Introduction

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The results of in vitro enzyme inhibition studies have proved to be useful as predictors of in vivo metabolic interactions between new chemical entities and existing drugs (or nutrients). Such studies are designed to answer questions concerning the isozymes responsible for metabolism, the chemical nature of the metabolites formed, and quantitative aspects of the biotransformation process. The latter includes an estimation of kinetic parameters that characterize the substrate and enzyme (e.g., V_max, K_m, and CL_intrinsic) as well as any inhibition process (e.g., K_i). Having an estimate of K_i, the inhibition constant, is quite useful in conjunction with knowledge of the actual or anticipated plasma concentrations of the new drug entity. Thus, the new agent is not likely to affect the metabolism of another drug if plasma concentrations of the former are much less than the value of K_i. The opposite conclusion also holds; an interaction in metabolism is likely if plasma concentrations exceed K_i.

The issue of how best to estimate the value of K_i, by comparing three different methods of analysis, has recently been reported (Kakkar et al., 1999). The most frequently used method, that of Dixon (Segel, 1975a), which relies on a linearized form of a nonlinear relationship, provides poor and unreliable estimates of K_i. The most robust method was that referred to as simultaneous nonlinear regression (SNLR), or the "direct" method (Cleland, 1963), in which all data (from control and inhibitors) are fit simultaneously to the full nonlinear competitive inhibition expression. Nimmo and Atkins (1976) were among the first investigators to suggest the advantages of the use of SNLR. Another method, referred to as K_m,app, or the "replot" method (Cleland, 1963), which combines nonlinear and linear regression analyses of the data, provided estimates of K_i similar to those obtained with the SNLR method.

Another important aspect to the practical estimation of K_i, especially in recent years, is the need to adapt methods to the current high-throughput demands of the pharmaceutical industry. Such information is important for reasons noted earlier and must be obtained in early discovery/development. Similar high-throughput efforts are being made to characterize other aspects of the very large number of new chemical entities being screened (e.g., membrane permeability, binding, and so on). What, ideally simple, strategies can be brought to bear to the routine estimation of K_i for the literally thousands of new chemical entities that need to be tested in in vitro systems with a wide array of enzymes and substrates? One simple response, other than improved efficiency in technology, is to reduce or minimize the total experimental effort. Preliminary simulations were conducted to address the possibility of limiting the number of inhibition experiments. The results (Kakkar et al., 1999) suggested that reduced experimental effort will provide good estimates of K_i. One purpose of the present report is to more thoroughly evaluate the minimal experimental design needed to obtain reliable and robust estimates of K_i (as well as V_max and K_m).

The first part of this study evaluates minimal experimental design strategies (containing four experimental cases). To conduct these simulations, we needed to assume an enzyme inhibition mechanism, and we have assumed competitive inhibition. However, for most new chemical entities, the mechanism of inhibition of metabolism, by endogenous or exogenous compounds, is not known in advance. There is a need to accurately determine the type of inhibition and the inhibition constant with the least amount of experimental effort. Therefore, the second part of this study was designed to test the ability of the SNLR method to differentiate between competitive and noncompetitive enzyme inhibition mechanisms. Turner and Brouwer (1997) used the SNLR method with data obtained from an in vitro study that examined probenecid-associated alterations in hepatic acetaminophen glucuronide formation. However, because those investigators did not have a priori knowledge of the enzyme inhibition mechanism, the use of the SNLR method to determine the type of inhibition is questionable, unless it can be proved to distinguish among the different types of inhibition. Therefore, the second purpose of this report was to evaluate the ability of the SNLR method to distinguish between mechanisms.

	Materials and Methods

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Evaluation of a Minimal Experimental Design

The full competitive inhibition equation was used in simulations to generate rates of metabolite formation (v) as a function of substrate concentration ([S]) in the absence (control) or presence of different inhibitor concentrations ([I]) and assuming one metabolite was formed (Segel, 1975b).

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where K_m and V_max represent the Michaelis constant and the maximal rate of metabolite formation, respectively, and K_i is the inhibition constant.

