Moment-Independent Sensitivity Analysis of Enzyme-Catalyzed Reactions with Correlated Model Parameters

Abstract

The dynamic models used for biological and chemical process analysis and design usually include a significant number of uncertain model parameters. Sensitivity analysis is frequently applied to provide quantitative information regarding the influence of the parameters, as well as their uncertainties, on the model output. Various techniques are available in the literature to calculate parameter sensitivities based on local derivatives or changes in dedicated statistical moments of the model output. However, these methods may lead to an inevitable loss of information for a proper sensitivity analysis and are not directly available for problems with correlated model parameters. In this work, we demonstrate the use of a moment-independent sensitivity analysis concept in the presence and absence of parameter correlations and investigate the correlation effect in more detail. Moment-independent sensitivity analysis calculates parameter sensitivities based on changes in the entire probability density distribution of the model output and is formulated independently of whether the parameters are correlated or not. Technically, a single-loop Monte Carlo simulation method in combination with polynomial chaos expansion is implemented to reduce the computational cost significantly. A sampling procedure derived from Gaussian copula formalism is used to generate sample points for arbitrarily correlated uncertain parameters. The proposed concept is demonstrated with a case study of an enzyme-catalyzed reaction network. We observe evident differences in the parameter sensitivities for cases with independent and correlated model parameters.