1
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McCormick LA, Cleary JM, Hancock WO, Rice LM. Interface-acting nucleotide controls polymerization dynamics at microtubule plus- and minus-ends. eLife 2024; 12:RP89231. [PMID: 38180336 PMCID: PMC10945504 DOI: 10.7554/elife.89231] [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] [Indexed: 01/06/2024] Open
Abstract
GTP-tubulin is preferentially incorporated at growing microtubule ends, but the biochemical mechanism by which the bound nucleotide regulates the strength of tubulin:tubulin interactions is debated. The 'self-acting' (cis) model posits that the nucleotide (GTP or GDP) bound to a particular tubulin dictates how strongly that tubulin interacts, whereas the 'interface-acting' (trans) model posits that the nucleotide at the interface of two tubulin dimers is the determinant. We identified a testable difference between these mechanisms using mixed nucleotide simulations of microtubule elongation: with a self-acting nucleotide, plus- and minus-end growth rates decreased in the same proportion to the amount of GDP-tubulin, whereas with interface-acting nucleotide, plus-end growth rates decreased disproportionately. We then experimentally measured plus- and minus-end elongation rates in mixed nucleotides and observed a disproportionate effect of GDP-tubulin on plus-end growth rates. Simulations of microtubule growth were consistent with GDP-tubulin binding at and 'poisoning' plus-ends but not at minus-ends. Quantitative agreement between simulations and experiments required nucleotide exchange at terminal plus-end subunits to mitigate the poisoning effect of GDP-tubulin there. Our results indicate that the interfacial nucleotide determines tubulin:tubulin interaction strength, thereby settling a longstanding debate over the effect of nucleotide state on microtubule dynamics.
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Affiliation(s)
- Lauren A McCormick
- Department of Biophysics and Biochemistry, the University of Texas Southwestern Medical CenterDallasUnited States
| | - Joseph M Cleary
- Department of Biomedical Engineering, Pennsylvania State UniversityState CollegeUnited States
| | - William O Hancock
- Department of Biomedical Engineering, Pennsylvania State UniversityState CollegeUnited States
| | - Luke M Rice
- Department of Biophysics and Biochemistry, the University of Texas Southwestern Medical CenterDallasUnited States
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2
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McCormick LA, Cleary JM, Hancock WO, Rice LM. Interface-acting nucleotide controls polymerization dynamics at microtubule plus- and minus-ends. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.05.03.539131. [PMID: 37205370 PMCID: PMC10187237 DOI: 10.1101/2023.05.03.539131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
GTP-tubulin is preferentially incorporated at growing microtubule ends, but the biochemical mechanism by which the bound nucleotide regulates the strength of tubulin:tubulin interactions is debated. The 'self-acting' (cis) model posits that the nucleotide (GTP or GDP) bound to a particular tubulin dictates how strongly that tubulin interacts, whereas the 'interface-acting' (trans) model posits that the nucleotide at the interface of two tubulin dimers is the determinant. We identified a testable difference between these mechanisms using mixed nucleotide simulations of microtubule elongation: with self-acting nucleotide, plus- and minus-end growth rates decreased in the same proportion to the amount of GDP-tubulin, whereas with interface-acting nucleotide, plus-end growth rates decreased disproportionately. We then experimentally measured plus- and minus-end elongation rates in mixed nucleotides and observed a disproportionate effect of GDP-tubulin on plus-end growth rates. Simulations of microtubule growth were consistent with GDP-tubulin binding at and 'poisoning' plus-ends but not at minus-ends. Quantitative agreement between simulations and experiments required nucleotide exchange at terminal plus-end subunits to mitigate the poisoning effect of GDP-tubulin there. Our results indicate that the interfacial nucleotide determines tubulin:tubulin interaction strength, thereby settling a longstanding debate over the effect of nucleotide state on microtubule dynamics.
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Affiliation(s)
- Lauren A McCormick
- Department of Biophysics and Biochemistry, the University of Texas Southwestern Medical Center, Dallas, TX
| | - Joseph M Cleary
- Department of Biomedical Engineering, Pennsylvania State University, University Park, PA
| | - William O Hancock
- Department of Biomedical Engineering, Pennsylvania State University, University Park, PA
| | - Luke M Rice
- Department of Biophysics and Biochemistry, the University of Texas Southwestern Medical Center, Dallas, TX
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3
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Amoah-Darko FL, White D. Modelling microtubule dynamic instability: Microtubule growth, shortening and pause. J Theor Biol 2022; 553:111257. [PMID: 36057342 DOI: 10.1016/j.jtbi.2022.111257] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2021] [Revised: 08/11/2022] [Accepted: 08/18/2022] [Indexed: 11/26/2022]
Abstract
Microtubules (MTs) are protein polymers found in all eukaryotic cells. They are crucial for normal cell development, providing structural support for the cell and aiding in the transportation of proteins and organelles. In order to perform these functions, MTs go through periods of relatively slow polymerization (growth) and very fast depolymerization (shortening), where the switch from growth to shortening is called a catastrophe and the switch from shortening to growth is called a rescue. Although MT dynamic instability has traditionally been described solely in terms of growth and shortening, MTs have been shown to pause for extended periods of time, however the reason for pausing is not well understood. Here, we present a new mathematical model to describe MT dynamics in terms of growth, shortening, and pausing. Typically, MT dynamics are defined by four key parameters which include the MT growth rate, shortening rate, frequency of catastrophe, and the frequency of rescue. We derive a mathematical expression for the catastrophe frequency in the presence of pausing, as well as expressions to describe the total time that MTs spend in a state of growth and pause. In addition to exploring MT dynamics in a control-like setting, we explore the implicit effect of stabilizing MT associated proteins (MAPs) and stabilizing and destabilizing chemotherapeutic drugs that target MTs on MT dynamics through variations in model parameters.
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Affiliation(s)
| | - Diana White
- Clarkson University, 8 Clarkson Avenue, Potsdam, NY, United States of America.
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4
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Kliuchnikov E, Klyshko E, Kelly MS, Zhmurov A, Dima RI, Marx KA, Barsegov V. Microtubule assembly and disassembly dynamics model: Exploring dynamic instability and identifying features of Microtubules' Growth, Catastrophe, Shortening, and Rescue. Comput Struct Biotechnol J 2022; 20:953-974. [PMID: 35242287 PMCID: PMC8861655 DOI: 10.1016/j.csbj.2022.01.028] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2021] [Revised: 01/26/2022] [Accepted: 01/27/2022] [Indexed: 12/21/2022] Open
Abstract
Microtubules (MTs), a cellular structure element, exhibit dynamic instability and can switch stochastically from growth to shortening; but the factors that trigger these processes at the molecular level are not understood. We developed a 3D Microtubule Assembly and Disassembly DYnamics (MADDY) model, based upon a bead-per-monomer representation of the αβ-tubulin dimers forming an MT lattice, stabilized by the lateral and longitudinal interactions between tubulin subunits. The model was parameterized against the experimental rates of MT growth and shortening, and pushing forces on the Dam1 protein complex due to protofilaments splaying out. Using the MADDY model, we carried out GPU-accelerated Langevin simulations to access dynamic instability behavior. By applying Machine Learning techniques, we identified the MT characteristics that distinguish simultaneously all four kinetic states: growth, catastrophe, shortening, and rescue. At the cellular 25 μM tubulin concentration, the most important quantities are the MT length L , average longitudinal curvatureκ long , MT tip width w , total energy of longitudinal interactions in MT latticeU long , and the energies of longitudinal and lateral interactions required to complete MT to full cylinderU long add andU lat add . At high 250 μM tubulin concentration, the most important characteristics are L ,κ long , number of hydrolyzed αβ-tubulin dimersn hyd and number of lateral interactions per helical pitchn lat in MT lattice, energy of lateral interactions in MT latticeU lat , and energy of longitudinal interactions in MT tipu long . These results allow greater insights into what brings about kinetic state stability and the transitions between states involved in MT dynamic instability behavior.
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Affiliation(s)
| | - Eugene Klyshko
- Department of Chemistry, University of Massachusetts, Lowell, MA 01854, USA
| | - Maria S. Kelly
- Department of Chemistry, University of Cincinnati, Cincinnati, OH 45221, USA
| | - Artem Zhmurov
- KTH Royal Institute of Technology, Stockholm, Sweden
| | - Ruxandra I. Dima
- Department of Chemistry, University of Cincinnati, Cincinnati, OH 45221, USA
| | - Kenneth A. Marx
- Department of Chemistry, University of Massachusetts, Lowell, MA 01854, USA
| | - Valeri Barsegov
- Department of Chemistry, University of Massachusetts, Lowell, MA 01854, USA
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5
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Nasedkin A, Ermilova I, Swenson J. Atomistic molecular dynamics simulations of tubulin heterodimers explain the motion of a microtubule. EUROPEAN BIOPHYSICS JOURNAL : EBJ 2021; 50:927-940. [PMID: 34215900 PMCID: PMC8448678 DOI: 10.1007/s00249-021-01553-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/18/2021] [Revised: 05/24/2021] [Accepted: 06/07/2021] [Indexed: 06/13/2023]
Abstract
Microtubules are essential parts of the cytoskeleton that are built by polymerization of tubulin heterodimers into a hollow tube. Regardless that their structures and functions have been comprehensively investigated in a modern soft matter, it is unclear how properties of tubulin heterodimer influence and promote the self-assembly. A detailed knowledge of such structural mechanisms would be helpful in drug design against neurodegenerative diseases, cancer, diabetes etc. In this work atomistic molecular dynamics simulations were used to investigate the fundamental dynamics of tubulin heterodimers in a sheet and a short microtubule utilizing well-equilibrated structures. The breathing motions of the tubulin heterodimers during assembly show that the movement at the lateral interface between heterodimers (wobbling) dominates in the lattice. The simulations of the protofilament curvature agrees well with recently published experimental data, showing curved protofilaments at polymerization of the microtubule plus end. The tubulin heterodimers exposed at the microtubule minus end were less curved and displayed altered interactions at the site of sheet closure around the outmost heterodimers, which may slow heterodimer binding and polymerization, providing a potential explanation for the limited dynamics observed at the minus end.