Normally distributed [N(0,1)] random error was added to the exact (i.e., perfect) metabolite formation rate data (v_exact). The normally distributed random errors were obtained from random numbers (rn) created in Excel. The following errors were added to each simulated perfect value of rate: 0.1 · rate · random number and 0.2 · rate · random number. The resulting values correspond to additive errors having 10 and 20% coefficient of variation (CV), respectively. The resulting value for rate is represented as v_obs = v_exact + (0.1 or 0.2) · v_exact · rn, where v_obs is the value for rate containing added error and was used in the subsequent analyses. A single set of parameter values [cited as an example by Copeland (1996) but using arbitrary units] was used throughout this study: K_m = 10 µM, V_max = 100 nmol · min¹ · mg protein¹, and K_i = 5 µM. Four cases were examined.

Case I. The control experiments incorporated six substrate concentrations (2.5, 5, 10, 25, 50, and 75 µM). The inhibition experiments were based on six substrate concentrations (10, 25, 100, 250, 500, and 1000 µM) in conjunction with a single inhibitor concentration of either 10 or 100 µM. This design results in one complete rate-versus-substrate concentration curve in the absence of inhibitor (i.e., control) and one curve in the presence of each inhibitor concentration (either 10 or 100 µM). Three rates of control (i.e., no inhibitor) metabolite formation were simulated per [S] (with error added) and averaged. These simulations were repeated 200 times to give 200 average rate-versus-[S] curves. One-half of this total was used as controls for one inhibitor concentration, and the other half was used for the other inhibitor concentration. This entire process was then repeated for each of the two inhibitor concentrations, resulting in 100 average rate-versus-[S] curves for each inhibitor concentration. The data were then analyzed as discussed later.

Case II. The control experiments were based on six substrate concentrations (2.5 to 75 µM), and 200 average rate-versus-[S] curves were generated (different from those in case I). The inhibition experiments were based on two separate substrate-inhibitor pairs: [S] of 25 µM and [I] of 10 µM or [S] of 250 µM and [I] of 100 µM. One hundred average rates of metabolite formation were generated for each of the substrate-inhibitor pairs. This design results in one complete rate-versus-substrate concentration curve for the control experiment. In this instance, however, and unlike case I, complete inhibition curves were not obtained (i.e., one substrate-one inhibitor pair in case II versus six substrate-one inhibitor pairs in case I).

Case III. The inhibition experiments were based on two separate substrate-inhibitor pairs: [S] of 25 µM and [I] of 10 µM or [S] of 250 µM and [I] of 100 µM. The substrate concentrations were chosen to encompass the smallest and largest K_m,app values corresponding to the selected inhibitor concentrations. The substrate concentrations for the substrate-inhibitor pairs were obtained from the K_m,app relationship (K_m,app = K_m (1+ [I]/K_i). One pair had a low substrate and low inhibitor concentration, and one pair had a high substrate and high inhibitor concentration. A substrate concentration similar to the value for K_m,app was desired, and therefore, the substrate concentration closest to that used in the full control was selected.

Case IV. The inhibition experiments were based on two separate substrate-inhibitor pairs: [S] of 25 µM and [I] of 10 µM or [S] of 250 µM and [I] of 100 µM. The control experiments were based on three substrate concentrations only (2.5, 10, and 75 µM). Two hundred average rate-versus-[S] curves were generated (different from those in cases I, II, and III). One hundred average rates of metabolite formation were generated for each of the substrate-inhibitor pairs. In this instance and unlike case I, complete inhibition curves were not obtained (i.e., one substrate-one inhibitor pair in case IV versus six substrate-one inhibitor pairs in case I). Furthermore, this design tested the use of a minimal number of substrate concentrations (n = 3) for the control experiment.

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Evaluation of Mechanism of Enzyme Inhibition

Six different sets of parameter values were obtained from the literature. Each of these six sets had a different combination of enzyme kinetic parameters for V_max, K_m, and K_i. The three parameters for each set were chosen so that the K_m/K_i ratios were low, medium, and high to correspond to weak, medium, and strong inhibitors, respectively. Each of three sets of values were used as input parameters in the competitive enzyme inhibition equation, and the other three sets were used in the noncompetitive enzyme inhibition equation (Table 2). For a single set of parameters, metabolite formation rates were generated in triplicate, with normally distributed random errors (10, 20, and 30% CV).

Conventional, Nonoptimal Design. Six substrate concentrations without inhibitor served as the control. Six substrate concentrations were paired separately with two inhibitor concentrations (low and high). The preceding was done for each of six parameter combinations (Table 2), and 10 data sets were generated for each combination and for each of three random errors. All metabolite formation rates were calculated in triplicate, and the resulting rates were averaged. Thus, 30 data sets were generated for each level of error, and triplicate metabolite formation rates for each substrate-inhibitor concentration pair were averaged to yield 10 data sets.

