scholarly journals Effective elasticity and persistence of strain in active filament-motor assemblies

2021 ◽  
Author(s):  
Arvind Gopinath ◽  
Raghunath Chelakkot ◽  
L Mahadevan
Keyword(s):  
Molecular Motors ◽  
Mean Field Theory ◽  
Persistence Length ◽  
Mean Field ◽  
Continuum Theory ◽  
Particle Collision ◽  
Duty Ratio ◽  
Length Scale ◽  
Correlated Activity ◽  
Shear Elasticity

Cross-linked, elastic, filamentous networks that are deformed by active molecular motors feature in several natural and synthetic settings. The effective active elasticity of these composite systems determines the length scale over which active deformations persist in fluctuating environments. This fundamental quantity has been studied in passive systems; however mechanisms determining and modulating this length-scale in active systems has not been clarified. Here, focusing on active arrayed filament-motor assemblies, we propose and analyze a minimal model in order to estimate the length scale over which imposed or emergent elastic deformations or stresses persist. We combine a mean-field continuum theory valid for weakly elastic assemblies with high dimensional Multi-Particle Collision (MPC) based Brownian simulations valid for moderate to strongly elastic and noisy systems. Integrating analytical and numerical results, we show that localized strains - steady or oscillatory - persist over well-defined length scales that dependent on motor activity, effective shear elasticity and filament extensibility. Extensibility is key even in very stiff filaments, and cannot be ignored when global deformations are considered. We clarify mechanisms by which motor derived active elasticity and passive shear elasticity of the filamentous backbone combine to effectively soften filaments. Surprisingly, the predictions of the mean-field theory agree qualitatively with results from stochastic discrete filament-motor model, even for moderately strong noise. We also find that athermal motor noise impacts the overall duty ratio of the motors and thereby the persistence length in these driven assemblies. Our study demonstrates how correlated activity in natural ordered active matter possesses a finite range of influence with clear testable experimental implications.

scholarly journals A one-dimensional modified TASEP model on a track of variable length: analytical and computational results

2021 ◽  
Vol 2090 (1) ◽  
pp. 012025
Author(s):  
B. Reed ◽  
E. Aldrich ◽  
L. Stoleriu ◽  
D.A. Mazilu ◽  
I. Mazilu
Keyword(s):  
Monte Carlo ◽  
Molecular Motors ◽  
Mean Field Theory ◽  
Mean Field ◽  
Limited Range ◽  
Field Methods ◽  
One Dimensional ◽  
Emergent Features ◽  
Simulation Results ◽  
Mean Field Methods

Abstract We present analytical solutions and Monte Carlo simulation results for a one-dimensional modified TASEP model inspired by the interplay between molecular motors and their cellular tracks of variable lengths, known as microtubules. Our TASEP model incorporates rules for changes in the length of the track based on the occupation of the first two sites. Using mean-field theory, we derive analytical results for the particle densities and particle currents and compare them with Monte Carlo simulations. These results show the limited range of mean-field methods for models with localized high correlation between particles. The variability in length adds to the complexity of the model, leading to emergent features for the evolution of particle densities and particle currents compared to the traditional TASEP model.

scholarly journals Filament extensibility and shear stiffening control persistence of strain and loss of coherence in cross-linked motor-filament assemblies

2018 ◽  
Author(s):  
Arvind Gopinath ◽  
Raghunath Chelakkot ◽  
L. Mahadevan
Keyword(s):  
Collective Behavior ◽  
Molecular Motors ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spatial Coordination ◽  
Elastic Filaments ◽  
Mechanical Information ◽  
Loss Of Coherence ◽  
Elastic Strains

AbstractCross-linked flexible filaments deformed by active molecular motors occur in many natural and synthetic settings including eukaryotic flagella, the cytoskeleton and in vitro motor assays. In these systems, an important quantity that controls spatial coordination and emergent collective behavior is the length scale over which elastic strains persist. We estimate this quantity in the context of ordered composites comprised of cross-linked elastic filaments sheared by active motors. Combining a mean-field theory valid for negligibly noisy systems with discrete simulations for noisy systems, we show that the effect of localized strains – be they steady or oscillatory – persist over distances determined by motor kinetics, motor elasticity and filament extensibility. The cut-off length that emerges from these effects controls the transmission of mechanical information and determines the criterion for spatially separated motor groups to stay synchronized. Our results generalize the notion of persistence in passive, Brownian filaments to active, cross-linked filaments.

