MP Representations of Biological Structures and Dynamics

The main theme of this Ph.D. thesis is focused on the solution of dynamical inverse problems in the context of Metabolic P systems (MP systems). Metabolic P systems, based on Paun's P systems, were introduced by Manca in 2004 for modelling metabolic systems by means of suitable multiset rewriting grammars. In such kind of grammars, multiset transformations are regulated, in a deterministic way, by particular functions called regulators. The key result presented in the thesis is the definition of a regression algorithm, called LGSS (Log-gain Stoichiometric Stepwise regression), which provides a complete statistical regression framework for dealing with inverse dynamical problems in the MP context. In particular, LGSS derives MP models from the time series of observed dynamics by combining and extending the log-gain principle, developed in the MP system theory, with the classical method of Stepwise Regression, which is a statistical regression technique based on least squares approximation and statistical F-tests. In the last part of the thesis, three applications of MP systems are also presented for discovering, by means of LGSS, the internal regulation logic of phenomena relevant in systems biology. Despite the differences between the considered phenomena, which comprise both metabolic and gene regulatory processes, in all the cases a model was found that exhibits good approximation of the observed time series and highlights results which are new or that have been only theorized before.