(184a) 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 that the strength and duration of signaling through a critical set of those pathways dictate the degree to which EMT occurs. Based on this conceptual model, we are developing a mathematical model of EMT in response to extracellular stimuli (EMT agonists) in human pancreas cancer cells wherein EMT regulation is formulated as a model-based control problem. By solving the control problem, we seek to predict optimal schedules of EMT agonist treatments that minimize overall doses while still achieving near-complete EMT.

To model the overall ligand-signal-phenotype system, we decomposed it into two subsystems in series: (i) a "signal response" subsystem (f₁), with ligand concentrations as inputs, and the relative abundances of downstream signaling molecules (e.g., phosphorylated ERK, STAT3) as responses, and (ii) a "phenotype response" subsystem (f₂) in which the signaling molecule abundances from f₁ serve as the inputs and EMT-related phenotypes (e.g., E-cadherin or vimentin expression) serve as responses. This natural decomposition facilitates modeling the overall system as a convolution of the two subsystems.

In this presentation, we will discuss our results on the identification of the ligand-signal-phenotype system and the solution of the control problem. Subsystem f₁ is represented with a non-linear dynamical systems model, 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 single-ligand inputs (EGF, HGF, and TGFβ) and two ligand combinations (EGF+TGFβ and HGF+TGFβ). The non-linear model structure allows us to capture the variations in signaling dynamics at different ligand input levels. Subsystem f₂ is represented with a partial least-squares regression (PLSR) model that predicts the phenotypic EMT response based on the dynamic signaling profiles. Even though the responses of more than 30 distinct species of signaling proteins are measured, PLSR models based only on three signaling proteins were selected to keep the number of parameters in the resulting model manageable. The selection was performed in two steps. First, every possible combination of three species was used to create a unique f₁and f₂. The signal combinations forming a pareto frontier based on the goodness of fit of f₁and f₂were chosen for further analysis. These combinations were further pruned based on their ease of pharmacological inhibition, motivated by an anticipated desire to experimentally test the model.

To implement our proposed approach for solving for optimized ligand trajectories (i.e., determine the minimal ligand dosing schedule that would lead to the phenotype of EMT induction), we solved the model-based optimal control problem using f₁ and f₂. This multi-objective optimization problem was formulated with a primary objective to minimize the total (time-integrated) dosage of ligands and a secondary objective to avoid overlapping dosing schedules (ideally, one ligand added at a time), with the desired EMT phenotype response as a constraint. The resulting non-linear programming problem was formulated and 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. We anticipate that future implementations of this modeling approach will be used to understand how best to schedule combinations of therapeutics that antagonize EMT with minimal dose-related toxicities.