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They may be set by us or by third party providers whose services we have added to our pages. If you do not allow these cookies, then some or all of these functionalities may not function properly. If possible, a sample of the assay medium after washing should be removed and the presence of any remaining compound evaluated by testing the medium in a binding assay.
Another check is the shape of the tracer binding curve — if test compound has been effectively removed, the curve will eventually reach the same level of binding as the control no compound in pre-incubation , assuming compound dissociation is not too slow.
If significant compound remains after the wash step, the curve will plateau below the no-compound control, as a result of equilibrium competition between residual compound and the tracer Figure 13 False positive long residence time resulting from incomplete washout in the kinetic washout assay.
Kinetic washout experiments assume there is no free compound remaining after the washout step, meaning the delay of tracer association results solely from more This minimizes the wash burden. If the concentration is too high, residual compound can bind the target in the tracer incubation. Measuring the dissociation rate constant of the test compound k 4 is the goal of the analysis.
There are two steps in the analysis. First, the control data are analyzed to obtain k 1 for the tracer control being the sample without compound in the pre-incubation. The data are fit to Eq. The analysis provides fitted values of k 4 ; B 0 the percentage of targets occupied by compound at the end of the pre-incubation phase ; and B max the total number of ligand binding sites.
Figure 12 shows representative graphs for compounds with varying RTs i. The shape and position of the curve makes intuitive sense. For the shortest RT 6 min , the compound curve is only slightly delayed compared with the control curve; there is minimal delay of tracer binding because the compound dissociates so rapidly, leaving target free to bind tracer Figure 12A.
At later time points, the plateau for the compound curve reaches the same level as the control. This is because, given enough time, all of the compound-target complexes break down, leaving all of the targets free to bind tracer. Note this argument assumes the concentration of free compound in the tracer incubation is too low to significantly occupy the tracer — see below for what happens when this is not the case. For a 60 min RT compound Fig 12B , there is a marked delay in tracer association, which is predicted because it takes time for the target to become available owing to the slow dissociation of the compound.
When the RT is long 3 hr , the curve is markedly biphasic Fig 12C. There is a small rapid burst of tracer binding at the start, and a slower rise phase. The slower rise phase represents tracer binding to targets that become available once the compound has dissociated from the target. Note the data analysis can give ambiguous results when the top of the curve is not reached over the timeframe of the assay.
This issue can be solved by fixing the B max value for the compound curve to that of the control. When the RT is very long, relative to the timeframe of the assay 36 hr vs 3 hr , a near-monophasic curve results, in which binding plateaus well below the control Fig 12D. In this case, the binding signal is effectively tracer binding only to the targets which were free at the end of the pre-incubation. Very few new targets become available because compound dissociation is so slow.
The association rate constant of test compound can be determined if multiple concentrations of test compound are run. An experiment of this type will return fitted values of the percentage of target population bound, B 0 , for each concentration of test compound, [I]. B 0 is plotted against [I] and the data are fit to the following equation:. The kinetic washout method assumes the free compound is so well washed out that no new target-compound complexes form in the tracer incubation step.
What happens when this is not the case? How do the data appear when the wash is inefficient and there is ample free compound remaining to bind the target in the tracer incubation?
Compounds with short RTs can appear to possess long RTs, giving false positives in lead optimization where the goal is a long RT compound. A worst-case scenario is presented in Figure 13 , using simulated data.
A compound with a short RT 6 min is dosed at a very high concentration in the compound pre-incubation step 1, nM, which is times the compound K d of 10 nM. This leaves compound in the well, at nM concentration, when the tracer is added. This concentration, at 10 times the K d , easily competes against the tracer. This results in strong inhibition of tracer binding red squares in Figure Alarmingly, the data resemble those for a compound with a much longer RT of 36 hr, run under the proper conditions, i.
Analysis of the 6 min RT compound data with the kinetic washout equation gives a fitted RT of 10 hr. These results show that incomplete washout of compound can result in a false positive long RT. Data in Figure 13 were simulated using Eq.
Data were fitted to the kinetic washout equation Eq. B max was constrained to that of the control curve 30 binding units. Often in binding kinetic studies the data do not fit well to the equations given in the preceding sections.
