(671b) Efficient Numerical Protocol for Design of Lumped and Distributed Parameter Systems Involving Certain Classes of Networks of Complex Chemical Reactions

Complex reactions are encountered in a variety of chemical transformations, such as halogenation, hydrogenation, oxidation, condensation, hydrolysis, polymerization, polymer degradation, and genome-scale metabolic networks. In living systems, complex reactions are responsible for formation and hydrolysis of polysaccharides, polypeptides, DNA, RNA, lipids, and hybrids of these. Many of the complex reaction schemes are parallel with respect to primary reactants and series with respect to intermediates. Dependence of the rates of the individual reactions on concentrations of reactants for that reaction leads to a large number of nonlinear conservation equations for participating species, requiring tedious numerical analysis for reactor design. A far more efficient protocol is presented here for reactor analysis and design focused on certain classes of complex reactions. The solution to the multi-reaction and multi-species problem is made easier by (i) identifying stoichiometric hyperplanes among species attributes (concentrations, moles, fluxes) based on characteristics of the stoichiometric matrix for the reaction scheme, (ii) obtaining binary relations among concentrations of some of the species by working with appropriate pairs of conservation equations. The required numerical effort is reduced drastically because of the analytical identification of binary relations among concentrations of some species. The advantages of this protocol are illustrated with suitable examples of complex reaction schemes considering the popular workhorses used in industry, namely batch reactor, CSTR, and plug flow and packed bed reactors. Analysis and design of reactors for conducting complex reactions is made very precise by this hybrid (analytical and numerical) approach. The characteristics of the complex reaction schemes, such as maxima in concentrations of intermediates and conditions under which they are attained, can be evaluated and studied conveniently using the hybrid approach. The protocol is attractive for handling large networks of complex reactions, such as those encountered in genome-scale metabolic networks and genome-proteome-metabolome interactions in living cell systems.