here we review experimental and theoretical studies on contractile active gels composed of actin filaments and myosin motors. Unlike other active soft matter systems, which tend to form ordered patterns, actin-myosin systems exhibit a generic tendency to contract. Experimental studies of reconstituted actin-myosin model systems have long suggested that a mechanical interplay between motor activity and the network's connectivity governs this contractile behavior. Recent theoretical models indicate that this interplay can be understood in terms of percolation models, extended to include effects of motor activity on the network connectivity. Based on concepts from percolation theory, we propose a state diagram that unites a large body of experimental observations. This framework provides valuable insights into the mechanisms that drive cellular shape changes and also provides design principles for synthetic active materials.
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Affiliation(s)
- José Alvarado
- Systems Biophysics Department, AMOLF, 1098 XG Amsterdam, The Netherlands.
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25
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Kinesin-5-independent mitotic spindle assembly requires the antiparallel microtubule crosslinker Ase1 in fission yeast. Nat Commun 2017; 8:15286. [PMID: 28513584 PMCID: PMC5442317 DOI: 10.1038/ncomms15286] [Citation(s) in RCA: 59] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2016] [Accepted: 03/13/2017] [Indexed: 12/04/2022] Open
Abstract
Bipolar spindle assembly requires a balance of forces where kinesin-5 produces outward pushing forces to antagonize the inward pulling forces from kinesin-14 or dynein. Accordingly, Kinesin-5 inactivation results in force imbalance leading to monopolar spindle and chromosome segregation failure. In fission yeast, force balance is restored when both kinesin-5 Cut7 and kinesin-14 Pkl1 are deleted, restoring spindle bipolarity. Here we show that the cut7Δpkl1Δ spindle is fully competent for chromosome segregation independently of motor activity, except for kinesin-6 Klp9, which is required for anaphase spindle elongation. We demonstrate that cut7Δpkl1Δ spindle bipolarity requires the microtubule antiparallel bundler PRC1/Ase1 to recruit CLASP/Cls1 to stabilize microtubules. Brownian dynamics-kinetic Monte Carlo simulations show that Ase1 and Cls1 activity are sufficient for initial bipolar spindle formation. We conclude that pushing forces generated by microtubule polymerization are sufficient to promote spindle pole separation and the assembly of bipolar spindle in the absence of molecular motors. Bipolar spindle assembly requires a balance of kinesin 14 pulling and kinesin 5 pushing forces. Here, the authors show that in fission yeast, spindle formation can occur in the absence of kinesin 5 (Cut7) and 14 (Pkl1) but requires the microtubule-associated protein Ase1 for spindle bipolarity.
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26
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Blackwell R, Edelmaier C, Sweezy-Schindler O, Lamson A, Gergely ZR, O’Toole E, Crapo A, Hough LE, McIntosh JR, Glaser MA, Betterton MD. Physical determinants of bipolar mitotic spindle assembly and stability in fission yeast. SCIENCE ADVANCES 2017; 3:e1601603. [PMID: 28116355 PMCID: PMC5249259 DOI: 10.1126/sciadv.1601603] [Citation(s) in RCA: 39] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2016] [Accepted: 12/05/2016] [Indexed: 05/10/2023]
Abstract
Mitotic spindles use an elegant bipolar architecture to segregate duplicated chromosomes with high fidelity. Bipolar spindles form from a monopolar initial condition; this is the most fundamental construction problem that the spindle must solve. Microtubules, motors, and cross-linkers are important for bipolarity, but the mechanisms necessary and sufficient for spindle assembly remain unknown. We describe a physical model that exhibits de novo bipolar spindle formation. We began with physical properties of fission-yeast spindle pole body size and microtubule number, kinesin-5 motors, kinesin-14 motors, and passive cross-linkers. Our model results agree quantitatively with our experiments in fission yeast, thereby establishing a minimal system with which to interrogate collective self-assembly. By varying the features of our model, we identify a set of functions essential for the generation and stability of spindle bipolarity. When kinesin-5 motors are present, their bidirectionality is essential, but spindles can form in the presence of passive cross-linkers alone. We also identify characteristic failed states of spindle assembly-the persistent monopole, X spindle, separated asters, and short spindle, which are avoided by the creation and maintenance of antiparallel microtubule overlaps. Our model can guide the identification of new, multifaceted strategies to induce mitotic catastrophes; these would constitute novel strategies for cancer chemotherapy.
