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- ENZYME ASSAY DEVELOPMENT FLOW CHART
- INTRODUCTION
- CONCEPT
- REAGENTS AND METHOD DEVELOPMENT
- DETECTION SYSTEM LINEARITY
- ENZYME REACTION PROGRESS CURVE
- MEASUREMENT OF KM AND VMAX
- DETERMINATION OF IC50 FOR INHIBITORS
- INHIBITION CONSTANT (KI)
- IC50 DETERMINATION FOR SAR
- OPTIMIZATION EXPERIMENTS
- ASSAY VALIDATION
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 (for a reference see “Enzyme Structure and Mechanism” by Alan Fersht, WH Freeman and Co., NY, 1985, pp327-330).
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 substrate and P is product(s). ES is an enzyme-substrate complex that is formed prior to the catalytic reaction. 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 (see “Enzyme Kinetics: Behavior and analysis of rapid equilibrium and steady state enzyme systems.” By Irwin H. Segel, John Wiley and Sons, NY 1975 for these mathematical derivations). 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
Vmax = maximal reaction rate
[S] = substrate concentration
Km = 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 Km 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 Km (see section on optimization experiments).
- Initial velocity is the initial linear portion of the enzyme reaction when less than 10% of the substrate has been depleted or less than 10% of the product has formed. Under these conditions, it is assumed that the substrate concentration does not significantly change and the reverse reaction does not contribute to the rate<./LI>
- Initial velocity depends on enzyme and substrate concentration and is the region of the cureve in which the velocity does not change with time. This is not a predetermined time and can vary depending on the reaction conditions.
- The reaction is non-linear with respect to enzyme concentration.
- There is an unknown concentration of substrate.
- There is a greater possibility of saturation of the detection system.
- The steady state or rapid equilibrium kinetic treatment is invalid.
Measuring the rate of an enzyme reaction when 10% or less of the substrate has been depleted is the first requirement for steady state conditions. At low substrate depletion (i.e. initial velocity conditions) the factors listed below that contribute to non-linear progression curves for enzyme reactions, do not have a chance to influence the reaction.
- Product inhibition
- Saturation of the enzyme with substrate decreases as reaction proceeds due to a decrease in concentration of substrate (substrate limitation)
- Reverse reaction contributes as concentration of product increases over time
- Enzyme may be inactivated due to instability at given pH or temperature
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:
- 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.
- Identify source and acquire native or surrogate substrates with appropriate sequence, chemical purity, and adequate available supply.
- Identify and acquire buffer components, co-factors and other necessary additives for enzyme activity measurements according to published procedures and/or exploratory research.
- Determine stability of enzyme activity under long-term storage conditions and during on bench experiments. Establish lot-to-lot consistency for long-term assays.
- Identify and acquire enzyme inactive mutants purified under identical conditions (if available) for comparison with wild type enzyme.
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.
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.
A reaction progress curve can be obtained by mixing an enzyme and it's 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.
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 0.5 X 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 below. 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.
- Keep temperature constant in the reaction by having all reagents equilibrated at the same temperature.
- Design an experiment so pH, ionic strength and composition of final buffer are constant. Initially use a buffer known for the enzyme of interest either by consulting the literature or by using the buffer recommended for the enzyme. This buffer could be further optimized in later stages of development.
- Perform the time course of reaction at three or four enzyme concentrations.
- Need to be able to measure the signal generated when 10% product is formed or to detect 10% loss of substrate.
- Need to measure signal at t=0 to correct for background (leave out enzyme or substrate).
For kinase assays, the background can be determined by leaving out the enzyme or the substrate. The condition resulting in the highest background level should be used. EDTA is not recommended for use as the background control during validation of a kinase assay. Once the assay has been validated, if the background measured with EDTA is the same than both the no enzyme and no substrate control, then EDTA could be used.
Once the initial velocity conditions have been established, the substrate concentration should be varied to generate a saturation curve for the determination of Kmmax values. Initial velocity conditions must be used. The Michaelis-Menten kinetic model shows that the Km = [S] at Vmax/2. In order for competitive inhibitors to be identified in a competition experiment that measures IC50 values, a substrate concentration around or below the Km must be used. Using substrate concentrations higher than the Km will make the identification of competitive inhibitors (a common goal of SAR) more difficult.
