Multiple Model-Informed Open-Loop Control of Uncertain Intracellular Signaling Dynamics

Computational approaches to tune the activation of intracellular signal transduction pathways both predictably and selectively will enable researchers to explore and interrogate cell biology with unprecedented precision. Techniques to control complex nonlinear systems typically involve the application of control theory to a descriptive mathematical model. For cellular processes, however, measurement assays tend to be too time consuming for real-time feedback control and models offer rough approximations of the biological reality, thus limiting their utility when considered in isolation. We overcome these problems by combining nonlinear model predictive control with a novel adaptive weighting algorithm that blends predictions from multiple models to derive a compromise open-loop control sequence. The proposed strategy uses weight maps to inform the controller of the tendency for models to differ in their ability to accurately reproduce the system dynamics under different experimental perturbations (i.e. control inputs). These maps, which characterize the changing model likelihoods over the admissible control input space, are constructed using preexisting experimental data and used to produce a model-based open-loop control framework. In effect, the proposed method designs a sequence of control inputs that force the signaling dynamics along a predefined temporal response without measurement feedback while mitigating the effects of model uncertainty. We demonstrate this technique on the well-known Erk/MAPK signaling pathway in T cells. In silico assessment demonstrates that this approach successfully reduces target tracking error by 52% or better when compared with single model-based controllers and non-adaptive multiple model-based controllers. In vitro implementation of the proposed approach in Jurkat cells confirms a 63% reduction in tracking error when compared with the best of the single-model controllers. This study provides an experimentally-corroborated control methodology that utilizes the knowledge encoded within multiple mathematical models of intracellular signaling to design control inputs that effectively direct cell behavior in open-loop.Author Summary: Most cell behavior arises as a response to external forces. Signals from the extracellular environment are passed to the cell's nucleus through a complex network of interacting proteins. Perturbing these pathways can change the strength or outcome of the signals, which could be used to treat or prevent a pathological response. While manipulating these networks can be achieved using a variety of methods, the ability to do so predictably over time would provide an unprecedented level of control over cell behavior and could lead to new therapeutic design and research tools in medicine and systems biology. Hence, we propose a practical computational framework to aid in the design of experimental perturbations to force cell signaling dynamics to follow a predefined response. Our approach represents a novel merger of model-based control and information theory to blend the predictions from multiple mathematical models into a meaningful compromise solution. We verify through simulation and experimentation that this solution produces excellent agreement between the cell readouts and several predefined trajectories, even in the presence of significant modeling uncertainty and without measurement feedback. By combining elements of information and control theory, our approach will help advance the best practices in model-based control applications for medicine.