Computationally Efficient Strategy for Modeling the Effect of Ion Current Modifiers

Electrophysiological studies often seek to relate changes in ion current properties caused by a chemical modifier to changes in cellular properties. Therefore, quantifying concentration-dependent effects of modifiers on ion currents is a topic of importance. In this paper, we sought a mathematical method for using ion current data to predict the effect of several theoretical ion current modifiers on cellular and tissue properties that is computationally efficient without compromising predictive power. We focused on the current as an example case due to its link to long QT syndrome and arrhythmias, but these methods should be generally applicable to other electrophysiological studies. We compared predictions using a Markov model with mass action binding of the modifiers to specific conformational states of the channel to predictions generated by two simplified models. We investigated scaling conductance, and found that although this method produced predictions that agreed qualitatively with the more complicated model, it did not generate quantitatively consistent predictions for all modifiers tested. Our simulations showed that a more computationally efficient Hodgkin-Huxley model that incorporates the effect of modifiers through functional changes in the current produced quantitatively consistent predictions of concentration-dependent changes in cell and tissue properties for all modifiers tested.

[1]  C Antzelevitch,et al.  I(NaCa) contributes to electrical heterogeneity within the canine ventricle. , 2000, American journal of physiology. Heart and circulatory physiology.

[2]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[3]  Andrew C. Zygmunt,et al.  Electrophysiological Effects of Ranolazine, a Novel Antianginal Agent With Antiarrhythmic Properties , 2004, Circulation.

[4]  E. Carmeliet Voltage- and time-dependent block of the delayed K+ current in cardiac myocytes by dofetilide. , 1992, The Journal of pharmacology and experimental therapeutics.

[5]  J. Hell,et al.  Regulation of Cardiac L-Type Calcium Channels by Protein Kinase A and Protein Kinase C , 2000, Circulation research.

[6]  E. Albuquerque,et al.  Macromolecular sites for specific neurotoxins and drugs on chemosensitive synapses and electrical excitation in biological membranes. , 1988, Ion channels.

[7]  B. Hille Ionic channels of excitable membranes , 2001 .

[8]  B. Fermini,et al.  The impact of drug-induced QT interval prolongation on drug discovery and development , 2003, Nature Reviews Drug Discovery.

[9]  T J Campbell,et al.  Inhibition of the human ether‐a‐go‐go‐related gene (HERG) potassium channel by cisapride: affinity for open and inactivated states , 1999, British journal of pharmacology.

[10]  E. Carmeliet Use-dependent block and use-dependent unblock of the delayed rectifier K+ current by almokalant in rabbit ventricular myocytes. , 1993, Circulation research.

[11]  A. Brown,et al.  Variability in the measurement of hERG potassium channel inhibition: effects of temperature and stimulus pattern. , 2004, Journal of pharmacological and toxicological methods.

[12]  James P. Keener,et al.  Mathematical physiology , 1998 .

[13]  R L Winslow,et al.  Molecular Interactions Between Two Long-QT Syndrome Gene Products, HERG and KCNE2, Rationalized by In Vitro and In Silico Analysis , 2001, Circulation research.

[14]  D. Marquardt An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[15]  Yasutaka Kurata,et al.  Roles of L-type Ca2+ and delayed-rectifier K+ currents in sinoatrial node pacemaking: insights from stability and bifurcation analyses of a mathematical model. , 2003, American journal of physiology. Heart and circulatory physiology.

[16]  J. M. Di Diego,et al.  Cisapride-Induced Transmural Dispersion of Repolarization and Torsade de Pointes in the Canine Left Ventricular Wedge Preparation During Epicardial Stimulation , 2003, Circulation.

[17]  M. Sanguinetti,et al.  Class III antiarrhythmic drugs block HERG, a human cardiac delayed rectifier K+ channel. Open-channel block by methanesulfonanilides. , 1996, Circulation research.

[18]  G. Bard Ermentrout,et al.  Modeling neural oscillations , 2002, Physiology & Behavior.

