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

Epithelial-Mesenchymal plasticity (EMP) is a key arm of cancer metastasis and is observed across many contexts. Cells undergoing EMP can reversibly switch between three classes of phenotypes: Epithelial (E), Mesenchymal (M), and Hybrid E/M. While a large number of multistable regulatory networks have been identified to be driving EMP in various contexts, the exact mechanisms and design principles that enable robustness in driving EMP across contexts are not yet fully understood. Here we investigated dynamic and structural robustness in EMP networks with regards to phenotypic distribution and plasticity. We use two different approaches to simulate these networks: a computationally inexpensive, parameter-independent continuous state space boolean 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 EMP networks are structurally and dynamically more robust as compared to their randomized counterparts, thereby highlighting their topological hallmarks. These features of robustness are governed by a balance 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 EMP networks. Significance StatementEpithelial-Mesenchymal plasticity (EMP) is a key arm of cancer metastasis. Despite extensive intra- and inter-tumor heterogeneity, the characteristics of EMP have been observed to be robust across multiple contexts. We hypothesize that topology of EMP regulatory networks contributes towards this robustness. Here, we measure the robustness of EMP in the form of its phenotypic heterogeneity and multistability and show that EMP networks are more robust to dynamical (change in kinetic parameters) and structural (change in network topology) perturbations as compared to their random network counterparts. Furthermore, we propose a network topology-based metric using the nature and length of feedback loops that explains the observed robustness. Our metric hence serves to quantify robustness in multistable EMP networks without simulating their dynamics.