An alternative approach to Michaelis-Menten kinetics that is based on the renormalization group.

We apply to Michaelis-Menten kinetics an alternative approach to the study of Singularly Perturbed Differential Equations, that is based on the Renormalization Group (SPDERG). To this aim, we first rebuild the perturbation expansion for Michaelis-Menten kinetics, beyond the standard Quasi-Steady-State Approximation (sQSSA), determining the 2nd order contributions to the inner solutions, that are presented here for the first time to our knowledge. Our main result is that the SPDERG 2nd order uniform approximations reproduce the numerical solutions of the original problem in a better way than the known results of the perturbation expansion, even in the critical matching region.

Application of a functional mathematical index for antibacterial and anticarcinogenic effects of tea catechins.

Tea leaves produce secondary metabolites that are involved in the defense of the plants against invading pathogens. In the case of green teas, these metabolites are polyphenolic compounds called catechins. Previous studies developed a mathematical formula called functional mathematical index (FMI) that was used to describe the quality of different olive oils and potatoes in terms of compositional parameters and antioxidative properties of individual components.

The total quasi-steady-state approximation for fully competitive enzyme reactions.

The validity of the Michaelis-Menten-Briggs-Haldane approximation for single enzyme reactions has recently been improved by the formalism of the total quasi-steady-state approximation. This approach is here extended to fully competitive systems, and a criterion for its validity is provided. We show that it extends the Michaelis-Menten-Briggs-Haldane approximation for such systems for a wide range of parameters very convincingly, and investigate special cases.