A mathematical approach to signaling, specificity and growth in yeast cell mating

In this dissertation we study the mating of Saccharomyces cerevisiae, yeast, through strict mathematical analyses. After a brief review of the relevant background in biology we first focus on what we call the specificity problem. Put simply, the specificity problem is: given that a cell receives many different signals, the transduction of which converges on many common intermediate messengers, how do cells distinguish signals and elicit appropriate responses? In particular we focus on the effect ultrasensitivity, the property of having switch-like responses, may have on specificity. The approach taken is to construct a simple ODE model and evaluate indicators that we show represent a quantification of the idea of specificity.;We find that ultrasensitive responses in a signaling pathway can provide significant advantages to specificity, but to achieve even a functioning level of specificity further biological mechanisms must be employed to insulate the pathways from one another. We examine some methods in optimizing the parameters for different signaling networks adjoined with different insulation mechanisms.;We also study the problem of projection formation in yeast mating. Here we model a two cell system through a series of coupled PDEs. The model represents the dynamics of the spatial distribution of key surface proteins known to influence cell growth during mating. As the exact mechanism for projection formation is unknown, we examine the properties of utilizing different growth functions and determine the advantages and shortcomings of each. Further we try to explain the behavior of several published genetic mutation in the mating pathway by making conjugate parameter variations in our model and examining the effect on growth.