On the Numerical Computation of Enzyme Kinetic Parameters

Abstract

We consider the enzyme kinetic reaction scheme originally proposed by V. HenriВ of single enzyme-substrate dynamics where two fractions of the enzyme - free and bound - are involved. Henri's scheme involves four concentrations and three rate constants and via the mass action law it is translated into a systemВ of four ODE's. On two case studies we demonstrate how the rate constants can be computed whenever time course experimental data are available. The obtained results are compared with analogous results implied by classical Michaelis-Menten model. Our approach focuses on the uncertainties in the experimental data, as well as on the use of contemporary computational tools such as CAS Mathematica.

Building reaction kinetic models for amiloid fibril growth

“…We see that the logistic model admits all three formulation types: the E-type (13), the D-type (11) or (12) and the R-type (10).…”

“…A possible "biological" interpretation of reaction network (10) in the context of population dynamics can be the following: the nutrient substrate (or species) U is utilized (consumed) by species (population) X leading to a reproduction of species X, thereby k is a specific growth rate of the process.…”

“…On the other side reaction network (22) can be seen as an extension of Verhulst reaction network (10) by involving an intermediate catalyst C.…”

“…Graphs of the solutions m, f of model (23) ues for the rate parameters and the initial conditions by fitting (some of) the solutions to available time course experimental measurements. Computational tools for the solution of this problem are proposed in [10], [11].…”

“…The transition of the aggregated monomer P into fibril according to reaction network (28 follows the Verhulst autocatalitic mechanism (10). Applying the mass action law we obtain the ODE system: dm/dt = −k + f m + k − c, df /dt = −k + f m + (k − + k c )c + k p f p, dc/dt = k + f m − (k − + k c )c, dp/dt = k c c − k p f p.…”