Reduced-Order Cue-Signal-Response Modeling for Angiogenic Cell Migration Control: A Principal Signal Approach

A cell’s behavior in response to stimuli is governed by a signaling network, called cue-signal-response. Endothelial Cells (ECs), for example, migrate towards the source of chemo-attractants by detecting cues (chemo-attractants and their concentration gradient), feeding them into an intra-cellular signaling network (coded internal state), and producing a response (migration). It is known that the cue-signal-response process is a nonlinear, dynamical system with high dimensionality and stochasticity. This paper presents a system dynamics approach to modeling the cue-signal-response process for the purpose of manipulating and guiding the cell behavior through feedback control. A Hammerstein type model is constructed by representing the entire process in two stages. One is the cue-to-signal process represented as a nonlinear feedforward map, and the other is the signal-to-response process as a stochastic linear dynamical system, which contains feedback loops and auto-regressive dynamics. Analysis of the signaling space based on Singular-Value Decomposition yields a set of reduced order synthetic signals, which are used as inputs to the dynamical system. A prediction-error method is used for identifying the model from experimental data, and an optimal system order is determined based on Akaike’s Information Criterion. The resultant low order model is capable of predicting the expected response to cues, and is directly usable for feedback control. The method is applied to an in vitro angiogenic process using microfluidic devices.