Weakly coupled, antiparallel, totally asymmetric simple exclusion processes

We study a system composed of two parallel totally asymmetric simple exclusion processes with open boundaries, where the particles move in the two lanes in opposite directions and are allowed to jump to the other lane with rates inversely proportional to the length of the system. Stationary density profiles are determined and the phase diagram of the model is constructed in the hydrodynamic limit, by solving the differential equations describing the steady state of the system, analytically for vanishing total current and numerically for nonzero total current. The system possesses phases with a localized shock in the density profile in one of the lanes, similarly to exclusion processes endowed with nonconserving kinetics in the bulk. Besides, the system undergoes a discontinuous phase transition, where coherently moving delocalized shocks emerge in both lanes and the fluctuation of the global density is described by an unbiased random walk. This phenomenon is analogous to the phase coexistence observed at the coexistence line of the totally asymmetric simple exclusion process, however, as a consequence of the interaction between lanes, the density profiles are deformed and in the case of asymmetric lane change, the motion of the shocks is confined to a limited domain.Comment: 14 pages, 15 figures, to appear in Phys. Rev.

FRESH: Fréchet similarity with hashing

This paper studies the r-range search problem for curves under the continuous Fréchet distance: given a dataset S of n polygonal curves and a threshold >0 , construct a data structure that, for any query curve q, efficiently returns all entries in S with distance at most r from q. We propose FRESH, an approximate and randomized approach for r-range search, that leverages on a locality sensitive hashing scheme for detecting candidate near neighbors of the query curve, and on a subsequent pruning step based on a cascade of curve simplifications. We experimentally compare FRESH to exact and deterministic solutions, and we show that high performance can be reached by suitably relaxing precision and recall

Traffic of Molecular Motors

Molecular motors perform active movements along cytoskeletal filaments and drive the traffic of organelles and other cargo particles in cells. In contrast to the macroscopic traffic of cars, however, the traffic of molecular motors is characterized by a finite walking distance (or run length) after which a motor unbinds from the filament along which it moves. Unbound motors perform Brownian motion in the surrounding aqueous solution until they rebind to a filament. We use variants of driven lattice gas models to describe the interplay of their active movements, the unbound diffusion, and the binding/unbinding dynamics. If the motor concentration is large, motor-motor interactions become important and lead to a variety of cooperative traffic phenomena such as traffic jams on the filaments, boundary-induced phase transitions, and spontaneous symmetry breaking in systems with two species of motors. If the filament is surrounded by a large reservoir of motors, the jam length, i.e., the extension of the traffic jams is of the order of the walking distance. Much longer jams can be found in confined geometries such as tube-like compartments.Comment: 10 pages, latex, uses Springer styles (included), to appear in the Proceedings of "Traffic and Granular Flow 2005

Self-organized density patterns of molecular motors in arrays of cytoskeletal filaments

The stationary states of systems with many molecular motors are studied theoretically for uniaxial and centered (aster-like) arrangements of cytoskeletal filaments using Monte Carlo simulations and a two-state model. Mutual exclusion of motors from binding sites of the filaments is taken into account. For small overall motor concentration, the density profiles are exponential and algebraic in uniaxial and centered filament systems, respectively. For uniaxial systems, exclusion leads to the coexistence of regions of high and low densities of bound motors corresponding to motor traffic jams, which grow upon increasing the overall motor concentration. These jams are insensitive to the motor behavior at the end of the filament. In centered systems, traffic jams remain small and an increase in the motor concentration leads to a flattening of the profile, if the motors move inwards, and to the build-up of a concentration maximum in the center of the aster if motors move outwards. In addition to motors density patterns, we also determine the corresponding patterns of the motor current.Comment: 48 pages, 8 figure

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.Comment: 20 pages, latex, 7 figures, 1 tabl

Microtubules gate tau condensation to spatially regulate microtubule functions.

Tau is an abundant microtubule-associated protein in neurons. Tau aggregation into insoluble fibrils is a hallmark of Alzheimer's disease and other types of dementia1, yet the physiological state of tau molecules within cells remains unclear. Using single-molecule imaging, we directly observe that the microtubule lattice regulates reversible tau self-association, leading to localized, dynamic condensation of tau molecules on the microtubule surface. Tau condensates form selectively permissible barriers, spatially regulating the activity of microtubule-severing enzymes and the movement of molecular motors through their boundaries. We propose that reversible self-association of tau molecules, gated by the microtubule lattice, is an important mechanism of the biological functions of tau, and that oligomerization of tau is a common property shared between the physiological and disease-associated forms of the molecule

Aspergillus Myosin-V Supports Polarized Growth in the Absence of Microtubule-Based Transport

In the filamentous fungus Aspergillus nidulans, both microtubules and actin filaments are important for polarized growth at the hyphal tip. Less clear is how different microtubule-based and actin-based motors work together to support this growth. Here we examined the role of myosin-V (MYOV) in hyphal growth. MYOV-depleted cells form elongated hyphae, but the rate of hyphal elongation is significantly reduced. In addition, although wild type cells without microtubules still undergo polarized growth, microtubule disassembly abolishes polarized growth in MYOV-depleted cells. Thus, MYOV is essential for polarized growth in the absence of microtubules. Moreover, while a triple kinesin null mutant lacking kinesin-1 (KINA) and two kinesin-3s (UNCA and UNCB) undergoes hyphal elongation and forms a colony, depleting MYOV in this triple mutant results in lethality due to a severe defect in polarized growth. These results argue that MYOV, through its ability to transport secretory cargo, can support a significant amount of polarized hyphal tip growth in the absence of any microtubule-based transport. Finally, our genetic analyses also indicate that KINA (kinesin-1) rather than UNCA (kinesin-3) is the major kinesin motor that supports polarized growth in the absence of MYOV