[19]  Mark E. Anderson,et al.  A calcium sensor in the sodium channel modulates cardiac excitability , 2002, Nature.

[20]  A. Camm,et al.  The potential for QT prolongation and pro-arrhythmia by non-anti-arrhythmic drugs: clinical and regulatory implications. Report on a Policy Conference of the European Society of Cardiology. , 2000, Cardiovascular research.

[21]  Yoram Rudy,et al.  Rate Dependence and Regulation of Action Potential and Calcium Transient in a Canine Cardiac Ventricular Cell Model , 2004, Circulation.

[22]  C. Antzelevitch,et al.  Characteristics of the delayed rectifier current (IKr and IKs) in canine ventricular epicardial, midmyocardial, and endocardial myocytes. A weaker IKs contributes to the longer action potential of the M cell. , 1995, Circulation research.

[23]  K. Borowicz,et al.  Remacemide--a novel potential antiepileptic drug. , 2003, Polish journal of pharmacology.

[24]  C Antzelevitch,et al.  Larger late sodium conductance in M cells contributes to electrical heterogeneity in canine ventricle. , 2001, American journal of physiology. Heart and circulatory physiology.

[25]  C F Starmer,et al.  Mechanisms of use-dependent block of sodium channels in excitable membranes by local anesthetics. , 1984, Biophysical journal.

[26]  L. Carlsson,et al.  Block of HERG‐Carried K+ Currents by the New Repolarization Delaying Agent H 345/52 , 2003, Journal of cardiovascular electrophysiology.

[27]  Antonio Zaza,et al.  Ionic currents during sustained pacemaker activity in rabbit sino‐atrial myocytes , 1997, The Journal of physiology.

[28]  M. Sanguinetti,et al.  A structural basis for drug-induced long QT syndrome. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[29]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[30]  J. Hancox,et al.  Inhibition of HERG K+ Current and Prolongation of the Guinea‐Pig Ventricular Action Potential by 4‐Aminopyridine , 2003, The Journal of physiology.

[31]  W. Trautwein,et al.  Calcium currents in single SA nodal cells of the rabbit heart studied with action potential clamp , 1989, Pflügers Archiv - European Journal of Physiology.

[32]  Glenn I. Fishman,et al.  Cyclic AMP regulates the HERG K+ channel by dual pathways , 2000, Current Biology.

[33]  D DiFrancesco,et al.  A model of cardiac electrical activity incorporating ionic pumps and concentration changes. , 1985, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[34]  K.H.W.J. ten Tusscher,et al.  Comments on 'A model for human ventricular tissue' : reply , 2005 .

[35]  C. Luo,et al.  A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. , 1991, Circulation research.

[36]  D. Koh,et al.  How noise and coupling induce bursting action potentials in pancreatic {beta}-cells. , 2005, Biophysical journal.

[37]  C Antzelevitch,et al.  The potential for QT prolongation and proarrhythmia by non-antiarrhythmic drugs: clinical and regulatory implications. Report on a policy conference of the European Society of Cardiology. , 2000, European heart journal.

[38]  R L Winslow,et al.  Cardiac sodium channel Markov model with temperature dependence and recovery from inactivation. , 1999, Biophysical journal.

[39]  G. Helmlinger,et al.  Preclinical cardiac safety assessment of pharmaceutical compounds using an integrated systems-based computer model of the heart. , 2006, Progress in biophysics and molecular biology.

[40]  D. Roden,et al.  K+ currents and K+ channel mRNA in cultured atrial cardiac myocytes (AT-1 cells). , 1994, Circulation research.

[41]  C. Starmer,et al.  Blockade of Rabbit Atrial Sodium Channels by Lidocaine Characterization of Continuous and Frequency-Dependent Blocking , 1989, Circulation research.

[42]  Robert F Gilmour,et al.  Contribution of IKr to Rate-Dependent Action Potential Dynamics in Canine Endocardium , 2004, Circulation research.