Molecular signaling observer and predictor: A framework for closed-loop control of cell behaviors having long time delay

Stable in vitro feedback control of cell behaviors using an observer to predict a cell´s future response to input cues based on real-time measurement of intracellular signaling molecules is presented. Biological cells, particularly mammalian cells, have a long latency time from receiving cues to producing output responses. Numerous steps of intracellular signal transductions are involved between cues and responses. This slow dynamics is a major obstacle for close-loop control based on measurement of the output response. This paper presents a promising approach to coping with the slow dynamics and forming a stable feedback loop. A molecular signaling observer and predictor is designed for estimating the intracellular state and predict the cell´s future response so that input cues can be accommodated proactively before observing the output response. First, a brief background description on relevant cell biology and in vitro micro-fluidics is provided, followed by the basic concept of molecular signaling observer and predictor. Cue-signal response processes are modeled as a time-delay system with noise dynamics. A k-step ahead predictor is obtained as a conditional mean, and a closed-loop control system is formed based on the future error of the predicted output response. Prediction error and its effect on control performance are analyzed. The method is applied to angiogenic endothelial cell sprouting and migration process. Numerical examples demonstrate the effectiveness of the method.