This Article 
 Bibliographic References 
 Add to: 
An Efficient Method for Modeling Kinetic Behavior of Channel Proteins in Cardiomyocytes
January/February 2012 (vol. 9 no. 1)
pp. 40-51
Chong Wang, University of Ulster, Coleraine
Peter Beyerlein, Technical University Wildau, Wildau
Heike Pospisil, Technical University Wildau, Wildau
Antje Krause, Bingen University of Applied Sciences, Bingen Am Rhein
Chris Nugent, University of Ulster, Jordanstown
Werner Dubitzky, University of Ulster, Jordanstown
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.

[1] J.A. Malmivuo and R. Plonsey, Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields. Oxford Univ. Press, 1995.
[2] C. Antzelevitch and W. Shimizu, “Cellular Mechanisms Underlying the Long QT Syndrome,” Current Opinion in Cardiology, vol. 17, no. 1, pp. 43-51, 2002.
[3] I. Splawski, “Spectrum of Mutations in Long-QT Syndrome Genes: KVLQT1, HERG, SCN5A, KCNE1, and KCNE2,” Circulation, vol. 102, no. 10, pp. 1178-1185, 2000.
[4] R. Horn, R., and C. Vanderburg, “Statistical Properties of Single Sodium Channels,” J. General Physiology, vol. 84, no. 4, pp. 505-534, 1984.
[5] C. Wang, A. Krause, C. Nugent, and W. Dubitzky, “Markov Modeling of Conformational Kinetics of Cardiac Ion Channel Proteins,” Lecture Notes in Computer Science, N. Maglaveras, I. Chouvarda, V. Koutkias, and R. Brause, eds., vol. 4345, pp. 116-127, Springer Berlin/Heidelberg, 2006.
[6] J. Wang, J. Onuchic, and P. Wolynes, “Statistics of Kinetic Pathways on Biased Rough Energy Landscapes with Applications to Protein Folding,” Physical Rev. Letters, vol. 76, no. 25, pp. 4861-4864, 1996.
[7] T. Ferrer, J. Rupp, D.R. Piper, and M. Tristani-Firouzi, “The S4-S5 Linker Directly Couples Voltage Sensor Movement to the Activation Gate in the Human Ether-Go-Go-Related Gene (hERG) K+ Channel,” J. Biological Chemistry, vol. 281, no. 18, pp. 12858-12864, 2006.
[8] N. Zandany, M. Ovadia, I. Orr, and O. Yifrach, “Direct Analysis of Cooperativity in Multisubunit Allosteric Proteins,” Proc. Nat'l Academy of Sciences USA, vol. 105, no. 33, pp. 11697-11702, 2008.
[9] Y. Rudy and J.R. Silva, “Computational Biology in the Study of Cardiac Ion Channels and Cell Electrophysiology,” Quarterly Rev. of Biophysics, vol. 39, pp. 57-116, 2006.
[10] V.E. Bondarenko, G.P. Szigeti, G.C.L. Bett, S.J. Kim, and R.L. Rasmusson, “Computer Model of Action Potential of Mouse Ventricular Myocytes,” Am. J. Physiology Heart and Circulatory Physiology, vol. 287, no. 3, pp. 1378-1403, 2004.
[11] K.H.W.J. ten Tusscher, D. Noble, P.J. Noble, and A.V. Panfilov, “A Model for Human Ventricular Tissue,” Am. J. Physiology Heart and Circulatory Physiology, vol. 286, no. 4, pp. 1573-1589, 2004.
[12] I. Najfeld and T. Havel, “Derivatives of the Matrix Exponential and Their Computation,” Advances in Applied Math., vol. 16, pp. 321-375, 1995.
[13] C. Van Loan, “Computing Integrals Involving the Matrix Exponential,” IEEE Trans. Automatic Control, vol. AC-23, no. 3, pp. 395-404, June 1978.
[14] C. Wang, P. Beyerlein, H. Pospisil, A. Krause, W. Dubitzky, and C. Nugent, “Interplay of Potassium Channels in Modulating the Action Potential of the Human Left Ventricle,” Computers in Cardiology, vol. 37, pp. 653-656, 2010.
[15] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing, second ed. Cambridge Univ. Press, 1992.
[16] Z. Zhou, Q. Gong, B. Ye, Z. Fan, J.C. Makielski, G.A. Robertson, and C.T. January, “Properties of HERG Channels Stably Expressed in HEK 293 Cells Studied at Physiological Temperature,” Biophysical J., vol. 74, no. 1, pp. 230-241, 1998.
[17] G. Berecki, J.G. Zegers, A.O. Verkerk, Z.A. Bhuiyan, B. de Jonge, M.W. Veldkamp, R. Wilders, and A.C. van Ginneken, “HERG Channel (Dys)Function Revealed by Dynamic Action Potential Clamp Technique,” Biophysical J., vol. 88, no. 1, pp. 566-578, 2005.
[18] S. Zicha, L. Xiao, S. Stafford, T.J. Cha, W. Han, A. Varro, and S. Nattel, “Transmural Expression of Transient Outward Potassium Current Subunits in Normal and Failing Canine and Human Hearts,” J. Physiology, vol. 561, no. 3, pp. 735-748, 2004.
[19] E. Vigmond, R.W. dos Santos, A. Prassl, M. Deo, and G. Plank, “Solvers for the Cardiac Bidomain Equations,” Progress in Biophysics and Molecular Biology, vol. 96, nos. 1-3, pp. 3-18, 2008.
[20] J. Stinstra, S. Roberts, J.B. Pormann, R. MacLeod, and C.S. Henriquez, “Computer Simulations of Cardiac Electrophysiology, a Model of 3D Propagation in Discrete Cardiac Tissue,” Computers in Cardiology, vol. 33, pp. 41-44, 2006.
[21] C. Wang, A. Krause, C. Nugent, and W. Dubitzky, “Focal Activity in Simulated LQT2 Models at Rapid Ventricular Pacing: Analysis of Cardiac Electrical Activity Using Grid-Based Computation,” Lecture Notes in Computer Science, J. Oliveira, V. Maojo, F. Martín-Sánchez, and A. Pereira, eds., vol. 3745, pp. 305-316, Springer Berlin/Heidelberg, 2005.
[22] W. Jangsangthong, E. Kuzmenkina, I.F.Y. Khan, J. Matthes, R. Hullin, and S. Herzig, “Inactivation of L-Type Calcium Channels Is Determined by the Length of the N Terminus of Mutant Subunits,” Pflgers Archiv: European J. Physiology, vol. 459, pp. 399-411, 2010.
[23] L. Xia, Y. Zhang, H. Zhang, Q. Wei, F. Liu, and S. Crozier, “Simulation of Brugada Syndrome Using Cellular and Three-Dimensional Whole-Heart Modeling Approaches,” Physiological Measurement, vol. 27, pp. 1125-1142, 2006.

Index Terms:
Cardiomyocyte, arrhythmia, channel protein, conformation, kinetic pathway, differential equations, Markov model.
Chong Wang, Peter Beyerlein, Heike Pospisil, Antje Krause, Chris Nugent, Werner Dubitzky, "An Efficient Method for Modeling Kinetic Behavior of Channel Proteins in Cardiomyocytes," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 9, no. 1, pp. 40-51, Jan.-Feb. 2012, doi:10.1109/TCBB.2011.84
Usage of this product signifies your acceptance of the Terms of Use.