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Affiliation(s)
- Robert Blackwell
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
- PULS Group, Department of Physics and Cluster of Excellence: Engineering of Advanced Materials, Friedrich-Alexander University Erlangen-Nurnberg, Nagelsbachstr. 49b, Erlangen, Germany
| | | | | | - Adam Lamson
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Zachary R. Gergely
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, CO 80309, USA
| | - Eileen O’Toole
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, CO 80309, USA
| | - Ammon Crapo
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Loren E. Hough
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - J. Richard McIntosh
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, CO 80309, USA
| | - Matthew A. Glaser
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Meredith D. Betterton
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, CO 80309, USA
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27
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Blackwell R, Sweezy-Schindler O, Edelmaier C, Gergely ZR, Flynn PJ, Montes S, Crapo A, Doostan A, McIntosh JR, Glaser MA, Betterton MD. Contributions of Microtubule Dynamic Instability and Rotational Diffusion to Kinetochore Capture. Biophys J 2016; 112:552-563. [PMID: 27692365 DOI: 10.1016/j.bpj.2016.09.006] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2016] [Revised: 08/08/2016] [Accepted: 09/06/2016] [Indexed: 11/27/2022] Open
Abstract
Microtubule dynamic instability allows search and capture of kinetochores during spindle formation, an important process for accurate chromosome segregation during cell division. Recent work has found that microtubule rotational diffusion about minus-end attachment points contributes to kinetochore capture in fission yeast, but the relative contributions of dynamic instability and rotational diffusion are not well understood. We have developed a biophysical model of kinetochore capture in small fission-yeast nuclei using hybrid Brownian dynamics/kinetic Monte Carlo simulation techniques. With this model, we have studied the importance of dynamic instability and microtubule rotational diffusion for kinetochore capture, both to the lateral surface of a microtubule and at or near its end. Over a range of biologically relevant parameters, microtubule rotational diffusion decreased capture time, but made a relatively small contribution compared to dynamic instability. At most, rotational diffusion reduced capture time by 25%. Our results suggest that while microtubule rotational diffusion can speed up kinetochore capture, it is unlikely to be the dominant physical mechanism for typical conditions in fission yeast. In addition, we found that when microtubules undergo dynamic instability, lateral captures predominate even in the absence of rotational diffusion. Counterintuitively, adding rotational diffusion to a dynamic microtubule increases the probability of end-on capture.
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Affiliation(s)
- Robert Blackwell
- Department of Physics, University of Colorado, Boulder, Colorado
| | | | | | - Zachary R Gergely
- Department of Physics, University of Colorado, Boulder, Colorado; Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, Colorado
| | - Patrick J Flynn
- Department of Physics, University of Colorado, Boulder, Colorado
| | - Salvador Montes
- Department of Physics, University of Colorado, Boulder, Colorado
| | - Ammon Crapo
- Department of Physics, University of Colorado, Boulder, Colorado
| | - Alireza Doostan
- Department of Aerospace Engineering Sciences, University of Colorado, Boulder, Colorado
| | - J Richard McIntosh
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, Colorado
| | - Matthew A Glaser
- Department of Physics, University of Colorado, Boulder, Colorado
| | - Meredith D Betterton
- Department of Physics, University of Colorado, Boulder, Colorado; Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, Colorado.
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Foster PJ, Fürthauer S, Shelley MJ, Needleman DJ. Active contraction of microtubule networks. eLife 2015; 4. [PMID: 26701905 PMCID: PMC4764591 DOI: 10.7554/elife.10837] [Citation(s) in RCA: 78] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2015] [Accepted: 12/20/2015] [Indexed: 01/08/2023] Open
Abstract
Many cellular processes are driven by cytoskeletal assemblies. It remains unclear how cytoskeletal filaments and motor proteins organize into cellular scale structures and how molecular properties of cytoskeletal components affect the large-scale behaviors of these systems. Here, we investigate the self-organization of stabilized microtubules in Xenopus oocyte extracts and find that they can form macroscopic networks that spontaneously contract. We propose that these contractions are driven by the clustering of microtubule minus ends by dynein. Based on this idea, we construct an active fluid theory of network contractions, which predicts a dependence of the timescale of contraction on initial network geometry, a development of density inhomogeneities during contraction, a constant final network density, and a strong influence of dynein inhibition on the rate of contraction, all in quantitative agreement with experiments. These results demonstrate that the motor-driven clustering of filament ends is a generic mechanism leading to contraction.
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Affiliation(s)
- Peter J Foster
- John A. Paulson School of Engineering and Applied Sciences, FAS Center for Systems Biology, Harvard University, Cambridge, United States
| | - Sebastian Fürthauer
- Courant Institute of Mathematical Science, New York University, New York, United States.,Department of Molecular and Cellular Biology, Harvard University, Cambridge, United States
| | - Michael J Shelley
- Courant Institute of Mathematical Science, New York University, New York, United States
| | - Daniel J Needleman
- John A. Paulson School of Engineering and Applied Sciences, FAS Center for Systems Biology, Harvard University, Cambridge, United States.,Department of Molecular and Cellular Biology, Harvard University, Cambridge, United States
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