We take a theoretical approach to a collection of problems in cell biology. A recent paper described an intriguing negative correlation between variability of the potential at which an action potential occurs and the rapidity of action potential initiation. Due to this antagonism, it is argued that Hodgkin-Huxley type models are unable to describe action potentials observed in cortical neurons in vivo.

In Chapter 2 we apply a method from theoretical physics to derive an analytical characterization of this problem. We analyze the probability distribution of onset potentials and derive the inverse relationship between onset span and onset rapidity. We find the relationship between onset span and onset rapidity depends on the level of synaptic background activity Hence we elucidate the regions of parameter space for which the Hodgkin-Huxley model is able to accurately describe the behavior of this system.

Nuclear pore complexes (NPCs) are highly selective filters that control the exchange of material between nucleus and cytoplasm. The principles that govern selective filtering by NPCs are not fully understood. Our analysis in Chapter 3 finds that transport receptors and their complexes are highly negatively charged. Moreover, NPC components that constitute the permeability barrier are positively charged. Electrostatic interactions between a transport receptor and the NPC could result in an energy gain of several k _BT, enabling significantly increased translocation rates relative to other cellular proteins. We suggest that negative charge is required for selective passage through the NPC.

The explosive growth in the number of protein sequences gives rise to the possibility of using natural variation in homologous protein sequences to find residues that control protein phenotypes. In many cases phenotypic changes are controlled by a group of residues, whose mutations are therefore correlated. In Chapter 4 we propose a methodology for incorporating functional and structural annotations of sequences into algorithms that detect correlated mutations, improving their efficacy at detecting these residue sets. This Bayesian approach uses annotations to define the prior probability that residues with different conservation levels are associated with each phenotype. Applying these principles to simulated and experimental data demonstrates the power of this approach.