On the Role of Interacting Particles and Limited Resources in the Regulation of Lattice Length Dynamics

Abstract

Motivated by the significant effect of particle–particle interactions on the driven stochastic transport system, we examine how interacting particles control the lattice polymerization and depolymerization dynamics under the restricted supply of involved resources. We carried out a theoretical analysis based on the simple mean-field and cluster mean-field theory to predict the fundamental role of interactions on the steady-state length dynamics. It has been detected that there is a strong correlation between the lattice length dynamics and the concentration of the total number of lattice sites in the reservoir. For lower and higher values of available resources, depolymerization and polymerization process dominates the lattice dynamics, respectively, while for intermediate values of resources we observe a competition between polymerization and depolymerization kinetics. Further, it is examined that for a specific range of interaction energy E, the system remains in low density phase, on the contrary, for its significantly higher value, the system transits to high-density phase. In contrast to the high density phase, it is observed that in low density phase, lattice length decreases with an increase in interaction strength. Finally, the theoretical outcomes are validated with extensive Monte Carlo simulations.