Modelling Signalling Networks with Incomplete Information about Protein Activation States: A P System Framework of the KaiABC Oscillator

Abstract

Reconstruction of signal transduction network models based on incomplete information about network structure and dynamical behaviour is a major challenge in current systems biology. In particular, interactions within signalling networks are frequently characterised by partially unknown protein phosphorylation and dephosphorylation cascades at a submolecular description level. For prediction of promising network candidates, reverse engineering techniques typically enumerate the reaction search space. Considering an underlying amount of phosphorylation sites, this implies a potentially exponential number of individual reactions in conjunction with corresponding protein activation states. To manage the computational complexity, we extend P systems with string-objects by a subclass for protein representation able to process wild-carded together with specific information about protein binding domains and their ligands. This variety of reactants works together with assigned term-rewriting mechanisms derived from discretised reaction kinetics. We exemplify the descriptional capability and flexibility of the framework by discussing model candidates for the circadian clock formed by the KaiABC oscillator found in the cyanobacterium Synechococcus elongatus. A simulation study of its dynamical behaviour demonstrates effects of superpositioned protein abundance courses based on regular expressions corresponding to dedicated protein activation states.