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Affiliation(s)
- Alexandr Nasedkin
- Department of Physics, Chalmers University of Technology, SE 41296 Göteborg, Sweden
| | - Inna Ermilova
- Department of Physics, Chalmers University of Technology, SE 41296 Göteborg, Sweden
| | - Jan Swenson
- Department of Physics, Chalmers University of Technology, SE 41296 Göteborg, Sweden
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6
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Abstract
Microtubules are dynamic cytoskeletal filaments composed of αβ-tubulin heterodimers. Historically, the dynamics of single tubulin interactions at the growing microtubule tip have been inferred from steady-state growth kinetics. However, recent advances in the production of recombinant tubulin and in high-resolution optical and cryo-electron microscopies have opened new windows into understanding the impacts of specific intermolecular interactions during growth. The microtubule lattice is held together by lateral and longitudinal tubulin-tubulin interactions, and these interactions are in turn regulated by the GTP hydrolysis state of the tubulin heterodimer. Furthermore, tubulin can exist in either an extended or a compacted state in the lattice. Growing evidence has led to the suggestion that binding of microtubule-associated proteins (MAPs) or motors can induce changes in tubulin conformation and that this information can be communicated through the microtubule lattice. Progress in understanding how dynamic tubulin-tubulin interactions control dynamic instability has benefitted from visualizing structures of growing microtubule plus ends and through stochastic biochemical models constrained by experimental data. Here, we review recent insights into the molecular basis of microtubule growth and discuss how MAPs and regulatory proteins alter tubulin-tubulin interactions to exert their effects on microtubule growth and stability.
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Affiliation(s)
- Joseph M Cleary
- Department of Biomedical Engineering, Pennsylvania State University, University Park, PA 16802, USA
| | - William O Hancock
- Department of Biomedical Engineering, Pennsylvania State University, University Park, PA 16802, USA.
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7
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Gudimchuk NB, Ulyanov EV, O'Toole E, Page CL, Vinogradov DS, Morgan G, Li G, Moore JK, Szczesna E, Roll-Mecak A, Ataullakhanov FI, Richard McIntosh J. Mechanisms of microtubule dynamics and force generation examined with computational modeling and electron cryotomography. Nat Commun 2020; 11:3765. [PMID: 32724196 PMCID: PMC7387542 DOI: 10.1038/s41467-020-17553-2] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2020] [Accepted: 07/08/2020] [Indexed: 01/15/2023] Open
Abstract
Microtubules are dynamic tubulin polymers responsible for many cellular processes, including the capture and segregation of chromosomes during mitosis. In contrast to textbook models of tubulin self-assembly, we have recently demonstrated that microtubules elongate by addition of bent guanosine triphosphate tubulin to the tips of curving protofilaments. Here we explore this mechanism of microtubule growth using Brownian dynamics modeling and electron cryotomography. The previously described flaring shapes of growing microtubule tips are remarkably consistent under various assembly conditions, including different tubulin concentrations, the presence or absence of a polymerization catalyst or tubulin-binding drugs. Simulations indicate that development of substantial forces during microtubule growth and shortening requires a high activation energy barrier in lateral tubulin-tubulin interactions. Modeling offers a mechanism to explain kinetochore coupling to growing microtubule tips under assisting force, and it predicts a load-dependent acceleration of microtubule assembly, providing a role for the flared morphology of growing microtubule ends.
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Affiliation(s)
- Nikita B Gudimchuk
- Department of Physics, Lomonosov Moscow State University, Moscow, Russia.
- Center for Theoretical Problems of Physicochemical Pharmacology, Russian Academy of Sciences, Moscow, Russia.
- Dmitry Rogachev National Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russia.
| | - Evgeni V Ulyanov
- Department of Physics, Lomonosov Moscow State University, Moscow, Russia
| | - Eileen O'Toole
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, CO, USA
| | - Cynthia L Page
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, CO, USA
| | - Dmitrii S Vinogradov
- Center for Theoretical Problems of Physicochemical Pharmacology, Russian Academy of Sciences, Moscow, Russia
| | - Garry Morgan
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, CO, USA
| | - Gabriella Li
- Department of Cell and Developmental Biology, University of Colorado School of Medicine, Aurora, CO, USA
| | - Jeffrey K Moore
- Department of Cell and Developmental Biology, University of Colorado School of Medicine, Aurora, CO, USA
| | - Ewa Szczesna
- Cell Biology and Biophysics Unit, National Institute of Neurological Disorders and Stroke, Bethesda, MD, USA
| | - Antonina Roll-Mecak
- Cell Biology and Biophysics Unit, National Institute of Neurological Disorders and Stroke, Bethesda, MD, USA
| | - Fazoil I Ataullakhanov
- Department of Physics, Lomonosov Moscow State University, Moscow, Russia
- Center for Theoretical Problems of Physicochemical Pharmacology, Russian Academy of Sciences, Moscow, Russia
- Dmitry Rogachev National Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russia
| | - J Richard McIntosh
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, CO, USA
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8
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Numerical Parameter Space Compression and Its Application to Biophysical Models. Biophys J 2020; 118:1455-1465. [PMID: 32070477 DOI: 10.1016/j.bpj.2020.01.023] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2019] [Revised: 12/07/2019] [Accepted: 01/14/2020] [Indexed: 11/20/2022] Open
Abstract
Physical models of biological systems can become difficult to interpret when they have a large number of parameters. But the models themselves actually depend on (i.e., are sensitive to) only a subset of those parameters. This phenomenon is due to parameter space compression (PSC), in which a subset of parameters emerges as "stiff" as a function of time or space. PSC has only been used to explain analytically solvable physics models. We have generalized this result by developing a numerical approach to PSC that can be applied to any computational model. We validated our method against analytically solvable models of a random walk with drift and protein production and degradation. We then applied our method to a simple computational model of microtubule dynamic instability. We propose that numerical PSC has the potential to identify the low-dimensional structure of many computational models in biophysics. The low-dimensional structure of a model is easier to interpret and identifies the mechanisms and experiments that best characterize the system.
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9
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Jonasson EM, Mauro AJ, Li C, Labuz EC, Mahserejian SM, Scripture JP, Gregoretti IV, Alber M, Goodson HV. Behaviors of individual microtubules and microtubule populations relative to critical concentrations: dynamic instability occurs when critical concentrations are driven apart by nucleotide hydrolysis. Mol Biol Cell 2019; 31:589-618. [PMID: 31577530 PMCID: PMC7202068 DOI: 10.1091/mbc.e19-02-0101] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Abstract
The concept of critical concentration (CC) is central to understanding the behavior of microtubules (MTs) and other cytoskeletal polymers. Traditionally, these polymers are understood to have one CC, measured in multiple ways and assumed to be the subunit concentration necessary for polymer assembly. However, this framework does not incorporate dynamic instability (DI), and there is work indicating that MTs have two CCs. We use our previously established simulations to confirm that MTs have (at least) two experimentally relevant CCs and to clarify the behavior of individuals and populations relative to the CCs. At free subunit concentrations above the lower CC (CCElongation), growth phases of individual filaments can occur transiently; above the higher CC (CCNetAssembly), the population’s polymer mass will increase persistently. Our results demonstrate that most experimental CC measurements correspond to CCNetAssembly, meaning that “typical” DI occurs below the concentration traditionally considered necessary for polymer assembly. We report that [free tubulin] at steady state does not equal CCNetAssembly, but instead approaches CCNetAssembly asymptotically as [total tubulin] increases, and depends on the number of stable MT nucleation sites. We show that the degree of separation between CCElongation and CCNetAssembly depends on the rate of nucleotide hydrolysis. This clarified framework helps explain and unify many experimental observations.
