| Summary: | In this dissertation, we consider a complex biological system known as cortical microtubule (CMT) system, where stochastic dynamics of the components (i.e., the CMTs) are defined in both space and time. CMTs have an inherent spatial dimension of their own, as their length changes over time in addition to their location. As a result of their dynamics in a confined space, they run into and interact with each other according to simple stochastic rules. Over time, CMTs acquire an ordered structure that is achieved without any centralized control beginning with a completely disorganized system. It is also observed that this organization might be distorted, when parameters of dynamicity and interactions change due to genetic mutation or environmental conditions. The main question of interest is to explore the characteristics of this system and the drivers of its self-organization, which is not feasible relying solely on biological experiments. For this, we replicate the system dynamics and interactions using computer simulations. As the simulations successfully mimic the organization seen in plant cells, we conduct an extensive analysis to discover the effects of dynamics and interactions on system characteristics by experimenting with different input parameters. To compare simulation results, we characterize system properties and quantify organization level using metrics based on entropy, average length and number of CMTs in the system. Based on our findings and conjectures from simulations, we develop analytical models for more generalized conclusions and efficient computation of system metrics. As a fist step, we formulate a mean-field model, which we use to derive sufficient conditions for organization to occur in terms of input parameters. Next, considering the parameter ranges that satisfy these conditions, we develop predictive methodologies for estimation of expected average length and number of CMTs over time, using a fluid model, transient analysis, and approximation algorithms tailored to our problem. Overall, we build a comprehensive framework for analysis and control of microtubule organization in plant cells using a wide range of models and methodologies in conjunction. This research also has broader impacts related to the fields of bio-energy, healthcare, and nanotechnology; in addition to its methodological contribution to stochastic modeling of systems with high-level spatial and temporal complexity.
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