Jianshu Cao of the Massachusetts Institute of Technology is supported by a Small Grant for Exploratory Research from the Theoretical and Computational Chemistry program for research to develop a method to decompose complex chemical reactions into irreducible schemes that provide the generic structures for a class of reactions and are invariant to changes made to the sub-schemes. The concept of irreducible generic schemes is helpful in the analysis and classification of dynamic behavior and facilitates the interpretation of experimental measurements. The work consists of three stages. 1. A first-order kinetic network is decomposed by identifying two kinetic motifs, i.e., sequential chain reactions and branching reactions. Systematically concatenating chain reactions and side-branches, the investigators can then reduce a complex reaction to its generic form, each link of which represents a sub-scheme associated with a complex waiting time distribution function. When a kinetic step is altered within a sub-scheme, the waiting time distribution function changes accordingly, but the overall generic scheme and related dynamic quantities will remain the same functional forms. 2. A high-order kinetic network is then expanded around its steady state solution to the rate equation, which retains the full non-linearity in the dynamic behavior of average concentration. The correlations and fluctuations near the steady state are approximated by a linear form for the solution, an approach directly related to stability analysis methods for dynamic behavior and response measurements. In linearized networks, the feed-back or feed-forward mechanism defines a third motif, which introduces non-locality into linear kinetics and is central for understanding multi-stability and oscillations. 3. In the last part of the research, a hierarchical treatment of non-linear kinetic networks with a full account of number statistics relevant to single cell experiments is being developed. The projection operator is being explored as a formal technique to systematically reduce a complex kinetic network to a generic scheme with non-linear couplings.
The work is having a broader impact through application of the resulting methods to complx reaction networks of interets in biology. Student training is also being positively impacted and Cao is making an effort to further disseminate the results of his research through a course he is developing for the Telluride Workshop.