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Affiliation(s)
- Erin M Jonasson
- Department of Chemistry and Biochemistry.,Department of Natural Sciences, Saint Martin's University, Lacey, WA 98503
| | - Ava J Mauro
- Department of Chemistry and Biochemistry.,Department of Applied and Computational Mathematics and Statistics, and.,Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003
| | - Chunlei Li
- Department of Applied and Computational Mathematics and Statistics, and
| | | | | | | | | | - Mark Alber
- Department of Applied and Computational Mathematics and Statistics, and.,Department of Mathematics, University of California, Riverside, Riverside, CA 92521
| | - Holly V Goodson
- Department of Chemistry and Biochemistry.,Department of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556
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10
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Kim T, Rice LM. Long-range, through-lattice coupling improves predictions of microtubule catastrophe. Mol Biol Cell 2019; 30:1451-1462. [PMID: 30943103 PMCID: PMC6724698 DOI: 10.1091/mbc.e18-10-0641] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
Microtubules are cylindrical polymers of αβ-tubulin that play critical roles in fundamental processes such as chromosome segregation and vesicular transport. Microtubules display dynamic instability, switching stochastically between growth and rapid shrinking as a consequence of GTPase activity in the lattice. The molecular mechanisms behind microtubule catastrophe, the switch from growth to rapid shrinking, remain poorly defined. Indeed, two-state stochastic models that seek to describe microtubule dynamics purely in terms of the biochemical properties of GTP- and GDP-bound αβ-tubulin predict the concentration dependence of microtubule catastrophe incorrectly. Recent studies provide evidence for three distinct conformations of αβ-tubulin in the lattice that likely correspond to GTP, GDP.Pi, and GDP. The incommensurate lattices observed for these different conformations raise the possibility that in a mixed nucleotide state lattice, neighboring tubulin dimers might modulate each other’s conformations and hence each other’s biochemistry. We explored whether incorporating a GDP.Pi state or the likely effects of conformational accommodation can improve predictions of catastrophe. Adding a GDP.Pi intermediate did not improve the model. In contrast, adding neighbor-dependent modulation of tubulin biochemistry improved predictions of catastrophe. Because this conformational accommodation should propagate beyond nearest-neighbor contacts, our modeling suggests that long-range, through-lattice effects are important determinants of microtubule catastrophe.
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Affiliation(s)
- Tae Kim
- Departments of Biophysics and Biochemistry, UT Southwestern Medical Center, Dallas, TX 75390
| | - Luke M Rice
- Departments of Biophysics and Biochemistry, UT Southwestern Medical Center, Dallas, TX 75390
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11
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Direct observation of individual tubulin dimers binding to growing microtubules. Proc Natl Acad Sci U S A 2019; 116:7314-7322. [PMID: 30804205 DOI: 10.1073/pnas.1815823116] [Citation(s) in RCA: 38] [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
The biochemical basis of microtubule growth has remained elusive for over 30 years despite being fundamental for both cell division and associated chemotherapy strategies. Here, we combine interferometric scattering microscopy with recombinant tubulin to monitor individual tubulins binding to and dissociating from growing microtubule tips. We make direct, single-molecule measurements of tubulin association and dissociation rates. We detect two populations of transient dwell times and determine via binding-interface mutants that they are distinguished by the formation of one interprotofilament bond. Applying a computational model, we find that slow association kinetics with strong interactions along protofilaments best recapitulate our data and, furthermore, predicts plus-end tapering. Overall, we provide the most direct and complete experimental quantification of how microtubules grow to date.
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12
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Manandhar A, Kang M, Chakraborty K, Loverde SM. Effect of Nucleotide State on the Protofilament Conformation of Tubulin Octamers. J Phys Chem B 2018; 122:6164-6178. [PMID: 29768004 DOI: 10.1021/acs.jpcb.8b02193] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
At the molecular level, the dynamic instability (random growth and shrinkage) of the microtubule (MT) is driven by the nucleotide state (GTP vs GDP) in the β subunit of the tubulin dimers at the MT cap. Here, we use large-scale molecular dynamics (MD) simulations and normal-mode analysis (NMA) to characterize the effect of a single GTP cap layer on tubulin octamers composed of two neighboring protofilaments (PFs). We utilize recently reported high-resolution structures of dynamic MTs to simulate a GDP octamer both with and without a single GTP cap layer. We perform multiple replicas of long-time atomistic MD simulations (3 replicas, 0.3 μs for each replica, 0.9 μs for each octamer system, and 1.8 μs total) of both octamers. We observe that a single GTP cap layer induces structural differences in neighboring PFs, finding that one PF possesses a gradual curvature, compared to the second PF which possesses a kinked conformation. This results in either curling or splaying between these PFs. We suggest that this is due to asymmetric strengths of longitudinal contacts between the two PFs. Furthermore, using NMA, we calculate mechanical properties of these octamer systems and find that octamer system with a single GTP cap layer possesses a lower flexural rigidity.
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Affiliation(s)
- Anjela Manandhar
- Department of Chemistry, College of Staten Island , City University of New York , 2800 Victory Boulevard , Staten Island , New York 10314 , United States.,Ph.D. Program in Biochemistry , The Graduate Center of the City University of New York , 365 Fifth Avenue , New York , New York 10016 , United States
| | - Myungshim Kang
- Department of Chemistry, College of Staten Island , City University of New York , 2800 Victory Boulevard , Staten Island , New York 10314 , United States
| | - Kaushik Chakraborty
- Department of Chemistry, College of Staten Island , City University of New York , 2800 Victory Boulevard , Staten Island , New York 10314 , United States
| | - Sharon M Loverde
- Department of Chemistry, College of Staten Island , City University of New York , 2800 Victory Boulevard , Staten Island , New York 10314 , United States.,Ph.D. Program in Biochemistry , The Graduate Center of the City University of New York , 365 Fifth Avenue , New York , New York 10016 , United States
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13
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White D, Honoré S, Hubert F. Exploring the effect of end-binding proteins and microtubule targeting chemotherapy drugs on microtubule dynamic instability. J Theor Biol 2017. [DOI: 10.1016/j.jtbi.2017.06.014] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
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14
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Zakharov P, Gudimchuk N, Voevodin V, Tikhonravov A, Ataullakhanov FI, Grishchuk EL. Molecular and Mechanical Causes of Microtubule Catastrophe and Aging. Biophys J 2016; 109:2574-2591. [PMID: 26682815 DOI: 10.1016/j.bpj.2015.10.048] [Citation(s) in RCA: 71] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2015] [Revised: 09/11/2015] [Accepted: 10/05/2015] [Indexed: 10/22/2022] Open
Abstract
Tubulin polymers, microtubules, can switch abruptly from the assembly to shortening. These infrequent transitions, termed "catastrophes", affect numerous cellular processes but the underlying mechanisms are elusive. We approached this complex stochastic system using advanced coarse-grained molecular dynamics modeling of tubulin-tubulin interactions. Unlike in previous simplified models of dynamic microtubules, the catastrophes in this model arise owing to fluctuations in the composition and conformation of a growing microtubule tip, most notably in the number of protofilament curls. In our model, dynamic evolution of the stochastic microtubule tip configurations over a long timescale, known as the system's "aging", gives rise to the nonexponential distribution of microtubule lifetimes, consistent with experiment. We show that aging takes place in the absence of visible changes in the microtubule wall or tip, as this complex molecular-mechanical system evolves slowly and asymptotically toward the steady-state level of the catastrophe-promoting configurations. This new, to our knowledge, theoretical basis will assist detailed mechanistic investigations of the mechanisms of action of different microtubule-binding proteins and drugs, thereby enabling accurate control over the microtubule dynamics to treat various pathologies.
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Affiliation(s)
- Pavel Zakharov
- Department of Physiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania
| | - Nikita Gudimchuk
- Center for Theoretical Problems of Physicochemical Pharmacology, Russian Academy of Sciences, Moscow, Russia; Moscow State University, Moscow, Russia; Federal Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russia
| | | | | | - Fazoil I Ataullakhanov
- Center for Theoretical Problems of Physicochemical Pharmacology, Russian Academy of Sciences, Moscow, Russia; Moscow State University, Moscow, Russia; Federal Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russia
| | - Ekaterina L Grishchuk
- Department of Physiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania.
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15
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Bowne-Anderson H, Hibbel A, Howard J. Regulation of Microtubule Growth and Catastrophe: Unifying Theory and Experiment. Trends Cell Biol 2016; 25:769-779. [PMID: 26616192 DOI: 10.1016/j.tcb.2015.08.009] [Citation(s) in RCA: 54] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2015] [Revised: 08/27/2015] [Accepted: 08/27/2015] [Indexed: 10/22/2022]
Abstract
Recent studies have found that microtubule-associated proteins (MAPs) can regulate the dynamical properties of microtubules in unexpected ways. For most MAPs, there is an inverse relationship between their effects on the speed of growth and the frequency of catastrophe, the conversion of a growing microtubule to a shrinking one. Such a negative correlation is predicted by the standard GTP-cap model, which posits that catastrophe is due to loss of a stabilizing cap of GTP-tubulin at the end of a growing microtubule. However, many other MAPs, notably Kinesin-4 and combinations of EB1 with XMAP215, contradict this general rule. In this review, we show that a more nuanced, but still simple, GTP-cap model, can account for the diverse regulatory activities of MAPs.
