Active chiral fluids

Active processes in biological systems often exhibit chiral asymmetries. Examples are the chirality of cytoskeletal filaments which interact with motor proteins, the chirality of the beat of cilia and flagella as well as the helical trajectories of many biological microswimmers. Here, we derive constitutive material equations for active fluids which account for the effects of active chiral processes. We identify active contributions to the antisymmetric part of the stress as well as active angular momentum fluxes. We discuss four types of elementary chiral motors and their effects on a surrounding fluid. We show that large-scale chiral flows can result from the collective behavior of such motors even in cases where isolated motors do not create a hydrodynamic far field.      

Random walks of cytoskeletal motors in open and closed compartments

Random walks of molecular motors, which bind to and unbind from cytoskeletal filaments, are studied theoretically. The bound and unbound motors undergo directed and nondirected motion, respectively. Motors in open compartments exhibit anomalous drift velocities. Motors in closed compartments generate stationary nonequilibrium states with spatially varying densities of the motor concentrations and currents. "Traffic jams" on the filaments lead to a maximum of the motor current at an optimal motor concentration. Quantitative estimates based on experimental data for bound motors indicate that these transport phenomena are accessible to experiments.     

Driven Diffusive Systems of Active Filament Bundles

The cytoskeleton is an important subsystem of cells that is involved for example in cell division and locomotion. It consists of filaments that are cross-linked by molecular motors that can induce relative sliding between filaments and generate stresses in the network. In order to study the effects of fluctuations on the dynamics of such a system we introduce here a new class of driven diffusive systems mimicking the dynamics of active filament bundles where the filaments are aligned with respect to a common axis. After introducing the model class we first analyze an exactly solvable case and find condensation. For the general case we perform a mean-field analysis and study the behavior on large length scales by coarse-graining. We determine conditions for condensation and establish a relation between the hopping rates and the tension generated in the bundle.     

Fluctuations, dynamics, and the stretch-coil transition of single actin filaments in extensional flows

Semiflexible polymers subject to hydrodynamic forcing play an important role in cytoskeletal motions in the cell, particularly when filaments guide molecular motors whose motions create flows. Near hyperbolic stagnation points, filaments experience a competition between bending elasticity and tension and are predicted to display suppressed thermal fluctuations in the extensional regime and a buckling instability under compression. Using a microfluidic cross-flow geometry, we verify these predictions in detail, including a fluctuation-rounded stretch-coil transition of actin filaments.     

Motility States of Molecular Motors Engaged in a Stochastic Tug-of-War

Intracellular transport is mediated by molecular motors that pull cargos along cytoskeletal filaments. Many cargos move bidirectionally and are transported by two teams of motors which move into opposite directions along the filament. We have recently introduced a stochastic tug-of-war model for this situation. This model describes the motion of the cargo as a Markov process on a two-dimensional state space defined by the numbers of active plus and active minus motors. In spite of its simplicity, this tug-of-war model leads to a complex dependence of the cargo motility on the motor parameters. We present new numerical results for the dependence on the number of involved motors. In addition, we derive a simple and intuitive sharp maxima approximation, from which one obtains the cargo motility state from only four simple inequalities. This approach provides a fast and reliable method to determine the cargo motility.     

Enhanced ordering of interacting filaments by molecular motors

We theoretically study the cooperative behavior of cytoskeletal filaments in motility assays in which immobilized motor proteins bind the filaments to substrate surfaces and actively pull them along these surfaces. Because of the mutual exclusion of the filaments, the coupled dynamics of filaments, motor heads, and motor tails leads to a nonequilibrium phase transition which generalizes the isotropic-nematic phase transition of the corresponding equilibrium system, the hard-rod fluid. Langevin dynamics simulations show that the motor activity enhances the tendency for nematic ordering. We develop a quantitative theory for the location of the phase boundary as a function of motor density. At high detachment forces of motors, we also observe filament clusters arising from blocking effects.     

Transport by Molecular Motors in the Presence of Static Defects

The transport by molecular motors along cytoskeletal filaments is studied theoretically in the presence of static defects. The movements of single motors are described as biased random walks along the filament as well as binding to and unbinding from the filament. Three basic types of defects are distinguished, which differ from normal filament sites only in one of the motors’ transition probabilities. Both stepping defects with a reduced probability for forward steps and unbinding defects with an increased probability for motor unbinding strongly reduce the velocities and the run lengths of the motors with increasing defect density. For transport by single motors, binding defects with a reduced probability for motor binding have a relatively small effect on the transport properties. For cargo transport by motors teams, binding defects also change the effective unbinding rate of the cargo particles and are expected to have a stronger effect.     

Generic theory of active polar gels: a paradigm for cytoskeletal dynamics

We develop a general theory for active viscoelastic materials made of polar filaments. This theory is motivated by the dynamics of the cytoskeleton. The continuous consumption of a fuel leads to a non equilibrium state characterized by the generation of flows and stresses. Our theory can be applied to experiments in which cytoskeletal patterns are set in motion by active processes such as those which are at work in cells.     

