Petr Kuzmič

DynaFit--a software package for enzymology.

Since its original publication, the DynaFit software package [Kuzmic, P. (1996). Program DYNAFIT for the analysis of enzyme kinetic data: Application to HIV proteinase. Anal. Biochem. 237, 260-273] has been used in more than 500 published studies. Most applications have been in biochemistry, especially in enzyme kinetics. This paper describes a number of recently added features and capabilities, in the hope that the tool will continue to be useful to the enzymological community. Fully functional DynaFit continues to be freely available to all academic researchers from http://www.biokin.com.

Mixtures of tight-binding enzyme inhibitors. Kinetic analysis by a recursive rate equation

When two or more tight-binding inhibitors are present in an enzyme assay, the equation that relates the initial velocity v to the concentration of reactants cannot be written in an algebraically explicit form. Rather, for n inhibitors it is an implicit polynomial equation of degree n + 1 with respect to v. The complexity of the polynomial coefficients dramatically increases with each added inhibitor. Solving the transcendental rate equation by traditional methods of numerical mathematics has proven tedious because of the sensitivity of these methods to initial estimates and because of the existence of multiple roots. However, the equation can be rearranged into a convenient recursive form, one in which the velocity appears on both sides and the solution is found iteratively. The algebraic form of the recursive rate equation is remarkably simple and differs from the rate equation for classical rather than tight-binding inhibition only by an added term. The numerical stability and the speed of convergence were tested on the case of two competitive inhibitors. Initial estimates of velocity that spanned 12 orders of magnitude converged within five iterations. The velocities computed with the recursive method for a single tight-binding inhibitor were identical with the values predicted by the Morrison equation. The method is used to analyze experimental data for the inhibition of rat liver dihydrofolate reductase by mixtures of the anticancer drug methotrexate and its metabolic precursor form, methotrexate-alpha-aspartate (a prodrug).

Mixed‐type noncompetitive inhibition of anthrax lethal factor protease by aminoglycosides

We report a detailed kinetic investigation of the aminoglycosides neomycin B and neamine as inhibitors of the lethal factor protease from Bacillus anthracis. Both inhibitors display a mixed‐type, noncompetitive kinetic pattern, which suggests the existence of multiple enzyme–inhibitor binding sites or the involvement of multiple structural binding modes at the same site. Quantitative analysis of the ionic strength effects by using the Debye–Hückel model revealed that the average interionic distance at the point of enzyme–inhibitor attachment is likely to be extremely short, which suggests specific, rather than nonspecific, binding. Only one ion pair seems to be involved in the binding process, which suggests the presence of a single binding site. Combining the results of our substrate competition studies with the ionic strength effects on the apparent inhibition constant, we propose that aminoglycoside inhibitors, such as neomycin B, bind to the lethal factor protease from B. anthracis in two different structural orientations. These results have important implications for the rational design of lethal factor protease inhibitors as possible therapeutic agents against anthrax. The strategies and methods we describe are general and can be employed to investigate in depth the mechanism of inhibition by other bioactive compounds.

Fluorescence displacement method for the determination of receptor-ligand binding constants

The equilibrium constant for the binding of a spectroscopically invisible ligand to its protein receptor can be determined in a competition experiment, by using a structural analog that contains a reporter group (fluorophor). A novel mathematical treatment of the multiple equilibria allows the analysis to be performed under tight-binding conditions. The equilibrium equation for mixtures of two mutually competitive tight-binding ligands can be expressed in a recursive form, a form in which the dependent variable appears on both sides and the solution is found iteratively. The algorithm is also applicable to the special case of weak binding, where the concentration of the bound ligand can be neglected in the mass balance. The fluorescence displacement method is demonstrated on the determination cyclophilin binding to cyclosporin A (CsA), in competition with its fluorescent derivative, [D-Lys(Dns)]8-CsA.

Practical robust fit of enzyme inhibition data.

Publisher Summary This chapter describes the practical robust fit of enzyme inhibition data. The analysis of enzyme inhibition data in the context of preclinical drug screening presents unique challenges to the data analyst. Outliers are data points that are affected by gross errors caused by malfunctioning volumetric equipment, by a human error in data entry, or by countless other possible mishaps. It is shown that Hubers Minimax approach to robust statistical estimation is particularly preferable over the conventional least-squares analysis. The ordinary least square (OLS) estimate of the model parameters is sensitive to the presence of outliers, which has led to the design of various alternatives. All good data points are assigned the same weight in the iteratively reweighted series of LS estimations, exactly as they are in OLS. The practical success of Hubers method applied even to relatively small data sets, such as those arising in preclinical screening, is due to the fact that the method behaves as OLS does if the data are good, but at the same time it gives the least absolute deviation treatment to suspected outliers, while maintaining 95% asymptotic efficiency. It is found that both standardized residuals and leverages play a role in the Hubers method of robust regression analysis, implemented as iteratively re-weighted least squares.

