Integrated Graph Propagation and Optimization with Biological Applications.

Mathematical models that utilize network representations have proven to be valuable tools for investigating biological systems. Often dynamic models are not feasible due to their complex functional forms that rely on unknown rate parameters. Network propagation has been shown to accurately capture the sensitivity of nodes to changes in other nodes; without the need for dynamic systems and parameter estimation. Node sensitivity measures rely solely on network structure and encode a sensitivity matrix that serves as a good approximation to the Jacobian matrix. The use of a propagation-based sensitivity matrix as a Jacobian has important implications for network optimization. This work develops Integrated Graph Propagation and OptimizatioN (IGPON), which aims to identify optimal perturbation patterns that can drive networks to desired target states. IGPON embeds propagation into an objective function that aims to minimize the distance between a current observed state and a target state. Optimization is performed using Broyden's method with the propagationbased sensitivity matrix as the Jacobian. IGPON is applied to simulated random networks, DREAM4 in silico networks, and over-represented pathways from STAT6 knockout data and YBX1 knockdown data. Results demonstrate that IGPON is an effective way to optimize directed and undirected networks that are robust to uncertainty in the network structure.