Continuation methods as a tool for parameter inference in models of biological oscillations: a case study in electrophysiology modeling

• We are often interested in calibrating biological models to stable periodic data. • Cardiac action potential models can converge slowly, which hinders inference. • Continuation methods efficiently identify stable limit cycles as parameters vary. • Inference with continuation instead of long model solves reduces computation by 70%. • Potential pitfalls in using continuation methods are discussed. Parameterizing mathematical models of biological systems often requires fitting to stable periodic data. In cardiac electrophysiology this typically requires converging to a stable action potential through long simulations. We explore this problem through the theory of dynamical systems, bifurcation analysis and continuation methods; under which a converged action potential is a stable limit cycle. Various attempts have been made to improve the efficiency of identifying these limit cycles, with limited success. We demonstrate that continuation methods can more efficiently infer the converged action potential as proposed model parameter sets change during optimization or inference routines. In an example electrophysiology model this reduces parameter inference computation time by 70%. We also discuss theoretical considerations and limitations of continuation method use in place of time-consuming model simulations. The application of continuation methods allows more robust optimization by making extra runs from multiple starting locations computationally tractable, and facilitates the application of inference methods such as Markov Chain Monte Carlo to gain more information on the plausible parameter space.