Partial differential equation models for intranuclear diffusion, inverse problems in nanobiology and cell cycle specific effects of anticancer drugs
In this dissertation we have applied partial differential equation models to various problems arising in biology. We investigated the diffusional motility of p53, a key tumor suppressor protein, in living cells using fluorescence recovery after photobleaching (FRAP). Diffusion of p53-GFP within the cell nucleus is well described by a mathematical model for diffusion of particles that bind temporarily to a spatially homogeneous immobile structure. An open problem is to understand how DNA-binding proteins find their specific target sequences in the genome. We argue that inverse problems for wave equations in elastic media can be directly applied to biophysical problems of fiber-ligand association. We have used age-structured models of population dynamics to understand the cytostatic and cytotoxic effects of the anticancer drug lapatinib. Our mathematical model is fully continuous with respect to time and maturity. We analyze mathematically two age-structured models of population dynamics. We show that a nonlinear population dynamic model based on chronological age must have a nontrivial equilibrium solution.