Viscous-fingering-like instability of cell fragments

We present a novel flow instability that can arise in thin films of cytoskeletal fluids if the friction with the substrate on which the film lies is sufficiently strong. We consider a two-dimensional, membrane-bound fragment containing actin filaments that polymerize at the edge and depolymerize in the fragment. Performing a linear stability analysis of the initial state due to perturbations of the fragment boundary, we find, in the limit of large friction, that the perturbed actin velocity and pressure fields obey the same laws governing the viscous fingering instability of an interface between immiscible fluids in a Hele-Shaw cell. A remarkable feature of this instability is that it is independent of the strength of the interaction between actin filaments and myosin motors.     

Collective alignment of polar filaments by molecular motors

We study the alignment of polar biofilaments, such as microtubules and actin, subject to the action of multiple molecular motors attached simultaneously to more than one filament. Focusing on a paradigm model of only two filaments interacting with multiple motors, we were able to investigate in detail the alignment dynamics. While almost no alignment occurs in the case of a single motor, the filaments become rapidly aligned due to the collective action of the motors. Our analysis shows that the alignment time is governed by the number of bound motors and the magnitude of the motors’ stepping fluctuations. We predict that the time scale of alignment is in the order of seconds, much faster than that reported for passive crosslink-induced bundling. In vitro experiments on the alignment of microtubules by multiple-motor covered beads are in qualitative agreement. We also discuss another mode of fast alignment of filaments, namely the cooperation between motors and passive crosslinks.     

What Laboratory-Produced Plasma Structures Can Contribute to the Understanding of Cosmic Structures Both Large and Small

The tradition of the classical 1901 work by Birkeland [1] on aurora phenomena by laboratory terrella experiments was resumed by Alfvén [2], Cowling [3], Ferraro et al. [4], and by Bennett [5] in his terrella experiments. In 1954 [6] when experimenters accidentally produced in the laboratory structures later identified as diamagnetic vortex filaments, and in 1961 [7] when filaments, later identified as current-carrying paramagnetic plasma vortex structures (which are both electric motors and dynamos), were observed in the Z and theta-pinch experiments, this tradition was being further reestablished. It has been successfully argued [6], [8], [11], [20] that both of these types of vortices are force-free minimum-free-energy structures that spontaneously spring to life as readily as do thousands of spherical bubbles and water droplets during the splash of a breaking water wave. The Birkeland aurora filaments are a hybrid combination of these two basic types (paramagnetic and diamagnetic) of plasma vortices. It is to be expected that such structures on a cosmic scale play an important role in the cosmos, and indeed they do in the formation of galaxies, stars, binary stars, solar systems, solar prominences, solar flares, solar wind, comet tails, cosmic "strings" in the Crab nebula, string-like galactic clusters, expansion of the Universe, giant galactic jets, cosmic rays, sunspots, vortex rolls in sunspot penumbra, twinkling of radio stars by the density fluctuations in the ionosphere, turbulence at the interface between the solar wind and the earth's magnetosphere, etc.     

Continuum description of the cytoskeleton: ring formation in the cell cortex

Motivated by the formation of ringlike filament structures in the cortex of plant and animal cells, we study the dynamics of a two-dimensional layer of cytoskeletal filaments and motor proteins near a surface by a general continuum theory. As a result of active processes, dynamic patterns of filament orientation and density emerge via instabilities. We show that self-organization phenomena can lead to the formation of stationary and oscillating rings. We present state diagrams that reveal a rich scenario of asymptotic behaviors and discuss the role of boundary conditions.     

Self-organization of treadmilling filaments

The cytoskeleton is an active network of polar filaments. The activity can lead to the polymerization of filaments at one end and depolymerization at the other. This phenomenon is called treadmilling and is essential for many cellular processes, in particular, the crawling of cells on a substrate. We develop a microscopic theoretical framework for describing systems of treadmilling filaments. We show that such systems can self-organize into structures observed in cell fragments, in particular, asters and moving spots.     

Asters, vortices, and rotating spirals in active gels of polar filaments

We develop a general theory for active viscoelastic materials made of polar filaments. This theory is motivated by the dynamics of the cytoskeleton. The continuous consumption of a fuel generates a nonequilibrium state characterized by the generation of flows and stresses. Our theory applies to any polar system with internal energy consumption such as active chemical gels and cytoskeletal networks which are set in motion by active processes at work in cells.     

Rheology of active-particle suspensions

We study the interplay of activity, order, and flow through a set of coarse-grained equations governing the hydrodynamic velocity, concentration, and stress fields in a suspension of active, energy-dissipating particles. We make several predictions for the rheology of such systems, which can be tested on bacterial suspensions, cell extracts with motors and filaments, or artificial machines in a fluid. The phenomena of cytoplasmic streaming, elastotaxis, and active mechanosensing find natural explanations within our model.     

Bistable helices

We extend elasticity theory of filaments to encompass systems, such as bacterial flagella, that display competition between two helical structures of opposite chirality. A general, fully intrinsic formulation of the dynamics of bend and twist degrees of freedom is developed using the natural frame of space curves, spanning from the inviscid limit to the viscously overdamped regime applicable to cellular biology. Aspects of front propagation found in flagella are discussed.