Semiminimal Design. Six substrate concentrations in the absence of inhibitor were used to generate rate of metabolite formation for the control experiment. Three pairs of substrate-inhibitor concentrations were used to generate metabolite rates with inhibitor (three different substrate concentrations paired with a particular inhibitor concentration). The inhibitor concentration chosen was the lower value used for each set of 10 data sets in the "conventional, nonoptimal" design. One hundred data sets were generated for each parameter set and for each random error where each metabolite rate was an average of three values.

Minimal Design. Three substrate concentrations in the absence of inhibitor were used to generate the rate of metabolite formation for the control experiment. Three pairs of substrate-inhibitor concentrations were used to generate metabolite rates with inhibitor, where there were three different substrate concentrations and a particular inhibitor concentration. Only one parameter set representing a medium competitive inhibitor was used to generate data sets with 20% CV. The parameter values for the competitive enzyme inhibition model were used to generate the 100 data sets: V_max = 2.6 nmol · min¹ · mg protein¹, K_m = 11.9 µM, and K_i = 12.1 µM.

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	Results

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Evaluation of a Minimal Experimental Design

Table 3 and Fig. 1 summarize the estimates obtained for K_i for cases I and II. The results for case I, in which there was a complete rate profile for the control and for one inhibitor concentration, are shown on the left side of Table 3. Excellent estimates of K_i were obtained for both methods of data analysis (SNLR and K_m,app) regardless of inhibitor concentration. There was, however, less variability associated with the higher inhibitor concentration as judged by percentage CV and range of values. There was a less than 2-fold range in the estimates of K_i for each method, and in all cases, the ranges encompassed the correct value (5 µM). This can be seen visually from the data shown in Fig. 1. In the "box and whisker" plots, the ends of the box encompass the interquartile range with the median value shown as the solid horizontal line. The "whiskers" represent the 10 and 90 percentiles, and the outlier points are beyond those ranges. Each box represents the results of 100 simulations.

View this table: [in this window] [in a new window]   TABLE 3 Determination of Ki values using two methods of analysis and two experimental designs (cases I and II) Parameter values: Ki = 5 µM; Km = 10 µM; Vmax = 100 nmol · min1 · mg protein1. Values are the mean of 100 average experiments. A random error of 10% CV was added to all values of rate (v).

View larger version (13K): [in this window] [in a new window]   Fig. 1.   "Box and whiskers" plots of Ki values determined by several methods of data analysis as a function of inhibitor concentration ([I], 10 or 100 µM) and level of random error (% CV). Each box represents the interquartile range, with the median value illustrated by the solid horizontal line. The "whiskers" represent the 10 and 90 percentile range. , individual values outside of that range. The horizontal dotted line represents the correct value for Ki (5 µM). SNLR and Km,app methods of analysis were examined in case I, whereas only SNLR analysis was examined in case II. See text for details.

These findings indicate that excellent estimates of K_i can be obtained from experimental rate-versus-substrate concentration data that include one control and one inhibitor concentration. In this design, there were six substrate concentrations in the absence of and in the presence of one inhibitor concentration with triplicate measurements obtained (i.e., a total of 36 experimental rate values).

Case II, which evaluated the SNLR method, further minimized the experimental effort by reducing the total number of inhibitor-substrate pairs from six (as used in case I) to one. In each case, however, a complete substrate control experiment was performed (six substrates; a total of 21 experimental rate values). The results for this minimal design are summarized in Table 3 and Fig. 1. The approach used in case II provides good estimates of K_i but with greater variability than that noted for case I. The range of the estimates, for the added 10% CV, is less than 3-fold, and in all cases, the ranges encompass the mean value. A considerably wider range in values is noted when greater random error (20% CV) is incorporated into the simulations (last two columns in Table 3 and two boxes on the right in Fig. 1). In the latter instance, an approximate 8-fold range in values is seen at an inhibitor concentration of 10 µM. In both cases, the higher inhibitor concentration resulted in smaller variability (compare percent CVs and range of values).

Conclusions similar to these can be made for the estimates of K_m and V_max, whose results are presented in Fig. 2. Excellent estimates of these parameters are obtained for both cases I and II, but there is less variability in the case I scenario. For case II, with the greater of the two levels of error (noted in the two boxes at the right in Fig. 2), K_m values range less than 3-fold, whereas estimates of V_max vary by about 20% from the mean.

