| Biological complexity emerges from the synthesis of biochemical, chemical and physical phenomena. In recent years there has been an intense effort in modeling various cellular systems of interest to understand how the observed complexity emerges from the underlying mechanisms. Most modeling approaches are based on a population description of the cells: these methods, though usually amenable to calculation, are only valid in the limit of large numbers of interacting cells. Many systems of interest involve the interaction of a relatively small number of cells; even biological systems composed of thousands of cells have spatially extended regions over which the number density of cells is small. For the latter cases, population descriptions are not valid and individual based models become a necessity. Such models, usually cellular automaton models, have been numerically studied in recent years; however, these models are not usually amenable to analytic calculation. The work presented in this thesis seeks to fulfill a gap in modeling approaches to the understanding of biocomplexity by constructing an individual based model on which analysis is possible, through the methods of statistical physics and the theory of stochastic processes. This model will be used to study the differences between individual based and population based models and the range of applicability of the latter. For the sake of comparison of the two, new efficient computational algorithms are devised for the simulation of both types of models. We finally complete our multiscale study of modeling by investigating the robustness of individual based models; this meaning a comparison of the results of different microscopic descriptions modeling the same underlying phenomena. |
