American Institute of Mathematical Sciences

Advanced
2011, 8(3): 861-873. doi: 10.3934/mbe.2011.8.861

Defining candidate drug characteristics for Long-QT (LQT3) syndrome

Aslak Tveito 1, , Glenn T. Lines 1, , Pan Li 2, and  Andrew McCulloch 3,

1. 

Center for Biomedical Computing, Simula Research Laboratory, P.O. Box 134, Lysaker 1325, Norway, Norway
2. 

Cardiac Bioelectricity & Arrhythmia Center, Washington University, St. Louis, MO 63130-4899, United States
3. 

Department of Bioengineering, University of California San Diego, United States

Received  September 2010 Revised  February 2011 Published  June 2011

Mutations of the SCN5A gene can significantly alter the function of cardiac myocyte sodium channels leading to increased risk of ventricular arrhythmia. Over the past decade, detailed Markov models of the action potential of cardiac cells have been developed. In such models, the effects of a drug can be treated as alterations in on- and off rates between open and inactivated states on one hand, and blocked states on the other hand. Our aim is to compute the rates specifying a drug in order to: (a) restore the steady-state open probability of the mutant channel to that of normal wild type channels; and (b) minimize the difference between whole cell currents in drugged mutant and wild type cells. The difference in the electrochemical state vector of the cell can be measured in a norm taking all components and their dynamical properties into account. Measured with this norm, the difference between the state of the mutant and wild-type cell was reduced by a factor of 36 after the drug was introduced and by factors of 4 over mexitiline and 25 over lidocaine. The results suggest the potential to synthesize more effective drugs based on mechanisms of action of existing compounds.
Keywords: optimization., markov models, Cardiac arrhythmia, drug design.
Mathematics Subject Classification: Primary: 92C50; Secondary: 92C4.
Citation: Aslak Tveito, Glenn T. Lines, Pan Li, Andrew McCulloch. Defining candidate drug characteristics for Long-QT (LQT3) syndrome. Mathematical Biosciences & Engineering, 2011, 8 (3) : 861-873. doi: 10.3934/mbe.2011.8.861
References:
[1]

C. Antzelevitch, Ionic, molecular, and cellular bases of qt-interval prolongation and torsade de pointes, Europace, 4 (2007), 4-15. Google Scholar

[2]

T. Brennan, M. Fink and B. Rodriguez, Multiscale modelling of drug-induced effects on cardiac electrophysiological activity, European Journal of Pharmaceutical Sciences, 36 (2009), 62-77. doi: 10.1016/j.ejps.2008.09.013.  Google Scholar

[3]

A. Burashnikov and C. Antzelevitch, A unique mechanism contributing to initiation of atrial fibrillation, Pacing Clin Electrophysiol, 29 (2006), 290-5. doi: 10.1111/j.1540-8159.2006.00336.x.  Google Scholar

[4]

C. E. Clancy and Y. Rudy, Linking a genetic defect to its cellular phenotype in a cardiac arrhythmia, Nature, 400 (1999), 566. doi: 10.1038/23034.  Google Scholar

[5]

C. E. Clancy, Z. I. Zhu and Y. Rudy, Pharmacogenetics and anti-arrhythmic drug therapy: A theoretical investigation, Am. J. Physiol. Heart Circ. Physiol., 292 (2007), H66-75. doi: 10.1152/ajpheart.00312.2006.  Google Scholar

[6]

L. Hondeghem and B. G. Katzung, Test of a model of antiarrhythmic drug action. Effects of quinidine and lidocaine on myocardial conduction, Circulation, 61 (1980), 1217-1224. Google Scholar

[7]

J. Keener and J. Sneyd, "Mathematical Physiology," Springer, 2009. Google Scholar

[8]

L. M. Livshitz and Y. Rudy, Regulation of Ca2+ and electrical alternans in cardiac myocytes: Role of CAMKII and repolarizing currents, Am. J. Physiol. Heart Circ. Physiol., 292 (2007), 2854-2866. doi: 10.1152/ajpheart.01347.2006.  Google Scholar

[9]

J. A. Nelder and R. Mead, A simplex method for function minimization, Computer Journal, 7 (1965), 308-313. Google Scholar

[10]

Denis Noble, Jeremy Levin and William Scott, Biological simulations in drug discovery, Drug Discovery Today, 4 (1999), 10-16. doi: 10.1016/S1359-6446(98)01277-X.  Google Scholar

[11]

Y. Rudy, Modelling the molecular basis of cardiac repolarization, Europace, 9 (2007), vi17-vi19. doi: 10.1093/europace/eum202.  Google Scholar

[12]

A. Tveito and G. T. Lines, A note on a method for determining advantageous properties of an anti-arrhythmic drug based on a mathematical model of cardiac cells, Mathematical Biosciences, 217 (2009), 167-173. doi: 10.1016/j.mbs.2008.12.001.  Google Scholar

