Microscopic modeling and simulation of lactose operon in Escherichia coli

This work deals with computer simulation of simple biological processes in simple cellular systems. The goal of our work is to produce a faithful simulation that tracks the evolution of a biological processes in both space and time. Our attempts have centered on metabolic processes in bacteria because these are well characterized systems. We have employed known models for processes involving simple nutrients, such as glucose and lactose, and enhanced those models by expanding the microscopic basis for the processes based on specifics of the chemistry and physics occurring within the cell.; In this work, models of the lactose operon genetic regulatory network are developed and investigated by both deterministic and stochastic methods. We first approached the lactose operon model by employing a system of ordinary differential equations taken from the literature with four changes which have not been considered in previous investigations. This model is conventional in that it incorporated only temporal changes in nutrient concentration and biological processes. Nonetheless; with this model we were able to predict the growth characteristics of bacteria on simple nutrients, i.e. glucose and lactose, and the diauxic growth curve in the presence of both glucose and lactose. The results were in good agreement with the available experimental data. These ordinary differential equations, especially with our modification, represented the limiting case, or uniform mixing approximation, for the more advanced spatial-temporal modeling effort in which we engaged.; Extending our modeling efforts to include the spatial elements of the cell involved the use of or, as needed, the development of various microscopic models of cellular processes that incorporated the correct elements of statistical mechanics and transport physics. As part of the process, while we were nominally stimulating a single cell, that cell was also representing some average of a large cell population. As a consequence, we introduced an average cell model to which allowed the following of evolution of processes in a single cell while also reflecting the average behavior of many cells.; In this final portion of our work, we developed spatial-temporal Monte Carlo methods to simulate the dynamical response of lactose operon. Several technical issues were addressed. The first involved finite size effects of the simulation volume. This is more complex and severe for the average cell model approach than the usual simulations of condensed matter. In order that the correct net nutrient flux flows to the cell as it would in the finite medium, we altered the dynamics of the nutrient flux in the finite simulation box using a technique that is completely original that we have called virtual space simulations. In addition, the stochastic implementation of the various boundary conditions developed and tested earlier proved complex and we found both exact and approximate methods for implementing the correct nutrient absorption dynamics at the boundary in Monte Carlo simulations.; The simulations of the stochastic models did not incorporate the full lactose operon model. That remains to be completed. Several tests in the stochastic simulation approach were done and compared to the numerical and analytic solutions in the idealized geometries investigated earlier. This serves primarily as a test of the correctness of the implementation of the boundary conditions and the virtual space methods.