Nonequilibrium phase transitions in the extraction of membrane tubes by molecular motors

Self-organized system-size oscillation of a stochastic lattice-gas model

The totally asymmetric simple exclusion process (TASEP) is a paradigmatic stochastic model for nonequilibrium physics, and has been successfully applied to describe active transport of molecular motors along cytoskeletal filaments. Building on this simple model, we consider a two-lane lattice-gas model that couples directed transport (TASEP) to diffusive motion in a semiclosed geometry, and simultaneously accounts for spontaneous growth and particle-induced shrinkage of the system's size. This particular extension of the TASEP is motivated by the question of how active transport and diffusion might influence length regulation in confined systems. Surprisingly, we find that the size of our intrinsically stochastic system exhibits robust temporal patterns over a broad range of growth rates. More specifically, when particle diffusion is slow relative to the shrinkage dynamics, we observe quasiperiodic changes in length. We provide an intuitive explanation for the occurrence of these self-organized temporal patterns, which is based on the imbalance between the diffusion and shrinkage speed in the confined geometry. Finally, we formulate an effective theory for the oscillatory regime, which explains the origin of the oscillations and correctly predicts the dependence of key quantities, such as the oscillation frequency, on the growth rate.

Asymmetric simple exclusion process with position-dependent hopping rates: Phase diagram from boundary-layer analysis

In this paper, we study a one-dimensional totally asymmetric simple exclusion process with position-dependent hopping rates. Under open boundary conditions, this system exhibits boundary-induced phase transitions in the steady state. Similarly to totally asymmetric simple exclusion processes with uniform hopping, the phase diagram consists of low-density, high-density, and maximal-current phases. In various phases, the shape of the average particle density profile across the lattice including its boundary-layer parts changes significantly. Using the tools of boundary-layer analysis, we obtain explicit solutions for the density profile in different phases. A detailed analysis of these solutions under different boundary conditions helps us obtain the equations for various phase boundaries. Next, we show how the shape of the entire density profile including the location of the boundary layers can be predicted from the fixed points of the differential equation describing the boundary layers. We discuss this in detail through several examples of density profiles in various phases. The maximal-current phase appears to be an especially interesting phase where the boundary layer flows to a bifurcation point on the fixed-point diagram.

Exclusion and Hierarchy of Time Scales Lead to Spatial Segregation of Molecular Motors in Cellular Protrusions

Molecular motors that carry cargo along biopolymer filaments within cells play a crucial role in the functioning of the cell. In particular, these motors are essential for the formation and maintenance of the cellular protrusions that play key roles in motility and specific functionalities, such as the stereocilia in hair cells. Typically, there are several species of motors, carrying different cargos, that share the same track. Furthermore, it was observed that in the mature stereocilia, the different motors occupy well-segregated bands as a function of distance from the tip. We use a totally asymmetric exclusion process model with two- and three-motor species, to study the conditions that give rise to such spatial patterns. We find that the well-segregated bands appear for motors with a strong hierarchy of attachment or detachment rates. This is a striking example of pattern formation in nonequilibrium, low-dimensional systems.

Modelling the effect of myosin X motors on filopodia growth

We present a numerical simulation study of the dynamics of filopodial growth in the presence of active transport by myosin X motors. We employ both a microscopic agent-based model, which captures the stochasticity of the growth process, and a continuum mean-field theory which neglects fluctuations. We show that in the absence of motors, filopodia growth is overestimated by the continuum mean-field theory. Thus fluctuations slow down the growth, especially when the protrusions are driven by a small number (10 or less) of F-actin fibres, and when the force opposing growth (coming from membrane elasticity) is large enough. We also show that, with typical parameter values for eukaryotic cells, motors are unlikely to provide an actin transport mechanism which enhances filopodial size significantly, unless the G-actin concentration within the filopodium greatly exceeds that of the cytosol bulk. We explain these observations in terms of order-of-magnitude estimates of diffusion-induced and advection-induced growth of a bundle of Brownian ratchets.

