Stochastic transport on flexible lattice under limited resources

Many theoretical models have tried to study the biological transport systems with the unbending paths in the framework of totally asymmetric simple exclusion processes. However, in most cases, these models ignore the three-dimensional (3D) conformation of the intracellular highways, in particular, microtubules and mRNAs and it is assumed that particles perform a motion along one-dimensional rigid paths connected with the reservoir of the infinite number of particles. In this work, we generalize the standard single lane exclusion process to analyze the transport of particles moving along a polymer-like flexible lattice plunged in a 3D reservoir with the finite number of particles which is a more realistic case both in physical as well as biological systems. We investigate the system dynamics by obtaining phase diagrams and density profiles with respect to the total number of particles. Moreover, we also study the effect of flexibility and finite resources on the steady-state system properties. It is also analyzed how the lattice occupancy affixes the 3D shape of the considered lattice under the influence of limited resources. Four stationary phases, including a shock phase, are reported. The interplay between the finite supply of particles and 3D environment with flexible lattice produces a novel feature in the form of back-and-forth phase transition. The study reveals that as a non-trivial effect on the system dynamics, the 3D environment counters the existence of bottleneck like situation arising through jamming of many particles on the lattice. (paper: classical statistical mechanics, equilibrium and non-equilibrium)