UCLA

Ordinary differential equation (ODE) models are often used to quantitatively describe and predict the dynamic responses of biological and other systems. Models with many parameters, limited measurement data and in need of quantification are typically unidentifiable from available input/output data. Even models that are structurally identifiable can be difficult to quantify in practice from limited data. For overparameterized models (OPMs), it is often helpful to simplify the model, by rationally reducing the dimensionality of the parameter space. This is done by finding a set of "key parameters" to estimate, a subset that best represents the dominant model dynamic responses. OPMs are often characterized by pairwise parameter correlations close to 1 in magnitude and at least some unacceptably large parameter estimation variances. The goal is to get the best fit possible with a smaller number of parameters, each with acceptable variances. Several published methods for selecting the key parameter subset are based on parameter sensitivity analysis and/or analysis of the parameter covariance matrix estimated from the input/output data.

We apply a combination of these methods to an overparameterized candidate model of tumor suppressor protein p53. The model comprises of 4 ODEs, 23 unknown parameters, and noisy output measurements of the 4 state variables and the input. Three least sensitive and highly correlated parameters were isolated from the analysis and fixed to nominal values. This reduced the parameter search space and yielded substantially improved numerical identifiability properties for the resulting simplified model which fitted the data equally well, using both global and local search algorithms.