[13]

S. Vecchietti, E. Grandi, S. Severi, I. Rivolta, C. Napolitano, S. G. Priori and S. Cavalcanti, In silico assessment of Y1795C and Y1795H SCN5A mutations: Implication for inherited arrhythmogenic syndromes, Am. J. Physiol. Heart Circ. Physiol., 292 (2007), 56-65. doi: 10.1152/ajpheart.00270.2006.  Google Scholar

[14]

D. W. Wang, K. Yazawa, N. Makita, Jr. A. L. George and P. B. Bennett, Pharmacological targeting of long qt mutant sodium channels, Journal of Clinical Investigation, 99 (1997), 1714-1720. doi: 10.1172/JCI119335.  Google Scholar

[15]

Zheng I. Zhu and Colleen E. Clancy, Genetic mutations and arrhythmia: Simulation from DNA to electrocardiogram, Journal of Electrocardiology, ISCE 32nd Annual Conference, 40 (2007), S47-S50. Google Scholar

show all references

References:
[1]

C. Antzelevitch, Ionic, molecular, and cellular bases of qt-interval prolongation and torsade de pointes, Europace, 4 (2007), 4-15. Google Scholar

[2]

T. Brennan, M. Fink and B. Rodriguez, Multiscale modelling of drug-induced effects on cardiac electrophysiological activity, European Journal of Pharmaceutical Sciences, 36 (2009), 62-77. doi: 10.1016/j.ejps.2008.09.013.  Google Scholar

[3]

A. Burashnikov and C. Antzelevitch, A unique mechanism contributing to initiation of atrial fibrillation, Pacing Clin Electrophysiol, 29 (2006), 290-5. doi: 10.1111/j.1540-8159.2006.00336.x.  Google Scholar

[4]

C. E. Clancy and Y. Rudy, Linking a genetic defect to its cellular phenotype in a cardiac arrhythmia, Nature, 400 (1999), 566. doi: 10.1038/23034.  Google Scholar

[5]

C. E. Clancy, Z. I. Zhu and Y. Rudy, Pharmacogenetics and anti-arrhythmic drug therapy: A theoretical investigation, Am. J. Physiol. Heart Circ. Physiol., 292 (2007), H66-75. doi: 10.1152/ajpheart.00312.2006.  Google Scholar

[6]

L. Hondeghem and B. G. Katzung, Test of a model of antiarrhythmic drug action. Effects of quinidine and lidocaine on myocardial conduction, Circulation, 61 (1980), 1217-1224. Google Scholar

[7]

J. Keener and J. Sneyd, "Mathematical Physiology," Springer, 2009. Google Scholar

[8]

L. M. Livshitz and Y. Rudy, Regulation of Ca2+ and electrical alternans in cardiac myocytes: Role of CAMKII and repolarizing currents, Am. J. Physiol. Heart Circ. Physiol., 292 (2007), 2854-2866. doi: 10.1152/ajpheart.01347.2006.  Google Scholar

[9]

J. A. Nelder and R. Mead, A simplex method for function minimization, Computer Journal, 7 (1965), 308-313. Google Scholar

[10]

Denis Noble, Jeremy Levin and William Scott, Biological simulations in drug discovery, Drug Discovery Today, 4 (1999), 10-16. doi: 10.1016/S1359-6446(98)01277-X.  Google Scholar

[11]

Y. Rudy, Modelling the molecular basis of cardiac repolarization, Europace, 9 (2007), vi17-vi19. doi: 10.1093/europace/eum202.  Google Scholar

[12]

A. Tveito and G. T. Lines, A note on a method for determining advantageous properties of an anti-arrhythmic drug based on a mathematical model of cardiac cells, Mathematical Biosciences, 217 (2009), 167-173. doi: 10.1016/j.mbs.2008.12.001.  Google Scholar

[13]

S. Vecchietti, E. Grandi, S. Severi, I. Rivolta, C. Napolitano, S. G. Priori and S. Cavalcanti, In silico assessment of Y1795C and Y1795H SCN5A mutations: Implication for inherited arrhythmogenic syndromes, Am. J. Physiol. Heart Circ. Physiol., 292 (2007), 56-65. doi: 10.1152/ajpheart.00270.2006.  Google Scholar

[14]

D. W. Wang, K. Yazawa, N. Makita, Jr. A. L. George and P. B. Bennett, Pharmacological targeting of long qt mutant sodium channels, Journal of Clinical Investigation, 99 (1997), 1714-1720. doi: 10.1172/JCI119335.  Google Scholar

[15]

Zheng I. Zhu and Colleen E. Clancy, Genetic mutations and arrhythmia: Simulation from DNA to electrocardiogram, Journal of Electrocardiology, ISCE 32nd Annual Conference, 40 (2007), S47-S50. Google Scholar

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