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Abstract

Many factors must be considered during the optimization of an enzyme assay. These include the choice of buffer and its composition, the type of enzyme and its concentration, as well as the type of substrate and concentrations, the reaction conditions, and the appropriate assay technology. The process of an enzyme assay optimization, in our experience, can take more than 12 weeks using the traditional one-factor-at-a-time approach. In contrast, the design of experiments (DoE) approaches have the potential to speed up the assay optimization process and provide a more detailed evaluation of tested variables. However, not all researchers are aware of DoE approaches or believe that it is easy to employ a DoE approach for the optimization of an assay. In order to facilitate enzyme assay developers to use DoE methodologies, we present in detail the steps required to identify in less than 3 days (1) the factors that significantly affect the activity of an enzyme and (2) the optimal assay conditions using a fractional factorial approach and response surface methodology. This is exemplified with the optimization of assay conditions for the human rhinovirus-3C protease, and the methodology used could be employed as a basic guide for the speedy identification of the optimum assay conditions for any enzyme.

Keywords

design of experiments assay optimization enzyme activity fractional factorial response surface methodology

Introduction

Enzymes that are involved in the pathogenesis and development of disease are important targets for many marketed drugs, which are designed mainly to inhibit such enzymes.¹ During the initial stages of any drug design project, large chemical libraries composed of a variety of molecules that differ in size and structure have to be screened in order to identify new leads and hits (i.e., inhibitors, bioactive compounds, and ligands).^2,3 Pharmaceutical companies perform more than 50 million biological assays (including enzyme assays) annually, despite the improvements in assay technology.⁴ Thus, the development of reliable enzyme assays for the identification of lead compounds is a major challenge in the initial stages of any drug development project.^2,3

The development of an in vitro enzyme assay requires consideration of several factors, including the purity of the enzyme, pH, viscosity and ionic strength of the reaction mixture, and the addition of co-factors or other buffer additives.⁵ Although methodologies for enzyme assays have been extensively reviewed (see Bisswanger⁶ and references cited therein), a further modification of procedure is most likely required in all cases, in order to adjust the assay to the special features of the target enzyme or in order to develop an assay for a newly discovered enzyme.⁶ During the optimization of an enzyme assay, the effects of the following factors are normally examined: (1) buffer composition, (2) pH, (3) temperature, (4) the concentration of divalent ions (e.g., Mg²⁺, Ca²⁺), (5) the concentration of ion salts (e.g., NaCl, KCl), (6) the type and concentration of reducing agents (e.g., DTT, β-mercaptoethanol), and (7) solvent concentration (e.g., DMSO, polyethylene glycol [PEG]).⁷ In addition to these, the choice of detection method for following an enzymatic reaction and the size of the reaction volume are also critical,^6,8 especially if there are budget and material limitations. Assays are miniaturized in order to reduce the consumption of reagents (and therefore the cost), and the effect of miniaturization on both the signal window and assay performance should be examined in each case,⁹ while the general guidelines for enzymatic assays for high-throughput screening (HTS) must be employed.⁷ Moreover, the suitability of HTS assays should be evaluated for biological and pharmacological relevance as well as for robustness of assay performance by quantitative methods.¹⁰ More information and guidelines for assay validation methods, analyses, and acceptance criteria are available at https://www.ncbi.nlm.nih.gov/books/NBK83783/.

