Pharmacology and Systems Therapeutics, Mount Sinai School of Medicine, New York, NY 10029, USA.
J Physiol. 2012 Jun 1;590(11):2555-67. doi: 10.1113/jphysiol.2011.223313. Epub 2012 Apr 10.
Across individuals within a population, several levels of variability are observed, from the differential expression of ion channels at the molecular level, to the various action potential morphologies observed at the cellular level, to divergent responses to drugs at the organismal level. However, the limited ability of experiments to probe complex interactions between components has hitherto hindered our understanding of the factors that cause a range of behaviours within a population. Variability is a challenging issue that is encountered in all physiological disciplines, but recent work suggests that novel methods for analysing mathematical models can assist in illuminating its causes. In this review, we discuss mathematical modelling studies in cardiac electrophysiology and neuroscience that have enhanced our understanding of variability in a number of key areas. Specifically, we discuss parameter sensitivity analysis techniques that may be applied to generate quantitative predictions based on considering behaviours within a population of models, thereby providing novel insight into variability. Our discussion focuses on four issues that have benefited from the utilization of these methods: (1) the comparison of different electrophysiological models of cardiac myocytes, (2) the determination of the individual contributions of different molecular changes in complex disease phenotypes, (3) the identification of the factors responsible for the variable response to drugs, and (4) the constraining of free parameters in electrophysiological models of heart cells. Together, the studies that we discuss suggest that rigorous analyses of mathematical models can generate quantitative predictions regarding how molecular-level variations contribute to functional differences between experimental samples. These strategies may be applicable not just in cardiac electrophysiology, but in a wide range of disciplines.
在人群中的个体中，观察到了几个层次的可变性，从分子水平上离子通道的差异表达，到细胞水平上观察到的各种动作电位形态，再到生物体水平上对药物的不同反应。然而，实验探测复杂相互作用的能力有限，迄今为止一直阻碍着我们对导致人群中一系列行为的因素的理解。变异性是一个具有挑战性的问题，在所有生理学科中都存在，但最近的工作表明，分析数学模型的新方法可以帮助阐明其原因。在这篇综述中，我们讨论了心脏电生理学和神经科学中的数学建模研究，这些研究增强了我们对许多关键领域变异性的理解。具体来说，我们讨论了参数敏感性分析技术，这些技术可以应用于根据模型群体内的行为生成定量预测，从而为变异性提供新的见解。我们的讨论集中在四个受益于这些方法的利用的问题上：（1）比较不同的心肌细胞电生理模型，（2）确定复杂疾病表型中不同分子变化的个体贡献，（3）确定导致药物反应可变性的因素，以及（4）限制心脏细胞电生理模型中的自由参数。我们讨论的研究表明，对数学模型的严格分析可以产生关于分子水平变化如何导致实验样本之间功能差异的定量预测。这些策略不仅可以应用于心脏电生理学，还可以应用于广泛的学科。
