Methods for fitting equations with two or more non-linear parameters

A method for conforming the pH dependence of the michaelis parameters of nonallosteric enzymes to four kinetic schemes

A nonlinear regression program for the analysis of the effect of pH on enzyme activity has been developed for the IBM micro range and compatible machines. The program conforms the V and Km pH profiles to one of four commonly occurring kinetic schemes. By using multiple linear regression the program computes initial estimates for the nonlinear search which are thus not required from the user. Two nonlinear optimization methods are included in order to effectively handle the nonnegativity constraints on the parameters. The program is user-friendly and provides plots of the fit and residual plots to help the user decide on the goodness of fit obtained. The program was coded in Turbo Pascal version 4.0 and runs on IBM micros or close compatibles with four types of graphics cards.

The analysis of enzyme progress curves by numerical differentiation, including competitive product inhibition and enzyme reactivation

A new method for analyzing steady-state enzyme kinetic data is presented. The technique, which is based on the numerical differentiation of the complete reaction curve, has several advantages over initial velocity and integrated Michaelis-Menten equation methods. The differentiated data are fit to the differential equation describing the appropriate kinetic scheme. This approach is particularly valuable in cases of strong competitive product inhibition and of changing concentrations of active enzyme. The method assumes a reversible reaction and is applicable to a very wide variety of steady-state kinetic schemes. A particular advantage of this approach over integrated methods is that it is independent of [S0] and hence of errors in [S0]. The combination of complete progress curve and computer analysis makes this approach very efficient with respect to both time and materials. Running on an IBM PC XT or equivalent microcomputer with an 8087 coprocessor, the analyses are very fast, the complete process usually being complete in a minute or two. The utility of the technique is demonstrated by application to both simulated and real data. We show that the differentiation of the progress curve for the ribonuclease-catalyzed hydrolysis of 2',3'-cyclic cytidine monophosphate reveals strong product inhibition by 3'-CMP, and this product inhibition accounts for the large discrepancies reported in the literature for the value of Km for this substrate. The method was also applied to determine the rate of reactivation of beta-lactamase which had been reversibly inactivated by cloxacillin. Since large numbers of data points are required for the numerical differentiation the method has become practical only with the advent of computer-acquired data systems.

A microcomputer program for fitting enzyme inhibition rate equations

This paper presents a computer program written in BASIC for fitting different enzyme inhibition kinetic models. The program, based on a nonlinear least-squares regression, can be run on any microcomputer with the CP/M operating system. Weighting of observed initial velocities is decided by the user by assessing constant variance, proportional variance or by incorporation of the variances calculated by a subroutine. The program also uses robust regression by bisquare weighting. All questions concerning data input, type of rate function, type of weight and the use of bisquare regression appear on the video display unit.

Analysis of progress curves for a highly concentrated Michaelian enzyme in the presence or absence of product inhibition

Methods are given for analysing the time course of an enzyme-catalysed reaction when the concentration of the enzyme itself is high, a situation which is often found in vivo. (1) The integrated form of the kinetic equation for a concentrated Michaelian enzyme in absence of product inhibition is given. Parameters are shown to be calculated easily using non-linear fitting procedures. (2) A general algorithm to analyse progress-curve data in more complex cases (i.e. when the analytical form of the integrated rate equation is not known or is exceedingly complex) is proposed. This algorithm may be used for any enzyme mechanism for which the differential form of the kinetic equation may be written analytically. We show that the method allows differentiation between the main types of product inhibition which may occur in the case of a highly concentrated Michaelian enzyme.

An evaluation of ways of using equilibrium dialysis to quantify the binding of ligand to macromolecule

1. The effect of systematic error (loss of ligand, complex or macromolecule) on three of the experimental designs by which equilibrium dialysis may be used to quantify the interaction of ligand and macromolecule is examined theoretically, and the design that is least sensitive to systematic error is identified. 2. Thirteen methods for fitting the binding isotherm to experimental data are compared by using them to analyse simulated data containing random error, and the most reliable method is identified.