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Affiliation(s)
| | - Anneke Hibbel
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden 01307, Germany; ETH Zurich, Institute for Biochemistry, HPM E8.1, Otto-Stern-Weg 3, 8093 Zurich, Switzerland
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16
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Piedra FA, Kim T, Garza ES, Geyer EA, Burns A, Ye X, Rice LM. GDP-to-GTP exchange on the microtubule end can contribute to the frequency of catastrophe. Mol Biol Cell 2016; 27:3515-3525. [PMID: 27146111 PMCID: PMC5221584 DOI: 10.1091/mbc.e16-03-0199] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2016] [Accepted: 04/26/2016] [Indexed: 11/11/2022] Open
Abstract
Microtubules are dynamic polymers of αβ-tubulin that have essential roles in chromosome segregation and organization of the cytoplasm. Catastrophe-the switch from growing to shrinking-occurs when a microtubule loses its stabilizing GTP cap. Recent evidence indicates that the nucleotide on the microtubule end controls how tightly an incoming subunit will be bound (trans-acting GTP), but most current models do not incorporate this information. We implemented trans-acting GTP into a computational model for microtubule dynamics. In simulations, growing microtubules often exposed terminal GDP-bound subunits without undergoing catastrophe. Transient GDP exposure on the growing plus end slowed elongation by reducing the number of favorable binding sites on the microtubule end. Slower elongation led to erosion of the GTP cap and an increase in the frequency of catastrophe. Allowing GDP-to-GTP exchange on terminal subunits in simulations mitigated these effects. Using mutant αβ-tubulin or modified GTP, we showed experimentally that a more readily exchangeable nucleotide led to less frequent catastrophe. Current models for microtubule dynamics do not account for GDP-to-GTP exchange on the growing microtubule end, so our findings provide a new way of thinking about the molecular events that initiate catastrophe.
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Affiliation(s)
- Felipe-Andrés Piedra
- Departments of Biophysics and Biochemistry, UT Southwestern Medical Center, Dallas, TX 75390
| | - Tae Kim
- Departments of Biophysics and Biochemistry, UT Southwestern Medical Center, Dallas, TX 75390
| | - Emily S Garza
- Departments of Biophysics and Biochemistry, UT Southwestern Medical Center, Dallas, TX 75390
| | - Elisabeth A Geyer
- Departments of Biophysics and Biochemistry, UT Southwestern Medical Center, Dallas, TX 75390
| | - Alexander Burns
- Departments of Biophysics and Biochemistry, UT Southwestern Medical Center, Dallas, TX 75390
| | - Xuecheng Ye
- Departments of Biophysics and Biochemistry, UT Southwestern Medical Center, Dallas, TX 75390
| | - Luke M Rice
- Departments of Biophysics and Biochemistry, UT Southwestern Medical Center, Dallas, TX 75390
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17
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Brownian dynamics of subunit addition-loss kinetics and thermodynamics in linear polymer self-assembly. Biophys J 2014; 105:2528-40. [PMID: 24314083 DOI: 10.1016/j.bpj.2013.10.009] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2013] [Revised: 09/23/2013] [Accepted: 10/16/2013] [Indexed: 11/23/2022] Open
Abstract
The structure and free energy of multistranded linear polymer ends evolves as individual subunits are added and lost. Thus, the energetic state of the polymer end is not constant, as assembly theory has assumed. Here we utilize a Brownian dynamics approach to simulate the addition and loss of individual subunits at the polymer tip. Using the microtubule as a primary example, we examined how the structure of the polymer tip dictates the rate at which units are added to and lost from individual protofilaments. We find that freely diffusing subunits arrive less frequently to lagging protofilaments but bind more efficiently, such that there is no kinetic difference between leading and lagging protofilaments within a tapered tip. However, local structure at the nanoscale has up to an order-of-magnitude effect on the rate of addition. Thus, the kinetic on-rate constant, integrated across the microtubule tip (kon,MT), is an ensemble average of the varying individual protofilament on-rate constants (kon,PF). Our findings have implications for both catastrophe and rescue of the dynamic microtubule end, and provide a subnanoscale framework for understanding the mechanism of action of microtubule-associated proteins and microtubule-directed drugs. Although we utilize the specific example of the microtubule here, the findings are applicable to multistranded polymers generally.
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18
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Bowne-Anderson H, Zanic M, Kauer M, Howard J. Microtubule dynamic instability: a new model with coupled GTP hydrolysis and multistep catastrophe. Bioessays 2013; 35:452-61. [PMID: 23532586 PMCID: PMC3677417 DOI: 10.1002/bies.201200131] [Citation(s) in RCA: 105] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
A key question in understanding microtubule dynamics is how GTP hydrolysis leads to catastrophe, the switch from slow growth to rapid shrinkage. We first provide a review of the experimental and modeling literature, and then present a new model of microtubule dynamics. We demonstrate that vectorial, random, and coupled hydrolysis mechanisms are not consistent with the dependence of catastrophe on tubulin concentration and show that, although single-protofilament models can explain many features of dynamics, they do not describe catastrophe as a multistep process. Finally, we present a new combined (coupled plus random hydrolysis) multiple-protofilament model that is a simple, analytically solvable generalization of a single-protofilament model. This model accounts for the observed lifetimes of growing microtubules, the delay to catastrophe following dilution and describes catastrophe as a multistep process.
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Affiliation(s)
- Hugo Bowne-Anderson
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
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19
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Bolterauer H, Limbach HJ, Tuszyński JA. Models of assembly and disassembly of individual microtubules: stochastic and averaged equations. J Biol Phys 2013; 25:1-22. [PMID: 23345684 DOI: 10.1023/a:1005159215657] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
In this paper we present solutions of the master equations for the microtubule length and show that the local probability for rescues or catastrophes can lead to bell-shaped length histograms. Conversely, as already known, non-local probabilities for these events result in exponential length histograms. We also derive master equations for a stabilizing cap and obtain a new boundary condition which provides an explanation of the results obtained in dilution and cutting experiments.
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Affiliation(s)
- H Bolterauer
- Institut für Theoretische Physik, Justus-Liebig Universität Gießen, Gießen, Germany
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20
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Margolin G, Gregoretti IV, Cickovski TM, Li C, Shi W, Alber MS, Goodson HV. The mechanisms of microtubule catastrophe and rescue: implications from analysis of a dimer-scale computational model. Mol Biol Cell 2011; 23:642-56. [PMID: 22190741 PMCID: PMC3279392 DOI: 10.1091/mbc.e11-08-0688] [Citation(s) in RCA: 70] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
ETOC: The behavior of a dimer-scale computational model predicts that short interprotofilament “cracks” (laterally unbonded regions between protofilaments) exist even at the tips of growing MTs and that rapid fluctuations in the depths of these cracks govern both catastrophe and rescue. Microtubule (MT) dynamic instability is fundamental to many cell functions, but its mechanism remains poorly understood, in part because it is difficult to gain information about the dimer-scale events at the MT tip. To address this issue, we used a dimer-scale computational model of MT assembly that is consistent with tubulin structure and biochemistry, displays dynamic instability, and covers experimentally relevant spans of time. It allows us to correlate macroscopic behaviors (dynamic instability parameters) with microscopic structures (tip conformations) and examine protofilament structure as the tip spontaneously progresses through both catastrophe and rescue. The model's behavior suggests that several commonly held assumptions about MT dynamics should be reconsidered. Moreover, it predicts that short, interprotofilament “cracks” (laterally unbonded regions between protofilaments) exist even at the tips of growing MTs and that rapid fluctuations in the depths of these cracks influence both catastrophe and rescue. We conclude that experimentally observed microtubule behavior can best be explained by a “stochastic cap” model in which tubulin subunits hydrolyze GTP according to a first-order reaction after they are incorporated into the lattice; catastrophe and rescue result from stochastic fluctuations in the size, shape, and extent of lateral bonding of the cap.
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Affiliation(s)
- Gennady Margolin
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA
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21
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Macroscopic simulations of microtubule dynamics predict two steady-state processes governing array morphology. Comput Biol Chem 2011; 35:269-81. [PMID: 22000798 DOI: 10.1016/j.compbiolchem.2011.06.002] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2011] [Revised: 05/10/2011] [Accepted: 06/17/2011] [Indexed: 01/21/2023]
Abstract
Microtubule polymers typically function through their collective organization into a patterned array. The formation of the pattern, whether it is a relatively simple astral array or a highly complex mitotic spindle, relies on controlled microtubule nucleation and the basal dynamics parameters governing polymer growth and shortening. We have investigated the interaction between the microtubule nucleation and dynamics parameters, using macroscopic Monte Carlo simulations, to determine how these parameters contribute to the underlying microtubule array morphology (i.e. polymer density and length distribution). In addition to the well-characterized steady state achieved between free tubulin subunits and microtubule polymer, we propose that microtubule nucleation and extinction constitute a second, interdependent steady state process. Our simulation studies show that the magnitude of both nucleation and extinction additively impacts the final steady state free subunit concentration. We systematically varied individual microtubule dynamics parameters to survey the effects on array morphology and find specific sensitivity to perturbations of catastrophe frequency. Altering the cellular context for the microtubule array, we find that nucleation template number plays a defining role in shaping the microtubule length distribution and polymer density.
