Parameter Uncertainty Analysis of a Mathematical Ion Channel Model

In mathematical modeling of cell physiological processes, measurements required for parameter determination are often available only as aggregated data in the literature. Physiological measurements contain relatively large observation errors due to intrinsic variations in physiological processes, and the errors cause uncertainties in parameter values. This paper reports analyses of the uncertainty in parameter estimates of a simple mathematical model of an ion channel from a set of published experimental data. A conventional approach for estimating model parameters from aggregated data is applying the method of least squares to a series of the mean values of measurements. The parameter estimates by the conventional method significantly differed from those by a statistical approach, maximum likelihood estimation considering the standard errors of the means. Exhaustive analyses on the likelihood of parameter values show high parameter uncertainties and wide distribution of parameter values with no significant differences in the likelihood. These results imply the importance of considering variances of observations and uncertainties in parameter estimates.