Molecular Polarizabilities and Orientational Ordering of Two Mesogens

1991 ◽  
Vol 46 (10) ◽  
pp. 858-864 ◽  
Author(s):  
M. Mitra ◽  
S. Paul ◽  
R. Paul
Keyword(s):  
Field Theory ◽  
Liquid Crystalline ◽  
Mean Field Theory ◽  
Orientational Order ◽  
Mean Field ◽  
Continuum Theory ◽  
Order Parameters ◽  
Liquid Phases ◽  
Molecular Polarizabilities ◽  
The Mean

AbstractThe refractive indices (no, ne) and densities of two mesogens have been measured in their liquid crystalline and liquid phases. The molecular polarizabilities (xo, xe) were evaluated by Vuks' and Neugebauer's relations. The polarizabilities thus obtained are compared with those estimated from the bond polarizabilities, and the orientational order parameters, <P2>, are compared with the mean field theory of Maier and Saupe, the modified mean field theory of Humphries, James and Luckhurst. and the continuum theory suggested by T. E. Faber. We have also calculated the three order parameters (<P2), τ, σ) describing the smectic A phase following McMillan's model. Possible causes of the discrepancy are discussed.

PHASE TRANSITION IN RIGID QED

1994 ◽  
Vol 09 (23) ◽  
pp. 4077-4099 ◽  
Author(s):  
MOUSTAFA AWADA ◽  
DAVID ZOLLER
Keyword(s):  
World Line ◽  
Mean Field Theory ◽  
Mean Field ◽  
Continuum Theory ◽  
Experimental Tests ◽  
Point Particle ◽  
Kinetic Term ◽  
Scale Invariant ◽  
Majorana Mass ◽  
Curvature Term

We present a new model of QED which exhibits two distinct phases. The model emerges in the first-quantized formalism where it is possible to generalize QED by adding the curvature of the world line to the usual kinetic term, the arc length action of the point particle. The Boltzmann factor associated with the curvature term favors rigid paths. The curvature term is not only scale-invariant and hence renormalizable but it is also the unique reparametrization-invariant term with second derivatives with this property. The new term transforms a single electron of mass m into an infinite number of particles with masses varying inversely with the spin (Majorana mass spectrum). The value of the bare curvature coupling determines which phase the theory is in. For bare curvature coupling α0 less than a certain critical coupling αc, we recover conventional QED as one phase where the curvature term is absent at large distance scales in the continuum theory. For α0 greater than αc, we have a new phase characterized by a curvature law. Using mean field theory methods, we determine αc to be of the order of one. We argue that the positronium spectrum in the strong curvature phase is approximately described by a Majorana mass formula. Even though the GSI experiments might not survive further experimental tests, we nevertheless examine the Majorana spectrum with the three observed narrow e+ e− peaks observed in the GSI experiments and make some possible new predictions.

A continuum theory of disorder in nematic liquid crystals IV. Application to lattice models+

1980 ◽  
Vol 370 (1743) ◽  
pp. 509-521 ◽  
Keyword(s):  
Mean Field Theory ◽  
Random Phase ◽  
Mean Field ◽  
Lattice Models ◽  
Continuum Theory ◽  
Wave Theory ◽  
Approximate Theory ◽  
Secondary Importance ◽  
Nearest Neighbours ◽  
The Mean