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22
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Margolin G, Goodson HV, Alber MS. Mean-field study of the role of lateral cracks in microtubule dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:041905. [PMID: 21599199 DOI: 10.1103/physreve.83.041905] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2010] [Revised: 01/22/2011] [Indexed: 05/04/2023]
Abstract
A link between dimer-scale processes and microtubule (MT) dynamics at macroscale is studied by comparing simulations obtained using computational dimer-scale model with its mean-field approximation. The novelty of the mean-field model (MFM) is in its explicit representation of inter-protofilament cracks, as well as in the direct incorporation of the dimer-level kinetics. Due to inclusion of both longitudinal and lateral dimer interactions, the MFM is two dimensional, in contrast to previous theoretical models of MTs. It is the first analytical model that predicts and quantifies crucial features of MT dynamics such as (i) existence of a minimal soluble tubulin concentration needed for the polymerization (with concentration represented as a function of model parameters), (ii) existence of steady-state growth and shortening phases (given with their respective velocities), and (iii) existence of an unstable pause state near zero velocity. In addition, the size of the GTP cap of a growing MT is estimated. Theoretical predictions are shown to be in good agreement with the numerical simulations.
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Affiliation(s)
- Gennady Margolin
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana 46556, USA
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23
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Gardner MK, Odde DJ. Stochastic simulation and graphic visualization of mitotic processes. Methods 2010; 51:251-6. [PMID: 20096783 PMCID: PMC2884048 DOI: 10.1016/j.ymeth.2010.01.021] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2010] [Accepted: 01/19/2010] [Indexed: 12/26/2022] Open
Abstract
Computational modeling can be extremely useful in interpreting experimental results. Here we describe how a relatively sophisticated stochastic model for microtubule dynamic instability in the mitotic spindle can be developed starting with straightforward rules and simple programming code. Once this model is developed, the method for comparing simulation results to experimental data must be carefully considered. The ultimate utility of any computational model relies on its predictive power and the ability to assist in designing new experiments. We describe how "deconstructing" the model through the use of quantitative animations contributes to a better qualitative understanding of model behavior. By extracting key qualitative elements of the model in this fashion, model predictions and new experiments can be more easily extracted from model results.
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Affiliation(s)
- Melissa K Gardner
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota 55455
| | - David J. Odde
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota 55455
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24
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25
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A thermodynamic model of microtubule assembly and disassembly. PLoS One 2009; 4:e6378. [PMID: 19668378 PMCID: PMC2719802 DOI: 10.1371/journal.pone.0006378] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2009] [Accepted: 06/05/2009] [Indexed: 01/13/2023] Open
Abstract
Microtubules are self-assembling polymers whose dynamics are essential for the normal function of cellular processes including chromosome separation and cytokinesis. Therefore understanding what factors effect microtubule growth is fundamental to our understanding of the control of microtubule based processes. An important factor that determines the status of a microtubule, whether it is growing or shrinking, is the length of the GTP tubulin microtubule cap. Here, we derive a Monte Carlo model of the assembly and disassembly of microtubules. We use thermodynamic laws to reduce the number of parameters of our model and, in particular, we take into account the contribution of water to the entropy of the system. We fit all parameters of the model from published experimental data using the GTP tubulin dimer attachment rate and the lateral and longitudinal binding energies of GTP and GDP tubulin dimers at both ends. Also we calculate and incorporate the GTP hydrolysis rate. We have applied our model and can mimic published experimental data, which formerly suggested a single layer GTP tubulin dimer microtubule cap, to show that these data demonstrate that the GTP cap can fluctuate and can be several microns long.
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26
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Schilstra MJ, Martin SR, Keating SM. Methods for simulating the dynamics of complex biological processes. Methods Cell Biol 2008; 84:807-42. [PMID: 17964950 DOI: 10.1016/s0091-679x(07)84025-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
In this chapter, we provide the basic information required to understand the central concepts in the modeling and simulation of complex biochemical processes. We underline the fact that most biochemical processes involve sequences of interactions between distinct entities (molecules, molecular assemblies), and also stress that models must adhere to the laws of thermodynamics. Therefore, we discuss the principles of mass-action reaction kinetics, the dynamics of equilibrium and steady state, and enzyme kinetics, and explain how to assess transition probabilities and reactant lifetime distributions for first-order reactions. Stochastic simulation of reaction systems in well-stirred containers is introduced using a relatively simple, phenomenological model of microtubule dynamic instability in vitro. We demonstrate that deterministic simulation [by numerical integration of coupled ordinary differential equations (ODE)] produces trajectories that would be observed if the results of many rounds of stochastic simulation of the same system were averaged. In Section V, we highlight several practical issues with regard to the assessment of parameter values. We draw some attention to the development of a standard format for model storage and exchange, and provide a list of selected software tools that may facilitate the model building process, and can be used to simulate the modeled systems.
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Affiliation(s)
- Maria J Schilstra
- Biological and Neural Computation Group, Science and Technology Research Institute, University of Hertfordshire, College Lane, Hatfield AL10 9AB, United Kingdom
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27
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Schek HT, Gardner MK, Cheng J, Odde DJ, Hunt AJ. Microtubule assembly dynamics at the nanoscale. Curr Biol 2007; 17:1445-55. [PMID: 17683936 PMCID: PMC2094715 DOI: 10.1016/j.cub.2007.07.011] [Citation(s) in RCA: 148] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2007] [Revised: 06/29/2007] [Accepted: 07/04/2007] [Indexed: 12/16/2022]
Abstract
BACKGROUND The labile nature of microtubules is critical for establishing cellular morphology and motility, yet the molecular basis of assembly remains unclear. Here we use optical tweezers to track microtubule polymerization against microfabricated barriers, permitting unprecedented spatial resolution. RESULTS We find that microtubules exhibit extensive nanometer-scale variability in growth rate and often undergo shortening excursions, in some cases exceeding five tubulin layers, during periods of overall net growth. This result indicates that the guanosine triphosphate (GTP) cap does not exist as a single layer as previously proposed. We also find that length increments (over 100 ms time intervals, n = 16,762) are small, 0.81 +/- 6.60 nm (mean +/- standard deviation), and very rarely exceed 16 nm (about two dimer lengths), indicating that assembly occurs almost exclusively via single-subunit addition rather than via oligomers as was recently suggested. Finally, the assembly rate depends only weakly on load, with the average growth rate decreasing only 2-fold as the force increases 7-fold from 0.4 pN to 2.8 pN. CONCLUSIONS The data are consistent with a mechanochemical model in which a spatially extended GTP cap allows substantial shortening on the nanoscale, while still preventing complete catastrophe in most cases.
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Affiliation(s)
- Henry T Schek
- European Molecular Biology Laboratory, Meyerhofstrasse 1, 69117, Heidelberg, Germany
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28
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Margolin G, Gregoretti IV, Goodson HV, Alber MS. Analysis of a mesoscopic stochastic model of microtubule dynamic instability. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:041920. [PMID: 17155109 DOI: 10.1103/physreve.74.041920] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2006] [Revised: 07/13/2006] [Indexed: 05/12/2023]
Abstract
A theoretical model of dynamic instability of a system of linear one-dimensional microtubules (MTs) in a bounded domain is introduced for studying the role of a cell edge in vivo and analyzing the effect of competition for a limited amount of tubulin. The model differs from earlier models in that the evolution of MTs is based on the rates of single-mesoscopic-unit (e.g., a heterodimer per protofilament) transformations, in contrast to postulating effective rates and frequencies of larger-scale macroscopic changes, extracted, e.g., from the length history plots of MTs. Spontaneous GTP hydrolysis with finite rate after polymerization is assumed, and theoretical estimates of an effective catastrophe frequency as well as other parameters characterizing MT length distributions and cap size are derived. We implement a simple cap model which does not include vectorial hydrolysis. We demonstrate that our theoretical predictions, such as steady-state concentration of free tubulin and parameters of MT length distributions, are in agreement with the numerical simulations. The present model establishes a quantitative link between mesoscopic parameters governing the dynamics of MTs and macroscopic characteristics of MTs in a closed system. Last, we provide an explanation for nonexponential MT length distributions observed in experiments. In particular, we show that the appearance of such nonexponential distributions in the experiments can occur because a true steady state has not been reached and/or due to the presence of a cell edge.
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Affiliation(s)
- Gennady Margolin
- Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, USA
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29
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Stukalin EB, Kolomeisky AB. Polymerization dynamics of double-stranded biopolymers: chemical kinetic approach. J Chem Phys 2006; 122:104903. [PMID: 15836354 DOI: 10.1063/1.1858859] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The polymerization dynamics of double-stranded polymers, such as actin filaments, is investigated theoretically using simple chemical kinetic models that explicitly take into account some microscopic details of the polymer structure and the lateral interactions between the protofilaments. By considering all possible molecular configurations, the exact analytical expressions for the growth velocity and dispersion for two-stranded polymers are obtained in the case of the growing at only one end, and for the growth from both polymer ends. Exact theoretical calculations are compared with the predictions of approximate multilayer models that consider only a finite number of the most relevant polymer configurations. Our theoretical approach is applied to analyze the experimental data on the growth and fluctuations dynamics of individual single actin filaments.