Application of the Van Slyke–Cullen irreversible mechanism in the analysis of enzymatic progress curves

For enzymatic progress curves conforming to the Michaelis-Menten mechanism E+Sright harpoon over left harpoonES-->E+P, the minimal fitting model cast as a system of numerically integrated differential equations is the simplified, irreversible Van Slyke-Cullen mechanism E+S-->ES-->E+P. The best-fit value of the bimolecular association rate constant is identical to the specificity constant kcat/KM. An illustrative example involves a fluorogenic continuous assay of the HIV protease, analyzed by the differential-equation oriented software package DYNAFIT [P. Kuzmic, Anal. Biochem. 237 (1996) 260].

Analysis of residuals from enzyme kinetic and protein folding experiments in the presence of correlated experimental noise.

Experimental data from continuous enzyme assays or protein folding experiments often contain hundreds, or even thousands, of densely spaced data points. When the sampling interval is extremely short, the experimental data points might not be statistically independent. The resulting neighborhood correlation invalidates important theoretical assumptions of nonlinear regression analysis. As a consequence, certain goodness-of-fit criteria, such as the runs-of-signs test and the autocorrelation function, might indicate a systematic lack of fit even if the experiment does agree very well with the underlying theoretical model. A solution to this problem is to analyze only a subset of the residuals of fit, such that any excessive neighborhood correlation is eliminated. Substrate kinetics of the HIV protease and the unfolding kinetics of UMP/CMP kinase, a globular protein from Dictyostelium discoideum, serve as two illustrative examples. A suitable data-reduction algorithm has been incorporated into software DYNAFIT [P. Kuzmic, Anal. Biochem. 237 (1996) 260-273], freely available to all academic researchers from http://www.biokin.com.

Long range electrostatic effects in pepsin catalysis

Abstract Binding of polycationic substrates and inhibitors to pepsin is a stepwise process. Fast nonspecific association, governed by long range electrostatic forces, is followed by slow surface diffusion into the active site.

Nonspecific Electrostatic Binding of Substrates and Inhibitors to Porcine Pepsin

Porcine pepsin has long been recognized to have primary and secondary specificity for hydrophobic amino acids, and the binding of low molecular weight inhibitors (e.g., aliphatic alcohols) is also dominated by hydrophobic interactions1. However, the long standing ‘hydrophobic dogma’ in pepsin catalysis was seriously challenged when Pohl and Dunn2 described a series of polycationic oligopeptides that are among the most reactive synthetic substrates known. These highly hydrophilic molecules should not be well accommodated in a hydrophobic active site. Moreover, the steady state kinetic parameters were remarkably sensitive to the acidity of the medium. As the pH was increased from pH 3 to 6, the specificity number kcat/Km increased by three to four orders of magnitude and approached values close to the diffusion limit. The catalytic turnover number kcat was much less affected by the increase in pH, and the Michaelis constant Km decreased accordingly, by three to four orders of magnitude. A typical pH profile of steady state kinetic parameters, for the substrate Lys-Lys-Ala-Lys-Phe-Phe(NO2)-Arg-Leu, is shown in Figure 1.

Optimal design for the dose–response screening of tight-binding enzyme inhibitors

Optimal experimental designs for the dose-response screening of enzyme inhibitors were studied within the framework of the Box-Lucas theory. If the enzyme concentration E is considered as a fixed constant, an exact two-point D-optimal design consists of a pair of inhibitor concentrations equal to I(1)=0 and I(2)=E+K, where K is the apparent inhibition constant. If the enzyme concentration is treated as an adjustable parameter, an empirical three-point D-optimal design consists of three inhibitor concentrations equal to I(1)=0, I(2)=E+3K, and I(3)=0.7E. These results were applied to design optimized, irregularly spaced concentration series for routine inhibitor screening. A heuristic Monte Carlo simulation study confirmed that the optimized dilution series is significantly more efficient than the classic series characterized by a constant dilution ratio. An online calculator to create optimized dilution series is freely available at http://www.biokin.com/design/.