Understanding Behavior of Biological Network via Invariant Computation

Abstract

It is of practical interest to know whether a biological network contains mass-preserving and state-preserving subnetworks. In a mass-preserving subnetwork, the total mass is constant and, therefore, bounded. In any state-preserving subnetwork biochemical reactions bring the subnetwork back to a given state. For instance, any reversible reaction forms a state-preserving subnetwork. In a large intricate biological network, it is rather cumbersome task to determine mass-preserving and state-preserving subnetworks. Akt and MAPK are important pathways regulating cell proliferation, differentiation, senescence and apoptosis. In the present research, we derive information from Reactome and KEGG databases as well as from existing literature, to date, to create rather detailed Petri net model of Akt and MAPK pathways and crosstalk one pathway to another and perform their qualitative analysis with computation of P-invariants and T-invariants to determine mass-preserving and state-preserving subnetworks. We also make deductions regarding the temporal behavior of both pathway.