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30
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Deymier PA, Yang Y, Hoying J. Effect of tubulin diffusion on polymerization of microtubules. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:021906. [PMID: 16196603 DOI: 10.1103/physreve.72.021906] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2005] [Revised: 05/02/2005] [Indexed: 05/04/2023]
Abstract
The dynamics of microtubules (MT's) growing from a nucleation center is simulated with a kinetic Monte Carlo model that includes tubulin diffusion. In the limit of fast diffusion (homogeneous tubulin concentration), MT growth is synchronous and bounded. The microtubules form an aster with a monotonously decreasing long-time distribution of lengths. Slow tubulin diffusion leads to rapid dephasing in the growth dynamics, unbounded growth of some MT's, spatial inhomogeneities, and morphological change toward a morphology with bounded short MT's located in the nucleation center and unbounded long MT's with narrowly distributed lengths. The transition from unbounded to bounded growth is driven by the competition between the reaction rate of the tubulin assembly and the tubulin's diffusion rate. While the present study reports the effect of the tubulin diffusion coefficient on the transition, the results of the simulations are qualitatively comparable to the morphological and dynamical changes of centrosome-nucleated MT's from interphase to mitosis in cellular systems where the transition is regulated by the reaction rates.
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Affiliation(s)
- P A Deymier
- Department of Materials Science and Engineering, The University of Arizona, Tucson, Arizona 85721, USA
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31
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VanBuren V, Cassimeris L, Odde DJ. Mechanochemical model of microtubule structure and self-assembly kinetics. Biophys J 2005; 89:2911-26. [PMID: 15951387 PMCID: PMC1366790 DOI: 10.1529/biophysj.105.060913] [Citation(s) in RCA: 176] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Microtubule self-assembly is largely governed by the chemical kinetics and thermodynamics of tubulin-tubulin interactions. An important aspect of microtubule assembly is that hydrolysis of the beta-tubulin-associated GTP promotes protofilament curling. Protofilament curling presumably drives the transition from tip structures associated with growth (sheetlike projections and blunt ends) to those associated with shortening (rams' horns and frayed ends), and transitions between these structures have been proposed to be important for growth-shortening transitions. However, previous models for microtubule dynamic instability have not considered such structures or mechanics explicitly. Here we present a three-dimensional model that explicitly incorporates mechanical stress and strain within the microtubule lattice. First, we found that the model recapitulates three-dimensional tip structures and rates of assembly and disassembly for microtubules grown under standard conditions, and we propose that taxol may stabilize microtubule growth by reducing flexural rigidity. Second, in contrast to recent suggestions, it was determined that sheetlike tips are more likely to undergo catastrophe than blunt tips. Third, partial uncapping of the tubulin-GTP cap provides a possible mechanism for microtubule pause events. Finally, simulations of the binding and structural effects of XMAP215 produced the experimentally observed growth and shortening rates, and tip structure.
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Affiliation(s)
- Vincent VanBuren
- Department of Biological Sciences, Lehigh University, Bethlehem, PA, USA
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32
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Molodtsov MI, Ermakova EA, Shnol EE, Grishchuk EL, McIntosh JR, Ataullakhanov FI. A molecular-mechanical model of the microtubule. Biophys J 2005; 88:3167-79. [PMID: 15722432 PMCID: PMC1305467 DOI: 10.1529/biophysj.104.051789] [Citation(s) in RCA: 73] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Dynamic instability of MTs is thought to be regulated by biochemical transformations within tubulin dimers that are coupled to the hydrolysis of bound GTP. Structural studies of nucleotide-bound tubulin dimers have recently provided a concrete basis for understanding how these transformations may contribute to MT dynamic instability. To analyze these ideas, we have developed a molecular-mechanical model in which structural and biochemical properties of tubulin are used to predict the shape and stability of MTs. From simple and explicit features of tubulin, we define bond energy relationships and explore the impact of their variations on integral MT properties. This modeling provides quantitative predictions about the GTP cap. It specifies important mechanical features underlying MT instability and shows that this property does not require GTP-hydrolysis to alter the strength of tubulin-tubulin bonds. The MT plus end is stabilized by at least two layers of GTP-tubulin subunits, whereas the minus end requires at least one; this and other differences between the ends are explained by asymmetric force balances. Overall, this model provides a new link between the biophysical characteristics of tubulin and the physiological behavior of MTs. It will also be useful in building a more complete description of MT dynamics and mechanics.
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Affiliation(s)
- Maxim I Molodtsov
- Molecular, Cellular, and Developmental Biology Department, University of Colorado, Boulder, Colorado, USA
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33
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Freed KF. Analytical solution for steady-state populations in the self-assembly of microtubules from nucleating sites. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:061916. [PMID: 12513326 DOI: 10.1103/physreve.66.061916] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2001] [Indexed: 05/24/2023]
Abstract
In addition to the biological importance of microtubules, which form a portion of the cellular cytoskeleton and a network for intracellular transport, the kinetics of microtubule self-assembly have generated great interest because individual microtubules exist in growing and decaying phases, with randomly occurring interconversions between them. Although a great deal is known concerning the microscopic details of these growth and decay processes, no description is available for the steady-state microtubule concentrations that are observed experimentally when microtubules are grown from nucleating sites. We generalize Hill's two-state model to include the dependence of the rates on tubulin concentration for systems where microtubules are grown from nucleating sites. An analytic solution is provided here to the resulting nonlinear, doubly infinite set of kinetic equations for the steady-state concentrations of both the growing and decaying phase microtubules as a function of the degree n of self-assembly and of the tubulin concentration. We also discuss the conditions for the stability of the steady state.
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Affiliation(s)
- Karl F Freed
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA
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34
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VanBuren V, Odde DJ, Cassimeris L. Estimates of lateral and longitudinal bond energies within the microtubule lattice. Proc Natl Acad Sci U S A 2002; 99:6035-40. [PMID: 11983898 PMCID: PMC122897 DOI: 10.1073/pnas.092504999] [Citation(s) in RCA: 166] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We developed a stochastic model of microtubule (MT) assembly dynamics that estimates tubulin-tubulin bond energies, mechanical energy stored in the lattice dimers, and the size of the tubulin-GTP cap at MT tips. First, a simple assembly/disassembly state model was used to screen possible combinations of lateral bond energy (DeltaG(Lat)) and longitudinal bond energy (DeltaG(Long)) plus the free energy of immobilizing a dimer in the MT lattice (DeltaG(S)) for rates of MT growth and shortening measured experimentally. This analysis predicts DeltaG(Lat) in the range of -3.2 to -5.7 k(B)T and DeltaG(Long) plus DeltaG(S) in the range of -6.8 to -9.4 k(B)T. Based on these estimates, the energy of conformational stress for a single tubulin-GDP dimer in the lattice is 2.1-2.5 k(B)T. Second, we studied how tubulin-GTP cap size fluctuates with different hydrolysis rules and show that a mechanism of directly coupling subunit addition to hydrolysis fails to support MT growth, whereas a finite hydrolysis rate allows growth. By adding rules to mimic the mechanical constraints present at the MT tip, the model generates tubulin-GTP caps similar in size to experimental estimates. Finally, by combining assembly/disassembly and cap dynamics, we generate MT dynamic instability with rates and transition frequencies similar to those measured experimentally. Our model serves as a platform to examine GTP-cap dynamics and allows predictions of how MT-associated proteins and other effectors alter the energetics of MT assembly.
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Affiliation(s)
- Vincent VanBuren
- Department of Biological Sciences, Lehigh University, 111 Research Drive, Bethlehem, PA 18015, USA
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35
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Arnal I, Karsenti E, Hyman AA. Structural transitions at microtubule ends correlate with their dynamic properties in Xenopus egg extracts. J Cell Biol 2000; 149:767-74. [PMID: 10811818 PMCID: PMC2174571 DOI: 10.1083/jcb.149.4.767] [Citation(s) in RCA: 98] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2000] [Accepted: 04/06/2000] [Indexed: 11/22/2022] Open
Abstract
Microtubules are dynamically unstable polymers that interconvert stochastically between growing and shrinking states by the addition and loss of subunits from their ends. However, there is little experimental data on the relationship between microtubule end structure and the regulation of dynamic instability. To investigate this relationship, we have modulated dynamic instability in Xenopus egg extracts by adding a catastrophe-promoting factor, Op18/stathmin. Using electron cryomicroscopy, we find that microtubules in cytoplasmic extracts grow by the extension of a two- dimensional sheet of protofilaments, which later closes into a tube. Increasing the catastrophe frequency by the addition of Op18/stathmin decreases both the length and frequency of the occurrence of sheets and increases the number of frayed ends. Interestingly, we also find that more dynamic populations contain more blunt ends, suggesting that these are a metastable intermediate between shrinking and growing microtubules. Our results demonstrate for the first time that microtubule assembly in physiological conditions is a two-dimensional process, and they suggest that the two-dimensional sheets stabilize microtubules against catastrophes. We present a model in which the frequency of catastrophes is directly correlated with the structural state of microtubule ends.
