Model-Based Control of Epithelial-Mesenchymal Transition through Signaling Regulation in Pancreas Cancer Cells

Epithelial-mesenchymal transition (EMT) is a normal cell developmental program that occurs aberrantly in numerous carcinomas and promotes chemoresistance. We hypothesize that various extracellular stimuli drive EMT through a conserved set of kinase-regulated signaling pathways, and the strength and duration of signaling through a critical set of those pathways dictate the degree to which EMT will occur. This allows us to develop a mathematical model of EMT in response to extracellular stimuli (EMT agonists) in human pancreas cancer cells, formulate EMT regulation as a model-based control problem, and solve the control problem to obtain the optimal schedule and dosage of combination therapies required to achieve the desired level of EMT.

To model the overall ligand-signal-phenotype system, we decompose it into two subsystems in series. (i) A “signal response” subsystem (f₁), whose inputs are the ligand concentrations, and the responses are the relative abundance of the signaling molecules, is followed by (ii) a “phenotype response” subsystem (f₂), for which the signals-the responses from f₁-serve as the stimuli which then stimulate the mesenchymal phenotypes as the response of f₂. This natural decomposition facilitates modeling the overall system as a convolution of the two subsystems, which also allows us to understand the dynamics of the intermediate signal responses.

In this presentation, we discuss our results on the identification of the ligand-signal-phenotype system and the solution of the control problem. Subsystem f₁ is represented with an autoregressive model with exogenous inputs (ARX), in which the parameters are estimated from time-series data obtained from the response of a subset of measurable signaling proteins to changes in three ligand inputs-epidermal growth factor (EGF), hepatocyte growth factor (HGF), and transforming growth factor-beta (TGF-β)-and two combinations of these-EGF+TGF-β and HGF+TGF-β. Subsystem f₂ is represented with a partial least-squares regression (PLSR) model that predicts the phenotypic EMT response (expression and localization of E-cadherin and vimentin) based on the dynamic signaling profiles. Even though the responses of more than 30 distinct species of signaling proteins are measured, to keep the number of parameters in the resulting model manageable, only three are selected for inclusion in the model. The selection is performed in two steps. First, every possible combination of three species is used to create a unique f₁ and a unique f₂. The signal combinations forming a pareto frontier based on the goodness of fit of f₁ and f₂ are chosen for further analysis. Subsequently, these combinations are pruned according to their physiological relevance (e.g., are they all practically druggable?).

As a proof-of-principle, we illustrate how to implement our proposed approach as follows: we solve a model-based optimal control problem using f₁ and f₂, i.e., determine the minimal ligand dosing schedule that would lead to the phenotype of EMT induction. This multi-objective optimization problem is formulated with a primary objective to minimize the total dosage of ligands and a secondary objective to avoid overlapping dosing schedules (ideally, one ligand is added at a time), with the desired EMT phenotype response as a constraint. The resulting mixed-integer linear program is solved using MATLAB.

The results of this study provide a new set of experimentally testable hypotheses on the time-dependent effects of exogenous ligands on a key set of intracellular signaling pathways and, subsequently, the effects of these signals on EMT. They also provide a new paradigm for developing a predictive understanding of how multivariate signaling processes control complex cell phenotypes by integrating data-driven modeling approaches such as PLSR with dynamic control system models. The primary benefit of such a paradigm is that it provides a quantitative, model-based framework for using the indicated predictive understanding, in reverse, to determine how best to manipulate the signaling processes to achieve desired phenotypic responses optimally.