Using the traditional one-factor-at-a-time (OFAT) approach can take 4 or more months to develop an assay, and assay development can become a bottleneck in drug discovery projects.¹¹ Using the OFAT approach, one gains information about a particular factor during the experiment without taking into account the interactions among the various factors that may affect enzyme activity. Statistical design of experiments (DoE) is a statistical tool that is used to evaluate much faster both the effect and the significance of experimental variables (independent variables) on a response (dependent variable).¹² The most critical step in all DoE approaches is the selection of variables (and their levels), which need to be examined since each design is a fit-for-purpose DoE.¹³ Among the various DoE designs, response surface methodology (RSM) is the most widely used, and it has been successfully employed for the design, development, improvement, and optimization of various processes and for the formulation of new products and upgrading of existing ones.¹⁴ Even though the automated liquid handling systems (robotics) are not designed for setting up DoE assays, and the pipetting required to set up a DoE assay manually is too complicated, DoE designs have several advantages over the traditional OFAT approach. DoE designs produce data that can be analyzed to draw more accurate conclusions regarding the assay, while at the same time they improve the quality of the assay and shorten the time of assay development/validation.^7,8 Most importantly, in assay development, DoE designs can be used for screening, characterization, optimization, and evaluation of assay robustness, whereas in assay validation, DoE can be used for confirmation studies and for assessing assay robustness.¹¹ It is worthwhile to mention that recent advances in automation could facilitate the development of DoE assays using automated liquid handling systems. Modern systems such as TTP Labtech’s (Melbourn, UK) dragonfly system, Labcyte’s (San Jose, CA) Echo Acoustic Liquid Handling Technology, and Tecan’s (Männedorf, Switzerland) liquid handling/automation systems (e.g., the Freedom EVO systems) are equipped with low-volume dispensers and acoustic liquid handling systems and have the potential to be used for DoE assay development and optimization. Thus, the software to design experiments on automaton is now more of a limitation than automation itself.

For the DoE approaches as well as for the analysis/evaluation of the results, several software packages (e.g., Design-Expert, Minitab, JMP) are available. However, in spite of their availability, the use of DoE approaches has been limited to chromatographic and electrochemical techniques, and there are only a few publications using DoE in enzyme assays. Interestingly, a survey carried out by HTStec in 2009¹⁵ revealed that researchers do not use DoE approaches to optimize a biological process because the majority of them believe that this kind of design is very difficult to employ. In addition, many researchers stated that they were not aware of DoE, while others did not fully understand the benefits of these approaches in assay development. On the other hand, others have suggested the use of DoE in the industry and that it should be taught in academia.¹⁶

The aim of this work is to demonstrate the benefits of the applications of DoE to enzymologists and, at the same time, provide a step-by-step guide that will encourage them to use DoE approaches. To this end, we have used the optimization of assay conditions for the human rhinovirus (HRV)-3C protease as a case study. HRV-3C protease, which plays an important role in viral infection (i.e., it catalyzes the generation of functional viral proteins and enzymes¹⁷), is a potential target for antiviral drug development. To identify novel inhibitors that bind selectively at the catalytic site of HRV-3C protease, it is necessary to have an assay suitable for the HTS of large libraries. Herein, we describe the layout of the statistical approaches used for (1) the identification of variables that significantly affect HRV-3C protease activity and (2) the further optimization of enzyme assay conditions. To this end, the colorimetric assay developed by Wang et al.¹⁷ was optimized using the DoE approach. The optimization of reaction conditions resulted in a 1.5-fold increase in the HRV-3C protease activity in a 96-well plate format that makes the assay suitable for HTS of enzyme inhibitors.

Materials and Methods

Materials

All chemicals were obtained from Sigma-Aldrich (St. Louis, MO), Thermo Fisher Scientific (Waltham, MA), or Macherey-Nagel (Düren, Germany). Recombinant HRV-3C protease was expressed in Escherichia coli (as a GST-tagged protein) and purified as previously described.¹⁸ Separation of HRV-3C protease from the GST tag was carried out using the Thrombin Clean Cleave Kit (Sigma) according to manufacturer’s instructions.

HRV-3C Protease Activity Assay

The activity of HRV-3C protease was assessed using the synthetic p-nitroanilide (pNA) peptide, EALFQ-pNA (Peptides International, Louisville, KY), which mimics the cleavage site of HRV-3C protease as previously described,¹⁷ with minor modifications. Briefly, 0.5 μΜ of the purified HRV-3C protease was incubated with 250 μΜ pNA peptide substrate in a final reaction volume of 100 μL. For the identification of factors that significantly affect the activity of HRV-3C protease, a fractional factorial approach was employed that included experiments under various reaction conditions using 50 mM of either Tris-HCl or HEPES buffer at different pH values and a range of concentrations of various additives as described in Results and Discussion. For the optimization of HRV-3C protease assay conditions using RSM, experiments were carried out at 30 °C in 50 mM HEPES buffer at different pH values and concentrations of DTT and glycerol as described in Results and Discussion. All buffers were supplemented with 150 mM NaCl and 0.5 mM EDTA. Peptide cleavage activity was assayed by optical density (OD) measurements at 405 nm, against a control sample that did not contain any enzyme.¹⁷ A different pNA standard curve (0–250 μΜ) was prepared for each reaction buffer ( Suppl. Fig. S1 ). All reactions were directly prepared in 96-microtiter plate wells and the OD measurements were monitored using a temperature-control microplate reader (PerkinElmer, Waltham, MA). One unit of protease activity was defined as the cleavage of 1 μmol/min of pNA peptide at 30 °C (or at the designated temperature as described in Results and Discussion).

