Regression analysis for constraining free parameters in electrophysiological models of cardiac cells.
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.
Sarkar
Amrita X
AX
Department of Pharmacology and Systems Therapeutics, Mount Sinai School of Medicine, New York, New York, USA.
Sobie
Eric A
EA
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
Nat Neurosci. 2004 Dec;7(12):1345-52
15558066
Philos Trans A Math Phys Eng Sci. 2009 Jun 13;367(1896):2161-79
19414451
J Physiol. 1962 Feb;160:317-52
14480151
J Theor Biol. 2008 Aug 7;253(3):544-60
18495166
J Neurophysiol. 2007 Dec;98(6):3749-58
17855581
J Physiol. 2005 Apr 15;564(Pt 2):411-9
15649977
Am J Physiol Heart Circ Physiol. 2004 Apr;286(4):H1573-89
14656705
Am J Physiol Heart Circ Physiol. 2008 Jun;294(6):H2565-75
18408122
Circ Res. 1991 Jun;68(6):1501-26
1709839
Am J Physiol Heart Circ Physiol. 2005 Jul;289(1):H398-413
15708964
PLoS Comput Biol. 2007 Oct;3(10):1871-78
17922568
Am J Physiol Heart Circ Physiol. 2000 Jul;279(1):H397-421
10899081
Biophys J. 2004 Nov;87(5):3351-71
15347581
Nat Rev Neurosci. 2006 Jul;7(7):563-74
16791145
Circ Res. 1994 Jun;74(6):1071-96
7514509
PLoS Comput Biol. 2008 Jan;4(1):e11
18208320
J Mol Cell Cardiol. 2001 May;33(5):851-72
11343410
Science. 1999 Jan 15;283(5400):381-7
9888852
Biophys J. 1998 Mar;74(3):1149-68
9512016
Prog Biophys Mol Biol. 2004 Jun-Jul;85(2-3):407-31
15142755
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Aug;68(2 Pt 1):021904
14525003
N Engl J Med. 2004 Mar 4;350(10):1013-22
14999113
Biotechnol J. 2008 May;3(5):639-47
18246569
Biophys J. 2009 Feb 18;96(4):1264-74
19217846
Am J Physiol Heart Circ Physiol. 2009 Oct;297(4):H1436-45
19648254
Circ Res. 1998 Jan 9-23;82(1):63-81
9440706
J Mol Cell Cardiol. 2008 Sep;45(3):420-8
18639555
J Gen Physiol. 1990 Jul;96(1):195-215
2170562
J Cell Sci. 1993 Dec;106 ( Pt 4):1153-68
8126097
Nature. 2006 Mar 23;440(7083):463-9
16554806
Circ Res. 1995 Jul;77(1):140-52
7788872
Am J Physiol Heart Circ Physiol. 2002 Jun;282(6):H2296-308
12003840
Prog Biophys Mol Biol. 2008 Jun-Jul;97(2-3):332-47
18395246
Front Neurosci. 2007 Oct 15;1(1):7-18
18982116
PLoS Comput Biol. 2006 Jul 21;2(7):e94
16848639
J Neurophysiol. 2003 Dec;90(6):3998-4015
12944532
J Neurosci. 2009 Apr 29;29(17):5573-86
19403824
J Physiol. 1952 Aug;117(4):500-44
12991237
Am J Physiol Heart Circ Physiol. 2002 Nov;283(5):H2074-101
12384487
Circ Res. 2006 May 26;98(10):1244-53
16728670
Biophys J. 1978 Jul;23(1):147-52
667303
J Physiol. 2009 Mar 15;587(Pt 6):1293-9
19153162
Biophys J. 2005 Dec;89(6):4096-110
16169970