Date of Award

Spring 2001

Document Type


Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Michael Recce

Second Advisor

Denis L. Blackmore

Third Advisor

Victoria Booth

Fourth Advisor

James A. McHugh

Fifth Advisor

Karl Swann


A major goal of modern cell biology is to understand the regulation of cell behavior in the reductive terms of all the molecular interactions. This aim is made explicit by the assertion that understanding a cell's response to stimuli requires a full inventory of details. Currently, no satisfactory explanation exists to explain why cells exhibit only a relatively small number of different behavioral modes.

In this thesis, a discrete dynamical model is developed to study interactions between certain types of signaling proteins. The model is generic and "connectionist" in nature and incorporates important concepts from the biology. The emphasis is on examining dynamic properties that occur on short-term time scales and are independent of gene expression. A number of modeling assumptions are made. However, the framework is flexible enough to be extended in future studies.

The dynamical states of the system are explored both computationally and analytically. Monte Carlo methods are used to study the state space of simulated networks over selected parameter regimes. Networks show a tendency to settle into fixed points or oscillations over a wide range of initial conditions. A genetic algorithm (GA) is also designed to explore properties of networks. It evolves a "population" of modeled cells, selecting and ranking them according to a fitness function, which is designed to mimic features of real biological evolution. An analogue of protein domain shuffling is used as the crossover operator and cells are reproduced asexually. The effects of changing the parameters of the GA are explored. A clustering algorithm is developed to test the effectiveness of the GA search at generating cells, which display a limited number of different behavioral modes. Stability properties of equilibrium states in small networks are analyzed. The ability to generalize these techniques to larger networks is discussed. Topological properties of networks generated by the GA are examined. Structural properties of networks are used to provide insight into their dynamic properties.

The dynamic attractors exhibited by such signaling networks may provide a framework for understanding why cells persist in only a small number of stable behavioral modes.

Included in

Mathematics Commons