New methods of determination of kinetic parameters of theoretical models from experimental data

Integral and integro-differential methods have been developed for determining unknown characteristics of a kinetic experiment, including the rates of chemical reactions, the initial concentrations of substances, and Michaelis constants. These methods are applicable to a wide class of reactions and are most efficient when the system of differential equations considered is linear with respect to all, or a group of, unknown parameters. For an open multienzyme system obeying the Michaelis-Menten system of equations that is nonlinear in unknown parameters, it is demonstrated how the initial system of equations can be transformed into a new system that is linear with respect to new variables functionally depending on the initial parameters. A method has been developed for reformulating the initial nonlinear problem of determining the unknown parameters into a linear one. In this method, the initial problem is immersed into the more general problem of identifying the coefficients of a differential equation such that the initial formula is one of the solutions of this equation. This method can also be used to determine kinetic parameters of theoretical models that are formulated in terms of both concentrations and activities. A method of complete identification of chemical kinetic problems has been analyzed for the case of the incomplete observability of some components of the reaction, and it has been concluded that the kinetics of the substrate and intermediates in a multistep consecutive reaction can be qualitatively and quantitatively reconstructed by monitoring its product provided that the product concentration is precisely determined.