The design of chemical reaction networks (CRNs) that couple to systems that phase separate is a promising avenue towards the realization of functional materials capable of displaying controlled non-equilibrium behaviors. However, how a particular CRN would affect the behaviors of a phase separating system is difficult to fully predict theoretically. In this paper, we analyze a mean field theory coupling CRNs to phase separating materials and expound on how the properties of the CRNs affect different classes of non-equilibrium behaviors. We examine the problem of achieving control over the size of phase separated condensates, by first considering tractable problems and illustrating the mathematical conditions leading to small wavelength instability. We then identify CRN motifs that are likely to yield size control by examining randomly generated networks and parameters. By analyzing the probabilities to observe particular states, we define simple design rules of CRNs that lead to desired non-equilibrium behavior. For example, we show that chemical interactions generating negative feedback facilitate size control, and that, similarly, chemical interactions should have effects counteracting those introduced by spatial interactions. We also adapt our mean field approach to the emergence of temporally oscillating patterns. Our results provide guidance toward the design of self-regulating material CRNs provide instructions to manage the formation, dissolution, and organization of compartments. arXiv preprint: arXiv:2207.10135, joint work with Dr. Dino Osmanovic.
Elisa Franco is an Associate Professor in Mechanical & Aerospace Engineering and Bioengieering at UCLA.
She holds a Ph.D. in Control and Dynamical Systems from the California Institute of Technology, and a Ph.D. in Automation from the University of Trieste, Italy. The research of the Franco group is in the areas of biological feedback and DNA/RNA nanotechnology, with focus on design, modeling, and synthesis of circuits and responsive materials using nucleic acids and proteins; their work is funded by the NSF, the DOE, the Sloan Foundation, and the Broad Stem Cell Research Center at UCLA. Prof. Franco received the NSF CAREER award, the Rose Hills Foundation Young Investigator award, and is a Hellman Fellow. Prof. Franco is a senior member of IEEE; she served as an associate editor with IEEE Control Systems Letters, and was an elected member of the IEEE Control Systems Society Board of Governors. She was also a council member of the Engineering Biology Research Center (EBRC).