Complex Media and Enzymatic Kinetics.

Enzymatic reactions in complex environments often take place with concentrations of enzyme comparable to that of substrate molecules. Two such cases occur when an enzyme is used to detect low concentrations of substrate/analyte or inside a living cell. Such concentrations do not agree with standard in vitro conditions, aimed at satisfying one of the founding hypotheses of the Michaelis-Menten reaction scheme, MM. It would be desirable to generalize the classical approach and show its applicability to complex systems. A permeable micrometrically structured hydrogel matrix was fabricated by protein cross-linking. Glucose oxidase enzyme (GOx) was embedded in the matrix and used as a prototypical system. The concentration of H2O2 was monitored in time and fitted by an accurate solution of the enzymatic kinetic scheme, which is expressed in terms of simple functions. The approach can also find applications in digital microfluidics and in systems biology where the kinetics response in the linear regimes often employed must be replaced.

Perturbation theory in the catalytic rate constant of the Henri-Michaelis-Menten enzymatic reaction.

The Henry-Michaelis-Menten (HMM) mechanism of enzymatic reaction is studied by means of perturbation theory in the reaction rate constant k (2) of product formation. We present analytical solutions that provide the concentrations of the enzyme (E), the substrate (S), as well as those of the enzyme-substrate complex (C), and the product (P) as functions of time. For k (2) small compared to k (-1), we properly describe the entire enzymatic activity from the beginning of the reaction up to longer times without imposing extra conditions on the initial concentrations E ( o ) and S ( o ), which can be comparable or much different.