Linda M. Boland, Principal Investigator

Simulations of Voltage-Dependent Ion Channel Gating

Voltage-gated ion channels regulate the electrical properties of excitable cells. These researchers were interested in understanding the mechanisms of ion channel opening and closing, which alters cellular excitability and biological signaling. Continuous-time, discrete-state Markov models were used to reconstruct experimentally measured ionic and gating currents from ion channels. Numerical time-integration of mathematical models was performed using an implicit method with a variable-step, variableorder backward differentiation time-stepper, a Newton nonlinear solver, and an iterative linear solver with simple reconditioning. A novel, inexpensive computational method for the estimation of asymptotic and finite-time gating charge was used in the lab. Experimental data was compared with simulations in order to estimate optimal parameter values that reconstruct the electrophysiological experiments. Regression analyses were carried out in parallel to improve the ability to find a true global optimal set of model parameters. These simulations proved useful in evaluating current hypotheses about channel gating mechanisms, making predictions, and generating ideas for new experiments in the lab.

This project further refined several models of potassium ion channel gating. Potassium channel gating was modeled by classical kinetic theory with voltage-dependent rate constants and the assumption that gating is a Markov process. This research used models to simulate the modification of inactivation gating by accessory (non-pore-forming) protein subunits or the modification of activation gating by drugs or biomolecules. Animated graphical outputs of the channel’s behavior under different experimental conditions were generated and compared to experimental data generated in ongoing electrophysiological and structure-function experiments. This process was expected to use a heuristic search for the most sensitive model parameters, which, in turn, were to be used as starting points for multiple nonlinear regression searches in the remaining parameter space. These researchers successfully developed three different models of potassium channel gating and applied these models to experimental data. The experimental data was simulated by the mathematical calculations of the model using user-defined criteria. The greatest challenge was selecting the best fit parameters. Since this was not achievable by trial and error, the research group continued to work on fitting the free parameters in the simulation using methods for error minimization. Supercomputer resources were critical to the development and testing of methods to search for the best fit parameter values.

Research Group

Anthony Varghese, Research Associate