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Warkotsch D, Christiansen H, Zierenberg J, Janke W. Pulling on grafted flexible polymers can cause twisted bundles. SOFT MATTER 2024; 20:4916-4927. [PMID: 38868862 DOI: 10.1039/d4sm00093e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2024]
Abstract
Bundles of semiflexible polymers can twist at low temperatures to balance energy gain from attraction and energy cost from bending. This raises the question whether twisting can be also observed for bundles of rather flexible grafted polymers stretched out by pulling force. Here, we address this question using Monte Carlo computer simulations of small bundles. Our data show that for weak forces F < Fl, intertwined globular conformations are favored, whereas for strong forces F > Fu, rod-like bundles emerge. In the intermediate force window Fl < F < Fu, bundles with a helical twist can be clearly identified. Applying a field to all monomers yields qualitatively the same effect. This suggests the conclusion that rather flexible polymers under pulling force or field behave effectively like semiflexible polymers without external pull.
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Affiliation(s)
- Dustin Warkotsch
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
| | - Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
| | - Johannes Zierenberg
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany.
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
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Matković J, Ghosh S, Ćosić M, Eibes S, Barišić M, Pavin N, Tolić IM. Kinetochore- and chromosome-driven transition of microtubules into bundles promotes spindle assembly. Nat Commun 2022; 13:7307. [PMID: 36435852 PMCID: PMC9701229 DOI: 10.1038/s41467-022-34957-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Accepted: 11/11/2022] [Indexed: 11/28/2022] Open
Abstract
Mitotic spindle assembly is crucial for chromosome segregation and relies on bundles of microtubules that extend from the poles and overlap in the middle. However, how these structures form remains poorly understood. Here we show that overlap bundles arise through a network-to-bundles transition driven by kinetochores and chromosomes. STED super-resolution microscopy reveals that PRC1-crosslinked microtubules initially form loose arrays, which become rearranged into bundles. Kinetochores promote microtubule bundling by lateral binding via CENP-E/kinesin-7 in an Aurora B-regulated manner. Steric interactions between the bundle-associated chromosomes at the spindle midplane drive bundle separation and spindle widening. In agreement with experiments, theoretical modeling suggests that bundles arise through competing attractive and repulsive mechanisms. Finally, perturbation of overlap bundles leads to inefficient correction of erroneous kinetochore-microtubule attachments. Thus, kinetochores and chromosomes drive coarsening of a uniform microtubule array into overlap bundles, which promote not only spindle formation but also chromosome segregation fidelity.
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Affiliation(s)
- Jurica Matković
- grid.4905.80000 0004 0635 7705Division of Molecular Biology, Ruđer Bošković Institute, Zagreb, Croatia
| | - Subhadip Ghosh
- grid.4808.40000 0001 0657 4636Department of Physics, Faculty of Science, University of Zagreb, Zagreb, Croatia
| | - Mateja Ćosić
- grid.4905.80000 0004 0635 7705Division of Molecular Biology, Ruđer Bošković Institute, Zagreb, Croatia
| | - Susana Eibes
- grid.417390.80000 0001 2175 6024Cell Division and Cytoskeleton, Danish Cancer Society Research Center, Copenhagen, Denmark
| | - Marin Barišić
- grid.417390.80000 0001 2175 6024Cell Division and Cytoskeleton, Danish Cancer Society Research Center, Copenhagen, Denmark ,grid.5254.60000 0001 0674 042XDepartment of Cellular and Molecular Medicine, Faculty of Health Sciences, University of Copenhagen, Copenhagen, Denmark
| | - Nenad Pavin
- grid.4808.40000 0001 0657 4636Department of Physics, Faculty of Science, University of Zagreb, Zagreb, Croatia
| | - Iva M. Tolić
- grid.4905.80000 0004 0635 7705Division of Molecular Biology, Ruđer Bošković Institute, Zagreb, Croatia
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Grill MJ, Kernes J, Slepukhin VM, Wall WA, Levine AJ. Directed force propagation in semiflexible networks. SOFT MATTER 2021; 17:10223-10241. [PMID: 33367438 DOI: 10.1039/d0sm01177k] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We consider the propagation of tension along specific filaments of a semiflexible filament network in response to the application of a point force using a combination of numerical simulations and analytic theory. We find the distribution of force within the network is highly heterogeneous, with a small number of fibers supporting a significant fraction of the applied load over distances of multiple mesh sizes surrounding the point of force application. We suggest that these structures may be thought of as tensile force chains, whose structure we explore via simulation. We develop self-consistent calculations of the point-force response function and introduce a transfer matrix approach to explore the decay of tension (into bending) energy and the branching of tensile force chains in the network.
