TESTING THE ROBUSTNESS OF THE STEADY-STATE CHARACTERISTICS OF A METABOLIC PATHWAY: PARAMETER SENSITIVITIES AS A BASIC FEATURE FOR MODEL VALIDATION

Abstract

Mathematical models are useful for analyzing metabolic problems. To build up these models, we need: (1) A scheme of the target system, (2) Measurements of concentrations and fluxes in steady-state, (3) The rate law of each reaction and (4) The set of differential equations that reflects the model behaviour. Usually, the rate-laws are identified from in vitro data, which could result in unrealistic models when compared with the behavior of the intact system. Hence, mathematical models must be carefully validated before one can trust their behavior. We can use different features of a biological system as a reference for validating a model. The steady-state robustness to parameter changes can be used as an index for such an evaluation. In this sense, a realistic model should reflect a fundamental property of a living system: small perturbations are compatible with system performance. We present an example of such analysis in the case of the ethanolic fermentation pathway of Saccharomyces cerevisiae. The parameter sensitivities of the model are computed in two experimental conditions and a diagnostic is made on the validity of the corresponding model. Translation of the mechanistic model into an S-system model facilitates the analysis of parameter sensitivity. After the analysis, a high parameter sensitivity suggest the need for a careful estimation of the involved parameters.