The main framework analysis for the most part of biological dynamics remains the theory of ordinary differential equations (ODEs). However, ODEs present some intrinsic limitations in the evaluation of the kinetic reaction rates. In contrast to ODEs, Metabolic P systems (MP systems), based on Pǎun's P systems, were introduced for modelling metabolic systems by means of suitable multiset rewriting grammars. In this work three applications of MP systems are presented, for discovering the internal regulation logic of three phenomena relevant in systems biology: i) the Goldbeter's mitotic oscillator; ii) the glucose/insulin dynamics in the Intravenous Glucose Tolerance Test; iii) the HER-2 oncogene-regulated transcriptome in human SUM-225 cells. Despite the differences between the considered phenomena, 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.
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