These equations assume the binding event is of the simplest form, a single-step, single site target-ligand interaction. When the data are not fit well by the equations it can indicate a more complicated binding mechanism. Such mechanisms often include two conformational states of the target, with different binding kinetics, giving rise to multiphasic time course curves for example, Figure Thanks to the efforts of investigators, equations are available to analyze more complex binding data to obtain estimates of the kinetic parameters.
While a detailed description is beyond the scope of this chapter, these mechanisms are introduced below and references are provided. Two conformational states of the target — binding kinetic data. Here there are two states of the target, which bind the ligand with different kinetics. Note the biphasic curves — there is an initial burst, followed by a slower phase of more Sometimes there is more than one conformational state of the target in the assay.
GPCRs are the classic example. In binding assays, the GPCR exists in two predominant conformations, the G-protein coupled state and the uncoupled state, which bind agonist ligands with different affinity 60 , 61 and with different binding kinetics 44 , This mechanism is represented by the following scheme:.
Note there is no interconversion between the states in this model. This mechanism gives rise to biphasic time course curves for ligand association and dissociation Figure 14 — there are two components to the curves, one fast and one slow An example of this mechanism and the data analysis is provided in refs 62 , The mechanism has been extended to handle the competition kinetic scenario i.
This mechanism is often encountered with enzymes. The ligand first binds the target in a loose complex. The complex then undergoes a conformational change, producing a tightly-bound complex. This is a mechanism of conformational induction — the ligand induces a new conformation of the target after binding to it. This mechanism is discussed in detail in refs 42 , 64 , The mechanism scheme is,. The first step is the same as the single-site binding mechanism described in Basic Principles of Ligand Binding Kinetics.
The second step is represented as an isomerization event. The shape of the curve depends on the technical properties of the assay. Sometimes the binding signal can be dependent on the conformation of the target, for example in fluorescence assays where fluorescence intensity or resonance energy transfer can change when the conformation of the target changes.
In some cases, the initial complex RL is not detected at all, for example in filtration radioligand binding assays where the loosely-bound complex dissociates during the filtration wash step. Under this condition, a monophasic association curve results but the plot of the observed rate versus the ligand concentration is a hyperbola rather than a straight line 42 , The mechanism has been extended to handle competition between a labeled tracer and an unlabeled test compound, as described in ref In this mechanism, the target consists of a dimer of identical subunits, each subunit containing a single binding site for the ligand.
Binding of ligand to one of the subunits within the dimer affects the binding kinetics of the ligand for the second subunit within the dimer. An equation for this model is derived in ref 67 , which also includes a detailed description of the manifestation of the model in the binding data. In the preceding material we assume a binding assay is available for the target.
Often this is not the case and instead all we have available is a functional assay, i. This is particularly true for new targets in drug discovery. Fortunately, methods are available to quantify the binding kinetics of inhibitor compounds from functional assays.
A detailed description is beyond the scope of this chapter but here the basics of the data analysis are presented together with references for further reading.
The binding kinetics of enzyme inhibitors and equations for analyzing the data have been extensively investigated and described 31 - Methods are available for quantifying inhibitor binding kinetics from enzyme activity assays.
The formation of product is measured over time in the absence and presence of the inhibitor. This is done under initial rate conditions, i. The data are then fit to equations to determine the RT.
For enzymes, analysis can be complicated by the myriad of mechanisms by which the inhibitor inhibits the enzyme, and so consultation with an expert in enzymology is recommended. The RT of enzyme inhibitors is often measured using the jump dilution method 32 , a variant of the washout method described above. Enzyme and inhibitor are incubated together to form the enzyme inhibitor complex. Then the reaction is diluted into a much larger volume of assay buffer containing the substrate and all the necessary reaction components.
The generation of product is then recorded over time. The jump dilution is designed to reduce the free inhibitor concentration sufficiently that it does not appreciably compete with substrate for the enzyme. Consequently, the inhibition that does occur in the substrate incubation is due to the pre-bound complexes from the inhibitor pre-incubation step; the complex needs to break down before the substrate can bind and product be formed. A vehicle control is included in the experiment in order to record enzyme activity without the inhibitor; the enzyme is pre-incubated with vehicle and diluted in the same way as the inhibitor sample.
