Interplay of positive and negative feedback loops governs robustness in multistable biological networks

Biological networks are widely reported to be robust to both external and internal perturbations. However, the exact mechanisms and design principles that enable robustness are not yet fully understood. Here we investigated dynamic and structural robustness in biological networks with regards to phenotypic distribution and plasticity. We use two different approaches to simulate these networks: a computationally inexpensive, parameter-independent continuous model, and an ODE-based parameter-agnostic framework (RACIPE), both of which yield similar phenotypic distributions. Using perturbations to network topology and by varying network parameters, we show that multistable biological networks are structurally and dynamically more robust as compared to their randomized counterparts. These features of robustness are governed by an interplay of positive and negative feedback loops embedded in these networks. Using a combination of the number of negative and positive feedback loops weighted by their lengths and sign, we identified a metric that can explain the structural and dynamical robustness of these networks. This metric enabled us to compare networks across multiple sizes, and the network principles thus obtained can be used to identify fragilities in large networks without simulating their dynamics. Our analysis highlights a network topology based approach to quantify robustness in multistable biological networks.