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Sen A, Chowdhury D, Kunwar A. Coordination, cooperation, competition, crowding and congestion of molecular motors: Theoretical models and computer simulations. ADVANCES IN PROTEIN CHEMISTRY AND STRUCTURAL BIOLOGY 2024; 141:563-650. [PMID: 38960486 DOI: 10.1016/bs.apcsb.2023.12.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/05/2024]
Abstract
Cytoskeletal motor proteins are biological nanomachines that convert chemical energy into mechanical work to carry out various functions such as cell division, cell motility, cargo transport, muscle contraction, beating of cilia and flagella, and ciliogenesis. Most of these processes are driven by the collective operation of several motors in the crowded viscous intracellular environment. Imaging and manipulation of the motors with powerful experimental probes have been complemented by mathematical analysis and computer simulations of the corresponding theoretical models. In this article, we illustrate some of the key theoretical approaches used to understand how coordination, cooperation and competition of multiple motors in the crowded intra-cellular environment drive the processes that are essential for biological function of a cell. In spite of the focus on theory, experimentalists will also find this article as an useful summary of the progress made so far in understanding multiple motor systems.
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Affiliation(s)
- Aritra Sen
- Department of Biosciences and Bioengineering, Indian Institute of Technology Bombay, Mumbai, Maharashtra, India
| | - Debashish Chowdhury
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India
| | - Ambarish Kunwar
- Department of Biosciences and Bioengineering, Indian Institute of Technology Bombay, Mumbai, Maharashtra, India.
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Bauer D, Ishikawa H, Wemmer KA, Hendel NL, Kondev J, Marshall WF. Analysis of biological noise in the flagellar length control system. iScience 2021; 24:102354. [PMID: 33898946 PMCID: PMC8059064 DOI: 10.1016/j.isci.2021.102354] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2020] [Revised: 03/16/2021] [Accepted: 03/19/2021] [Indexed: 02/06/2023] Open
Abstract
Any proposed mechanism for organelle size control should be able to account not only for average size but also for the variation in size. We analyzed cell-to-cell variation and within-cell variation of length for the two flagella in Chlamydomonas, finding that cell-to-cell variation is dominated by cell size, whereas within-cell variation results from dynamic fluctuations. Fluctuation analysis suggests tubulin assembly is not directly coupled with intraflagellar transport (IFT) and that the observed length fluctuations reflect tubulin assembly and disassembly events involving large numbers of tubulin dimers. Length variation is increased in long-flagella mutants, an effect consistent with theoretical models for flagellar length regulation. Cells with unequal flagellar lengths show impaired swimming but improved gliding, raising the possibility that cells have evolved mechanisms to tune biological noise in flagellar length. Analysis of noise at the level of organelle size provides a way to probe the mechanisms determining cell geometry.
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Affiliation(s)
- David Bauer
- Department of Biochemistry & Biophysics, University of California, San Francisco, 600 16th St., San Francisco, CA, USA
| | - Hiroaki Ishikawa
- Department of Biochemistry & Biophysics, University of California, San Francisco, 600 16th St., San Francisco, CA, USA
| | - Kimberly A. Wemmer
- Department of Biochemistry & Biophysics, University of California, San Francisco, 600 16th St., San Francisco, CA, USA
| | - Nathan L. Hendel
- Department of Biochemistry & Biophysics, University of California, San Francisco, 600 16th St., San Francisco, CA, USA
| | - Jane Kondev
- Department of Physics, Brandeis University, Abelson-Bass-Yalem Building, 97-301, Waltham, MA, USA
| | - Wallace F. Marshall
- Department of Biochemistry & Biophysics, University of California, San Francisco, 600 16th St., San Francisco, CA, USA
- Center for Cellular Construction, University of California, San Francisco, 600 16th St., San Francisco, CA, USA
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Fai TG, Mohapatra L, Kar P, Kondev J, Amir A. Length regulation of multiple flagella that self-assemble from a shared pool of components. eLife 2019; 8:e42599. [PMID: 31596235 PMCID: PMC6863624 DOI: 10.7554/elife.42599] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2018] [Accepted: 10/08/2019] [Indexed: 11/24/2022] Open
Abstract
The single-celled green algae Chlamydomonas reinhardtii with its two flagella-microtubule-based structures of equal and constant lengths-is the canonical model organism for studying size control of organelles. Experiments have identified motor-driven transport of tubulin to the flagella tips as a key component of their length control. Here we consider a class of models whose key assumption is that proteins responsible for the intraflagellar transport (IFT) of tubulin are present in limiting amounts. We show that the limiting-pool assumption is insufficient to describe the results of severing experiments, in which a flagellum is regenerated after it has been severed. Next, we consider an extension of the limiting-pool model that incorporates proteins that depolymerize microtubules. We show that this 'active disassembly' model of flagellar length control explains in quantitative detail the results of severing experiments and use it to make predictions that can be tested in experiments.
