Chapter 10 - DynaFit—A Software Package for Enzymology
Introduction
DynaFit (Kuzmič, 1996) is a software package for the statistical analysis of experimental data that arise in biochemistry (e.g., enzyme kinetics; Leskovar et al., 2008), biophysics (protein folding; Bosco et al., 2009), organic chemistry (organic reaction mechanisms; Storme et al., 2009), physical chemistry (guest–host complexation equilibria; Gasa et al., 2009), food chemistry (fermentation dynamics; Van Boekel, 2000), chemical engineering (bio-reactor design; Von Weymarn et al., 2002), environmental science (bio-sensors for heavy metals; Le Clainche and Vita, 2006), and related areas.
The common features of these diverse systems are that (a) the underlying theoretical model is based on the mass action law (Guldberg and Waage, 1879); (b) the model can be formulated in terms of stoichiometric equations; and (c) the experimentally observable quantity is a linear function of concentrations or, more generally, populations of reactive species.
The main use of DynaFit is in establishing the detailed molecular mechanisms of the physical, chemical, or biological processes under investigation. Once the molecular mechanism has been identified, DynaFit can be used for routine quantitative determination of either microscopic rate constants or thermodynamic equilibrium constants that characterize individual reaction steps.
DynaFit can be used for the statistical analysis of three different classes of experiments: (1) the progress of chemical or biochemical reactions over time; (2) the initial rates of enzyme reaction, under either the rapid-equilibrium or the steady-state approximations (Segel, 1975); and (3) equilibrium ligand-binding studies.
Regardless of the type of experiment, the main benefit of using the DynaFit package is that it allows the investigator to specify the fitting model in the biochemical notation (e.g., E + S <==> E.S --> E + P) instead of mathematical notation (e.g., v = kcat[E]0[S]0/([S]0 + Km)).
For example, to fit a set of initial rates of an enzyme reaction to a steady-state kinetic model for the “Bi Bi Random” mechanism (Segel, 1975, p. 647) (Scheme 10.1), the investigator can specify the following text in the DynaFit input file:
[data]
data = rates
approximation = steady-state
[mechanism]
E + A <==> E. A : k1 k2
E. A + B <==> E. A. B : k3 k4
E. A. B <==> E. B + A : k5 k6
E. B <==> E + B : k7 k8
E. A. B --> E + P + Q : k9
[constants]
k8 = (k1 k3 k5 k7) / (k2 k4 k6)
. . .
The program will internally derive the initial rate law corresponding to this steady-state reaction mechanism (or any arbitrary mechanism), and perform the least-squares fit of the experimental data. This allows the investigator to focus exclusively on the biochemistry, rather than on the mathematics. Using exactly equivalent notation, one can analyze equilibrium binding data, such as those arising in competitive ligand displacement assays, or time-course data from continuous assays.
Importantly, the DynaFit algorithm does not make any assumptions regarding the relative concentrations of reactants. Specifically, it is no longer necessary to assume that the enzyme concentration is negligibly small compared to the concentrations of reactants (substrates and products) and modifiers (inhibitors and activators). This feature is especially valuable for the kinetic analysis of “slow, tight” enzyme inhibitors (Morrison and Walsh, 1988, Szedlacsek and Duggleby, 1995, Williams and Morrison, 1979).
Since its original publication (Kuzmič, 1996), DynaFit has been utilized in more than 500 journal articles. In the intervening time, many new features have been added. The main purpose of this report is to give a brief sampling of several newly added capabilities, which might be of interest specifically to the enzymological community. The survey of DynaFit updates is by no means comprehensive; the full program documentation is available online (http://www.biokin.com/dynafit).
This article has been divided into four parts. The first three parts touch on the three main types of experiments: (1) equilibrium ligand binding studies; (2) initial rates of enzyme reactions; and (3) the time course of enzyme reactions. The fourth and last part contains a brief overview of selected data-analytical approaches, which are common to all three major experiment types.
Section snippets
Equilibrium Binding Studies
DynaFit can be used to fit, or to simulate, equilibrium binding data. The main purpose is to determine the number of distinct noncovalent molecular complexes, the stoichiometry of these complexes in terms of component molecular species, and the requisite equilibrium constants.
The most recent version of the software includes features and capabilities that go beyond the original publication (Kuzmič, 1996). For example, DynaFit can now be used to analyze equilibrium binding data involving—at least
Initial Rates of Enzyme Reactions
The study of initial rates of enzyme-catalyzed reactions defines the traditional approach to mechanistic enzymology (Segel, 1975). Earlier versions of the DynaFit software package (Kuzmič, 1996) were suitable for the analysis of initial-rate data under the rapid equilibrium approximation (Kuzmič, 2006), where it is assumed that the chemical steps in an enzyme mechanism are negligibly slow in comparison with all association and dissociation steps.
The current version of DynaFit extends the
Time Course of Enzyme Reactions
DynaFit (Kuzmič, 1996) was initially developed to process the time course of “slow, tight” (Morrison and Walsh, 1988, Szedlacsek and Duggleby, 1995, Williams and Morrison, 1979) enzyme inhibition assays. In the intervening period, a number of features and capabilities had been added to further facilitate the analysis of reaction dynamics. For example, DynaFit can now be used to analyze “double-mixing” stopped-flow experiments (Williams et al., 2004). Microscopic rate constants can be
General Methods and Algorithms
This section briefly summarizes selected features and capabilities added to the DynaFit software package since its original publication (Kuzmič, 1996). These general algorithms are applicable to all types of experimental data (progress curves, initial rates, and complex equilibria) being analyzed.
This selection of added features is not exhaustive, but it emphasizes some of the most difficult tasks in the analysis of biochemical data:
- •
How do we know where to start (the initial estimate problem);
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Concluding Remarks
DynaFit (Kuzmič, 1996) has proved quite useful in a number of projects, as is evidenced by the number of journal publications that cite the program. It is hoped that the software will continue to enable innovative research. This section offers a few closing comments on DynaFit enhancements currently in development.
Acknowledgments
Klára Briknarová and Jill Bouchard (University of Montana) are gratefully acknowledged for sharing their as yet unpublished NMR titration data. Jan Antosiewicz (Warsaw University) provided stimulating discussions and procured the PNP inhibition data for testing the statistical-factors feature in DynaFit; the raw experimental data were made available by Beata Wielgus-Kutrowska, Agnieszka Bzowska, and Katarzyna Breer (Warsaw University). Stephen Bornemann and his colleagues (John Innes Center,
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