On sustaining robustness of molecular pathway circuits of the HSR network of E. coli under spatial configuration

In systems biology, the robustness of molecular circuits has been intensively studied. Especially, the temporal dynamics mechanism of robust molecular circuits has been verified by experimental evidences. But its spatial dynamics mechanism is still an open problem yet. To solve this problem, it is necessary to introduce the communication channel into the dynamics model based on the spatial configuration of molecular circuits. In this paper, we study how the robustness of molecular circuits constructed by signaling pathways is sustained. The information-theoretic model called network coding is presented to formalize the molecular pathway circuits to introduce the channel unit into the controller of the signaling pathway, which is a networked control system (NCS). By using the Heat Shock Response (HSR) network of the model organism E. coli as an example of robust molecular pathway circuits, we quantitatively analyze its robustness behavior under channel delay and show the robustness is sustained under the stochastic channel of intra-cellular communication. The result on the robustness of molecular circuits under the spatial configuration is significant for designing and controlling engineered molecular circuits in vivo by synthetic biological technology. It is concluded that the robustness mechanism of signaling pathway networks may contribute to the application of molecular circuits in the molecular biomedical engineering systems built by the means of synthetic biology.