Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Regular Article: Derivatives of the Matrix Exponential and Their Computation
Advances in Applied Mathematics
Markov modeling of conformational kinetics of cardiac ion channel proteins
ISBMDA'06 Proceedings of the 7th international conference on Biological and Medical Data Analysis
ISBMDA'05 Proceedings of the 6th International conference on Biological and Medical Data Analysis
Approximate bisimulations for sodium channel dynamics
CMSB'12 Proceedings of the 10th international conference on Computational Methods in Systems Biology
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Characterization of the kinetic and conformational properties of channel proteins is a crucial element in the integrative study of congenital cardiac diseases. The proteins of the ion channels of cardiomyocytes represent an important family of biological components determining the physiology of the heart. Some computational studies aiming to understand the mechanisms of the ion channels of cardiomyocytes have concentrated on Markovian stochastic approaches. Mathematically, these approaches employ Chapman-Kolmogorov equations coupled with partial differential equations. As the scale and complexity of such subcellular and cellular models increases, the balance between efficiency and accuracy of algorithms becomes critical. We have developed a novel two-stage splitting algorithm to address efficiency and accuracy issues arising in such modeling and simulation scenarios. Numerical experiments were performed based on the incorporation of our newly developed conformational kinetic model for the rapid delayed rectifier potassium channel into the dynamic models of human ventricular myocytes. Our results show that the new algorithm significantly outperforms commonly adopted adaptive Runge-Kutta methods. Furthermore, our parallel simulations with coupled algorithms for multicellular cardiac tissue demonstrate a high linearity in the speedup of large-scale cardiac simulations.