Ion Transport from Physics to Physiology: the Missing Rungs in the Ladder
A Former Electrophysiologist Revisits Diffusive GatingDaniel Sigg
What defines common ground between ion channel researchers and molecular dynamicists? Resolving the times scale problem between opening-closing events, which are measured in milliseconds, and crystal structure-based molecular dynamics simulations, which run on the femtosecond-nanosecond time scale, will require phenomenological gating models that operate on intermediate time scales. The thermodynamics and kinetics of simple bridging models were of interest to me when I was a graduate student, and given recent rapid advances on the molecular dynamics side, it is an excellent time to revisit these topics from the experimentalists perspective. The discrete-state master equation (Q-matrix) has long been the mainstay of describing and modeling ion channel data. It is a purely kinetic equation, though equilibrium probabilities may be obtained by solving peqQ = 0. Despite its utility as a complete theory, the Q-matrix method is starting to outlive its usefulness as gating models grow larger and more complex with the number of moving parts that can be experimentally resolved. Thermodynamic-based models offer an alternative, more flexible approach. Here, the potential of interest is the chemical potential of the channel, characterized as a free energy landscape of metastable states and dividing barriers constructed from a suitable set of reaction coordinates q. The presence of macroscopic fluctuations requires a statistical mechanical description, utilizing a coarse-grained partition function Z that is made up of equilibrium constants and allosteric factors. Z can often be expressed simply, even for models possessing a large number of gating particles. Kinetics are calculated on the fine time scale using a diffusion equation like the Smoluchowski equation, which requires a potential of mean force W(q) and diffusion coefficient D(q) as inputs. This provides the connection to molecular dynamics, which can provide W and D. The transition from a fast diffusion landscape to a slow Q-matrix formulation is achieved through various calculations, most straightforwardly by assigning rate constant values to the inverse mean first passage time between states. Practical demonstrations of the thermodynamic approach to analyzing electrophysiological data will be presented, and simulated data from a toy lattice model will be used to illustrate the proposed bridge between dynamic simulation and data-based modeling.