Intra-cellular traffic: bio-molecular motors on filamentary tracks

Abstract

Molecular motors are macromolecular complexes which use some form of input energy to perform mechanical work. The filamentary tracks, on which these motors move, are made of either proteins (e.g., microtubules) or nucleic acids (DNA or RNA). Often, many such motors move simultaneously on the same track and their collective properties have superficial similarities with vehicular traffic on highways. The models we have developed provide "unified" description: in the low-density limit, a model captures the transport properties of a single motor while, at higher densities the same model accounts for the collective spatio-temporal organization of interacting motors. By drawing analogy with vehicular traffic, we have introduced novel quantities for characterizing the nature of the spatio-temporal organization of molecular motors on their tracks. We show how the traffic-like intracellular collective phenomena depend on the mechano-chemistry of the corresponding individual motors.

Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport

“…Perhaps the simplest models of active biological transport are those of isolated molecular motors that move along one-dimensional tracks such as actin, microtubules, DNA, or RNA. Motors are enzymes such as dynein, kinesin, and myosin that hydrolyze molecules such as ATP or GTP, turning the free energy released to directed motion along their one-dimensional substrate [272,273]. Motoring is necessary for sustaining cell functions such as mediating cell swimming and motility and intracellular transport of biomolecules, particularly at length scales where diffusion is not efficient, or where spatial specificity is required.…”

Multiple phase transitions in a system of exclusion processes with limited reservoirs of particles and fuel carriers

“…Mean-field methods have also been extensively used [16], since they are easily tractable and yield a good approximation in many cases. There has been much extension of this simple model, for example variable hopping rates (site or particle dependent) [21,22,23], extended particles which cover more than one site [6,24], branching lattices [25,26], particles which have multiple internal states [27,28,29], as well as a TASEP with a constrained reservoir of particles [9,10,11,12].…”

Thermodynamics of Constant Curvature Black Holes Through Semiclassical Tunneling

“…Given the "radial" derivative of the action, given by equation (23), it is straightforward to calculate the imaginary part of the action, which is related to the Hawking temperature through the tunneling probability Γ ∝ e −ImI = e −E/T . While there are a number of techniques which have been introduced for this step [44][45][46][47][48][49][50][51], we will here follow the ideas recently summarized in [52]. In particular, it is found that there are two separate contributions to the imaginary part of the action: one coming from the discontinuity of the time coordinate ∆t, and another coming from a pole, at the horizon, which arises when integrating the radial part of the action.…”