Parallel stochastic simulation of biochemical reaction systems

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University of Alabama Libraries

Chemical reactions of various scales occur in nature and in our bodies. As technology has improved, researchers have gained access to in-depth knowledge about the relationships between the moving parts of a chemical reaction system. This has led to a multitude of studies by researchers who strive to understand the background and behavior of these systems both experimentally and mathematically. Computational biology allows us the opportunity to study chemical processes from a model-based approach, in which algorithms are used to simulate and interpret biological systems to validate our models with data when available. A number of biological processes such as interactions between molecules, cells, organs, and tissues in the body can be modeled mathematically, making it useful in medicine, biology, chemistry, biophysics, statistics, genomics, and more. Mathematically, biochemical processes can be modeled deterministically and stochastically. The Reaction Rate Equations (RREs), in the form of a system of ODEs, are used to model deterministically. The Chemical Master Equation (CME), in the form of a Markov Chain, is used to solve stochastically. When the CME becomes computationally expensive, methods such as the Stochastic Simulation Algorithm (SSA), the Tau-Leap Method (Tau-Leap), the First Reaction Method (FRM), and the Delay Stochastic Simulation Algorithm (DSSA) are used to simulate the change in population of the species in a system over time. For accuracy when examining the resulting data, models are simulated many times in order to produce probability distributions of the involved species. An increase in the size and complexity of a system, leads to an increase in the computational time needed to simulate a model. Parallel processing is used to speed up the computational time of simulating biochemical processes via the aforementioned methods. The numerical results can be illustrated for various models found in science.

Electronic Thesis or Dissertation
Mathematics, Applied mathematics, Cellular biology