Markov Chains Meet Molecular Motors

Abstract

Transportation of important cargoes inside the cells of living organism is critical for several cellular functions. Most form of cargo transportation inside the cells is accomplished by teams of nanometer sized proteins called molecular motors. These proteins walk on filamentous tracks inside the cells while carrying a common cargo from its source to destination. Malfunctions in this process could lead to several life-threatening maladies ranging from neurodegenerative diseases to cancers. Thus, fundamental understanding of how molecular motors coordinate the transport of a common cargo is of immense scientific importance. Due to small sizes and stochastic nature of these motor proteins, experiments often lack the spatial and temporal resolutions to investigate the intracellular cargo transport process with molecular details. Mathematical modeling provides a helping hand and can not only add to the information obtained experimentally, but also guide future experiment design, thereby helping us understand the genesis of diseases and aid to the discovery of cures. In this thesis, we have utilized the theory of Markov chains to mathematically model intracellular cargo transport process by teams of molecular motors. Backed by the mathematical theory, we developed a numerical framework which improves upon the existing methodologies and enables us to numerically compute the biologically important statistics of the cargo transport by teams of motor proteins in a more realistic setting on a regular desktop PC. In contrast, previous methodologies regularly employed supercomputing clusters to obtain these statistics. Thus our methods are more accessible to biophysicists studying molecular motors but lacking the access to appropriate computational infrastructure. Further, we develop toy models to mathematically analyze the cargo transport process by two molecular motors replicating the well known "tug of war" and "coordinated movement" type scenarios during multi-motor cargo transport. Our results show that the cargo transport velocities could display non-trivial characteristics and phase transitions depending on certain experimental parameters which is an unexpected phenomenon. The methods developed here are not only limited to modeling cargo transport by molecular motors but also serve as a stepping stone for modeling more general class of processes where a group of stochastic agents accomplishes a common goal.