Chemical Reaction Network (CRN)

Chemical Reaction Networks

Chemical reaction network theory is an area of applied mathematics that attempts to model the behavior of real-world chemical systems. Its primary applications are in biochemistry and theoretical chemistry, however it has also attracted interest from pure mathematicians due to the interesting problems that arise from the networks and mathematical structures involved. CRN models utilize dynamical properties of simple mathematical or chemical abstractions of particles. The can form quite complex dynamical systems, some capable of simple or advanced computation . Some assumed properties common to most if not all CRN systems: concentrations of reactants cannot be negative or zero, the rate of change of a given reactant or product type is assumed to be continuously differentiable, and many kinetic and physical considerations are often addressed via rules that pertain to mass action and reaction rates, among others. Many of the results in studies of CRNs involve the dynamics of the simulated reactor, such as the number of steady states, the stability of steady states, persistence of various species of reactants and products, network structure and temporal dynamics are often investigated as well. Artificial chemistries, models of early autopoiesis, are frequently concerned with the network structure, temporal and population dynamics of simple models of abstractions of prebiotic particles.

Computer Science Relevance

Due to the large number of chemical species that can be generated from relatively few chemical components and the numerous kinetic factors that must be taken into consideration when simulating a CRN, an active area of research within the CRN field is how to more simply and accurately model the network interactions. When modeling CRN's, many physical considerations must be left out due to an incomplete understanding of their mechanisms and to save computation cycles. To this end, Markov chain models are frequently used to describe the stochastic dynamics of networks of chemical reactants. These are of particular utility and interest when combined with Monte Carlo estimation techniques.