Determination of the Michaelis–Menten constant (K_M) and maximum velocity (V_max) before and after optimization of reaction conditions, as described in Results and Discussion, was carried out using 0.5 μΜ HRV-3C protease with incresing concentrations of pNA peptide (0–600 μΜ). All assays were performed in triplicate. The kinetic parameters K_M and V_max were calucated by fitting the data by nonlinear regression to the classic Michaelis–Menten steady-state model (eq 1) using Prism v7.0 (GraphPad, La Jolla, CA):

v_{o} = \frac{V_{m a x} \times S}{K_{M} + S}

(1)

where v_o is the initial velocity (μmol/mL/min), V_max is the maximum reaction velocity (μmol/mL/min), and S is the substrate concentration (μΜ). The turnover number (k_cat) was caculated assuing a molecular mass of 20.5 kDa.

Determination of Z′ Factor

The Z′ factor is a statistical parameter that is employed to assess the quality of an HTS assay.^10,19 The Z′ factor was calculated based on the following equation:

Z^{'} = 1 - 3 \times \frac{σ_{p} + σ_{n}}{μ_{p} - μ_{n}}

(2)

where σ_p and σ_c are the standard deviations of the positive and negative controls, respectively, and μ_p and μ_n are their respective means.

The assay was carried out with a final concentration of 0.5 μΜ HRV-3C protease and 250 μΜ pNA substrate in a final volume of 100 μL either in the previously described assays conditions (25 mM HEPES, pH 7.5, 150 mM NaCl, 1 mM EDTA, 6 mM DTT at 30 °C for 30 min)¹⁷ or in the optimized reaction conditions as described in Results and Discussion. Negative controls contained assay buffer in place of HRV-3C protease.

Statistical Design of Experiments

The software package Design-Expert v7 (Stat-Ease Inc., Minneapolis, MN) was used to design the DoE approaches, statistically analyze the results, and plot the three-dimensional (3-D) response surface graphs as described in Results and Discussion.

Results and Discussion

Strategy to Optimize the Reaction Conditions for HRV-3C Protease

The colorimetric assay for the determination of enzymatic activity of HRV-3C protease using a pNA synthetic peptide mimicking its native cleavage site has been previously described.¹⁷ Cleavage of pNA peptide between glutamine and pNA by the protease releases a yellow-colored pNA product (λ_max = 405 nm). It should be noted that to avoid false-positive or false-negative results due to buffer additive or traces of additives (i.e., DTT, EDTA, glycerol), we first evaluated any color interference by these compounds. None of these agents at the concentrations used affected the amount of yellow color produced (data not shown). Other key additives that may interfere, like detergents (to avoid protein aggregation), DMSO (used for the storage of compounds), and reducing agents (used to prevent oxidation of cysteine residues), are currently under investigation in our laboratory.

When we performed the assay under the previously described reactions conditions¹⁷ (25 mM HEPES, pH 7.5, 150 mM NaCl, 1 mM EDTA, 6 mM DTT at 30 °C for 30 min), the activity of HRV-3C protease was found to be equal to 487 ± 5.2 U/mL. Under these assay conditions, the kinetic parameters K_M, V_max, and K_cat were determined to be 244.6 ± 18 μΜ, 908 ± 31 μmol/mL/min, and 30 × 10⁻³ s⁻¹, respectively, while a Z′ value of 0.78 was obtained. We subsequently performed a screening-and-optimization DoE investigation to determine which reaction conditions could increase the activity of the protease. At first, we employed a fractional factorial design to identify factors that significantly affected enzyme activity. This was followed by the identification of optimal assay conditions using RSM. The specific steps taken for these approaches are described below.

