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

Abstract

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.

Resolving Early Signaling Events in T-Cell Activation Leading to IL-2 and FOXP3 Transcription

“…As the inhibitor concentrations increase, a threshold is crossed, resulting in more forceful inhibition: 10 µg/mL for sanguinarine and 1 µg/mL for U0126. The phospho-Erk simulations show good agreement with the time course and dose response observations originally reported by Perley et al [41]. Figure 5.…”

“…Appendix 1 also lists the rate equations, parameter values and summarizes the reactions primarily in terms of protein binding, phosphate group transfers and kinase and phosphatase activation. The part of the model representing the TCR-mediated Erk pathway is based on the ordinary differential equation (ODE) model developed by Zheng [40] with updates in Perley et al [41]. The Zheng model takes into account the major events of early T-cell signaling leading to the activation of the protein tyrosine kinases Zap70 and SFK, the downstream Erk pathway, as well as negative feedback regulation by phosphatase SHP1.…”

“…These reactions (R 11 -R 19 ) are modeled using the first-and second-order mass action kinetic equations of the base model presented by Zheng [40]. The kinetic parameters in this module are fitted to Erk phosphorylation data presented by Perley et al [41]. Figure 5A,B shows the changes in the Erk phosphorylation with different doses of the MKP inhibitor sanguinarine and Mek1/2 inhibitor U0126.…”

“…Samples of phospho-Erk were taken at indicated times relative to the inhibitor doses and measured via western blot. The data shown are the means and standard errors from at least three independent experiments (data source: [41]).…”

A Computational Study of the Effects of Syk Activity on B Cell Receptor Signaling Dynamics

“…Computational modeling allows us to gain insight into Syk’s impact that was not previously possible with experimentation alone. We have developed a model built on a T cell receptor (TCR) signaling model originally created by Zheng et al [ 2 ] and later expanded and used by Perley et al [ 3 ] for cellular level control. Perley’s success in using Zheng’s model for prediction and open-loop control made it an ideal candidate to adapt for our B cell study.…”