Date of Award

Spring 2009

Document Type


Degree Name

Doctor of Philosophy (PhD)


Computational Analysis and Modeling

First Advisor

Andrei Paun


The ideas expressed in this work pertain to biochemical modeling. We explore our technique, the Nondeterministic Waiting Time algorithm, for modeling molecular signaling cascades. The algorithm is presented with pseudocode along with an explanation of its implementation. The entire source code can be found in the Appendices. This algorithm builds on earlier work from the lab of Dr. Andrei Nun, the advisor for this dissertation. We discuss several important extensions including: (i) a heap with special maintenance functions for sorting reaction waiting times, (ii) a nondeterministic component for handling reaction competition, and (iii) a memory enhancement allowing slower reactions to compete with faster reactions.

Several example systems are provided for comparisons between modeling with systems of ordinary differential equations, the Gillespie Algorithm, and our Nondeterministic Waiting Time algorithm. Our algorithm has a unique ability to exhibit behavior similar to the solutions to systems of ordinary differential equations for certain models and parameter choices, but it also has the nondeterministic component which yields results similar stochastic methods (e.g., the Gillespie Algorithm).

Next, we turn our attention to the Fas-mediated apoptotic signaling cascade. Fas signaling has important implications in the research of cancer, autoimmune and neurodegenerative disorders. We provide an exhaustive account of results from the Nondeterministic Waiting Time algorithm in comparison to solutions to the system of ordinary differential equations described by another modeling group. Our work with the Fas pathway led us to explore a new model, focusing on the effects of HIV-1 proteins on the Fas signaling cascade. There is extensive information in the literature on the effects of the HIV-1 proteins on this pathway. The model described in this work represents the first attempt ever made in modeling Fas-induced apoptosis in latently infected T cells.

There are several extensions for the Fas model discussed at the end of the work. Calcium signaling would be an interesting avenue to investigate, building on some recent results reported in the literature. For the HIV model, there are several extensions discussed. We also suggest a new direction for the Nondeterministic Waiting Time algorithm exploring parallelization options.