The role of filament length, finite-extensibility and motor force dispersity in stress relaxation and buckling mechanisms in non-sarcomeric active gels

Chronology of motor-mediated microtubule streaming

We introduce a filament-based simulation model for coarse-grained, effective motor-mediated interaction between microtubule pairs to study the time-scales that compose cytoplasmic streaming. We characterise microtubule dynamics in two-dimensional systems by chronologically arranging five distinct processes of varying duration that make up streaming, from microtubule pairs to collective dynamics. The structures found were polarity sorted due to the propulsion of antialigned microtubules. This also gave rise to the formation of large polar-aligned domains, and streaming at the domain boundaries. Correlation functions, mean squared displacements, and velocity distributions reveal a cascade of processes ultimately leading to microtubule streaming and advection, spanning multiple microtubule lengths. The characteristic times for the processes extend over three orders of magnitude from fast single-microtubule processes to slow collective processes. Our approach can be used to directly test the importance of molecular components, such as motors and crosslinking proteins between microtubules, on the collective dynamics at cellular scale.

The Effects of the Interplay between Motor and Brownian Forces on the Rheology of Active Gels

Active gels perform key mechanical roles inside the cell, such as cell division, motion, and force sensing. The unique mechanical properties required to perform such functions arise from the interactions between molecular motors and semiflexible polymeric filaments. Molecular motors can convert the energy released in the hydrolysis of ATP into forces of up to piconewton magnitudes. Moreover, the polymeric filaments that form active gels are flexible enough to respond to Brownian forces but also stiff enough to support the large tensions induced by the motor-generated forces. Brownian forces are expected to have a significant effect especially at motor activities at which stable noncontractile in vitro active gels are prepared for rheological measurements. Here, a microscopic mean-field theory of active gels originally formulated in the limit of motor-dominated dynamics is extended to include Brownian forces. In the model presented here, Brownian forces are included accurately, at real room temperature, even in systems with high motor activity. It is shown that a subtle interplay, or competition, between motor-generated forces and Brownian forces has an important impact on the mass transport and rheological properties of active gels. The model predictions show that at low frequencies the dynamic modulus of active gels is determined mostly by motor protein dynamics. However, Brownian forces significantly increase the breadth of the relaxation spectrum and can affect the shape of the dynamic modulus over a wide frequency range even for ratios of motor to Brownian forces of more than a hundred. Since the ratio between motor and Brownian forces is sensitive to ATP concentration, the results presented here shed some light on how the transient mechanical response of active gels changes with varying ATP concentration.

Force percolation of contractile active gels

Living systems provide a paradigmatic example of active soft matter. Cells and tissues comprise viscoelastic materials that exert forces and can actively change shape. This strikingly autonomous behavior is powered by the cytoskeleton, an active gel of semiflexible filaments, crosslinks, and molecular motors inside cells. Although individual motors are only a few nm in size and exert minute forces of a few pN, cells spatially integrate the activity of an ensemble of motors to produce larger contractile forces (∼nN and greater) on cellular, tissue, and organismal length scales. Here we review experimental and theoretical studies on contractile active gels composed of actin filaments and myosin motors. Unlike other active soft matter systems, which tend to form ordered patterns, actin-myosin systems exhibit a generic tendency to contract. Experimental studies of reconstituted actin-myosin model systems have long suggested that a mechanical interplay between motor activity and the network's connectivity governs this contractile behavior. Recent theoretical models indicate that this interplay can be understood in terms of percolation models, extended to include effects of motor activity on the network connectivity. Based on concepts from percolation theory, we propose a state diagram that unites a large body of experimental observations. This framework provides valuable insights into the mechanisms that drive cellular shape changes and also provides design principles for synthetic active materials.

Microscopic origins of anisotropic active stress in motor-driven nematic liquid crystals

The cytoskeleton, despite comprising relatively few building blocks, drives an impressive variety of cellular phenomena ranging from cell division to motility. These building blocks include filaments, motor proteins, and static crosslinkers. Outside of cells, these same components can form novel materials exhibiting active flows and nonequilibrium contraction or extension. While dipolar extensile or contractile active stresses are common in nematic motor-filament systems, their microscopic origin remains unclear. Here we study a minimal physical model of filaments, crosslinking motors, and static crosslinkers to dissect the microscopic mechanisms of stress generation in a two-dimensional system of orientationally aligned rods. We demonstrate the essential role of filament steric interactions which have not previously been considered to significantly contribute to active stresses. With this insight, we are able to tune contractile or extensile behavior through the control of motor-driven filament sliding and crosslinking. This work provides a roadmap for engineering stresses in active liquid crystals. The mechanisms we study may help explain why flowing nematic motor-filament mixtures are extensile while gelled systems are contractile.

Determination of linear viscoelastic properties of an entangled polymer melt by probe rheology simulations

Particle rheology is used to extract the linear viscoelastic properties of an entangled polymer melt from molecular dynamics simulations. The motion of a stiff, approximately spherical particle is tracked in both passive and active modes. We demonstrate that the dynamic modulus of the melt can be extracted under certain limitations using this technique. As shown before for unentangled chains [Karim et al., Phys. Rev. E 86, 051501 (2012)PLEEE81539-375510.1103/PhysRevE.86.051501], the frequency range of applicability is substantially expanded when both particle and medium inertia are properly accounted for by using our inertial version of the generalized Stokes-Einstein relation (IGSER). The system used here introduces an entanglement length d_{T}, in addition to those length scales already relevant: monomer bead size d, probe size R, polymer radius of gyration R_{g}, simulation box size L, shear wave penetration length Δ, and wave period Λ. Previously, we demonstrated a number of restrictions necessary to obtain the relevant fluid properties: continuum approximation breaks down when d≳Λ; medium inertia is important and IGSER is required when R≳Λ; and the probe should not experience hydrodynamic interaction with its periodic images, L≳Δ. These restrictions are also observed here. A simple scaling argument for entangled polymers shows that the simulation box size must scale with polymer molecular weight as M_{w}^{3}. Continuum analysis requires the existence of an added mass to the probe particle from the entrained medium but was not observed in the earlier work for unentangled chains. We confirm here that this added mass is necessary only when the thickness L_{S} of the shell around the particle that contains the added mass, L_{S}>d. We also demonstrate that the IGSER can be used to predict particle displacement over a given timescale from knowledge of medium viscoelasticity; such ability will be of interest for designing nanoparticle-based drug delivery.

Multiscale modeling and simulation of microtubule-motor-protein assemblies

Microtubules and motor proteins self-organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven out of equilibrium by adenosine triphosphate-consuming motor proteins. Microscopic motor activity causes polarity-dependent interactions between motor proteins and microtubules, but how these interactions yield larger-scale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubule-motor systems in which Brownian dynamics simulations of polar microtubules driven by motors are used to study microscopic organization and stresses created by motor-mediated microtubule interactions. We identify polarity-sorting and crosslink tether relaxation as two polar-specific sources of active destabilizing stress. We then develop a continuum Doi-Onsager model that captures polarity sorting and the hydrodynamic flows generated by these polar-specific active stresses. In simulations of active nematic flows on immersed surfaces, the active stresses drive turbulent flow dynamics and continuous generation and annihilation of disclination defects. The dynamics follow from two instabilities, and accounting for the immersed nature of the experiment yields unambiguous characteristic length and time scales. When turning off the hydrodynamics in the Doi-Onsager model, we capture formation of polar lanes as observed in the Brownian dynamics simulation.