This talk summarizes some very preliminary theoretical ideas and calculations regarding the structure and evolution of ion channels. The overarching question is the extent to which it is possible to understand biological details by positing a design principle, and searching for solutions that maximize the design under desired constraints. The great advantage of ion channels in this regard is that they are individual proteins whose function has long been known and is readily inferred through voltage measurements. The kinetic schemes of ion channels (regulating membrane permeability to ions) have been studied for more than 50 years, and in general can be quite complex. Why are they this way?
As a specific example, I will discuss our efforts in the last few weeks to calculate the optimal kinetic schemes of sodium and potassium channels (including voltage dependent activation barriers) to maximize the propagation velocity of the action potential, a question inspired by an old paper of Hodgkin.
Examples of questions we would like to answer include: to what extent do design principles dictate the details of the kinetic schemes of the sodium and the potassium channel, such as (a) the symmetry of the sodium and potassium channels (or lack thereof), as reflected in their kinetic schemes ; (b) the coupling of sodium channel kinetics to potassium channel kinetics; or (c) activation/inactivation of the channels themselves.