Data are then analyzed using an appropriate equation to determine the RT for example, Eq. The activity of GPCRs is measured by recording the signaling pathways these receptors stimulate. Signaling is initiated by binding of an activating ligand an agonist to the GPCR.
This provides an assay of activity that can be used to quantify the kinetics of inhibitor binding to the GPCR i. A straightforward qualitative method for measuring antagonist RT is available employing the washout method Figure 15 35 , This procedure, called recovery of agonist responsiveness, uses the washout procedure described in Compound Washout Method.
Cells bearing the receptor are pre-incubated with antagonist long enough for the receptor-antagonist complex to form, then the free antagonist is removed by washing. The cells are then incubated for various times during which the antagonist will dissociate. Following this, agonist is applied and a rapid signaling assay is conducted e. The strength of the signal provides a readout of antagonist binding — the more antagonist that is bound, the lower the signaling by the agonist.
The amount of signal is plotted against the time after antagonist washout. Over time, the response increases owing to dissociation of the antagonist, freeing the receptor to bind the agonist and so generate a signal.
The time it takes the response to recover can be used as an assessment of the RT of the compound for the receptor. This is usually quantified as the half-time. However, the relationship between recovery time and RT is not one-to-one, owing to the pharmacological phenomenon of receptor reserve which dissociates the degree of receptor occupancy from the degree of functional response.
The recovery time is a relative measure of RT, useful for ranking compounds. Technical considerations in this assay include the use of a short duration signaling assay so that antagonist does not appreciably dissociate during the signaling assay , and effective washout of the antagonist to avoid false positive long RTs as described in Compound Washout Method.
Recovery of agonist responsivity method for measuring antagonist residence time. In this method for signal-transducing receptors, the agonist signal is used to assess occupancy by the antagonist Receptor-antagonist complexes are formed during a more More sophisticated methods are available for quantifying binding kinetics in GPCR functional assays.
These require a familiarity with receptor theory. One method utilizes the phenomenon of insurmountability, a property of slowly-dissociating antagonists in functional assays in which the antagonist reduces the maximal response to the agonist 36 , Alternatively, if there is no receptor reserve in the functional assay the signaling time course can be directly fitted using an analogue of the competition kinetics equation The kinetics of target-ligand interaction provide an additional dimension to the understanding of drug target function and the optimization of novel therapeutics.
This chapter enables the newcomer to quantify binding kinetics, specifically how to measure the rate constants for ligand association and dissociation. Analysis is straightforward for direct target-ligand binding assays. More advanced data analysis is required for indirect competition binding assays for quantifying binding kinetics of the large numbers of compounds encountered in modern drug discovery. This analysis, within the range of expertise of most investigators, is taught in easy-to-use step-by-step guides, and aided by guidance on troubleshooting and data interpretation.
More complex scenarios are introduced, including complex binding mechanisms and the measurement of binding kinetics in functional assays for enzymes and GPCRs.
By describing how to quantify binding kinetics, this chapter will aid investigators in applying and evaluating the role of the temporal dimension of binding activity to their targets of interest. The equations used to analyze the data are derived from first principles applied to the binding mechanism diagrams The equations define the concentration of target-ligand complex as a function of time.
They are used to fit the time course data to estimate the rate constant values for the binding interaction. In this section, the techniques for deriving the basic binding equations are presented, for the direct target-ligand binding interactions See Equations for Direct Target-Ligand Binding Kinetics Analysis.
Next, the competition kinetics equation is presented, used for measuring unlabeled test compound binding kinetics in competition with a labeled tracer ligand see Original Competition Kinetics Equation. This equation has been adapted to allow for rapid competitor dissociation See Adaptation for Rapidly-Dissociating Compounds , and for pre-incubation of target with compound Pre-incubating with Test Compound.
Finally, an equation for analyzing data from the washout kinetics method is described. This mechanism is a single-site, single-step reversible binding interaction between ligand L and target R. The binding kinetics are defined by the association rate constant k 1 and dissociation rate constant k 2. For ligand depletion conditions, use Eq.
The goal is an equation that defines the concentration of target-ligand complex [ R L ] as a function of time t and the mechanism parameters of interest k 1 and k 2. We start by writing equations that describe the rate of formation and the rate of breakdown of the target-ligand complex.
