Joseph Cooley, Supercomputing Institute Undergraduate Intern
Anthony Varghese, Research Associate
Voltage-gated ion channels regulate the electrical properties of excitable cells. This work is interested in understanding the mechanisms of ion channel opening and closing that alters cellular excitability and biological signaling. To this end, these researchers are studying potassium channel gating for potassium channels comprised of single (homomeric) or multiple (heteromeric) subunits. They also express potassium channels harboring site-directed mutations and/or large structural changes as a way to address the relationship between protein structure and function. Continuous-time, discrete-state Markov models are being used to experimentally reconstruct measured ionic and gating currents from potassium channels. Numerical time-integration of mathematical models is performed using an implicit method with a variable-step, variable-order backward differentiation time-stepper, 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 is being used in the lab. The ion channel simulations are useful in evaluating current hypotheses about channel gating mechanisms, making predictions and generating ideas for new experiments in the lab.
A Markov chain model was used to express ion channel gating as a system of differential algebraic equations with voltage-dependent transitions between the states in the activation pathway. The equations were solved using a variable time step, variable order, numerical integrator (DASPK). Shown are simulations of (A) ionic current through potassium channels and (B) gating currents from the voltage-dependent rearrangements of the potassium channel proteins as they respond to membrane depolarization and open a potassium-selective pore.
The model has now been tested and fully implemented with several data sets for potassium channel gating with single (homomeric) and multisubunit (heteromeric) composition. Experimental data is now being compared with simulations in order to estimate optimal parameter values that reconstruct the electrophysiological experiments. A heuristic search is being implemented for the most sensitive model parameters that, in turn, are used as starting points for multiple nonlinear regression searches in the remaining parameter space. These regression analyses are done in parallel to improve the ability to find a true global optimal set of model parameters. Further simulations and parameter estimation are needed for experimental data collected under different test conditions.
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URL: http://www.msi.umn.edu/about/publications/annualreport/ar2000/depts/MedSchool/Physiology/boland.html |
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