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.

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 Modeling and Simulation of Synchronous Threshold in Vent Collective Behavior

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yaofeng Zhang ◽  
Renbin Xiao
Keyword(s):  
Collective Behavior ◽  
Mean Field Theory ◽  
Mean Field ◽  
Mathematic Model ◽  
Homogeneous Group ◽  
The Social ◽  
Multi Agent ◽  
Group 3 ◽  
Global Coupling ◽  
Local Coupling

With the strengthening of the social contradiction, the outbreak of vent collective behavior tends to be frequent. The essence of vent collective behavior is emergence of synchronization. In order to explore the threshold of consensus synchronization in vent collective behavior, a mathematic model and a corresponding simulation model based on multi-agent are proposed. The results of analysis by mean field theory and simulation experiments show the following. (1) There is a thresholdKcfor consensus synchronization in global-coupling and homogeneous group, and when the system parameterKis greater thanKc, consensus synchronization emerge. Otherwise the system cannot achieve synchronization. The conclusion is verified by further study of multiagent simulation. (2) Compared with the global-coupling situation, the process of synchronization is delayed in local-coupling and homogeneous group. (3) For local-coupling and heterogeneous group, consensus dissemination can achieve synchronization only when the effects of the parameters meet the threshold requirements of consensus synchronization.

scholarly journals Resilience through diversity: Loss of neuronal heterogeneity in epileptogenic human tissue renders neural networks more susceptible to sudden changes in synchrony

2021 ◽  
Author(s):  
Scott Rich ◽  
Homeira Moradi Chameh ◽  
Jeremie Lefebvre ◽  
Taufik A Valiante
Keyword(s):  
Cortical Neurons ◽  
Neural Circuits ◽  
Mean Field Theory ◽  
Mean Field ◽  
Cellular Heterogeneity ◽  
Dynamical Structure ◽  
Activation Functions ◽  
Pathological Changes ◽  
Mathematical Analyses

AbstractA myriad of pathological changes associated with epilepsy can be recast as decreases in cell and circuit heterogeneity. We propose that epileptogenesis can be recontextualized as a process where reduction in cellular heterogeneity renders neural circuits less resilient to transitions into information-poor, over-correlated seizure states. We provide in vitro, in silico, and mathematical support for this hypothesis. Patch clamp recordings from human layer 5 (L5) cortical neurons demonstrate significantly decreased biophysical heterogeneity of excitatory neurons in seizure generating areas (epilepetogenic zone). This decreased heterogeneity renders model neural circuits prone to sudden dynamical transitions into synchronous, hyperactive states (paralleling ictogenesis) while also explaining counter-intuitive differences in population activation functions (i.e., FI curves) between epileptogenic and non-epileptogenic tissue. Mathematical analyses based in mean-field theory reveal clear distinctions in the dynamical structure of networks with low and high heterogeneity, providing the theoretical undergird for how ictogenic dynamics accompany a reduction in biophysical heterogeneity.

scholarly journals Hopf Bifurcation in Mean Field Explains Critical Avalanches in Excitation-Inhibition Balanced Neuronal Networks: A Mechanism for Multiscale Variability

2020 ◽  
Vol 14 ◽  
Author(s):  
Junhao Liang ◽  
Tianshou Zhou ◽  
Changsong Zhou
Keyword(s):  
Hopf Bifurcation ◽  
Large Scale ◽  
Neural Circuits ◽  
Mean Field Theory ◽  
Mean Field ◽  
Stable State ◽  
Population Level ◽  
Field Equations ◽  
Public Data

Cortical neural circuits display highly irregular spiking in individual neurons but variably sized collective firing, oscillations and critical avalanches at the population level, all of which have functional importance for information processing. Theoretically, the balance of excitation and inhibition inputs is thought to account for spiking irregularity and critical avalanches may originate from an underlying phase transition. However, the theoretical reconciliation of these multilevel dynamic aspects in neural circuits remains an open question. Herein, we study excitation-inhibition (E-I) balanced neuronal network with biologically realistic synaptic kinetics. It can maintain irregular spiking dynamics with different levels of synchrony and critical avalanches emerge near the synchronous transition point. We propose a novel semi-analytical mean-field theory to derive the field equations governing the network macroscopic dynamics. It reveals that the E-I balanced state of the network manifesting irregular individual spiking is characterized by a macroscopic stable state, which can be either a fixed point or a periodic motion and the transition is predicted by a Hopf bifurcation in the macroscopic field. Furthermore, by analyzing public data, we find the coexistence of irregular spiking and critical avalanches in the spontaneous spiking activities of mouse cortical slice in vitro, indicating the universality of the observed phenomena. Our theory unveils the mechanism that permits complex neural activities in different spatiotemporal scales to coexist and elucidates a possible origin of the criticality of neural systems. It also provides a novel tool for analyzing the macroscopic dynamics of E-I balanced networks and its relationship to the microscopic counterparts, which can be useful for large-scale modeling and computation of cortical dynamics.

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 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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