Investigation of Complex Intracellular Dynamics using the Ribosome Flow Model

Abstract

Movement is an important part of life. For example, in a central and fundamental process known as gene expression, there is a movement of biological particles called RNA polymerases on the DNA strand to produce messenger RNA (mRNA). Then, ribosomes move sequentially along an mRNA molecule and decode it to produce functional proteins. In intracellular transport within living organisms, motor proteins move along microtubules to transport cargo from one location to another. Another prominent example is the vehicular traffic in a city, where people or goods are transported to another place via pathways. these Understanding complex transport phenomena has been a significant area of research in mathematics, biology, and physics. It requires developing appropriate mathematical and computational models to analyze the flow of particles in these systems. Over the years, the Ribosome Flow Model (RFM), obtained via a mean-field approximation of a its stochastic model called the Totally Asymmetric Simple Exclusion Process (TASEP), has provided a rigorous mathematical framework for the analysis. It is a deterministic, continuous-time model for analyzing the flow of interacting particles, and dynamics are described by ordinary differential equations (ODEs). It is amenable to both mathematical and numerical analysis. The results of the RFM analysis can be used to model and engineer gene expression. In this thesis, we rely on the framework of RFM to model and analyze the dynamical flow of particles along an ordered chain of sites encapsulating various biologically observed features. We specifically focus on formulating a system of non-linear ordinary differential equations, where the densities of each site on a lattice serve as the state variables and understand their asymptotic behavior. Exploring cooperative irreducible systems of ODEs with a first integral exhibiting positive gradient, we leverage results on the global phase portrait of such systems in our proposed models. Additionally, contraction theory proves to be a powerful tool for establishing asymptotic properties, such as convergence to steady-state and entrainment to a periodic excitation. There are certain types of uncertainties present in the system leading to variability in the parameters modeling the dynamics. In this direction, we develop a framework to understand the flux of particle flow in the transport system having different site capacities. Next, drawing inspiration from complex cellular processes like intracellular transport where particles having extended length interact through binding and repelling actions and can detach along the microtubule, we investigate the impact of interactions and detachment phenomena on the output rate. Further, motivated by experimental studies on collision-stimulated abortive termination of ribosomes, we develop a modeling framework to analyze the production rate under various circumstances. Next, we derive a network model for large-scale translation in and to the cell that attachment. encapsulates important cellular properties like ribosome drop-off We explore the effects of ribosome drop-off on production rates understand how drop-off influences the total production rate in the system. Moving ahead, we develop a closed network system modeling simultaneous particle movement along tracks with varying capacities in a resource-limited environment. This facilitates the study of competition for shared resources and the development of network models with feedforward and feedback connections between the tracks. Inspired by real-world systems where entry rates into a lane are influenced by nearby pools’ occupancy, we develop a model where parallel lanes are strategically connected to in multiple finite pools. This model takes into account the distribution of particles a local neighborhood. In summary, we develop mathematical models that capture intricate features of several biological and physical systems. These frameworks yield deeper insights into how parameters influence system dynamics, enhancing our comprehension of the underlying processes.