An algebraic approach to challenges on identification problems in systems biology (Recent developments on inverse problems for partial differential equations and their applications)

Abstract

This paper is twofold. A challenge appearing in identification problems, in particular unidentifiability problems in parameter estimations, in the field of systems biology is introduced with an example of PBPK models in the first section. In the second section, an algebraic and algebro-geometric approach to the challenge in a wider context is explained. More precisely, a method to extract a geometric structure that is uniquely determined by observed time series data and unidentifiable state-space models as an algebraic variety is introduced. Our method is based on differential algebra. An application of the proposed method for analysis of viral dynamics during therapy is briefly described.