Identifiability of Nonlinear Biological Models

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DESCRIPTION (provided by applicant): Mathematical models of biological systems are essential to the quantitative understanding of physiological and pathophysiological mechanisms in humans and animals. Physiologically plausible models, the structure of which reflect available knowledge and assumptions about the systems, are usually nonlinear and characterized by a large number of unknown parameters. Examples of such models are enzyme kinetics and pharmacokinetic-pharmacodynamic models. Before performing an experiment to estimate these unknown parameters from the data, the following question arises: will the data we are about to collect (usually at a substantial expense) contain enough information to precisely and unequivocally estimate (for example, via least squares or maximum likelihood) all the unknown parameters of the postulated model? This question, set in the (theoretical) context of an error-free model structure and noise-free data, is usually referred to as the a priori global identifiability problem. Despite its theoretical nature, it is an essential, but often overlooked, prerequisite for model parameter estimation from real data. The solution of the identifiability problem is however in general very difficult, since one needs to solve a system of nonlinear algebraic equations which is increasing in number of terms and nonlinearity degree with the model order. The specific aims of this application focus on the development of an algorithm and a software tool to test a priori global identifiability of nonlinear compartmental models, a very inclusive class of ordinary nonlinear differential equation models based on conservation of mass. These models are widely used to study the kinetics of endogenous (e.g. substrates, hormones, enzymes) and exogenous (e.g., drugs, radiotracers) substances in living systems. The problem has been solved for a very limited set of models, but no solution exists in the general case. We will develop an algorithm based on computer algebra which allows to decrease the system complexity, thus providing the number of solutions for each parameter of the model. The software we propose to develop will be based on the client-server architecture paradigm, and will be open source, user-friendly and platform-independent. Such a tool would be very useful in experiment design. The software will also help in defining minimal input-output experimental configurations to assure a priori global identifiability: this is particularly important in clinical studies where severe constraints exist on experiment design, i.e. the number of inputs and outputs is limited for ethical and practical reasons.