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Affiliation(s)
- Isabelle Arnal
- Cell Biology Program, European Laboratory of Molecular Biology, 69117 Heidelberg, Germany
- Max Planck Institut for Molecular Cell Biology and Genetics, Dresden D-01307, Germany
| | - Eric Karsenti
- Cell Biology Program, European Laboratory of Molecular Biology, 69117 Heidelberg, Germany
| | - Anthony A. Hyman
- Max Planck Institut for Molecular Cell Biology and Genetics, Dresden D-01307, Germany
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36
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Sept D, Tuszyńskit JA. A Landau-Ginzburg Model of the Co-existence of Free Tubulin and Assembled Microtubules in Nucleation and Oscillations Phenomena. J Biol Phys 2000; 26:5-15. [PMID: 23345708 PMCID: PMC3456188 DOI: 10.1023/a:1005225911159] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
A link is shown between reaction-diffusion kinetics for microtubuleassembly and time-dependent Landau-Ginzburg phenomenology. In the latter,microtubule assembly is treated as a first-order phase transition using apostulated Landau-Ginzburg free energy expansion. The results establish aconnection between the oscillations observed in experiment and the phasediagram for microtubule assembly. The model also predicts a specific heatbehavior which could be verified experimentally.
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Affiliation(s)
- D Sept
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA 92093-036 U.S.A
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Bolterauer H, Limbach HJ, Tuszyński JA. Microtubules: strange polymers inside the cell. BIOELECTROCHEMISTRY AND BIOENERGETICS (LAUSANNE, SWITZERLAND) 1999; 48:285-95. [PMID: 10379541 DOI: 10.1016/s0302-4598(99)00011-2] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
This paper provides a consistent approach (within a one-dimensional approximation) to the description of the evolution of the microtubule length at both low- and high-density concentrations. We derive general master-type equations which are based on the key chemical reactions involved in the assembly and disassembly of microtubules. The processes included are: polymerization and depolymerization of a single protein dimer, catastrophic disassembly affecting an a piori arbitrary number of dimers, and a rescue event. Solutions of the derived equations are compared with the existing experimental data. Important conclusions linking the emergence of bell-shaped histograms with the nature of catastrophe and rescue phenomena are drawn. Finally, we briefly discuss the emergence of coherent phenomena in microtubule polymerization, i.e., a transition to collective oscillations in the assembly and disassembly effects.
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Affiliation(s)
- H Bolterauer
- Institut für Theoretische Physik, Justus-Liebig Universität Giessen, Germany
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38
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Abstract
Microtubule assembly is a complex process with individual microtubules alternating stochastically between extended periods of assembly and disassembly, a phenomenon known as dynamic instability. Since the discovery of dynamic instability, molecular models of assembly have generally assumed that tubulin incorporation into the microtubule lattice is primarily reaction-limited. Recently this assumption has been challenged and the importance of diffusion in microtubule assembly dynamics asserted on the basis of scaling arguments, with tubulin gradients predicted to extend over length scales exceeding a cell diameter, approximately 50 microns. To assess whether individual microtubules in vivo assemble at diffusion-limited rates and to predict the theoretical upper limit on the assembly rate, a steady-state mean-field model for the concentration of tubulin about a growing microtubule tip was developed. Using published parameter values for microtubule assembly in vivo (growth rate = 7 microns/min, diffusivity = 6 x 10(-12) m2/s, tubulin concentration = 10 microM), the model predicted that the tubulin concentration at the microtubule tip was approximately 89% of the concentration far from the tip, indicating that microtubule self-assembly is not diffusion-limited. Furthermore, the gradients extended less than approximately 50 nm (the equivalent of about two microtubule diameters) from the microtubule tip, a distance much less than a cell diameter. In addition, a general relation was developed to predict the diffusion-limited assembly rate from the diffusivity and bulk tubulin concentration. Using this relation, it was estimated that the maximum theoretical assembly rate is approximately 65 microns/min, above which tubulin can no longer diffuse rapidly enough to support faster growth.
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Affiliation(s)
- D J Odde
- Department of Chemical Engineering, Michigan Technological University, Houghton 49931, USA.
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Symmons MF, Martin SR, Bayley PM. Dynamic properties of nucleated microtubules: GTP utilisation in the subcritical concentration regime. J Cell Sci 1996; 109 ( Pt 11):2755-66. [PMID: 8937993 DOI: 10.1242/jcs.109.11.2755] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
Microtubule assembly kinetics have been studied quantitatively under solution conditions supporting microtubule dynamic instability. Purified GTP-tubulin (Tu-GTP) and covalently cross-linked short microtubule seeds (EGS-seeds; Koshland et al. (1988) Nature 331, 499) were used with and without biotinylation. Under sub-critical concentration conditions ([Tu-GTP] < 5.3 microM), significant microtubule growth of limited length was observed on a proportion of the EGS-seeds by immuno-electron microscopy. A sensitive fluorescence assay for microtubule GDP production was developed for parallel assessment of GTP utilisation. This revealed a correlation between the detected microtubule growth and the production of tubulin-GDP, deriving from the shortening phase of the dynamic microtubules. This correlation was confirmed by the action of nocodazole, a specific inhibitor of microtubule assembly, that was found to abolish the GDP release. The variation of the GDP release with tubulin concentration (Jh(c) plot) was determined below the critical concentration (Cc). The GDP production observed was consistent with the elongation of the observed seeded microtubules with an apparent rate constant of 1.5 × 10(6) M-1 second-1 above a threshold of approximately 1 microM tubulin. The form of this Jh(c) plot for elongation below Cc is reproduced by the Lateral Cap model for microtubule dynamic instability adapted for seeded assembly. The behaviour of the system is contrasted with that previously studied in the absence of detectable microtubule elongation (Caplow and Shanks (1990) J. Biol. Chem. 265, 8935–8941). The approach provides a means of monitoring microtubule dynamics at concentrations inaccessible to optical microscopy, and shows that essentially the same dynamic mechanisms apply at all concentrations. Numerical simulation of the subcritical concentration regime shows dynamic growth features applicable to the initiation of microtubule growth in vivo.
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Affiliation(s)
- M F Symmons
- Division of Physical Biochemistry, National Institute for Medical Research, London, UK
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Flyvbjerg H, Holy TE, Leibler S. Microtubule dynamics: Caps, catastrophes, and coupled hydrolysis. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:5538-5560. [PMID: 9965740 DOI: 10.1103/physreve.54.5538] [Citation(s) in RCA: 89] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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41
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Odde DJ, Cassimeris L, Buettner HM. Kinetics of microtubule catastrophe assessed by probabilistic analysis. Biophys J 1995; 69:796-802. [PMID: 8519980 PMCID: PMC1236309 DOI: 10.1016/s0006-3495(95)79953-2] [Citation(s) in RCA: 111] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
Microtubules are cytoskeletal filaments whose self-assembly occurs by abrupt switching between states of roughly constant growth and shrinkage, a process known as dynamic instability. Understanding the mechanism of dynamic instability offers potential for controlling microtubule-dependent cellular processes such as nerve growth and mitosis. The growth to shrinkage transitions (catastrophes) and the reverse transitions (rescues) that characterize microtubule dynamic instability have been assumed to be random events with first-order kinetics. By direct observation of individual microtubules in vitro and probabilistic analysis of their distribution of growth times, we found that while the slower growing and biologically inactive (minus) ends obeyed first-order catastrophe kinetics, the faster growing and biologically active (plus) ends did not. The non-first-order kinetics at plus ends imply that growing microtubule plus ends have an effective frequency of catastrophe that depends on how long the microtubules have been growing. This frequency is low initially but then rises asymptotically to a limiting value. Our results also suggest that an additional parameter, beyond the four parameters typically used to describe dynamic instability, is needed to account for the observed behavior and that changing this parameter can significantly affect the distribution of microtubule lengths at steady state.
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Affiliation(s)
- D J Odde
- Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, New Jersey 08855, USA
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42
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Odde DJ, Buettner HM. Time series characterization of simulated microtubule dynamics in the nerve growth cone. Ann Biomed Eng 1995; 23:268-86. [PMID: 7631981 DOI: 10.1007/bf02584428] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
The process of neurite outgrowth is critically dependent on proper microtubule assembly. However, characterizing the dynamics of microtubule assembly and their quantitative relationship to neurite outgrowth is a difficult task. The difficulty can be reduced by using time series analysis which has broad application in characterizing the dynamics of stochastic, or "noisy," behaviors. Here we apply time series analysis to quantitatively compare simulated microtubule assembly and neurite outgrowth in vitro. Microtubule length life histories were simulated assuming constant growth and shrinkage rates coupled with random selection of growth and shrinkage times, a formulation based on the dynamic instability model of microtubule assembly. Net length displacements of simulated microtubules were calculated at discrete, evenly spaced times, and the resulting time series were characterized by both spectral and autocorrelation analysis. Depending on the sampling rate and the dynamic parameters, simulated microtubules exhibited significant autocorrelation and periodicity. To make a comparison to neurite outgrowth, we characterized the dynamic behavior of simulated microtubule populations and found it was not significantly different from that of single microtubules. The net displacements of rat superior cervical ganglion neurite tips were measured and characterized using time series methods. Their behavior was consistent with the microtubule dynamics for appropriate simulation parameters and sampling rates. Our results show that time series analysis can provide a useful tool for quantitative characterization of microtubule dynamics and neurite outgrowth and for assessing the relationship between them.