View larger version (18K): [in this window] [in a new window]   Fig. 2.   "Box and whiskers" plots of Vmax (y-axis on left) and Km (y-axis on right) determined by the SNLR and Km,app methods of data analysis as a function of inhibitor concentration ([I], 10 or 100 µM) and level of random error (% CV). The horizontal dotted line represents the correct values for Vmax (100 nmol · min1 · mg protein1) and Km (10 µM).

Table 4 summarizes the results obtained from one of the experimental designs used in case III for two levels of error. That table presents the results obtained with a low substrate-inhibitor concentration pair (25 and 10 µM). Those parameter estimates are provided as a function of the number of substrate concentrations and pairing of those concentrations for the control experiment. Good estimates of V_max, K_m, and K_i were obtained for even the least demanding experimental protocol at 20% CV; three substrate concentrations were used for the control experiment. In the latter instance, for the low substrate-inhibitor concentration pair, the estimates of V_max, K_m, and K_i, at 20% CV; (ratio of maximum to minimum value) were 102.79 ± 9.40 (1.29), 10.56 ± 2.15 (2.03), and 4.91 ± 1.16 (1.99), respectively. When the high substrate-inhibitor concentration pair was used, the corresponding estimates at 20% CV were 106.42 ± 16.58 (1.66), 11.31 ± 2.61 (2.01), and 6.43 ± 2.62 (3.01), respectively. The results indicate that a minimal design (i.e., a total of 12 experimental rate values) consisting of three averaged substrate concentrations for the control and an averaged single substrate-inhibitor pair (either low or high concentrations) gives good estimates of enzyme kinetic parameters. This minimal design was evaluated further in case IV, in which 100 averaged data sets were analyzed.

In case IV, data sets with 20% CV random error were analyzed. Table 5 summarizes results obtained from fitting the data obtained from the minimal experimental design used in case IV (20% CV). The K_i estimates ranged from 2.23 to 23.66 µM (~11-fold range) and 2.49 to 17.97 µM (~7-fold range) for the low and high substrate-inhibitor concentration pairs, respectively. V_max and K_m estimates from the minimal experimental design (low or high substrate-inhibitor concentration pairs) had a 2- and 4-fold range of values, respectively. The range of values associated with the high substrate-inhibitor concentration pair were smaller (especially for K_i estimates) than the corresponding ranges for the analysis of the data sets based on the low substrate-inhibitor concentration pair.

Evaluation of Mechanism of Enzyme Inhibition

Conventional, Nonoptimal Design. The SNLR method correctly identified the enzyme inhibition mechanism for each data set for all three levels of random error (10, 20, and 30% CV). Because there were three parameter sets each for competitive and noncompetitive enzyme inhibition mechanisms, 10 data sets each for every parameter set, and three random errors, the SNLR method correctly identified 90 data sets as belonging to a competitive and 90 data sets as belonging to a noncompetitive enzyme inhibition model. Table 6 indicates that for all three inhibitors (strong, medium, and weak) and for each type of inhibition, the SNLR method gave good estimates for all three parameters. However, the percent CV of the corresponding parameter estimates in the inhibition models did not follow any specific pattern. The ranking of percent CV for K_i estimates within the competitive inhibition model did follow the expected pattern: 1, 2, and 3 for high, medium, and low values for the ratio K_m/K_i, respectively, for all three levels of added random errors. For noncompetitive enzyme inhibition, there was no difference in percent CV across the three data sets for any of the three levels of added random error.

Semiminimal Design. The mean estimates of V_max, K_m, and K_i using the SNLR method were very close to the true values at all three levels of random error. Table 7 lists the results obtained from fitting the data to the SNLR method with 30% CV random error. The variability in parameter estimates increased as the level of random error increased. The variability associated with the three parameters in ascending order was: V_max < K_m < K_i. The range of estimates widened as the level of random error increased. At 10% CV, the greatest range was less than 2-fold (for estimating K_i; K_i = 4 µM, competitive model). At a 20% CV, the greatest range was less than 5-fold (for estimating K_i; K_i = 4 µM, competitive model). At a 30% CV, the greatest range was about 8-fold (for estimating K_i; K_i = 12.1 µM, competitive model).

