Executive Summary : | Biological systems display a wide array of exquisite and sophisticated behaviours. A careful investigation of the underlying chemistry is warranted to understand the intricate behaviour exhibited by them. Dynamical properties like persistence, bifurcations and oscillations play a vital role in many of the processes at the cellular level. For example, the property of persistence is responsible for homeostasis, which is the ability to maintain the internal environment with change in external conditions. Oscillations can invoke the use of positive feedback loops, which form a critical component of many cellular processes. It turns out that there exists multiple networks that can generate the same dynamical system. We call such networks dynamically equivalent realizations. Network identification is therefore a difficult problem; however certain aspects can be salvaged by imposing additional constraints on the network structure. One of the objectives of this grant proposal is to identify these constraints, which may be either algebraic or geometric. For example, one may ask for the reaction network having the smallest number of reactions that generates a given dynamical system. In addition, there exists various types of inclusions between different families of reaction networks that are dynamically equivalent. The grant proposal seeks to discern these inclusions and exploit their properties to design computationally efficient algorithms for identifying certain special networks. In particular, the design of such algorithms would contribute to CoNtRol, which is a reliable online software for performing computations on reaction networks. |