One obvious issue is the small sample sizes that are typical of most studies. In a typical experiment performed by an electrophysiologist in the laboratory, it is quite difficult to treat variability in a rigorous manner. We wish to emphasize, however, that the strategies we advocate for understanding variability are potentially applicable in diverse fields.
Since our particular expertise is in cardiac electrophysiology, most of the examples we discuss are from studies in this area. The primary message of this review is that newly developed methods for analysing mathematical models can help to understand and predict the mechanisms underlying such functional variability. Muscle fibres will have different contraction strengths, neurons of the same type will exhibit different firing patterns, pancreatic β-cells will secrete differing amounts of insulin in response to the same glucose stimulus. Investigators in all fields of physiology, or indeed biological sciences more generally, must confront the fact that different experimental samples will demonstrate variable function. This variability can be substantial even within a population that would be considered normal or healthy, and it can become significantly more pronounced when a mixed population of healthy and diseased individuals is considered. 1991) (3) at the organ level where there is a range of normal heart rates, ECG metrics and cardiac outputs ( Taylor & Lipsitz, 1997) and finally (4) at the organismal level where administration of the same therapy can produce dramatically different outcomes in different individuals ( Kannankeril et al. 2007) (2) at the cellular level in the form of variable action potential waveforms ( Antzelevitch et al. When we consider the electrophysiology of the heart, this variability may manifest itself: (1) at the molecular level as differential expression of membrane ion channels ( Gaborit et al. Variability between members of the same species runs across different levels of organization. These strategies may be applicable not just in cardiac electrophysiology, but in a wide range of disciplines. 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.
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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. 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. 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. 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. 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. Abstract 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.
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