View larger version (44K): [in this window] [in a new window]   Fig. 3.   Column plots showing the percentage of data sets correctly identified as a function of %CV and parameter sets (sets 1-3 for competitive and noncompetitive mechanisms). Each column represents a total of 300 experiments. The semiminimal design using the SNLR method was followed. Correct Vmax (nmol · min1 · mg protein1), Km (µM), and Ki (µM) values used in the parameter sets were as follows: competitive, set 1, 0.34 (Vmax), 20 (Km), and 0.4 (Ki); set 2, 2.6 (Vmax), 11.9 (Km), and 12.1 (Ki); and set 3, 0.14 (Vmax), 0.34 (Km), and 4 (Ki); noncompetitive, set 1, 13.7 (Vmax), 30 (Km), and 0.6 (Ki); set 2, 0.6 (Vmax), 67.5 (Km), and 84.4 (Ki); and set 3, 0.1 (Vmax, nmol · min1 · mg S-91), 0.35 (Km), and 36 (Ki).

Minimal Design. The SNLR method correctly identified the appropriate model for 98 of 100 data sets for the parameter set examined (V_max = 2.6 nmol · min¹ · mg protein¹, K_m = 11.9 µM, and K_i = 12.1 µM; competitive inhibition model) at 20% CV. The SNLR method gave good estimates of the enzymatic parameters: V_max = 2.63 ± 0.241 (2.06-3.22) nmol · min¹ · mg protein¹, K_m = 12.2 ± 2.17 (7.56-16.9) µM, and K_i = 12.7 ± 3.14 (6.85-23.4) µM.

	Discussion

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The purpose of the present investigation was to assess the practicality of reducing the experimental burden in estimating the enzyme kinetic parameters K_i, K_m, and V_max and distinguishing between competitive and noncompetitive enzyme inhibition mechanisms. The estimation of K_i was of particular interest because of the approaches currently relied on in its estimation. The SNLR method was applied to four designs and the K_m,app method was applied to one design to evaluate approaches for optimizing experimental effort. Although both methods of analysis perform equally well when complete inhibition curves are obtained (i.e., case I), the former approach is preferred because it is easier to implement. Furthermore, only the SNLR method lends itself to minimal experimental designs in which only one inhibitor-substrate pair is used. The minimal design results in reasonably accurate but variable estimates of K_i; estimates of K_m and V_max are more robust.

According to Cleland (1967), at least four substrate concentrations are needed in the control experiment to obtain reliable estimates of V_max and K_m. The minimal design examined (three averaged rates of substrate metabolism for the control experiment; case IV), gave good estimates of V_max and K_m. The averaged single substrate-inhibitor concentration data provides not only estimates of K_i but also estimates of V_max and K_m.

In case III, 10 averaged data sets were fitted for the minimal design. A preliminary study, using the minimal designs in case III, compared estimates of enzyme kinetic parameters obtained from 100 averaged data sets (average of 300 experiments) to estimates obtained from 10 randomly chosen sets of 30 experiments per data set (i.e., 10 experiments done in triplicate). Comparison of the box and whiskers plots of the estimated enzyme kinetic parameters indicated that the interquartile range (box) encompassed the true estimates for virtually all of the 10 data sets for V_max, K_m, and K_i (data not shown). Therefore, in case III, only 10 averaged data sets were used per design. Results from case III led to the final minimal design explored in case IV. For consistency, 100 averaged data sets were fitted for each substrate-inhibitor concentration pair (low and high), using the SNLR method, to obtain the full range of parameter estimates.

An assumption behind the designs used in this theoretical study is that the investigator has an estimate of K_m (from preliminary studies or from the literature). If the K_m value is known to be about 10 µM (value used in first part of this report), the control experiment should include a substrate concentration near 10 µM. To encompass the full range of the control reaction rates (v), a low [ca. (1/8)K_m; 2.5 µM) and high (ca. 8 · K_m; 75 µM) substrate concentrations should be used. Only one combination of a three-substrate minimal design for the control experiment was examined. There is only one six-substrate minimal design for the control. There are three combinations for the five- and four-substrate minimal designs for the control experiment if substrate concentrations of 2.5, 10, and 75 µM are fixed. In case III, no single combination of substrate concentrations in the five- or four-substrate minimal design was clearly superior in estimating V_max, K_m, and K_i.

Are the resulting estimates sufficiently accurate to allow this dramatic reduction in the total number of experiments (from 108 to 12 in case IV)? For screening purposes, the answer is yes; a reasonable estimate of K_i is obtained. However, if more accurate estimates of the parameters are required, more inhibitor-substrate pairs or additional complete inhibition curves are needed.

