Steady states of a microtubule assembly in a confined geometry

Govindan, Bindu S.; Spillman, William B.

doi:10.1103/physreve.70.032901

Cited by 26 publications

(28 citation statements)

References 11 publications

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“…Many mathematical models have been formulated in the past, based on this two state approach to explore dynamic instability and its applications, eg., microtubule oscillations [17,18], dynamics under confinement [19,20], search for targets [20][21][22] and the effects of regulators [23,24]. Let us denote by T the time until catastrophe (referred to as the catastrophe time), starting from a rescue event at T = 0.…”

Section: Catastrophe Time Distributionmentioning

confidence: 99%

Effects of aging in catastrophe on the steady state and dynamics of a microtubule population

Jemseena

Gopalakrishnan

2015

Phys. Rev. E

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Several independent observations have suggested that catastrophe transition in microtubules is not a first-order process, as is usually assumed. Recent in vitro observations by Gardner et al.[ M. K. Gardner et al., Cell 147, 1092 showed that microtubule catastrophe takes place via multiple steps and the frequency increases with the age of the filament. Here, we investigate, via numerical simulations and mathematical calculations, some of the consequences of age dependence of catastrophe on the dynamics of microtubules as a function of the aging rate, for two different models of aging: exponential growth, but saturating asymptotically and purely linear growth. The boundary demarcating the steady state and non-steady state regimes in the dynamics is derived analytically in both cases. Numerical simulations, supported by analytical calculations in the linear model, show that aging leads to non-exponential length distributions in steady state. More importantly, oscillations ensue in microtubule length and velocity. The regularity of oscillations, as characterized by the negative dip in the autocorrelation function, is reduced by increasing the frequency of rescue events. Our study shows that age dependence of catastrophe could function as an intrinsic mechanism to generate oscillatory dynamics in a microtubule population, distinct from hitherto identified ones.

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Section: Catastrophe Time Distributionmentioning

confidence: 99%

Effects of aging in catastrophe on the steady state and dynamics of a microtubule population

Jemseena

Gopalakrishnan

2015

Phys. Rev. E

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“…In the case where the experimentally determined f c (L) and f c (L) cannot be approximated by analytically integrable functions, one may have to resort to numer-ical methods to solve the integral. We would like to note that there are already (theoretical) studies that include microscopic details of the catastrophe mechanism and/or more states than the two growing and shrinking states (41,42), as well as effects due to closed systems and/or due to a cell edge and/or due to a limited pool of free tubulin (17,(43)(44)(45)(46)(47). Including those effects also leads, in general, to nonexponential (peaked) MT length distributions, whose shapes are, however, implicit to the assumptions of each model.…”

Section: Appendix Amentioning

confidence: 99%

Providing Positional Information with Active Transport on Dynamic Microtubules

Tischer

Wolde

Dogterom

2010

Biophysical Journal

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Microtubules (MTs) are dynamic protein polymers that change their length by switching between growing and shrinking states in a process termed dynamic instability. It has been suggested that the dynamic properties of MTs are central to the organization of the eukaryotic intracellular space, and that they are involved in the control of cell morphology, but the actual mechanisms are not well understood. Here, we present a theoretical analysis in which we explore the possibility that a system of dynamic MTs and MT end-tracking molecular motors is providing specific positional information inside cells. We compute the MT length distribution for the case of MT-length-dependent switching between growing and shrinking states, and analyze the accumulation of molecular motors at the tips of growing MTs. Using these results, we show that a transport system consisting of dynamic MTs and associated motor proteins can deliver cargo proteins preferentially to specific positions within the cell. Comparing our results with experimental data in the model organism fission yeast, we propose that the suggested mechanisms could play important roles in setting length scales during cellular morphogenesis.

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“…The simplest way to explicitly consider the cell boundary is by imposing a maximum filament length l * such that l ≤ l * as in [142], where a two-state model has been considered. In this work it is assumed that the MT directly turns into the shrinking state, if the MT hits the cell boundary.…”

Section: Dynamic Mts In Finite Volumementioning

confidence: 99%

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

2015

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Cells are the elementary units of living organisms, which are able to carry out many vital functions. These functions rely on active processes on a microscopic scale. Therefore, they are strongly out-of-equilibrium systems, which are driven by continuous energy supply. The tasks that have to be performed in order to maintain the cell alive require transportation of various ingredients, some being small, others being large. Intracellular transport processes are able to induce concentration gradients and to carry objects to specific targets. These processes cannot be carried out only by diffusion, as cells may be crowded, and quite elongated on molecular scales. Therefore active transport has to be organized.The cytoskeleton, which is composed of three types of filaments (microtubules, actin and intermediate filaments), determines the shape of the cell, and plays a role in cell motion. It also serves as a road network for a special kind of vehicles, namely the cytoskeletal motors. These molecules can attach to a cytoskeletal filament, perform directed motion, possibly carrying along some cargo, and then detach.It is a central issue to understand how intracellular transport driven by molecular motors is regulated. The interest for this type of question was enhanced when it was discovered that intracellular transport breakdown is one of the signatures of some neuronal diseases like the Alzheimer.We give a survey of the current knowledge on microtubule based intracellular transport. Our review includes on the one hand an overview of biological facts, obtained from experiments, and on the other hand a presentation of some modeling attempts based on cellular automata. We present some background knowledge on the original and variants of the TASEP (Totally Asymmetric Simple Exclusion Process), before turning to more application oriented models. After addressing microtubule based transport in general, with a focus on in vitro experiments, and on cooperative effects in the transportation of large cargos by multiple motors, we concentrate on axonal transport, because of its relevance for neuronal diseases. Some important characteristics of axonal transport is that it takes place in a confined environment; Besides several types of motors are involved, that move in opposite directions. It is a challenge to understand how this bidirectional transport is organized. We review several features that could contribute to the efficiency of bidirectional transport in the axon, including in particular the role of motor-motor interactions and of the dynamics of the underlying microtubule network. Finally, we also discuss some open questions that may be relevant for future research in this field.

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Steady states of a microtubule assembly in a confined geometry

Cited by 26 publications

References 11 publications

Effects of aging in catastrophe on the steady state and dynamics of a microtubule population

Effects of aging in catastrophe on the steady state and dynamics of a microtubule population

Providing Positional Information with Active Transport on Dynamic Microtubules

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

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