From first principles, the rate of formation is the product of the free ligand concentration, free target concentration and the association rate constant:. The rate of breakdown is the product of the target-ligand complex concentration and the dissociation rate constant:. The next step is to write the equation that defines the rate of change of the target-ligand complex concentration over time, after target and ligand are mixed together. This is a differential equation. This equation contains two time-dependent terms, [RL] the species we are measuring, the y axis value of the time course and [R].
Note that [L], the free ligand concentration, is constant over time because it is not depleted by formation of [RL]. The derivation proceeds by removing the second time-dependent term [R].
This is done using a common mathematical maneuver in pharmacology and enzymology, the conservation of mass equation. This simply expresses the target species in the system as a function of a constant, the total concentration of targets, [R] TOT. Note that [R] TOT is constant over time. In the context of a binding assay, it is convenient to express [R] TOT in terms of the total number of binding sites for the ligand, termed B max.
B max is equal to [ R ] T O T for targets with a single binding site, so we can write,. This step requires facility with integral calculus. Fortunately, in this case the integral is well known and the integration can be done directly, giving:. This equation is adapted to analyze the data, as follows.
First of all, it can be expressed in a general form. This general form is an equation found in curve fitting programs, and is the association exponential equation Eq. Time course data are analyzed with Eq. In Prism, Eq. This plot is a straight line with gradient of k 1 Figure 3B so the data are analyzed by linear regression. The fitted value of the gradient is equal to k 1. In the dissociation assay, the target-ligand complex is formed, and then the decay of the target-ligand complex is measured over time after an experimental intervention that blocks the association interaction the dissociation phase.
Association can be blocked by washing out the unbound ligand, or, when a labeled ligand is being used, addition of a large excess of unlabeled ligand. The mechanism in the dissociation phase of the experiment is simply breakdown of the target-ligand complex:.
The equation defining the dissociation time course is derived using the same strategy as described above for the association process. The rate of change of the target-ligand complex over time is simply the rate of decay of the complex:. Note the negative sign, indicating [RL] is declining over time. The next step is to obtain the analytic form, and this is done directly by integration, giving the equation used to analyze the data Eq.
This equation is used to analyze dissociation time course data Figure 2B. In the competition kinetics assay, an unlabeled compound is competed against a labeled tracer ligand for binding to the target.
The analysis assumes the two ligands bind the same site on the target and that the binding events are simple single-site, single-step reversible interactions. The equations assume minimal depletion of the free ligand concentration for both the labeled and unlabeled ligand. The mechanism is illustrated in Figure 4 and shown schematically below:. By convention, k 1 and k 2 are the association and dissociation rate constants, respectively, of the labeled ligand L , with k 3 and k 4 being the corresponding rates for the unlabeled test ligand I.
In the original, commonly-used method, target is exposed simultaneously to both ligands i. The data take the form of the time course of labeled ligand binding in the presence of the unlabeled compound Figure 6. The equation describing these data is a bi-exponential equation and is rather complex to the uninitiated investigator, but it is a straightforward analytical equation where [RL] is a function of time and mechanism parameters.
The equation, Eq. The original papers describing the equation are refs. Occasionally the unlabeled test compound dissociates too rapidly for the analysis method to quantify k 4 reliably Limits of Sensitivity. A false fit results, where the program fits a curve to the data well, but that returns unrealistic estimates of k 3 and k 4 see Box 5 , bottom graph and data table.
Effectively, the compound is immediately and constantly at equilibrium with free targets. The analysis method can be adapted to quantify the binding affinity of such a compound from the time course data.
The equation for this analysis is Eq. K i is the equilibrium binding affinity of the unlabeled test compound. The original competition kinetics equation assumes target is exposed simultaneously to test compound and tracer ligand 18 , An equation is also available that assumes the target is pre-incubated with a test compound before the tracer is added 53 , The equation is a close analogue of the original equation — it is extended to include a term for binding of compound during the pre-incubation.
The equation Eq. The terms are defined in the section Original Competition Kinetics Equation. An equation is also available that assumes the tracer is pre-incubated with the target before an unlabeled test compound is added Here t PI is the pre-incubation time with tracer and t the x value is time after compound addition. An alternative method for measuring unlabeled compound RT is the washout method, popular for certain classes of targets such as protein kinases In this experiment, compound is pre-incubated with target to allow target-compound complexes to form Figure Next, the free unbound compound is washed out, leaving the compound-target complexes in the well.