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Affiliation(s)
- Maximilian J Grill
- Institute for Computational Mechanics, Technical University of Munich, 85748 Garching, Germany
| | - Jonathan Kernes
- Department of Physics & Astronomy, University of California, Los Angeles, 90095, USA.
| | - Valentin M Slepukhin
- Department of Physics & Astronomy, University of California, Los Angeles, 90095, USA.
| | - Wolfgang A Wall
- Institute for Computational Mechanics, Technical University of Munich, 85748 Garching, Germany
| | - Alex J Levine
- Department of Physics & Astronomy, University of California, Los Angeles, 90095, USA.
- Department of Chemistry & Biochemistry, University of California, Los Angeles, 90095, USA
- Department of Computational Medicine, University of California, Los Angeles, 90095, USA
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Slepukhin VM, Grill MJ, Hu Q, Botvinick EL, Wall WA, Levine AJ. Topological defects produce kinks in biopolymer filament bundles. Proc Natl Acad Sci U S A 2021; 118:e2024362118. [PMID: 33876768 PMCID: PMC8053966 DOI: 10.1073/pnas.2024362118] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022] Open
Abstract
Bundles of stiff filaments are ubiquitous in the living world, found both in the cytoskeleton and in the extracellular medium. These bundles are typically held together by smaller cross-linking molecules. We demonstrate, analytically, numerically, and experimentally, that such bundles can be kinked, that is, have localized regions of high curvature that are long-lived metastable states. We propose three possible mechanisms of kink stabilization: a difference in trapped length of the filament segments between two cross-links, a dislocation where the endpoint of a filament occurs within the bundle, and the braiding of the filaments in the bundle. At a high concentration of cross-links, the last two effects lead to the topologically protected kinked states. Finally, we explore, numerically and analytically, the transition of the metastable kinked state to the stable straight bundle.
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Affiliation(s)
- Valentin M Slepukhin
- Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1596;
| | - Maximilian J Grill
- Institute for Computational Mechanics, Technical University of Munich, 80333 Munich, Germany
| | - Qingda Hu
- Department of Biomedical Engineering, University of California, Irvine, CA 92697-2730
- Center for Complex Biological Systems, University of California, Irvine, CA 92697-2280
| | - Elliot L Botvinick
- Department of Biomedical Engineering, University of California, Irvine, CA 92697-2730
- Center for Complex Biological Systems, University of California, Irvine, CA 92697-2280
- Beckman Laser Institute, University of California, Irvine, CA 92697-2730
| | - Wolfgang A Wall
- Institute for Computational Mechanics, Technical University of Munich, 80333 Munich, Germany
| | - Alex J Levine
- Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1596
- Department of Chemistry and Biochemistry, University of California, Los Angeles, CA 90095-1596
- Department of Biomathematics, University of California, Los Angeles, CA 90095-1596
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Noh G, Benetatos P. Tensile elasticity of a freely jointed chain with reversible hinges. SOFT MATTER 2021; 17:3333-3345. [PMID: 33630011 DOI: 10.1039/d1sm00053e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Many biopolymers exhibit reversible conformational transitions within the chain, which affect their bending stiffness and their response to a stretching force. For example, double stranded DNA may have denatured "bubbles" of unzipped single strands which open and close randomly. In other polymers, the transitions may be due to the reversible attachment and detachment of ligands on ligand-receptor complexes along the backbone. Semiflexible bundles under tension formed by the reversible attachment of cross-linkers, on a coarse-grained level, exhibit similar behaviour. The simplest theoretical model which captures what the above mentioned systems have in common is a freely jointed chain (FJC) with reversible hinges. Each hinge can be open, as in the usual FJC, or closed forcing the adjacent segments to align (stretch). In this article, we analyse it in the Gibbs ensemble. Remarkably, even though the usual FJC in the thermodynamic limit exhibits ensemble equivalence, the reversible FJC exhibits ensemble inequivalence. Even though a mean field treatment suggests a continuous phase transition to a fully hinged state at a certain force, the generating function method ("necklace model") shows that there is no phase transition. However, there is a crossover between the two states with clearly different responses. In the low force (linear response) regime, the reversible FJC has higher tensile compliance than its usual counterpart. In contrast, in the strong force regime, the tensile compliance of the reversible FJC is much lower than that of the usual FJC.
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Affiliation(s)
- Geunho Noh
- Department of Physics, Kyungpook National University, Bukgu, 80 Daehakro, Daegu 41566, Korea.
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