Part 1: Screening Experiments to Identify Statistically Significant Factors

When optimizing assay reactions, the first question to ask is, “What variables should we examine?” A screening test is needed, therefore, to identify the factors (variables) that significantly affect the reaction (response) and thus reduce the long list of potential factors to a manageable few. It should be noted that the meaning of the terms of the DoE approaches that are used here are summarized in Supplemental Table S1 .

A two-level design is usually employed in order to identify the most important factors. Two-level designs are those in which all factors have only two values, while the effects of both categorical and continuous factors on the response can be examined simultaneously. Thus, to examine k factors at two levels, 2^k combinations (experiments) are required. The 2^k full (or complete) factorial design uses all 2^k combinations. When there are many factors to be examined as to whether they are important for the reaction, the number of experiments to perform using a 2^k full factorial approach becomes very large and too expensive to implement. In this case, it is recommended to examine only a fraction (e.g., one-half or one-quarter) of the full factorial approach. Thus, the $2_{R}^{k - p}$ fractional factorial design (where k is the number of factors, p represents the size of the fraction of the 2^k full factorial, and R is the resolution of the method) is widely used in order to identify the main factors affecting the reaction without losing information regarding possible interactions among factors. Design resolution (R) shows how clearly the effects can be separated in a design (the higher, the better), and resolution IV designs are the preferred ones. In addition, Plackett–Burman designs, a type of two-level fractional factorial design for studying N – 1 variables in N experiments (where N is a multiple of 4), are widely employed to identify the factors that statistically significantly affect a process. The specific steps taken to identify the assay factors that significantly affect the activity of HRV-3C protease using a two-level fractional factorial approach are described below.

Step 1: Selection of the screening variables. A major concern in setting up or optimizing a biological assay is the selection of factors to be tested and their ranges to use. Normally, if there is literature available, one starts with factors reported previously to be required for the activity of the same or similar enzyme. The concentration range of the selected factors to be tested should then be chosen carefully and should be large enough to cause an obvious alteration in the measured response, but not so large that the process will “fall off a cliff” and produce unusable data.

In the case of the HRV-3C protease used in this study, one categorical factor, that is, buffer composition (Tris-HCl and HEPES), and seven continuous factors—reaction pH, temperature, and time, as well as the concentrations of NaCl, DTT, EDTA, and glycerol—were selected for an initial screening. The low (–) and high (+) values of these factors to be tested were as follows: pH 7 and 8; temperature, 25 and 30 °C; time, 20 and 40 min; NaCl concentration, 150 and 500 mM; DTT concentration, 1 and 10 mM; EDTA concentration, 0.5 and 5 mM; and glycerol concentration, 2% and 10% v/v. The high and low levels of variables were selected as follows: for pH, DTT, EDTA, and incubation time, we used the standard conditions (7.5, 6 mM, 0.5 mM, and 30 min, respectively) as a starting point and we increased and decreased their values. However, for the activity of HRV-3C protease at least 150 mM NaCl is required;^17,18 thus, we used this salt concentration as the low level. In addition, we selected 30 °C as the high level of reaction temperature because at this temperature denaturation is not an issue and effective thermosetting is not required, while the assay is carried out at a temperature closer to the in vivo temperature of 37 °C. It should be noted that glycerol is not included in the standard assay condition, but we wanted to examine whether its presence affects the HRV-3C protease activity because glycerol is widely used to enhance the stability of many proteins.¹⁸ Based on preliminary experiments, the presence of 0.5 μΜ purified protease was sufficient to determine its activity under these conditions (data not shown).

Step 2: Selection of a two-level factorial approach. For the initial screening, we selected eight factors while only 1/16 (p = 4) of the full factorial was chosen to test; thus, a total of $\frac{1}{16} \times 2^{8} = 2^{8 - 4} = 16$ runs were required. The 16 different runs of the $2_{I V}^{8 - 4}$ factorial design used in this work and the results are presented in Table 1 .

