Heterogeneity in cancer dynamics: A convex formulation to dissect dynamic trajectories and infer LTV models of networked systems

Breast cancer tumors have inherently heterogeneous cell types that respond differently to treatments. Although there is a wealth of studies describing canonical cell signaling networks, little is known about how these networks operate in different cancer cells and treatments. This paper proposes a method to split a set of responses gathered from experiments on different cancer cells up into common and specific components. The key to this retrieval is the derivation of a linear timevarying model of the shared dynamics among the different cell lines. A convex optimization problem is derived that retrieves both the model and the common and specific responses without a priori information. The method is tested on synthetic data, and verifies known facts when tested on a biological data set with protein expression data from breast cancer experiments. The technique can be used to analyze specific responses to understand what treatments can be combined to persistently treat a heterogeneous cancer tumor. The linear time-varying model sheds light on how proteins interact over time.