Next, a tracer ligand is added and tracer binding recorded over time. The pre-bound compound delays association of the tracer Figure 11 graph. This is because the compound first has to dissociate before tracer can bind. An equation, Eq. The association rate constant of unlabeled test compound k 3 can be determined if multiple concentrations of compound are run in the assay.
Analysis using Eq. The B 0 value can then be plotted versus the compound concentration [I], and the data analyzed using the following equation:. Any altered, transformed, or adapted form of the work may only be distributed under the same or similar license to this one.
Turn recording back on. National Center for Biotechnology Information , U. Search term. Author Information Authors Sam R. Corresponding author. Abstract Biological and therapeutic agents exert their actions by interacting with specific molecular targets.
Introduction Therapeutic molecules exert their action by interacting with specific molecular targets. Download video file. Table 1. Kinetic analysis methods for direct target-ligand binding assays. Applicable to targets where technology is available to directly measure target-ligand interaction. Competition kinetics: Quantifying kinetics by competition against a tracer ligand. This competition method can be used to quantify binding kinetics. Compound washout method.
An indirect method popular for kinase enzymes is the compound washout method, in which target and compound are pre-incubated, then compound washed out, and compound dissociation recorded by its ability to slow association of a tracer ligand. Complex binding mechanisms. Sometimes the ligand binding mechanism is complex, for example involving multiple conformational states of the target.
These more complex binding mechanisms and methods to measure their kinetics are introduced here. Binding kinetics from functional assays. For some targets, only a functional assay is available e. Theoretical description of target-ligand binding and the equations used to analyze the data. Basic Principles of Ligand Binding Kinetics Most drugs bind their target by the classic bimolecular interaction.
The interaction can be written schematically as: Figure 1. Figure 2. Kinetic Analysis Methods for Direct Target-Ligand Binding Assays The goal is to measure the association rate constant k 1 and dissociation rate constant k 2. Figure 3. Box 1: Association rate constant assay considerations.
Box 2 Troubleshooting the association rate constant measurement. Box 3 Troubleshooting dissociation rate constant measurement. Competition Kinetics: Quantifying Kinetics by Competition Against a Tracer Ligand Introduction The sections above assume a direct method for measuring ligand binding to the target. Figure 5.
Figure 6. Assay Setup The typical assay consists of five conditions Box 4. For three concentrations, the following calculation is used Box 4 Experimental setup for unlabeled ligand competition kinetics assay.
Box 5 Troubleshooting the competition kinetics assay. Data Analysis The goal of the data analysis is determination of k 3 and k 4 , the association and dissociation rate constant of the unlabeled test compound. The analysis proceeds in a series of steps: 1.
Subtraction of nonspecific binding. Fitting the control curve to determine k 1. Shape of the Curves Can Diagnose the Residence Time of the Test Compound An interesting observation is immediately obvious on inspecting the data in Figure 6 — the curves are of an unusual shape. Figure 7. Limits of Sensitivity Like any other assay, there are limits to the sensitivity of the competition kinetics approach, specifically for quantifying the RT.
Figure 8. Figure 9. Pre-incubating With Test Compound The order of reagent addition is constrained in the original competition kinetics method. Figure Pre-incubating with Tracer An alternative way of setting up the assay is to pre-incubate target with tracer to allow target-tracer complexes to form, followed by addition of unlabeled test compound.
Compound Washout Method Introduction A popular method for measuring unlabeled compound RT is the washout method, frequently employed for kinase enzyme targets. Experimental Considerations Technically, the experiment must be performed carefully for the method to provide unambiguous results on the dissociation rate of the compound.
Data Analysis to Quantify the Compound Residence Time Measuring the dissociation rate constant of the test compound k 4 is the goal of the analysis. False-Positive Long Residence Time Resulting from Incomplete Washout The kinetic washout method assumes the free compound is so well washed out that no new target-compound complexes form in the tracer incubation step. Free Consultation. The drug discovery and development process is long and expensive with more failures than successes.
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