Asymmetric exclusion process with global hopping

We study a one-dimensional totally asymmetric simple exclusion process with one special site from which particles fly to any empty site (not just to the neighboring site). The system attains a nontrivial stationary state with a density profile varying over the spatial extent of the system. The density profile undergoes a nonequilibrium phase transition when the average density passes through the critical value 1-[4(1-ln2)](-1)=0.185277..., viz., in addition to the discontinuity in the vicinity of the special site, a shock wave is formed in the bulk of the system when the density exceeds the critical density.

Processivity and collectivity of biomolecular motors extracting membrane nanotubes

Biomolecular motors can pull and viscously drag membranes. The resulting elongations include cell protrusions, tether networks, and sensorial tentacles. Here we focus on the extraction of a single tube from a vesicle. Via a force balance coupled to binding kinetics, we analytically determine the phase diagram of tube formation as function of the motor processivity, the surface viscosity of the membrane η'(m), and the density of motors on the vesicle ρ. Three tubulation mechanisms are identified: (i) tip pulling, due to the accumulation of motors at the leading edge of the membrane, (ii) viscous drag, emergent from the translation of motors along the tube, and (iii) hybrid extraction, such that tip pulling and viscous drag are equally important. For experimental values of η'(m) and ρ, we find that the growth of bionanotubes tends to be driven by viscous forces, whereas artificial membranes are dominated by tip pulling.

Cooperativity of self-organized Brownian motors pulling on soft cargoes

We study the cooperative dynamics of Brownian motors moving along a one-dimensional track when an external load is applied to the leading motor, mimicking molecular motors pulling on membrane-bound cargoes in intracellular traffic. Due to the asymmetric loading, self-organized motor clusters form spontaneously. We model the motors with a two-state noise-driven ratchet formulation and study analytically and numerically the collective velocity-force and efficiency-force curves resulting from mutual interactions, mostly hard-core repulsion and weak (nonbinding) attraction. We analyze different parameter regimes including the limits of weak noise, mean-field behavior, rigid coupling, and large numbers of motors, for the different interactions. We present a general framework to classify and quantify cooperativity. We show that asymmetric loading leads generically to enhanced cooperativity beyond the simple superposition of the effects of individual motors. For weakly attracting interactions, the cooperativity is mostly enhanced, including highly coordinated motion of motors and complex nonmonotonic velocity-force curves, leading to self-regulated clusters. The dynamical scenario is enriched by resonances associated to commensurability of different length scales. Large clusters exhibit synchronized dynamics and bidirectional motion. Biological implications are discussed.

Bidirectional transport on a dynamic lattice

Bidirectional variants of stochastic many particle models for transport by molecular motors show a strong tendency to form macroscopic clusters on static lattices. Inspired by the fact that the microscopic tracks for molecular motors are dynamical, we study the influence of different types of lattice dynamics on stochastic bidirectional transport. We observe a transition toward efficient transport (corresponding to the dissolution of large clusters) controlled by the lattice dynamics.

Dynamical phase transition of a one-dimensional transport process including death

Motivated by biological aspects related to fungus growth, we consider the competition of growth and corrosion. We study a modification of the totally asymmetric exclusion process, including the probabilities of injection alpha and death of the last particle delta . The system presents a phase transition at deltac(alpha), where the average position of the last particle L grows as sqrt[t]. For delta>deltac, a nonequilibrium stationary state exists while for delta<deltac the asymptotic state presents a low density and max current phases. We discuss the scaling of the density and current profiles for parallel and sequential updates.

Mechanism of membrane nanotube formation by molecular motors

Membrane nanotubes are ubiquitous in eukaryotic cells due to their involvement in the communication between many different membrane compartments. They are very dynamical structures, which are generally extended along the microtubule network. One possible mechanism of tube formation involves the action of molecular motors, which can generate the necessary force to pull the tubes along the cytoskeleton tracks. However, it has not been possible so far to image in living organisms simultaneously both tube formation and the molecular motors involved in the process. The reasons for this are mainly technological. To overcome these limitations and to elucidate in detail the mechanism of tube formation, many experiments have been developed over the last years in cell-free environments. In the present review, we present the results, which have been obtained in vitro either in cell extracts or with purified and artificial components. In particular, we will focus on a biomimetic system, which involves Giant Unilamellar Vesicles, kinesin-1 motors and microtubules in the presence of ATP. We present both theoretical and experimental results based on fluorescence microscopy that elucidate the dynamics of membrane tube formation, growth and stalling.