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Affiliation(s)
- Thomas G Fai
- Department of MathematicsBrandeis UniversityWalthamUnited States
| | | | - Prathitha Kar
- Paulson School of Engineering and Applied SciencesHarvard UniversityCambridgeUnited States
| | - Jane Kondev
- Department of PhysicsBrandeis UniversityWalthamUnited States
| | - Ariel Amir
- Paulson School of Engineering and Applied SciencesHarvard UniversityCambridgeUnited States
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Bojer M, Graf IR, Frey E. Self-organized system-size oscillation of a stochastic lattice-gas model. Phys Rev E 2018; 98:012410. [PMID: 30110755 DOI: 10.1103/physreve.98.012410] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2018] [Indexed: 11/07/2022]
Abstract
The totally asymmetric simple exclusion process (TASEP) is a paradigmatic stochastic model for nonequilibrium physics, and has been successfully applied to describe active transport of molecular motors along cytoskeletal filaments. Building on this simple model, we consider a two-lane lattice-gas model that couples directed transport (TASEP) to diffusive motion in a semiclosed geometry, and simultaneously accounts for spontaneous growth and particle-induced shrinkage of the system's size. This particular extension of the TASEP is motivated by the question of how active transport and diffusion might influence length regulation in confined systems. Surprisingly, we find that the size of our intrinsically stochastic system exhibits robust temporal patterns over a broad range of growth rates. More specifically, when particle diffusion is slow relative to the shrinkage dynamics, we observe quasiperiodic changes in length. We provide an intuitive explanation for the occurrence of these self-organized temporal patterns, which is based on the imbalance between the diffusion and shrinkage speed in the confined geometry. Finally, we formulate an effective theory for the oscillatory regime, which explains the origin of the oscillations and correctly predicts the dependence of key quantities, such as the oscillation frequency, on the growth rate.
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Affiliation(s)
- Mareike Bojer
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany.,Department of Physics, Technische Universität München, D-85748 Garching, Germany
| | - Isabella R Graf
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany
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A deterministic model for one-dimensional excluded flow with local interactions. PLoS One 2017; 12:e0182074. [PMID: 28796838 PMCID: PMC5552133 DOI: 10.1371/journal.pone.0182074] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2017] [Accepted: 05/26/2017] [Indexed: 11/21/2022] Open
Abstract
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental model for the unidirectional flow of particles along a one-dimensional lattice of sites with nearest-neighbor interactions between the particles. The flow between consecutive sites is governed by a “soft” simple exclusion principle and by attracting or repelling forces between neighboring particles. Using tools from contraction theory, we prove that the model admits a unique steady-state and that every trajectory converges to this steady-state. Analysis and simulations of the effect of the attracting and repelling forces on this steady-state highlight the crucial role that these forces may play in increasing the steady-state flow, and reveal that this increase stems from the alleviation of traffic jams along the lattice. Our theoretical analysis clarifies microscopic aspects of complex multi-particle dynamic processes.
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Graf IR, Frey E. Generic Transport Mechanisms for Molecular Traffic in Cellular Protrusions. PHYSICAL REVIEW LETTERS 2017; 118:128101. [PMID: 28388182 DOI: 10.1103/physrevlett.118.128101] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2016] [Indexed: 06/07/2023]
Abstract
Transport of molecular motors along protein filaments in a half-closed geometry is a common feature of biologically relevant processes in cellular protrusions. Using a lattice-gas model we study how the interplay between active and diffusive transport and mass conservation leads to localized domain walls and tip localization of the motors. We identify a mechanism for task sharing between the active motors (maintaining a gradient) and the diffusive motion (transport to the tip), which ensures that energy consumption is low and motor exchange mostly happens at the tip. These features are attributed to strong nearest-neighbor correlations that lead to a strong reduction of active currents, which we calculate analytically using an exact moment identity, and might prove useful for the understanding of correlations and active transport also in more elaborate systems.
