Chapter 23 Fitting Enzyme Kinetic Data with KinTek Global Kinetic Explorer
Section snippets
Background
Fitting kinetic data based upon numerical integration of rate equations has several advantages over conventional fitting to mathematical functions derived by analytical solution of the rate equations (Barshop et al., 1983, Johnson et al., 2009a, Johnson et al., 2009b, Zimmerle and Frieden, 1989). In particular, by fitting primary data directly to a model by computer simulation, all aspects of the data are included in the fitting process including rates as well as amplitudes of the reactions
Challenges of Fitting by Simulation
There are two competing challenges to fitting data based upon computer simulation; namely, a model must be complete enough to provide an adequate description of the underlying mechanism, but not more complex than can be supported by the data. A complete model is required so that the data fitting is built upon a realistic mechanism without unsupported simplifying assumptions. Even with a realistic minimal model, not all of the rate constants may be known or constrained by the data. Accordingly,
Methods
In fitting kinetic data there is no substitute for a sound understanding of the principles in the design and interpretation of experiments. Nonetheless, by use of kinetic simulators in general and KinTek Explorer in particular, many of the pitfalls in interpretation can be avoided. Every week models are published that are simply not consistent with the data. These errors could be avoided by fitting data using computer simulation because all elements of the data must be consistent with the model
Progress Curve Kinetics
Standard steady-state kinetic analysis is based upon the error-prone estimates of initial velocities, restricting data to the first 10–20% of the reaction and the need to measure initial slope before the reaction starts to become nonlinear. The initial velocities must then be plotted as a function of substrate (and perhaps inhibitor) concentrations and then fit to another set of equations to extract kcat and Km values, all the while being careful to propagate error estimates. These
Fitting Full Progress Curves
In fitting steady-state or full progress curve kinetics, all that can be determined are kcat and Km values, possibly in both the forward and reverse directions depending upon the reversibility of the reaction and the properties of the data. Accordingly, one can only fit the data to extract two or four constants. However, the minimal model (Scheme 23.1) contains three steps and six rate constants. One easy approach is to simply fit to a model with all six rate constants as variable parameters
Slow Onset Inhibition Kinetics
In this example, we consider data collected in the steady state involving slow-onset inhibition. The data shown in Fig. 23.5 were generously provided by Vern Schramm and Andrew Murkin of the Albert Einstein College of Medicine from their work in developing transition state analog inhibitors of purine nucleoside phosphorylase (PNPase) (Kicska et al., 2002). These unpublished data show the increase in absorbance with time in the presence of various concentrations of the DADMe-ImmH inhibitor with
Summary
The two examples for data fitting serve to illustrate the use of KinTek Explorer in fitting data to derive steady-state kinetic constants and the rates of slow onset inhibition. In these cases, the fitting based upon simulation is fast and reliable. By fitting the parameters of the model directly to the data, simplifying assumptions and errors are eliminated.
Standard error analysis during nonlinear regression is not reliable and it fails to reveal when parameters are seriously underconstrained.
Acknowledgments
Supported by KinTek Corporation (www.kintek-corp.com)
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