A robust controller of dynamic networks and its verification by the simulation of the heat shock response network with reliable signal transmission

In this paper, a class of dynamic networks that widely exist in nature, such as signaling networks in cells, is modeled as a controller, in which the quantitative relation among principal factors is explicitly given. A reduction method with respect to the controller is proposed to transform a dynamic network into a minimum controller with only two variables and two units: a feedforward unit and a feedback unit. Here the feedforward unit is formulated as a combination of exponential functions, and the feedback unit as a polynomial function. The features of the robust controller on the aspects of non-smoothness and computational complexity are discussed. As an example to demonstrate the feasibility of the controller designed by the method proposed in this paper, the heat shock response (HSR) network of E. coli is simulated for its robustness to testify the effectiveness of the controller. The simulation result of the transmission process of the HSR network suggests that the designed controller is an efficient CAD (computer-aided design) tool for developing molecular communication systems using cells in vivo.