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Affiliation(s)
- Isabella R Graf
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, D-80333 Munich, Germany
| | - Erwin Frey
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, D-80333 Munich, Germany
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Pinkoviezky I, Gov NS. Exclusion and Hierarchy of Time Scales Lead to Spatial Segregation of Molecular Motors in Cellular Protrusions. PHYSICAL REVIEW LETTERS 2017; 118:018102. [PMID: 28106430 DOI: 10.1103/physrevlett.118.018102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2016] [Indexed: 06/06/2023]
Abstract
Molecular motors that carry cargo along biopolymer filaments within cells play a crucial role in the functioning of the cell. In particular, these motors are essential for the formation and maintenance of the cellular protrusions that play key roles in motility and specific functionalities, such as the stereocilia in hair cells. Typically, there are several species of motors, carrying different cargos, that share the same track. Furthermore, it was observed that in the mature stereocilia, the different motors occupy well-segregated bands as a function of distance from the tip. We use a totally asymmetric exclusion process model with two- and three-motor species, to study the conditions that give rise to such spatial patterns. We find that the well-segregated bands appear for motors with a strong hierarchy of attachment or detachment rates. This is a striking example of pattern formation in nonequilibrium, low-dimensional systems.
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Affiliation(s)
- I Pinkoviezky
- Department of Chemical Physics, Weizmann Institute of Science, P.O. Box 26, Rehovot 76100, Israel
| | - N S Gov
- Department of Chemical Physics, Weizmann Institute of Science, P.O. Box 26, Rehovot 76100, Israel
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Yochelis A, Ebrahim S, Millis B, Cui R, Kachar B, Naoz M, Gov NS. Self-organization of waves and pulse trains by molecular motors in cellular protrusions. Sci Rep 2015; 5:13521. [PMID: 26335545 PMCID: PMC4558574 DOI: 10.1038/srep13521] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2015] [Accepted: 07/29/2015] [Indexed: 11/13/2022] Open
Abstract
Actin-based cellular protrusions are an ubiquitous feature of cells, performing a variety of critical functions ranging from cell-cell communication to cell motility. The formation and maintenance of these protrusions relies on the transport of proteins via myosin motors, to the protrusion tip. While tip-directed motion leads to accumulation of motors (and their molecular cargo) at the protrusion tip, it is observed that motors also form rearward moving, periodic and isolated aggregates. The origins and mechanisms of these aggregates, and whether they are important for the recycling of motors, remain open puzzles. Motivated by novel myosin-XV experiments, a mass conserving reaction-diffusion-advection model is proposed. The model incorporates a non-linear cooperative interaction between motors, which converts them between an active and an inactive state. Specifically, the type of aggregate formed (traveling waves or pulse-trains) is linked to the kinetics of motors at the protrusion tip which is introduced by a boundary condition. These pattern selection mechanisms are found not only to qualitatively agree with empirical observations but open new vistas to the transport phenomena by molecular motors in general.
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Affiliation(s)
- A Yochelis
- Department of Solar Energy and Environmental Physics, Swiss Institute for Dryland Environmental and Energy Research, Blaustein Institutes for Desert Research (BIDR), Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 84990, Israel
| | - S Ebrahim
- Laboratory of Cell Structure and Dynamics, NIDCD, National Institutes of Health, 50 South Drive, Bethesda, MD 20892-8027, USA
| | - B Millis
- Laboratory of Cell Structure and Dynamics, NIDCD, National Institutes of Health, 50 South Drive, Bethesda, MD 20892-8027, USA
| | - R Cui
- Laboratory of Cell Structure and Dynamics, NIDCD, National Institutes of Health, 50 South Drive, Bethesda, MD 20892-8027, USA
| | - B Kachar
- Laboratory of Cell Structure and Dynamics, NIDCD, National Institutes of Health, 50 South Drive, Bethesda, MD 20892-8027, USA
| | - M Naoz
- Department of Chemical Physics, Weizmann Institute of Science, P.O.B. 26, Rehovot, Israel 76100
| | - N S Gov
- Department of Chemical Physics, Weizmann Institute of Science, P.O.B. 26, Rehovot, Israel 76100
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