title: Regression analysis for constraining free parameters in electrophysiological models of cardiac cells.
abstract: A major challenge in computational biology is constraining free parameters in mathematical models. Adjusting a parameter to make a given model output more realistic sometimes has unexpected and undesirable effects on other model behaviors. Here, we extend a regression-based method for parameter sensitivity analysis and show that a straightforward procedure can uniquely define most ionic conductances in a well-known model of the human ventricular myocyte. The model's parameter sensitivity was analyzed by randomizing ionic conductances, running repeated simulations to measure physiological outputs, then collecting the randomized parameters and simulation results as "input" and "output" matrices, respectively. Multivariable regression derived a matrix whose elements indicate how changes in conductances influence model outputs. We show here that if the number of linearly-independent outputs equals the number of inputs, the regression matrix can be inverted. This is significant, because it implies that the inverted matrix can specify the ionic conductances that are required to generate a particular combination of model outputs. Applying this idea to the myocyte model tested, we found that most ionic conductances could be specified with precision (R(2) > 0.77 for 12 out of 16 parameters). We also applied this method to a test case of changes in electrophysiology caused by heart failure and found that changes in most parameters could be well predicted. We complemented our findings using a Bayesian approach to demonstrate that model parameters cannot be specified using limited outputs, but they can be successfully constrained if multiple outputs are considered. Our results place on a solid mathematical footing the intuition-based procedure simultaneously matching a model's output to several data sets. More generally, this method shows promise as a tool to define model parameters, in electrophysiology and in other biological fields.
authors.affiliation: Department of Pharmacology and Systems Therapeutics, Mount Sinai School of Medicine, New York, New York, USA.
authors.forename: Amrita X
authors.initials: AX
authors.lastname: Sarkar
authors.forename: Eric A
authors.initials: EA
authors.lastname: Sobie
mesh_terms: D000200:Action Potentials / Q000502:physiology; D000818:Animals; D001499:Bayes Theorem; D054849:Cardiac Electrophysiology / Q000379:methods*; D019295:Computational Biology / Q000379:methods; D003198:Computer Simulation; D004285:Dogs; D006333:Heart Failure / Q000503:physiopathology; D006352:Heart Ventricles / Q000166:cytology; D006801:Humans; D008955:Models, Cardiovascular; D015999:Multivariate Analysis; D032383:Myocytes, Cardiac / Q000502:physiology*; D012044:Regression Analysis
references.citation: Nat Neurosci. 2004 Dec;7(12):1345-52
references.pmid: 15558066
references.citation: Philos Trans A Math Phys Eng Sci. 2009 Jun 13;367(1896):2161-79
references.pmid: 19414451
references.citation: J Physiol. 1962 Feb;160:317-52
references.pmid: 14480151
references.citation: J Theor Biol. 2008 Aug 7;253(3):544-60
references.pmid: 18495166
references.citation: J Neurophysiol. 2007 Dec;98(6):3749-58
references.pmid: 17855581
references.citation: J Physiol. 2005 Apr 15;564(Pt 2):411-9
references.pmid: 15649977
references.citation: Am J Physiol Heart Circ Physiol. 2004 Apr;286(4):H1573-89
references.pmid: 14656705
references.citation: Am J Physiol Heart Circ Physiol. 2008 Jun;294(6):H2565-75
references.pmid: 18408122
references.citation: Circ Res. 1991 Jun;68(6):1501-26
references.pmid: 1709839
references.citation: Am J Physiol Heart Circ Physiol. 2005 Jul;289(1):H398-413
references.pmid: 15708964
references.citation: PLoS Comput Biol. 2007 Oct;3(10):1871-78
references.pmid: 17922568
references.citation: Am J Physiol Heart Circ Physiol. 2000 Jul;279(1):H397-421
references.pmid: 10899081
references.citation: Biophys J. 2004 Nov;87(5):3351-71
references.pmid: 15347581
references.citation: Nat Rev Neurosci. 2006 Jul;7(7):563-74
references.pmid: 16791145
references.citation: Circ Res. 1994 Jun;74(6):1071-96
references.pmid: 7514509
references.citation: PLoS Comput Biol. 2008 Jan;4(1):e11
references.pmid: 18208320
references.citation: J Mol Cell Cardiol. 2001 May;33(5):851-72
references.pmid: 11343410
references.citation: Science. 1999 Jan 15;283(5400):381-7
references.pmid: 9888852
references.citation: Biophys J. 1998 Mar;74(3):1149-68
references.pmid: 9512016
references.citation: Prog Biophys Mol Biol. 2004 Jun-Jul;85(2-3):407-31
references.pmid: 15142755
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Aug;68(2 Pt 1):021904
references.pmid: 14525003
references.citation: N Engl J Med. 2004 Mar 4;350(10):1013-22
references.pmid: 14999113
references.citation: Biotechnol J. 2008 May;3(5):639-47
references.pmid: 18246569
references.citation: Biophys J. 2009 Feb 18;96(4):1264-74
references.pmid: 19217846
references.citation: Am J Physiol Heart Circ Physiol. 2009 Oct;297(4):H1436-45
references.pmid: 19648254
references.citation: Circ Res. 1998 Jan 9-23;82(1):63-81
references.pmid: 9440706
references.citation: J Mol Cell Cardiol. 2008 Sep;45(3):420-8
references.pmid: 18639555
references.citation: J Gen Physiol. 1990 Jul;96(1):195-215
references.pmid: 2170562
references.citation: J Cell Sci. 1993 Dec;106 ( Pt 4):1153-68
references.pmid: 8126097
references.citation: Nature. 2006 Mar 23;440(7083):463-9
references.pmid: 16554806
references.citation: Circ Res. 1995 Jul;77(1):140-52
references.pmid: 7788872
references.citation: Am J Physiol Heart Circ Physiol. 2002 Jun;282(6):H2296-308
references.pmid: 12003840
references.citation: Prog Biophys Mol Biol. 2008 Jun-Jul;97(2-3):332-47
references.pmid: 18395246
references.citation: Front Neurosci. 2007 Oct 15;1(1):7-18
references.pmid: 18982116
references.citation: PLoS Comput Biol. 2006 Jul 21;2(7):e94
references.pmid: 16848639
references.citation: J Neurophysiol. 2003 Dec;90(6):3998-4015
references.pmid: 12944532
references.citation: J Neurosci. 2009 Apr 29;29(17):5573-86
references.pmid: 19403824
references.citation: J Physiol. 1952 Aug;117(4):500-44
references.pmid: 12991237
references.citation: Am J Physiol Heart Circ Physiol. 2002 Nov;283(5):H2074-101
references.pmid: 12384487
references.citation: Circ Res. 2006 May 26;98(10):1244-53
references.pmid: 16728670
references.citation: Biophys J. 1978 Jul;23(1):147-52
references.pmid: 667303
references.citation: J Physiol. 2009 Mar 15;587(Pt 6):1293-9
references.pmid: 19153162
references.citation: Biophys J. 2005 Dec;89(6):4096-110
references.pmid: 16169970