The Role of Multifilament Structures and Lateral Interactions in Dynamics of Cytoskeleton Proteins and Assemblies

Li, Xin; Kolomeisky, Anatoly B.

doi:10.1021/acs.jpcb.5b01219

Cited by 12 publications

(17 citation statements)

References 35 publications

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“…As long as this constraint is satisfied, the update rules can be chosen following local detailed balance R + /R − = e −βǫ , where R + is the rate of a process that has a positive energy cost ǫ and R − is the rate of the reverse process. The filaments are modeled as rigid rod-like polymers, composed of monomers of length d [27,[36][37][38]. In Fig.…”

Section: Description Of the Modelmentioning

confidence: 99%

Interplay between surface and bending energy helps membrane protrusion formation

Sadhu

Chatterjee

2019

Phys. Rev. E

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We consider a one-dimensional elastic membrane, which is pushed by growing filaments. The filaments tend to grow by creating local protrusions in the membrane and this process has surface energy and bending energy costs. Although it is expected that with increasing surface tension and bending rigidity, it should become more difficult to create a protrusion, we find that for a fixed bending rigidity, as the surface tension increases, protrusions are more easily formed. This effect also gives rise to non-trivial dependence of membrane velocity on the surface tension, characterized by a dip and a peak. We explain this unusual phenomenon by studying in detail the interplay of the surface and the bending energy and show that this interplay is responsible for a qualitative shape change of the membrane, which gives rise to the above effect. * rajkumar.sadhu@bose.res.in

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Section: Description Of the Modelmentioning

confidence: 99%

Interplay between surface and bending energy helps membrane protrusion formation

Sadhu

Chatterjee

2019

Phys. Rev. E

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“…In this paper we have provided a theoretical framework to understand and predict the cooperative effects in the maximum force generation by multiple motors or filaments, for a broad class of models. It is now appreciated, at least theoretically, that the stall force of individual cytoskeletal filaments or molecular motors, when they push together against some obstacle, is not additive in general [31,32,57]. In this paper, we have provided several pointers to show that this non-additivity of the stall forces (f (N )…”

Section: Discussionmentioning

confidence: 93%

“…Some of these theoretical studies have demonstrated that the stall force of multiple, non-interacting filaments without ATP/GTP dynamics, scales linearly with the number of filaments [26,[28][29][30]54]. In contrast, a few other recent papers quite clearly report that inclusion of ATP/GTP hydrolysis can lead to either enhanced or reduced cooperativity in the maximum force generated by multiple growing filaments; the stall forces need not always scale with the number of filaments [31,[56][57][58]. In other words, the stall forces of individual filaments are non-additive in general, that is, the collective stall force produced by N number of filaments (denoted by f (N ) s ) is not just a simple sum of individual stall forces of single filaments (i.e., f (N )…”

Section: Introductionmentioning

confidence: 99%

Sufficient conditions for the additivity of stall forces generated by multiple filaments or motors

Bameta

Das

et al. 2017

Phys. Rev. E

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Molecular motors and cytoskeletal filaments work collectively most of the time under opposing forces. This opposing force may be due to cargo carried by motors or resistance coming from the cell membrane pressing against the cytoskeletal filaments. Some recent studies have shown that the collective maximum force (stall force) generated by multiple cytoskeletal filaments or molecular motors may not always be just a simple sum of the stall forces of the individual filaments or motors. To understand this excess or deficit in the collective force, we study a broad class of models of both cytoskeletal filaments and molecular motors. We argue that the stall force generated by a group of filaments or motors is additive, that is, the stall force of N number of filaments (motors) is N times the stall force of one filament (motor), when the system is in equilibrium at stall. Conversely, we show that this additive property typically does not hold true when the system is not at equilibrium at stall. We thus present a novel and unified understanding of the existing models exhibiting such nonaddivity, and generalise our arguments by developing new models that demonstrate this phenomena. We also propose a quantity similar to thermodynamic efficiency to easily predict this deviation from stall-force additivity for filament and motor collectives.

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“…Most of the mathematical models that dealt with polymerization-driven force generation do not explicitly consider the wall movements. Rather, the presence of wall is encapsulated in the growth rate and detachment rate of the filament [16,17,[19][20][21]. In these 'Brownian ratchet' models, the filament in contact with the wall is assumed to grow with an on-rate proportional to exp (−qf δ/k B T ) and off-rate proportional to exp (−(q − 1)f δ/k B T ) with 'q' being the load sharing factor.…”

Section: Mathematical Formalism: Fokker-planck Equationsmentioning

confidence: 99%

Force generation by polymerizing filaments revisited: diffusive interaction leads to nonlinear force-number scaling

Valiyakath

Gopalakrishnan

2017

Preprint

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Polymers growing against a barrier generate force and push it forward. We study here force generation by a bundle of N rigid polymers growing in parallel against a diffusing, rigid, flat barrier, resembling a bundle of microtubules. To estimate the polymerization force, the barrier is subjected to a force f acting against the direction of growth of the polymers and the mean velocity VN (f ) of the filament assembly is computed. The maximum polymerization force (alias stall force) f N s is deduced from the condition VN (f N s ) = 0. This problem has been studied in the literature earlier, but two important aspects have escaped attention: (a) free diffusion of monomers is hindered by the barrier, even when it is far from the growing tips and (b) parallel filaments could interact through the monomer density field ("diffusive coupling"), leading to negative interference between them. In our model, both these effects are investigated in detail. A mathematical treatment based on a set of continuum Fokker-Planck equations for combined filament-wall dynamics suggests that the barrier reduces the influx of monomers to the growing polymer tip, thereby reducing the growth velocity and also the stall force, but it doesn't affect the scaling of the stall force with number, i.e., f N s = N f 1 s . However, Brownian dynamics simulations show that the linear scaling holds only when the filaments are far apart; when they are arranged close together, forming a bundle, sublinear scaling of force with number appears. We argue that the nonlinear scaling could be attributed to diffusive interaction between the growing tips which becomes significant when the tips are close together. These conclusions, initially established for simple flat-faced polymers, are also found to hold true for microtubules with their characteristic hollow cylindrical geometry and rugged tip structure. In particular, simulations show conclusively that the stall force of a single microtubule is a fraction of the combined stall force of the 13 protofilaments. This result is supported by a simple analytical estimate of the force using diffusive coupling theory, and is in agreement with earlier experimental observations.

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The Role of Multifilament Structures and Lateral Interactions in Dynamics of Cytoskeleton Proteins and Assemblies

Cited by 12 publications

References 35 publications

Interplay between surface and bending energy helps membrane protrusion formation

Interplay between surface and bending energy helps membrane protrusion formation

Sufficient conditions for the additivity of stall forces generated by multiple filaments or motors

Force generation by polymerizing filaments revisited: diffusive interaction leads to nonlinear force-number scaling

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