Automatic deduction of key data
Key data are extracted from the curves and presented in table format. For each type of inhibition the time point of Dmax[P] between inhibited and uninhibited reactions, the observed inhibition (%) at that point, the associated amount of substrate conversion (%), and the value of Dmax[P] (mM) are given (Fig. S1). Figure 1. Simulated progress curves and differences between inhibited and uninhibited reactions. (Left) Simulated progress curves for competitive (blue trace), uninhibited (black trace) reactions, and the difference (D[P]) between the two reactions (red trace). Dmax[P] is indicated by a dashed vertical line. (Right) D[P] between inhibited and uninhibited enzyme reactions for competitive (yellow), uncompetitive (green), noncompetitive (orange), and mixed (blue) inhibition. In the simulation tool, progress curves for all types of inhibition are shown as in the left panel. Reaction parameters and variables can be entered and the results will be directly displayed in the graphs. Entered reaction conditions were: [S] = Km = 0.25Kmp = 10[I] = 400[Eo] = 100 mM; [Po] = 0 mM; kcat = 0.5 s21; enzyme t(1/2) = 24 hours; Kic = Kiu = Ki-non = 5 mM for competitive, uncompetitive, and non-competitive inhibition; and Kiu = 5Kic = 15 mM for mixed inhibition.inhibitor (Fig. 4). Kinetic parameters were derived by leastsquares model fitting. As a comparison, an experiment to determine kinetic parameters with initial reaction rates at increasing substrate concentrations was also performed (Fig. 4). Curve fitting gave a good data-to-model agreement, for both progress curves and the initial reaction rate experiment, and kinetic parameters derived with the two methods were very similar. Thus, Km was determined to be 3.6 mM and kcat to be 0.43 sec21 by progress curves analysis and to be 3.9 mM and 0.45 sec21 by the initial rate method. (One reason for the successful determination of Km by the progress curve method was the possibility to use a relatively high [So] of ,5 Km.) Comparing the experimentally observed Dmax[P] and the time point when it occurred, with the corresponding values predicted by the tool, gave deviations of only 0.17 mM (2%) and a 90 seconds (3%), respectively.
Simple usage
In the tool the user is presented to three differently colored blocks (for competitive, uncompetitive, and mixed inhibition) in which reactions parameters and variables can be adjusted (Fig. 5). Various curves are directly simulated in response to changed parameters. Adjustable cells/values are shown in red and other cells are locked for editing. Each block also has a table presenting important key data (Dmax[P] along with the associated time point, % Substrate, % Inhibition, and IC’50) that are automatically deduced in response to adjusted parameters. The corresponding data at defined time points can also be extracted by entering time points in the column headers of an adjacent table (also coupled to graphs). This helps the user to identify an optimal window of observation. For each type of inhibition the corresponding reaction equations are given. Non-competitive inhibition is not directly included but can be accounted for setting Kic = Kiu, realizing that this is a special case of mixed inhibition.
Figure 2. Inhibition as a function of substrate conversion. Observed inhibition (%) as a function of the degree of substrate conversion (%) of the uninhibited reference reaction for competitive (yellow), uncompetitive (green), non-competitive (orange), and mixed (blue) inhibition. In the simulation tool, time points can be entered (see Fig. S1) to directly study the effects in the graphs, where observed inhibition is also plotted against reaction time. Entered reaction conditions were: [S] = K m = 0.25K m p = 10[I] = 400[E o ] = 100 m M; [Po] = 0 mM; kcat = 0.5 s21; enzyme t(1/2) = 24 hours; Kic = Kiu = Ki-non = 5 mM for competitive, uncompetitive, and non-competitive inhibition; and Kiu = 5Kic = 15 mM for mixed inhibition. Figure 3. Observed inhibitor potency (IC’50) as a function of substrate depletion. The graph shows IC’50 as a function of the degree of substrate conversion of the uninhibited reference reaction for competitive (yellow), uncompetitive (green), non-competitive (orange), and mixed (blue) inhibition. In the tool, the graph is directly coupled to user adjustable reaction variables and parameters. At initial reaction conditions, IC’50 equals IC50. Entered reaction conditions were: [S] = Km = 0.25Kmp = 10[I] = 400[Eo] = 100 mM; [Po] = 0 mM; kcat = 0.5 s21; enzyme t(1/2) = 24 hours; Kic = Kiu = Ki-non = 5 mM for competitive, uncompetitive, and non-competitive inhibition; and Kiu = 5Kic = 15 mM for mixed inhibition.
Discussion
A tool for the simulation and comparative analysis of enzymatic progress curves for common types of inhibition has been developed. The tool can be downloaded as supplemental material (Simulation Tool S1) or obtained from the author. The tool provides accurate simulation of experimental progress curves (Fig. 4) – given that the enzyme system under study can be approximated by the underlying model, as in any simulation approach. Reaction parameters and concentrations can be adjusted to directly observe the effects on displayed progress curves and essential data are deduced and clearly presented (Figs. S1 & 5). The tool is particularly intended to support experimental design and to facilitate interpretation of data obtained in end-point assays, e.g. in HTS for enzyme inhibitors. In these processes the tool can be used to: study the effect of reaction conditions on the choice of observation window (see Table 1), tune reaction condition in favor of a particular type of inhibition, investigate the amount of substrate turn-over that can be allowed to increase the assay signal without severely affecting observed inhibition, adapt assay conditions to an enzyme with pronounced product inhibition, or to guide the selection of hit cut-off criteria while accounting for product inhibition, reaction reversibility, and substrate turn-over. Importantly, the tool has a dedicated purpose in HTS assay design, is simple to use, and only requires basic knowledge in enzyme kinetics. This is in contrast to other more advanced simulation software for more general usage, which are also considerably more complex, e.g. Dynafit [11,12], Fitsim/ Kinsim [8,9], and Gepasi [13,14] with its successor Copasi [15]. A general observation that emerges when using the simulation tool is that Dmax[P] occurs at the end of the linear phase of the uninhibited reference reaction (cf. Figs. 1 & S1).
