Theoretical and computational analyses of stochastic transport processes in complex system

Abstract

Inspired by the stochastic transport processes occurring in complex systems, this thesis focuses on the understanding of the mechanisms of such processes using the theoretical and computational tools. A biological cell is a perfect example of a naturally arisen complex system, where a large number of biological processes occur. In many aspects, the situation within a cell is comparable to a large urban city with its highly energetic life, which is an example of a physical complex system. Similar to the role played by vehicles or cars in vehicular transport processes, the molecular motors or motor proteins perform various functions in many biological processes, such as intracellular transport, cell division, etc. Both in vivo and in vitro single-molecular motor experiments have provided a good insight over the mechanochemical properties of motor proteins. However, motor proteins work in a larger team, and their collective behavior is not yet well understood. Recent experiments on kinesin motor proteins reveal that they remain attached to the microtubule for a longer time resulting in the formation of clusters. This indicates the presence of short-range and relatively weak attractive energy. Also, some experiments indicate the presence of weak repulsive interaction between motor proteins. These intermolecular interactions are known to influence the microscopic properties of motor proteins, such as transition rates of reversible chemical transitions, binding and unbinding rates, and many more, thus suggesting an important role for interactions in the collective behaviour of molecular motors. In the thesis, we utilized a variant of non-equilibrium stochastic model, namely totally asymmetric simple exclusion process (TASEP), to understand the collective properties of many particle interacting systems. The dynamics in the model are governed by a simple Poisson process. The incorporation of each new dynamic and microscopic property of motor proteins required modifications in the TASEP model. We explored each system with appropriate theoretical and computational methods. We have mainly employed the cluster mean-field theory and its generalisations that capture the correlations between clusters of size two or more and various numerical techniques where explicit results are not possible to obtain. Parallelly, the theoretical results are validated with the extensively performed Monte Carlo simulations. The theoretical and computational outcomes give justification not only to the experimental observations but also provide new challenges for the experiments. We computed the stationary phase diagrams, density, particle and correlations profiles. Motivated by the experimental investigations, we firstly focused on the collective behavior of interacting particles moving on single channel TASEP under both periodic and open boundary conditions. The correlations in the system are assimilated using twocluster mean-field and three-cluster mean-field theory. Generally, in the biological transport processes such as RNA translation and vesicular locomotion by molecular motors, the participating molecules are larger than their step size. Stimulated by these observations, we also analyzed one-channel interacting TASEP with extended particles by mapping the results of single sized particles. Since the motor proteins attach and detach themselves from the microtubules and also interact among themselves, we captured this phenomena by constructing a lattice-gas model where particles interact among themselves as well as stochastically attach and detach from the lattice. We developed a theoretical approach called correlated cluster mean-field theory, which work very well for such non-conservative driven diffusive systems. Motivated by the motion of particles in the multichannels offered in vehicular and biological transport and inter as well as intra lane interactions, we then worked on an open two-channel symmetrically coupled interactive TASEP model that incorporates interaction in thermodynamically consistent way. We observed the effect of different controlling parameters on the particle maximal current, density profiles and correlations. Lastly, we investigated the totally asymmetric simple exclusion process with interacting particles on network junctions. The work is motivated by biological transport phenomena that exhibit complex network behavior where several molecular fluxes converge to a special junction and also another fluxes move out from it in different directions. We observed the effect of the number of incoming and outgoing segments on the stationary phase diagrams as well as on the correlations of the system. We utilized the two-cluster mean field theory and the explicit vertex framework to determine all the dynamical properties of the system. Along with the theoretical and computational analysis, we have mostly provided the physical justification and microscopic arguments to the computed theoretical results.