HSM - a hybrid system based approach for modelling intracellular networks

The paper proposes a hybrid system based approach for modelling of intracellular networks and introduces a restricted subclass of hybrid systems - HSM - with an objective of still being able to provide sufficient power for the modelling of biological systems, while imposing some restrictions that facilitate analysis of systems described by such models. The use of hybrid system based models has become increasingly popular, likely due to the facts that: 1) they provide sufficiently powerful mathematical formalism to describe biological processes of interest and do it in a 'natural way' from the biological perspective; 2) there are well established mathematical techniques as well as supporting software tools for analysing such models. However often these models are very dependent on the quantitative parameters of the system (concentrations of proteins, their growth functions etc.) that are seldom exactly known, instead of more limited information of the system that can be observed in practice (directions of change in concentrations, but not the exact values etc.). As a result these models may work well for simulation of the system (prediction of its state starting from some initial conditions), but are too complicated for prediction of all possible qualitatively different behaviours a modelled system might have. With HSM we try to propose a hybrid system based formalism that is still sufficiently powerful for description of biological systems, while being as restricted as possible to facilitate the analysis of the systems described. We separate between the quantitative system parameters and their qualitative values that can be observed in practice. For HSM we provide an algorithm that analyses the system without the need to know the exact parameter values. We apply our model and analysis methods to a well-studied gene network of λ-phage. The phage has two well-known qualitatively different behaviours - lysis and lysogeny. We show that our model has an attractor structure that corresponds well to these two behaviours and that these are the only stable behaviours that can be exhibited by the system. The algorithm also generates (in principle biologically verifiable) hypotheses about the mutations of λ-phage that should change its observable behaviour.