Browsing by Author "Turner, Jesse Hosea, III"
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Item A quantitative study of the lac operon(2005) Turner, Jesse Hosea, III; Cox, Steven J.The lac operon has been key in the study of genetic regulation. Consisting of three structural genes and a regulatory domain, the lac operon controls the manufacture of lactose-digesting enzymes in E. coli bacteria. The mechanisms through which it is repressed and activated are standard and apply to many operons in other genetic settings. As a result, scientists believe understanding the lac operon will help to decipher how more complicated genetic regulatory systems behave. A large amount of quantitative data has been generated from the lac operon, a consequence of both its small size and tractability. A variety of mathematical models have been employed to examine this data. Here, we will investigate how bifurcation theory, reverse engineering, and Gillespie's stochastic simulation method have all been used to uncover some aspect of the lac operon. Conclusions drawn from the results of these models promise to reveal new information about this operon.Item Multi-scale behavior in chemical reaction systems: Modeling, applications, and results(2008) Turner, Jesse Hosea, III; Cox, Dennis D.Four major approaches model the time dependent behavior of chemical reaction systems: ordinary differential equations (ODE's), the &tgr;-leap algorithm, stochastic differential equations (SDE's), and Gillespie's stochastic simulation algorithm (SSA). ODE's are simulated the most quickly of these, but are often inaccurate for systems with slow rates and molecular species present in small numbers. Under ideal conditions, the SSA is exact, but computationally inefficient. Unfortunately, many reaction systems exhibit characteristics not well captured individually by any of these methods. Therefore, hybrid models incorporating aspects from all four must be employed. The aim is to construct an approach that is close in accuracy to the SSA, useful for a wide range of reaction system examples, and computationally efficient. The Adaptive Multi-scale Simulation Algorithm (AMSA) uses the SSA for slow reactions, SDE's for medium-speed reactions, ODE's for fast reactions, and the tau-leap algorithm for non-slow reactions involving species small in number. This article introduces AMSA and applies it to examples of reaction systems involving genetic regulation. A thorough review of existing reaction simulation algorithms is included. The computational performance and accuracy of AMSA's molecular distributions are compared to those of the SSA, which is used as the golden standard of accuracy. The use of supercomputers can generate much larger data sets than serial processors in roughly the same amount of computational time. Therefore, multi-processor machines are also employed to assess the accuracy of AMSA simulations.