For kinase assays, the Km 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 Km value using initial velocity conditions. However, it would be best to determine Km 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.
- If Km >>> [S], then the velocity is very sensitive to changes in substrate concentrations. If [S] >>> Km, then the velocity is insensitive to changes in substrate concentration. A substrate concentration around or below the Km is ideal for determination of competitive inhibitor activity.
- Km is constant for a given enzyme and substrate, and can be used to compare enzymes from different sources.
- If Km seems “unphysiologically” high then there may be activators missing from the reaction that would normally lower the Km in vivo, or that the enzyme conditions are not optimum.
- Measure the initial velocity of the reaction at substrate concentrations between 0.2-5.0 Km. If available, uses the Km 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 Km 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 Km. Make sure there are multiple points above and below the Km
- For enzymes with more than one substrate, measure the Km of the substrate of interest with the other substrate at saturating concentrations. This is also an iterative process. Once the second Km is measured, it is necessary to check that the first Km was measured under saturating 2nd substrate concentrations.
- Fit the data to a rectangular hyperbola function using non-linear regression analysis. Traditional linearized methods to measure Km s should not be used.
Figures 4 and 5 demonstrate a typical procedure to determine the Km 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
The initial velocity (vo) 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, vo) 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 below.
Figure 5. Initial velocity versus substrate concentration
The Vmax and Km for the system is calculated from the nonlinear regression analysis. The meaning of each term is shown in Figure 5. The Km 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/vo vs. 1/[S], should not be used for calculating the Km and Vmax 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 kcat. The kcat value can be determined from saturation data (Figure 5) from the following equation:
where [E]i is the initial enzyme concentration and Vmax is the maximum velocity determined from the saturation hyperbola.
For kinase reactions where the Km for ATP and substrate need to be determined, it is best if a multi-dimensional analysis is used to measure both Km’s simultaneously. An example is shown in Figure 6 below.
Figure 6. Simultaneous determination of Km 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.
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.
A simple method for assessing the mode of inhibition is given in Lai and Wu (2003). In this case the mode of inhibition can be evaluated by holding the inhibitor constant at an IC50 concentration and varying the substrate. The behavior of the curves obtained under these conditions will point to the mode of inhibition. Some example data of this type of experiment is given below of a kinase inhibitor that competes with the ATP-binding site but is non-competitive with respect to the substrate binding site.
The inhibitor was kept constant and either the ATP or the peptide substrate was varied. It can be seen that the inhibition can be completely relieved through increasing the ATP concentration. However, the inhibition is not effected by increasing the peptide substrate. According to the model shown in Lai and Wu (2003) this is consistent with an inhibitor that is competitive with respect to ATP and non-competitive with respect to the peptide substrate.
For simple competitive inhibition the Cheng-Pursoff equation can be used provided that the Km for the substrate under the assay conditions is known e.g.:
- 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, Chapter 9, Copeland, R.A., 2nd Edition, 2000).
- 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.
- 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 Km and the amount of product produced have the greatest effect on the measured IC50. The figure below demonstrates the effect of both substrate concentration and percent conversion on measured IC50 values for a competitive inhibitor.
Figure 7. Effect of substrate concentration and % conversion on the IC50 for an inhibitor
Figure 7 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 Ki = 1.0 for a competitive inhibitor with no product inhibition.
Buffer composition can have significant effects on enzymatic activities. Some buffer components can also affect compound inhibitory activities. Various components in the buffer can be used as factors to modify in a statistical optimization experiment. 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.
Parameters such as substrate Km and control inhibitor IC50’s need to be determined in 3 separate experiments to assess variability. Refer to Section IIB to assess variability the assay.
- Copeland, Robert A. Enzymes: A practical introduction to structure, mechanism and data analysis. Wiley-VCH, NY, 2nd Edition, 2000.
- Segel, Irwin H. Enzyme Kinetics: Behavior and analysis of rapid equilibrium and steady state enzyme systems. John Wiley and Sons, NY 1975.
- Dixon, M. and Webb, E.C. Enzymes, 3rd Edition. Academic Press, NY 1979.
- Lai C-J-,Wu JC A Simple Kinetic Method for Rapid Mechanistic Analysis of Reversible Enzyme Inhibitors. Assays and Drug Dev. Technologies. 2003;1(4):527-535.
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