An approximate theory of nematic disorder, reminiscent of the spin wave theory of ferromagnetic disorder, was put forward in previous papers in this series. Predictions based upon it are here compared with accurate results for two lattice models: (a) a model in which the interaction which causes molecules to align is between nearest neighbours only, which Zannoni (1979) has investigated by computer simulation, and (b) a model in which the interaction is of very long range, to which the mean field theory ofMaier & Saupe (1958,1959, i960) is applicable. At temperatures not too close to the nematic-isotropic transition temperature Tc the theory predicts the magnitude of S2 with remarkable precision for both models, though no adjustable parameters are involved. It also predicts correctly the magnitude and the range of the short-range order that is characteristic of model (a). Since some of the discrepancies that become apparent as Tc is approached can be attributed to an approximation of rather secondary importance - neglect of the effect that misalignment entropy may have on the Frank stiffness constants of a nematic - it looks as though the theory can safely be used to describe real nematics at temperatures such that S 2 exceeds, say, 0.5. A prediction that S 4 (= (P 4 (cos 0))) is equal to however, which is certainly correct for both models at very low temperatures, begins to fail, though not dramatically, when S2 reaches about 0.7. This failure is attributed to errors in the random phase approximation, to which the other results of the theory are relatively insensitive.

A continuum theory of disorder in nematic liquid crystals. I

1977 ◽  
Vol 353 (1673) ◽  
pp. 247-259 ◽  
Keyword(s):  
Ground State ◽  
Order Parameter ◽  
Nematic Phase ◽  
Mean Field Theory ◽  
Orientational Order ◽  
Mean Field ◽  
Continuum Theory ◽  
Wave Theory ◽  
Debye Theory ◽  
The Continuum

An alternative to the Maier-Saupe mean field theory of orientational order in nematics is suggested. It is a theory of disorder rather than order, analogous to the spin-wave theory of ferromagnetism. That is to say, the nematic is treated as a continuum with a perfectly aligned ground state, in which a spectrum of distortion modes involving splay, twist and bend are thermally excited with amplitudes determined by the Frank stiffness constants K 1 , K 2 and K 3 . It is argued that there cannot be more than 2 N independent modes, where N is the number of molecules, and a cut-off is applied to the spectrum accordingly, resembling the cut-off used in the Debye theory of solids. The theory is used to predict values for the con­ventional order parameter S 2 (= < P 2 (cos θ )>) and for higher order para­meters such as S 4 (= <P4(cos θ )>) in terms of K 1 , K 2 and K 3 , and the results agree adequately with experiment. Like the Maier-Saupe theory, the continuum theory suggests a minimum value for S 2 below which the nematic phase cannot be stable or even meta-stable. Refinements that might help to improve the agreement are discussed.

scholarly journals Pseudogaps: introducing the length scale into dynamical mean-field theory

2006 ◽  
Vol 32 (4) ◽  
pp. 398-405 ◽  
Author(s):  
E. Z. Kuchinskii ◽  
I. A. Nekrasov ◽  
M. V. Sadovskii
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Dynamical Mean Field Theory ◽  
Length Scale

scholarly journals A general one-dimensional traffic model for motion of molecular motors on microtubules of variable length

2021 ◽  
Vol 2090 (1) ◽  
pp. 012024
Author(s):  
E. Aldrich ◽  
B. Reed ◽  
L. Stoleriu ◽  
D.A. Mazilu ◽  
I. Mazilu
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Steady State ◽  
Molecular Motors ◽  
Particle Density ◽  
Mean Field Theory ◽  
Mean Field ◽  
Variable Length ◽  
Traffic Model ◽  
One Dimensional

Abstract We present a traffic model inspired by the motion of molecular motors along microtubules, represented by particles moving along a one-dimensional track of variable length. As the particles move unidirectionally along the track, several processes can occur: particles already on the track can move to the next open site, additional particles can attach at unoccupied sites, or particles on the track can detach. We study the model using mean-field theory and Monte Carlo simulations, with a focus on the steady-state properties and the time evolution of the particle density and particle currents. For a specific range of parameters, the model captures the microtubule instability observed experimentally and reported in the literature. This model is versatile and can be modified to represent traffic in a variety of biological systems.

Mean field theory of n-layer unbinding

1993 ◽  
Vol 3 (3) ◽  
pp. 385-393 ◽  
Author(s):  
W. Helfrich
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field
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