A computational method to preclude multistationarity in networks of interacting species

Modeling and analysis of complex systems are important aspects of understanding systemic behavior. In the lack of detailed knowledge about a system, we often choose modeling equations out of convenience and search the (high-dimensional) parameter space randomly to learn about model properties. Qualitative modeling sidesteps the issue of choosing specific modeling equations and frees the inference from specific properties of the equations. We consider classes of ordinary differential equation (ODE) models arising from interactions of species/entities, such as (bio)chemical reaction networks or ecosystems. A class is defined by imposing mild assumptions on the interaction rates. In this framework, we investigate whether there can be multiple positive steady states in some ODE models in a given class.

We have developed and implemented a method to decide whether any ODE model in a given class cannot have multiple steady states. The method runs efficiently on models of moderate size. We tested the method on a large set of models for gene silencing by sRNA interference and on two publicly available databases of biological models, KEGG and Biomodels. We recommend that this method is used as (i) a pre-screening step for selecting an appropriate model and (ii) for investigating the robustness of non-existence of multiple steady state for a given ODE model with respect to variation in interaction rates.

Scripts and examples in Maple are available in the Supplementary Information.

wiuf@math.ku.dk

Supplementary data are available at Bioinformatics online.