Verification of multistability in gene regulation networks: A combinatorial approach

Bi- or even multistable behavior is a recurrent phenomenon in gene regulation networks. These networks have the capacity to operate in two or more distinct modes in a stable manner. In this work, we consider gene regulation networks with known interaction structure but unknown reaction kinetics. Additionally, it is assumed that several distinct operation modes were observed experimentally whereby also the measurements of the individual protein concentrations are uncertain. For this setup, the important question of model validation is addressed: Can the given network structure in principle reproduce the observed operation modes? To approach this problem, the work builds on an existing modeling framework which is appropriate to deal with uncertain gene regulation networks. By regarding each operation mode as a forward-invariant set in the state space and with the notion of compatible intervals, it is shown how the validation problem can be translated into a combinatorial one. An algorithm is developed which can efficiently solve the new problem. Finally, the well-known bistable lactose utilization network is analyzed with this new method.