Abstract

Enzymes are important drug targets. Many marketed drugs today function through inhibition of enzymes mediating disease phenotypes. To design, develop and validate robust enzymatic assays for HTS applications, it is critical to have a thorough understanding of the enzyme biochemistry and the kinetics of enzyme action. This chapter contains basic concepts in enzyme kinetics, selection of appropriate substrates for assay design and the estimation and significance of K_m and V_max, the intrinsic kinetic parameters of enzyme targets. These concepts are addressed in the context of drug discovery and HTS assay development.

Enzyme Assay Development Flow Chart

Introduction

Enzyme inhibitors are an important class of pharmacological agents. Often these molecules are competitive, reversible inhibitors of substrate binding. This section describes the development and validation of assays for identification of competitive, reversible inhibitors. In some cases other mechanisms of action may be desirable which would require a different assay design. A separate approach should be used if seeking a non-competitive mechanism that is beyond the scope of this document and should be discussed with an enzymologist and chemist (1).

Concept

Enzymes are biological catalysts involved in important pathways that allow chemical reactions to occur at higher rates (velocities) than would be possible without the enzyme. Enzymes are generally globular proteins that have one or more substrate binding sites. The kinetic behavior for many enzymes can be explained with a simple model proposed during the 1900's:

where E is an enzyme, S is a substrate and P is a product (or products). ES is an enzyme-substrate complex that is formed prior to the catalytic reaction. Term k₁ is the rate constant for enzyme-substrate complex (ES) formation and k_-1 is the dissociation rate of the ES complex. In this model, the overall rate-limiting step in the reaction is the breakdown of the ES complex to yield product, which can proceed with rate constant k₂. The reverse reaction (E + P → ES) is generally assumed to be negligible.

Assuming rapid equilibrium between reactants (enzyme and substrate) and the enzyme-substrate complex resulted in mathematical descriptions for the kinetic behavior of enzymes based on the substrate concentration (2). The most widely accepted equation, derived independently by Henri and subsequently by Michaelis and Menten, relates the velocity of the reaction to the substrate concentration as shown in the equation below, which is typically referred to as the Michaelis-Menten equation:

where

v = rate if reaction

V_max = maximal reaction rate

S.

= substrate concentration

K_m = Michaelis-Menten constant

For an enzymatic assay to identify competitive inhibitors, it is essential to run the reaction under initial velocity conditions with substrate concentrations at or below the K_m value for the given substrate. The substrate should either be the natural substrate or a surrogate substrate, like a peptide, that mimics the natural substrate. The optimal pH and buffer component concentrations should be determined before measuring the K_m (see Optimization Experiments).

Reagents and Method Development

For any enzyme target, it is critical to ensure that the appropriate enzyme, substrate, necessary co-factors and control inhibitors are available before beginning assay development. The following requirements should be addressed during the method design phase:

1.

Identity of the enzyme target including amino acid sequence, purity, and the amount and source of enzyme available for development, validation and support of screening/SAR activities. One should also ensure that contaminating enzyme activities have been eliminated. Specific activities should be determined for all enzyme lots.

2.

Identify source and acquire native or surrogate substrates with appropriate sequence, chemical purity, and adequate available supply.

3.

Identify and acquire buffer components, co-factors and other necessary additives for enzyme activity measurements according to published procedures and/or exploratory research.

4.

Determine stability of enzyme activity under long-term storage conditions and during on bench experiments. Establish lot-to-lot consistency for long-term assays.

5.

Identify and acquire enzyme inactive mutants purified under identical conditions (if available) for comparison with wild type enzyme.

Detection System Linearity

Instrument capacity needs to be determined by detecting signal from product and plotting it versus product concentration. Figure 1 below demonstrates what can happen if a detection system has a limited linear range. In the Capacity 20 trace, the system becomes non-linear at concentrations of product that are greater than 10% of the total product generated. This limited linear range would severely compromise measurements, since it is essential that the enzyme reaction condition be within the linear portion of the instrument capacity. Subsequent assay analysis would be affected if the enzyme reaction were performed outside of this linear portion. The Capacity 100 trace represents a more ideal capability of an instrument that allows a broad range of product to be detected.

Figure 1:

Signal saturation can lead to false measurements of assay parameters, such as K_m

The linear range of detection for an instrument can be determined using various concentrations of product and measuring the signal. Plotting the signal obtained (Y-axis) versus the amount of product (X-axis) yields a curve that can be used to identify the linear portion of detection for the instrument.

Enzyme Reaction Progress Curve

A reaction progress curve can be obtained by mixing an enzyme and its substrate together and measuring the subsequent product that is generated over a period of time. The initial velocity region of the enzymatic reaction needs to be determined and subsequent experiments should be conducted in this linear range, where less than 10% of the substrate has been converted to product. If the reaction is not in the linear portion, the enzyme concentration can be modified to retain linearity during the course of the experiments. Both of these steps (modifying the enzyme and analyzing the reaction linearity) can be conducted in the same experiment. An example is shown below in Figure 2.