There is another experimental approach that should be considered for further reducing experimental burden (please see Acknowledgment). It is likely that a laboratory will use certain substrates and inhibitors to test specific isozymes in an established enzyme preparation. If that is the case, there should be a substantial amount of historical enzyme kinetic data for those probe or test substrates. Such baseline data can be relied on in the same manner that analytical controls are used: to determine whether the system is "within control" limits and to apply average parameter values. To determine whether the enzyme system is behaving "normally" (relative to historical value), it is only necessary to test one control substrate concentration (perhaps in triplicate). If the resulting metabolite formation rate is within the historical control limits, there is no need to test additional substrate concentrations. "Out of control" values would indicate a problem with the enzyme system, and additional experiments would have to be performed.

In this context, data analysis may be approached in several ways. Assuming that the experimental metabolite formation rate (in the absence of inhibitor) is within control limits, the associated historical average values for V_max and K_m (updated with new data) may be applied to the data obtained from the substrate-inhibitor experiments. In this instance, however, V_max and K_m are fixed as constants in the appropriate relationship (i.e., competitive or noncompetitive inhibition), which is solved for K_i. Alternatively, if the experimental metabolite formation rate is within control limits, the former single value may be simultaneously analyzed with the rate data obtained from the substrate-inhibitor experiment. This approach requires a priori knowledge of or an assumption of the mechanism of inhibition. Furthermore, a reasonable range of control values must apply as would be expected for pure isozymes and rodent liver preparations. It is unlikely that a similar relatively narrow control range of values will apply to human liver because of the expected highly variable nature of hepatic enzyme activity among human subjects.

The SNLR method was able to identify the correct enzyme inhibition model. The K_m,app method can, in theory, be used for that purpose. This can be done by comparing V_max and K_m values for the control and inhibition experiments; V_max should remain constant for a competitive model and K_m should remain constant for a noncompetitive model. However, when the variability in the data is high, both V_max and K_m values will vary, and therefore, the most correct model may not be selected. The data may appear to be derived from a mixed-type inhibition mechanism. In that situation, the SNLR method should be used to confirm the model. The SNLR method is superior to the K_m,app method in terms of reliably estimating the inhibition parameters and speed of analysis and of identifying the correct inhibition model.

After establishing that the SNLR method was able to correctly identify the true model, a minimal experimental design was explored (i.e., six substrates for control and one substrate-inhibitor pair). The SNLR method gave good parameter estimates when fit to the correct model, but the AIC values for the correct and the incorrect models were nearly identical for all data sets. Therefore, an additional substrate-inhibitor pair was added (i.e., same inhibitor concentrations and an additional substrate concentration). Even though the AIC values were different for most of the data sets with 10% CV, some of the data sets with 20% CV identified the incorrect mechanism. Therefore, a "semiminimal" inhibitor design was examined. In that approach, there were six different substrate concentrations paired with no inhibitor (control) and three pairs of substrate-inhibitor concentrations, using three different substrate concentrations and the same inhibitor concentration.

The "semiminimal" design was successful in discriminating between the two enzyme inhibition mechanisms even for data with 30% CV added random error. In the case of a strong inhibitor, the SNLR method was better at estimating the correct model compared with estimates for medium and weak inhibitors. The latter was especially apparent for data with 30% CV.

Results from the case IV design in the first portion of this report indicated that the number of substrate concentrations used in the control can be reduced to three. Therefore, the "minimal design" in the second part of this report involved three substrate concentrations paired with no inhibitor (control) and three substrate-inhibitor concentration pairs. Data with 20% level of error were used. The SNLR method was shown to be better at identifying the correct model for a strong versus medium and weak inhibitors. Because the SNLR method was equally capable of identifying the models belonging to the two types of inhibitions and inhibitors (medium and weak), a parameter set belonging to a medium competitive inhibitor was used. The results show that the "minimal design" was successful.

Competitive and noncompetitive enzyme inhibition models are the most commonly observed inhibitory mechanisms other than, perhaps, mixed models. It is possible that when the data generated have large errors, even though the inhibitory mechanisms are competitive or noncompetitive, investigators conclude the model to be of mixed type because of a lack of clear-cut distinction. Models such as uncompetitive are quite rare in single enzyme-catalyzed reactions. If preliminary studies indicate that the data belong to a certain type of enzyme inhibition model other than the two examined in the present study, the AIC values generated from the fit of the data to other models using the SNLR method can be compared with finding the "best" model describing the data.