| In this dissertation, we will present numerical and analytic evidence in how scaffold proteins facilitated in multisite protein phosphorylation can affect the number of steady states. In particular, we are looking for ways for this system to have more than one steady state; a phenomenon known as bistability. In our first model, we assumed uniform concentrations in the entire region, an ODE model. We start with a simplified scheme, using rapid equilibrium approximation, to determine the quasi-steady states and if bistability can be exhibited. Using the information from rapid equilibrium approximation, we generalized the approximation, as a result of concentration regimes, where the total concentration of one component is significantly larger than another, in the general scheme. The general scheme, using distributive mechanism, is widely used as the representation for this reaction network. In both schemes, we determine if bistability can be exhibited by solving the steady states using the most accurate and efficient numerical techniques and approximations, which include reduction to polynomial equations and an efficient method for an exhaustive search for parameters. In this model, we provide evidence on the possibilities and conditions needed for scaffold to induce bistability in multisite protein phosphorylation.;Recent biological evidence has shown that scaffold protein are specific to areas of the cell, such as the plasma membrane (13). We incorporate this in to our second model. Using our simplified scheme, we localized scaffold binding only on the plasma membrane, the outer region of our domain, along with the diffusion of non-scaffold components. We show bistability can be exhibited in to regions where it would not be if localization and diffusion were not present. We solve the steady states of this partial differential, reaction-diffusion equation using standard techniques of time evolution and Gauss-Seidel iteration. Using this model, we show that bistability can have long range effects in a cell. |