Figure 2:

Plateau is due to substrate depletion

In this set of data, product is measured at various times for three different concentrations of enzyme and one substrate concentration. The curves for the 1x and 2x relative levels of enzyme reach a plateau early, due to substrate depletion. To extend the time that the enzyme-catalyzed reaction exhibits linear kinetics, the level of enzyme can be reduced, as shown for the 0.5x curve. These curves are used to define the amount of enzyme, which can be used to maintain initial velocity conditions over a given period of time. These time points should be used for subsequent experiments.

Note that all three of the reaction progress curves shown in the example above approach a similar maximum plateau value of product formation. This is an indication that the enzyme remains stable under the conditions tested. A similar experiment performed when enzyme activity decreases during the reaction is shown in Figure 3. In this case, the maximum plateau value of product formed does not reach the same for all levels of tested enzyme, likely due to enzyme instability over time.

Figure 3:

Plateau is due to loss of enzyme activity (note: plateaus do not converge)

Measurement of K_m and V_max

Once the initial velocity conditions have been established, the substrate concentration should be varied to generate a saturation curve for the determination of K_m and V_max values. Initial velocity conditions must be used. The Michaelis-Menten kinetic model shows that the K_m = [S] at V_max/2. In order for competitive inhibitors to be identified in a competition experiment that measures IC₅₀ values, a substrate concentration around or below the K_m must be used. Using substrate concentrations higher than the K_m will make the identification of competitive inhibitors (a common goal of SAR) more difficult.

For kinase assays, the K_m for ATP should be determined using saturating concentrations of the substrate undergoing phosphorylation. Subsequent reactions need to be conducted with optimum ATP concentration, around or below the K_m value using initial velocity conditions. However, it would be best to determine K_m for ATP and specific substrate simultaneously. This would allow maximum information to be gathered during the experiment as well as address any potential cooperativity between substrate and ATP.

A requirement for steady state conditions to be met means that a large excess of substrate over enzyme is used in the experiment. Typical ratios of substrate to enzyme are greater than 100 but can approach one million.

How to measure K_m

• Measure the initial velocity of the reaction at substrate concentrations between 0.2-5.0 K_m. If available, use the K_m reported in the literature as a determinant of the range of concentration to be used in this experiment. Use 8 or more substrate concentrations.
• Measuring K_m is an iterative process. For the first iteration, use six substrate concentrations that cover a wide range of substrate concentrations, to get an initial estimate. For subsequent iterations, use eight or more substrate concentrations between 0.2-5.0 K_m. Make sure there are multiple points above and below the K_m.
• For enzymes with more than one substrate, measure the K_m of the substrate of interest with the other substrate at saturating concentrations. This is also an iterative process. Once the second K_m is measured, it is necessary to check that the first K_m was measured under saturating second substrate concentrations.
• Fit the data to a rectangular hyperbola function using non-linear regression analysis. Traditional linearized methods to measure K_m’s should not be used.

Figures 4 and 5 demonstrate a typical procedure to determine the K_m for a substrate. In Figure 4, reaction product is measured at various times for 8 different levels of substrate. The product generated (Y-axis) is plotted against the reaction time (X-axis). Each curve represents a different concentration of substrate. Note that all the curves are linear, indicating that initial velocity conditions (<10% of substrate conversion) have been met.

Figure 4.

Reaction progress curves at 8 substrate concentrations

Figure 5.

Initial velocity versus substrate concentration

The initial velocity (v_o) for each reaction progress curve is equivalent to the slope of the line, which is defined as the change in the product formed divided by the change in time. This is expressed by the equation below and can be calculated using linear regression or other standard linear method:

The resulting slopes (initial velocity, v_o) for each of the reaction progress curves are plotted on the Y-axis versus the concentration of substrate (X-axis) and a nonlinear regression analysis using a rectangular hyperbola model is performed as shown in Figure 5.

The V_max and K_m for the system is calculated from the nonlinear regression analysis. The meaning of each term is shown in Figure 5. The K_m is the substrate concentration which results in an initial reaction velocity that is one-half the maximum velocity determined under saturating substrate concentrations.

Linear transformations, such as a double reciprocal Lineweaver-Burke plot of the initial velocity/substrate concentration data (i.e. 1/v_o vs. 1/[S], should not be used for calculating the K_m and V_max from saturation type experiments such as those described above. These linear transformations tend to distort the error involved with the measurement and were used before programs that can perform nonlinear regression analysis were widely available.

An additional parameter, often seen in the literature, which can sometimes be useful to describe the efficiency of an enzyme, is the catalytic constant (or turnover number) that is termed k_cat. The k_cat value can be determined from saturation data (Figure 5) from the following equation:

Where [E]_i is the initial enzyme concentration and V_max is the maximum velocity determined from the saturation hyperbola.