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Affiliation(s)
- D J Odde
- Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, NJ 08855-0909, USA
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Hyman AA, Chrétien D, Arnal I, Wade RH. Structural changes accompanying GTP hydrolysis in microtubules: information from a slowly hydrolyzable analogue guanylyl-(alpha,beta)-methylene-diphosphonate. J Biophys Biochem Cytol 1995; 128:117-25. [PMID: 7822409 PMCID: PMC2120325 DOI: 10.1083/jcb.128.1.117] [Citation(s) in RCA: 198] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
We have used cryoelectron microscopy to try to understand the structural basis for the role of GTP hydrolysis in destabilizing the microtubule lattice. We have measured a structural difference introduced into microtubules by replacing GTP with guanylyl-(alpha,beta)-methylene-diphosphonate (GMPCPP). In a stable GMPCPP microtubule lattice, the moiré patterns change and the tubulin subunits increase in size by 1.5 A. This information provides a clue to the role of hydrolysis in inducing the structural change at the end of a microtubule during the transition from a growing to a shrinking phase.
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Affiliation(s)
- A A Hyman
- Cell Biology Program, European Molecular Biology Laboratory, Heidelberg, Germany
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44
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Abstract
BACKGROUND Microtubules polymerized from pure tubulin show the unusual property of dynamic instability, in which both growing and shrinking polymers coexist at steady state. Shortly after its addition to a microtubule end, a tubulin subunit hydrolyzes its bound GTP. Studies with non-hydrolyzable analogs have shown that GTP hydrolysis is not required for microtubule assembly, but is essential for generating a dynamic polymer, in which the subunits at the growing tip have bound GTP and those in the bulk of the polymer have bound GDP. It has been suggested that loss of the 'GTP cap' through dissociation or hydrolysis exposes the unstable GDP core, leading to rapid depolymerization. However, evidence for a stabilizing cap has been very difficult to obtain. RESULTS We developed an assay to determine the minimum GTP cap necessary to stabilize a microtubule from shrinking. Assembly of a small number of subunits containing a slowly hydrolyzed GTP analog (GMPCPP) onto the end of dynamic microtubules stabilized the polymer to dilution. By labeling the subunits with rhodamine, we measured the size of the cap and found that as few as 40 subunits were sufficient to stabilize a microtubule. CONCLUSIONS On the basis of statistical arguments, in which the proportion of stabilized microtubules is compared to the probability that when 40 GMPCPP-tubulin subunits have polymerized onto a microtubule end, all protofilaments have added at least one GMPCPP-tubulin subunit, our measurements of cap size support a model in which a single GTP subunit at the end of each of the 13 protofilaments of a microtubule is sufficient for stabilization. Depolymerization of a microtubule may be initiated by an exposed tubulin-GDP subunit at even a single position. These results have implications for the structure of microtubules and their means of regulation.
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Affiliation(s)
- D N Drechsel
- Department of Biochemistry and Biophysics, University of California, San Francisco 94143-0448, USA
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45
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Flyvbjerg H, Holy TE, Leibler S. Stochastic dynamics of microtubules: A model for caps and catastrophes. PHYSICAL REVIEW LETTERS 1994; 73:2372-2375. [PMID: 10057043 DOI: 10.1103/physrevlett.73.2372] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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46
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Marx A, Mandelkow E. A model of microtubule oscillations. EUROPEAN BIOPHYSICS JOURNAL : EBJ 1994; 22:405-21. [PMID: 8149923 DOI: 10.1007/bf00180162] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Simulations of microtubule oscillations have been obtained by a kinetic model including nucleation of microtubules, elongation by addition of GTP-loaded tubulin dimers, disassembly into oligomers, and dissolution of oligomers followed by nucleotide exchange at the free dimers. Dynamic instability is described by the on and off rates for dimer association in the growth phase, the rate of rapid shortening, and the transition rates for catastrophe and rescue. The latter are assumed to be completely determined by the current state of the system ("short cap hypothesis"). Microtubule oscillations and normal polymerizations measured by time-resolved X-ray scattering were used to test the model. The model is able to produce oscillations without further assumptions. However, in order to obtain good fits to the experimental data one requires an additional mechanism which prevents rapid desynchronization of the microtubules. One of several possible mechanisms that will be discussed is the destabilization of microtubules by the products of disassembly.
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Affiliation(s)
- A Marx
- Max-Planck-Unit for Structural Molecular Biology, DESY, Hamburg, Germany
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47
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Martin SR, Schilstra MJ, Bayley PM. Dynamic instability of microtubules: Monte Carlo simulation and application to different types of microtubule lattice. Biophys J 1993; 65:578-96. [PMID: 8218889 PMCID: PMC1225761 DOI: 10.1016/s0006-3495(93)81091-9] [Citation(s) in RCA: 94] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
Dynamic instability is the term used to describe the transition of an individual microtubule, apparently at random, between extended periods of slow growth and brief periods of rapid shortening. The typical sawtooth growth and shortening transition behavior has been successfully simulated numerically for the 13-protofilament microtubule A-lattice by a lateral cap model (Bayley, P. M., M. J. Schilstra, and S. R. Martin. 1990. J. Cell Sci. 95:33-48). This kinetic model is now extended systematically to other related lattice geometries, namely the 13-protofilament B-lattice and the 14-protofilament A-lattice, which contain structural "seams". The treatment requires the assignment of the free energies of specific protein-protein interactions in terms of the basic microtubule lattice. It is seen that dynamic instability is not restricted to the helically symmetric 13-protofilament A-lattice but is potentially a feature of all A- and B-lattices, irrespective of protofilament number. The advantages of this general energetic approach are that it allows a consistent treatment to be made for both ends of any microtubule lattice. Important features are the predominance of longitudinal interactions between tubulin molecules within the same protofilament and the implication of a relatively favorable interaction of tubulin-GDP with the growing microtubule end. For the three lattices specifically considered, the treatment predicts the dependence of the transition behavior upon tubulin concentration as a cooperative process, in good agreement with recent experimental observations. The model rationalizes the dynamic properties in terms of a metastable microtubule lattice of tubulin-GDP, stabilized by the kinetic process of tubulin-GTP addition. It provides a quantitative basis for the consideration of in vitro microtubule behaviour under both steady-state and non-steady-state conditions, for comparison with experimental data on the dilution-induced disassembly of microtubules. Similarly, the effects of small tubulin-binding molecules such as GDP and nonhydrolyzable GTP analogues are readily treated. An extension of the model allows a detailed quantitative examination of possible modes of substoichiometric action of a number of antimitotic drugs relevant to cancer chemotherapy.
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Affiliation(s)
- S R Martin
- Division of Physical Biochemistry, National Institute for Medical Research, Mill Hill, London, England
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49
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Hyman AA, Salser S, Drechsel DN, Unwin N, Mitchison TJ. Role of GTP hydrolysis in microtubule dynamics: information from a slowly hydrolyzable analogue, GMPCPP. Mol Biol Cell 1992; 3:1155-67. [PMID: 1421572 PMCID: PMC275679 DOI: 10.1091/mbc.3.10.1155] [Citation(s) in RCA: 279] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
The role of GTP hydrolysis in microtubule dynamics has been reinvestigated using an analogue of GTP, guanylyl-(alpha, beta)-methylene-diphosphonate (GMPCPP). This analogue binds to the tubulin exchangeable nucleotide binding site (E-site) with an affinity four to eightfold lower than GTP and promotes the polymerization of normal microtubules. The polymerization rate of microtubules with GMPCPP-tubulin is very similar to that of GTP-tubulin. However, in contrast to microtubules polymerized with GTP, GMPCPP-microtubules do not depolymerize rapidly after isothermal dilution. The depolymerization rate of GMPCPP-microtubules is 0.1 s-1 compared with 500 s-1 for GDP-microtubules. GMPCPP also completely suppresses dynamic instability. Contrary to previous work, we find that the beta--gamma bond of GMPCPP is hydrolyzed extremely slowly after incorporation into the microtubule lattice, with a rate constant of 4 x 10(-7) s-1. Because GMPCPP hydrolysis is negligible over the course of a polymerization experiment, it can be used to test the role of hydrolysis in microtubule dynamics. Our results provide strong new evidence for the idea that GTP hydrolysis by tubulin is not required for normal polymerization but is essential for depolymerization and thus for dynamic instability. Because GMPCPP strongly promotes spontaneous nucleation of microtubules, we propose that GTP hydrolysis by tubulin also plays the important biological role of inhibiting spontaneous microtubule nucleation.
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Affiliation(s)
- A A Hyman
- Department of Pharmacology, University of California, San Francisco 94143
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50
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Gildersleeve R, Cross A, Cullen K, Fagen A, Williams RC. Microtubules grow and shorten at intrinsically variable rates. J Biol Chem 1992. [DOI: 10.1016/s0021-9258(18)42399-x] [Citation(s) in RCA: 86] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022] Open
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