Model-based control of epithelial-mesenchymal transition through signaling regulation in pancreas cancer cells

Introduction::
The properly coordinated activation of specific signaling pathways over time in response to agonists is required to drive cell phenotypes efficiently. Identifying the rules for such coordination would enable the optimized induction or antagonism of phenotypes with minimal system input, but methods to decode these complex multivariate biological control problems do not exist. We addressed this issue for signaling control of the epithelial–mesenchymal transition (EMT), a cell developmental program that occurs aberrantly in carcinomas to promote chemoresistance. We hypothesize that the diverse growth factors that drive EMT operate primarily through a critical set of conserved kinase-regulated signaling pathways and that the strength and duration of those pathways dictate EMT response. Here, we describe the development of a systems engineering mathematical model of pancreas cancer cell EMT in response to different growth factor agonists and an experimentally validated model-based control framework to predict optimal schedules of EMT agonists that minimize overall doses while achieving near-complete EMT.




Materials and Methods:: Computational model: We modeled the overall growth factor–signal–phenotype system as 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 signaling molecule abundances from f₁ serve as inputs and EMT-related phenotypes (E-cadherin and vimentin expression) serve as responses. Subsystem f₁ is represented with a non-linear dynamical systems model, having terms describing input-driven signal augmentation, endogenous negative feedback, and signal decay. Model parameters are estimated from the response of a set of measurable signaling proteins to changes in three growth factor inputs (EGF, HGF, and TGFβ1) and their combinations. Subsystem f₂ is represented with a partial least-squares regression (PLSR) model that predicts phenotypic EMT responses based on dynamic signaling profiles.

Experiments: HPAF-II human pancreas cancer cells were maintained in RPMI medium supplemented with 10% fetal bovine serum, 1 mM L-glutamine, 100 units/mL penicillin, and 100 μg/mL streptomycin. Recombinant human EGF, HGF, and TGFβ1 were used at 50 ng/mL, 50 ng/mL, and 10 ng/mL, respectively. Lysates were prepared at six time points and analyzed by Luminex primarily for phosphorylated proteins. E-cadherin and vimentin expression were measured 48 hr after ligand treatments by immunofluorescence microscopy with quantitative image analysis using custom CellProfiler pipelines. In ligand switching experiments to test the process optimization predictions, cells were washed with PBS before adding ligand-supplemented medium.

Results, Conclusions, and Discussions:: We developed a mathematical model of ligand-driven EMT and used it to solve an open-loop control problem where the objective was to maximize EMT while minimizing overall ligand dosage. Model training was successful, with f₁ root mean square errors less than 30% for training and validation steps, f₁ models exhibiting asymptotic stability, and f₂ goodness of prediction Q²Y ≥ 0.7 for all versions of the model selected. Here, version refers to a model built with a subset of signaling molecules; we developed all possible three-signal model versions and selected an ensemble of the best subject to the aforementioned criteria. To test the model’s utility for control predictions, we focused on EGF and TGFβ1 because they drive similar levels of HPAF-II EMT and cooperate synergistically. Optimization problems were formulated and solved using a global solver to determine how to maximize EMT subject to the constraints that only one ligand could be used at a time (to reduce overall dosage) and that only one ligand switch could be made. The model predicted that dosing first with TGFβ for 3.25 hr followed by EGF up to 48 hr maximizes EMT within model constraints. The EMT predicted for that ligand trajectory is notably greater than for the converse trajectory of EGF for 3.25 hr followed by TGFβ and approaches the predicted limiting behavior of EMT induction for continual dosing of both ligands to within 20%. Experimental tests validated model predictions, demonstrating, for example, that the fraction of vimentin-positive cells observed at 48 hr was similar for the optimal ligand trajectory and for continual dosing of both ligands (Figure 1).

This work provides a new paradigm for developing quantitative predictions for how multivariate signaling processes regulate complex cell phenotypes by integrating data-driven modeling approaches with dynamic control system models. This approach provides a framework for deploying the model in reverse to determine how to manipulate process inputs optimally to achieve desired phenotypic responses. Future implementations of our EMT modeling approach will be used to predict how best to schedule combinations of small molecule drugs that antagonize EMT to promote PDAC chemoresponse with minimal dose-related toxicities.


Acknowledgements (Optional): : This work is supported by the National Cancer Institute, Cancer Systems Biology Consortium, Grant number: NCI U01 CA243007, PI: Matthew Lazzara

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