Shev MacNamara

Learn More
Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and(More)
When the heat equation and wave equation are approximated by ut = −Ku and utt = −Ku (discrete in space), the solution operators involve e−Kt, √K, cos(√Kt), and sinc( √ Kt). We compute these four matrices and find accurate approximations with a variety of boundary conditions. The second difference matrix K is Toeplitz (shift-invariant) for Dirichlet boundary(More)
Models of chemical kinetics in which some reactions are much faster than others are often treated by a type of quasi-steady-state approximation (QSSA). The total QSSA (tQSSA) was introduced for models of Michaelis-Menten enzyme kinetics and shown to be valid over a wider parameter regime than the usual QSSA. Here, we extend the tQSSA to the(More)
We analyze the governing partial differential equations of a model of pole-to-pole oscillations of the MinD protein in a bacterial cell. The sensitivity to extrinsic noise in the parameters of the model is explored. Our analysis shows that overall, the oscillations are robust to extrinsic perturbations in the sense that small perturbations in reaction(More)
The role of mathematical models of signaling networks is showcased by examples from Drosophila development. Three models of consecutive stages in dorsoventral patterning are presented. We begin with a compartmental model of intracellular reactions that generates a gradient of nuclear-localized Dorsal, exhibiting constant shape and dynamic amplitude. A(More)