A Theory of Decomposition of Complex Chemical Networks using the Hill   Functions
  The design and synthesis of complex and large mimicked biochemical networks de novo is an unsolved problem in synthetic biology. To address this limitation without resorting to ad hoc computations and experiments, a predictive mathematical theory is required to reduce these complex chemical networks into natural physico-chemical expressions. Here we provide a theory that offers a physico-chemical expression for a large chemical network that is almost arbitrarily both nonlinear and complex. Unexpectedly, the theory demonstrates that such networks can be decomposed into reactions based solely on the Hill equation, a simple chemical logic gate. This theory, analogous to implemented electrical logic gates or functional algorithms in a computer, is proposed for implementing regulated sequences of functional chemical reactions, such as mimicked genes, transcriptional regulation, signal transduction, protein interaction, and metabolic networks, into an artificial designed chemical network. 
Eisuke Chikayama and R. Craig Everroad
physics.bio-ph q-bio.MN