For kinase reactions where the K_m for ATP and substrate need to be determined, it is best if a multi-dimensional analysis is used to measure both K_m’s simultaneously. An example is shown in Figure 6.

Figure 6.

Simultaneous determination of K_m for ATP and specific substrate

If this method is used, it is important to demonstrate that in the extreme conditions (particularly low substrate, high ATP concentrations) the linearity of the instrument is maintained. In addition, it is important that linearity of the reaction is maintained at all conditions. Proper background controls must be used. The best condition would be a combination of the best signal to noise ratio while maintaining the substrate and ATP concentration as low as possible. Consult with a biochemist and statistician experienced in these techniques to ensure appropriate data analysis methods are utilized.

Determination of IC₅₀ for Inhibitors

Concentration-response plots are used to determine the effects of an inhibitor on an enzymatic reaction. These experiments are performed at constant enzyme and substrate concentrations and are the primary type of analysis performed for structure-activity relationship (SAR) measurements for compounds of interest.

A typical concentration-response plot is shown in Figure 7. Fractional activity (Y-axis) is plotted as a function of inhibitor concentration (X-axis). The data are fit using a standard four-parameter logistic nonlinear regression analysis.

Figure 7.

Concentration-Response plot for an enzyme inhibitor

The concentration of compound that results in 50% inhibition of maximal activity is termed the IC₅₀ (inhibitor concentration yielding 50% inhibition). It is important to use enough inhibitor concentrations to provide well-defined top and bottom plateau values. These parameters are critical for the mathematical models used to fit the data. Other criteria for successful concentration-response curves are listed in the discussion below.

IC₅₀ Determination for SAR

• Use a minimum of 10 inhibitor concentrations for an accurate IC₅₀ determination. Equally spaced concentration ranges (i.e. 3-fold or half-log dilutions) provide the best data sets for analysis.
• Ideally, half the data points on the IC₅₀ curve are above the IC₅₀ value and half are below the IC₅₀ value, including a minimum and maximum signal.
• The lower limit for determining an IC₅₀ is ½ the enzyme concentration (tight binding inhibitors, 3).
• Screening strategies for defining an initial SAR include: determination of the % inhibition at a single concentration; determination of the % inhibition at a high and a low concentration of inhibitor; and finally, determination of an apparent IC₅₀ using fewer concentrations.

Criteria for reporting IC₅₀’s

• The maximum % inhibition should be greater than 50%.
• Top and bottom values should be within 15% of theory.
• The 95% confidence limits for the IC₅₀ should be within a 2-5 fold range.

Since the IC₅₀ value is the most common result reported for enzymatic assays, it is important to understand how experimental conditions affect IC₅₀ determinations. Generally the concentrations of substrate relative to the K_m and the amount of product produced have the greatest effect on the measured IC₅₀. Figure 8 demonstrates the effect of both substrate concentration and percent conversion on measured IC₅₀ values for a competitive inhibitor.

Figure 8.

Effect of substrate concentration and % conversion on the IC₅₀ for an inhibitor

Figure 8 shows the effect of both substrate concentration and % conversion on measured IC₅₀ values. Increased substrate conversion as well as increased substrate concentrations will increase the resulting IC₅₀ value for a given inhibitor. The data were modeled assuming K_i = 1.0 for a competitive inhibitor with no product inhibition.

Optimization Experiments

Published literature information should be used in selecting these factors. For example a factorial design experiment could be conducted while varying:

• Divalent cations, for example Ca²⁺, Mg²⁺, Mn²⁺
• Salts, for example NaCl, KCl
• EDTA
• Reducing agents such as βME, DTT, glutathione
• Bovine serum albumin
• Detergents such as Triton, CHAPS
• DMSO
• Buffer source, for example HEPES vs. acetate
• pH

In addition to assay conditions, enzyme stability may be affected if appropriate measures are not taken during long-term storage. Many enzymes need to be stored at -70°C to maintain activity, but freeze-thaw cycles are not recommended. Other enzymes can be stored for long periods of time at -20°C using an additive in the storage buffer such as 50% glycerol.

The presence of carrier proteins in the buffer (bovine serum albumin, ovalbumin, others…) as well as use of polypropylene plates (or non-binding polystyrene plates) may be essential to retain proper enzyme activity.

Enzyme instability can also occur during an assay, as demonstrated previously in Figure 3. This type of instability can occur if the active conformation of the enzyme is not stable in the chosen assay conditions of pH, temperature, ionic strength, etc. In addition, for enzymes that are dimerized, a large dilution into assay buffer may result in inactivation.

Assay Validation

Parameters such as substrate K_m and control inhibitor IC₅₀’s need to be determined in three separate experiments to assess variability. Refer to HTS Assay Validation to assess variability of the assay.

References

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