Step 3: Identification of the factors that significantly affect the response. The data from Table 1 were automatically used by the Design-Expert software to produce the plots of Figure 1A(i,ii) (i.e., half-normal plot and Pareto chart) in order to assess the statistical significance of each variable on protease activity. More information on how to create these plots is available at https://www.statease.com/docs/v11/contents/analysis/select-effects.html. In more detail, each variable can be evaluated for its statistical significance by a half-normal probability plot that uses the estimated effect of each factor in order to identify the important ones. For our example, the factors pH (B), reaction time (D), DTT concentration (F), and glycerol concentration (H) produced significant effects as shown in Figure 1A (i). To further assess the significance of each factor, the Pareto chart was employed. As illustrated in Figure 1A (ii), the Pareto chart shows that the pH (B), time (D), DTT concentration (F), and glycerol concentration (H) lie above the Bonferroni limit (i.e., it is highly probable that they are statistically significant). Guidelines on how to identify factors that significantly affect a process using the Pareto chart/Bonferroni limit are available at https://www.statease.com/docs/v11/navigation/pareto-chart.html. Consequently, the statistically significant variables (pH, time, DTT and glycerol concentrations) were further investigated to determine the ranges that should be used for optimal activity using RSM as described in the following paragraphs.

Table 1.

Fractional Factorial Experimental Design for the Identification of Factors That Significantly Affect the Activity of HRV-3C Protease.

Run	A: Buffer	B: pH	C: Temperature (°C)	D: Time (min)	E: NaCl (mM)	F: DTT (mM)	E: EDTA (mM)	H: Glycerol (% v/v)	Activity (U/mL)
1	Tris^a	7	25	20	150	1	0.5	2	426.1
2	HEPES^b	7	25	20	500	1	5	10	337.2
3	Tris	8	25	20	500	10	0.5	10	156.0
4	HEPES	8	25	20	150	10	5	2	202.3
5	Tris	7	30	20	500	10	5	2	369.4
6	HEPES	7	30	20	150	10	0.5	10	315.3
7	Tris	8	30	20	150	1	5	10	207.4
8	HEPES	8	30	20	500	1	0.5	2	214.5
9	Tris	7	25	40	150	10	5	10	400.3
10	HEPES	7	25	40	500	10	0.5	2	470.4
11	Tris	8	25	40	500	1	5	2	360.7
12	HEPES	8	25	40	150	1	0.5	10	305.7
13	Tris	7	30	40	500	1	0.5	10	494.7
14 ^c	HEPES	7	30	40	150	1	5	2	576.7
15	Tris	8	30	40	150	10	0.5	2	359.9
16	HEPES	8	30	40	500	10	5	10	264.4

50 mM Tris-HCl.

50 mM HEPES.

The optimal assay conditions are indicated in bold.

Figure 1.

(A) Identification of the factors with a statistically significant effect on the activity of HRV-3C protease. (i) Adjusted half-normal probability plot with significant factors selected: pH (B), time (D), glycerol concentration (H), and DTT concentration (F). In a half-normal plot, the effects of nonsignificant (unimportant) factors have a normal distribution centered near zero, while the effects of significant (important) factors are significantly removed from zero. The farther away a factor is from the diagonal line, the greater its effect on the response. (ii) The Pareto chart identified factors B, D, H, and F lying above the Bonferroni limit, and they are designated as truly significant coefficients. Pareto charts examine the t value of the effect at two limit lines, that is, the Bonferroni limit line (t value of effect = 3.72829) and the t limit line (t value of effect = 2.20099). Factors that have t values above the Bonferroni line are considered truly significant, whereas factors with a t value between the Bonferroni line and t limit line are possibly significant, while those with a t value of effect below the t-limit line are statistically insignificant and not considered any further. (B) Diagnostic plots for the evaluation of the accuracy of the regression model for HRV-3C protease activity. (i) Normal (%) probability plot of the “Studentized” residuals for the model. (ii) Predicted values of HRV-3C protease activity versus actual values.

Part 2: Optimization of HRV-3C Protease Activity Using Response Surface Methodology

Once the key factors affecting a process are identified, an RSM design can then be employed to further optimize the process. RSM designs fit the experimental data with a second-order equation for the response, and if a maximum or minimum exists within the region of the key factors, RSM will find it.¹⁴ The main steps followed to identify the optimal assay conditions for HRV-3C protease using RSM are described below.

