A Case for Using Signal Transition Graphs for Analysing and Refining Genetic Networks

In order to understand and analyse genetic regulatory networks (GRNs), the complex control structures which regulate cellular systems, well supported qualitative formal modelling techniques are required. In this paper, we make a case that biological systems can be qualitatively modelled by speed-independent circuits. We apply techniques from asynchronous circuit design, based on Signal Transition Graphs (STGs), to modelling, visualising and analysing GRNs. STGs are a Petri net based model that has been extensively used in asynchronous circuit design. We investigate how the sufficient conditions ensuring that an STG can be implemented by a speed-independent circuit can be interpreted in the context of GRNs. We observe that these properties provide important insights into a model and highlight areas which need to be refined. Thus, STGs provide a well supported formal framework for GRNs that allows realistic models to be incrementally developed and analysed. We demonstrate the proposed STG approach with a case study of constructing and analysing a speed-independent circuit specification for the lysis-lysogeny switch in phage λ.