Step 1: Selection of an RSM design. The most widely used designs are the central composite design (CCD)¹³ and the Box–Behnken design (BBD)¹³ ( Suppl. Fig. S2 ). The CCD is based on two-level factorial designs, and each numeric factor is examined at five level points: two axial (±α), two factorial (±1), and one central (0). Thus, all factors are examined at levels –α, –1, 0, 1, and +α. In general, the ±1 factorial points define the limits for the area of interest where the optimum value of the response is believed to exist. The value of α determines the location of axial points in the experimental domain, while the axial points (±α) will typically be outside this limit to ensure that even the extreme axial runs are within the area of operability.²⁰ Depending on the α value, the design is rotatable, orthogonal, spherical, or face-centered.²⁰ The value of α depends on the number of factors and is calculated by the formula $α = 2^{k / 4}$ , where k is the number of factors. Thus, for two, three, and four variables, the α value is equal to 1.41, 1.68, and 2.00, respectively. Regardless of the axial distance, the center points are replicated four to six times to get a good estimation of the experimental error. For the HRV-3C protease in this study, a four-factor, five-level central composite rotatable design (CCRD) was applied. It should be noted the face-centered CCD is the simplest design to perform, as it requires running the process at only three levels of each variable. However, in our laboratory we prefer the CCRDs in spite of the fact that they require the process at five levels of each variable. The main disadvantage of face-centered designs is that they give poor precision for estimating pure quadratic coefficients. On the contrary, CCRDs, by using axial points that give new extremes for the low and high settings for all factors, have different magnitudes of prediction error.

Step 2: Selection of variables levels and of the axial distance α: We subsequently examined the four aforementioned important factors at low (–1) and high (+1) level and α value equal to 2, as follows: A: pH (7.4 and 8.2); B: incubation time (30 and 50 min); C: DTT concentration (4 and 10 mM); and D: glycerol concentration (5% and 15% v/v). The –α, –1, 0, 1, and +α levels of the four variables selected for experiments in the CCRD were as follows: pH (7, 7.4, 7.8, 8.2, 8.6), reaction time (min) (20, 30, 40, 50, 60), DTT concentration (mM) (1, 4, 7, 10, 13), and glycerol concentration (% v/v) (0, 5, 10, 15, 20). Overall, 30 experiments consisting of 16 cubic points, 8 axial points, and 6 central points were carried out. The 30 different combinations of the factors used in this work and the results are summarized in Table 2 .

Step 3: Generation of the regression equation. The data obtained from the experiments carried out using the parameters ( Table 2 ) were fitted automatically by the software to a response surface model, which for these data is the following equation:

\begin{array}{l} Y [HRV - 3 C activity (U / mL)] = + 629.28 - 39.90 A \\ + 26.94 B + 48.30 C + 9.75 D + 3.11 AB + 0.69 AC \\ + 0.21 AD + 11.83 BC - 22.58 BD - 5.40 CD - 31.42 A^{2} \\ + 9.10 B^{2} - 72.25 C^{2} - 35.34 D^{2} \end{array}

(3)

where Y represents the response, that is, the activity in U/mL of the HRV-3C protease enzyme, and A, B, C, and D are the mathematical model terms for the four factors, that is, pH, time, DTT concentration, and glycerol concentration, respectively.

Step 4: Statistical analysis of the results and evaluation of the fitted mathematical model. The terms used to validate the mathematical model as well as to assess the impact of the variables on HRV-3C protease activity are summarized in Supplemental Table S2 . The results of the regression analysis and analysis of variance (ANOVA) for the model are presented in Supplemental Table S3 .

The quality of the fitted mathematical model (eq 3) was evaluated by using “Lack of Fit test” and “Adj R-Squared.” The “Lack of Fit F-value” of 2.46 indicates that the lack of fit is not significant relative to the pure error, while the “Lack of Fit p-value” of 0.1666 indicates that all data are fitted well to the model. Moreover, the “Pred R-Squared” of 0.6871 was in good agreement with the “Adj R-Squared” of 0.8797. The “Adeq Precision” of 18.111 indicates an acceptable signal-to-noise ratio.

The adequacy of the fitted model (eq 3) was also verified by the normal (%) probability plot of the “Studentized” residual, as illustrated in Figure 1B (i); as shown, the errors of the model were normally distributed and insignificant. Moreover, as illustrated in Figure 1B(ii) the experimental and predicted values for the activity of HRV-3C protease are close. The predicted and actual values for the activity of HRV-3C protease are also illustrated in Table 2 .

The impact of variables on HRV-3C protease activity was evaluated by using the F tests following ANOVA and a p value of <0.05 for determining whether differences are statistically significant ( Suppl. Tables S3 ). The analysis revealed that the activity of the tested protease was significantly (p < 0.05) affected by the linear coefficients A, B, and C; by the quadratic factors A², C², and D²; and by the interaction of factor B with D.

Step 5: Generation of model graphs and determination of optimal conditions. To visualize and further examine the effects of the tested factors (and their interactions) on HRV-3C protease activity, the fitted second-order equation is presented as a 3-D plot (response surface plot). A 3-D response surface plot is the graphical representation of the relationships between three variables, that is, two independent variables on the x and y axes (the others are kept at their center points) and the response on the z axis, which is shown as a smooth 3-D surface plot ( Fig. 2 ). Each plot in Figure 2 provides information on the relation between HRV-3C protease activity and each factor and facilitates the identification of the best reaction conditions. According to these graphs, when pH ranges from 7.0 to 8.6, the activity of the tested protease first increases and then decreases, while the enzyme is more active when the pH is close to 7.6. Based on these graphs, higher protease activity could theoretically be achieved when incubation time is outside the experimental region (>50 min). Moreover, an increase of glycerol and DTT concentration above 15% and 9 mM, respectively, had a negative effect on HRV-3C protease activity, whereas the maximum enzyme activity (~700 U/mL) was obtained at values close to their central points for both factors (10% and 7 mM, respectively). The model developed for the determination of HRV-3C protease activity exhibits adequate sensitivity as it can detect the effect of small fluctuations of the variables on the response.

Step 6: Numerical optimization. The reaction conditions to maximize the protease activity were further optimized using the point optimization feature of Design-Expert software (see Antoniou et al.¹⁸ and references cited therein), which predicted a maximum enzyme activity of 751 U/mL at the following conditions: buffer pH 7.5, reaction time equal to 60 min, and DTT and glycerol concentrations of 9.2 mM and 6.5% (v/v), respectively. When these assay conditions were tested experimentally, an activity of 732 U/mL was obtained, in good agreement with the predicted activity. Under optimal assay conditions, the K_M, V_max, and K_cat were 194.2 ± 13 μΜ, 1215 ± 35 μmol/mL/min, and 41 × 10⁻³ s⁻¹, respectively, whereas a Z′ factor of 0.92 was obtained, indicating good reproducibility.

Table 2.

Central Composite Matrix with Actual and Predicted Responses of HRV-3C Protease Activity.

Run	Factors				Response
	Actual Values				HRV-3C Activity (U/mL)
	A	B	C	D	Actual	Predicted
1	7.4	30.0	4.0	5.0	482.9	442.1
2	8.2	30.0	4.0	5.0	382.5	354.3
3	7.4	50.0	4.0	5.0	509.6	511.3
4	8.2	50.0	4.0	5.0	458.9	435.9
5	7.4	30.0	10.0	5.0	539.6	524.5
6	8.2	30.0	10.0	5.0	439.9	439.4
7	7.4	50.0	10.0	5.0	690.5	641.0
8	8.2	50.0	10.0	5.0	555.5	568.4
9	7.4	30.0	4.0	15.0	537.4	517.2
10	8.2	30.0	4.0	15.0	418.7	430.2
11	7.4	50.0	4.0	15.0	533.5	496.0
12	8.2	50.0	4.0	15.0	413.7	421.5
13	7.4	30.0	10.0	15.0	593.0	577.9
14	8.2	30.0	10.0	15.0	502.9	493.7
15	7.4	50.0	10.0	15.0	583.3	604.1
16	8.2	50.0	10.0	15.0	529.6	532.3
17	7.0	40.0	7.0	10.0	528.3	583.4
18	8.6	40.0	7.0	10.0	433.5	423.8
19	7.8	20.0	7.0	10.0	575.8	611.8
20 ^a	7.8	60.0	7.0	10.0	710.2	719.6
21	7.8	40.0	1.0	10.0	202.1	243.7
22	7.8	40.0	13.0	10.0	433.0	436.9
23	7.8	40.0	7.0	0.0	419.9	468.4
24	7.8	40.0	7.0	20.0	510.6	507.4
25	7.8	40.0	7.0	10.0	599.5	629.3
26	7.8	40.0	7.0	10.0	601.1	629.3
27	7.8	40.0	7.0	10.0	645.7	629.3
28	7.8	40.0	7.0	10.0	667.4	629.3
29	7.8	40.0	7.0	10.0	624.0	629.3
30	7.8	40.0	7.0	10.0	638.0	629.3

The optimal assay conditions are indicated in bold.

Figure 2.

Response surface plots generated from the quadratic model of eq 3, showing the effect on HRV-3C protease activity of changing two factors at a time while the rest are fixed at their central points. The effect of interactions between factors was considered significant if the p value obtained from ANOVA was <0.05 ( Suppl. Table S3 ). (A) Effect of pH and reaction time. The effect of interaction between pH and time on enzyme activity was not significant (p = 0.7425) but had a positive influence since the model coefficient term AB from eq 3 had a positive sign. (B) Effect of pH and DTT concentration. The effect of interaction between these factors was not significant (p = 0.9415), but it may positively affect protease activity since the model coefficient term AC of eq 3 had a positive sign. (C) Effect of pH and glycerol concentration. The effect of interaction of these factors was not significant (p = 0.9821). However, the positive sign of the AD term in eq 3 implies a positive influence on protease activity. (D) Effect of reaction time and DTT concentration. The effect of interaction of these factors was insignificant (p = 0.2222). However, the positive sign of the term BC in eq 3 indicates a positive impact on protease activity. (E) Effect of reaction time and glycerol concentration. The effect of interaction of these two factors was significant (p = 0.0281) and had a negative impact on enzyme activity since the model term BD in eq 3 had a negative sign. (F) Effect of DTT concentration and glycerol concentration. Although the effect of interaction of the two factors was not significant (p = 0.5699), the negative sign of the model term CD in eq 3 suggests that these two factors in combination may negatively affect the enzyme activity.

In conclusion, DoE is a powerful tool that is gaining success in the optimization of any process that is affected by multiple factors. In this study, we ran the optimization of assay conditions of the HRV-3C protease in only 2 days, with one only scientist, and an approximately 50% increase of activity was achieved after identification of the optimal reaction conditions (the enzyme activity before and after optimization was 487 and 732 U/mL, respectively). Kinetic studies revealed that under optimal conditions, the affinity (reciprocal of K_M) of HRV-3C protease against pNA peptide substrate, V_max, and k_cat increase by 25.8%, 33.8%, and 36.7%, respectively, (p < 0.001). Most importantly, our modified assay demonstrated a significantly higher Z′ factor (0.92) compared with assay under the standard reaction conditions (Z′ factor 0.78), indicating that the former is probably more suitable for identifying HRV-3C protease inhibitors. The Z′ test is the most important statistical test to assess the assay quality as it takes into account both the signal window and assay viability.¹⁰ This final assessment of assay performance confirmed the efficiency of the developed assay for screening potential inhibitors of HRV-3C protease. It should be noted that the kinetic parameters should be balanced with the assay window when DoE is employed for the optimization of assay conditions.

Supplemental Material

DS_DISC830084 – Supplemental material for A General Guide for the Optimization of Enzyme Assay Conditions Using the Design of Experiments Approach

Supplemental material, DS_DISC830084 for A General Guide for the Optimization of Enzyme Assay Conditions Using the Design of Experiments Approach by Favour Chinyere Onyeogaziri and Christos Papaneophytou in SLAS Discovery

Footnotes

Acknowledgements

We thank Professor Catherine Demoliou for her support and critical review of the manuscript.

Supplemental material is available online with this article.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Christos Papaneophytou

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