A Perspective on the Kinetics of Covalent and Irreversible Inhibition

Abstract

The clinical and commercial success of covalent drugs has prompted a renewed and more deliberate pursuit of covalent and irreversible mechanisms within drug discovery. A covalent mechanism can produce potent inhibition in a biochemical, cellular, or in vivo setting. In many cases, teams choose to focus on the consequences of the covalent event, defined by an IC₅₀ value. In a biochemical assay, the IC₅₀ may simply reflect the target protein concentration in the assay. What has received less attention is the importance of the rate of covalent modification, defined by k_inact/K_I. The k_inact/K_I is a rate constant describing the efficiency of covalent bond formation resulting from the potency (K_I) of the first reversible binding event and the maximum potential rate (k_inact) of inactivation. In this perspective, it is proposed that the k_inact/K_I should be employed as a critical parameter to identify covalent inhibitors, interpret structure-activity relationships (SARs), translate activity from biochemical assays to the cell, and more accurately define selectivity. It is also proposed that a physiologically relevant k_inact/K_I and an (unbound) AUC generated from a pharmacokinetic profile reflecting direct exposure of the inhibitor to the target protein are two critical determinants of in vivo covalent occupancy. A simple equation is presented to define this relationship and improve the interpretation of covalent and irreversible kinetics.

Introduction

Covalent inhibitors are increasingly being considered a viable option in drug discovery. This resurgence has been led, in part, by the success of several drugs designed to treat acute and chronic diseases covering a number of therapeutic areas, including anti-infectives, cancer, gastrointestinal, central nervous system, cardiovascular, and inflammation. ¹ Often cited examples of successful drugs include aspirin, penicillin, omeprazole, clopidogrel, and ibrutinib. In 2005, a retrospective look at all marketed drugs in the Food and Drug Administration Orange Book revealed that 35% of enzymes (25/71) are irreversibly inhibited by a drug and 76% (19/25) of those form a covalent bond to the target protein. ² Many of these pharmaceutical agents have excellent safety records. ³ These drugs are often derived from natural products that form covalent bonds with target proteins.^4,5 As a result, covalent bond formation has been a successful and safe strategy used by nature and the pharmaceutical industry to alter disease pharmacology. It might be surprising to learn that acrylamides, the most common reactive functional group included in covalent inhibitors, are present in coffee, cereal, bread, French fries, and potato chips.^6–8 While there are efforts to reduce acrylamide levels in these foods, they are clearly not toxic. Why? Similar to pharmaceutical drugs, the difference between safety and toxicity depends on the administered (or consumed) dose. As credited to Paracelsus, the 16th-century founder of toxicology, “the dose makes the poison.”

In response to the increased interest in covalent inhibitors, several reports have presented the risks and rewards of their pursuit.^1,3,9,10 The primary risk is the potential for nonspecific reactivity with proteins, DNA, or small molecules (e.g., glutathione), which could produce an acute or delayed toxicological event.^11–13 Some of these idiosyncratic events result in an immune response to the covalently modified cellular macromolecule. ¹⁴ The discovery of drugs that can be administered at lower doses could decrease the risk of these events.^15,16 Despite these potential issues, covalent inhibitors can produce very specific, targeted effects with excellent biochemical and cellular potencies, even in the presence of high concentrations of competing ligand. In addition, they can produce a pharmacodynamic effect that endures beyond what the pharmacokinetic profile would predict. In an effort to identify the proper therapeutic window between a specific and nonspecific effect, reports have provided guidance on how drug discovery groups may best characterize the cellular pharmacology of these inhibitors. ¹⁷ Activity-based protein profiling (ABPP) has become a powerful tool to evaluate the covalent inhibition of serine hydrolases, kinases, phosphatases, histone deacetylases, cytochrome P450s, and proteases (aspartyl, metallo, and cysteine).^18–25 The irreversibility of covalent bond formation makes it an accessible and powerful tool to interrogate their cellular pharmacology. What has received less attention is the importance of the kinetics or rate of covalent bond formation. For example, the incorporation of k_inact/K_I during a structure-activity relationship (SAR) campaign is often recommended but infrequently applied. The k_inact/K_I is a second-order rate constant describing the efficiency of covalent bond formation. In this report, a perspective is presented regarding the risks of an overreliance on IC₅₀ values. A comprehensive understanding of the kinetics of covalent and irreversible inhibition, as defined by k_inact/K_I, can have a significant impact on how to identify covalent inhibitors, understand SAR, translate their activity to the cell, interpret selectivity, view an optimal pharmacokinetic profile, and estimate in vivo target occupancy.

Kinetic Mechanism of Covalent Inhibition

In small-molecule drug discovery, there are two general categories of covalent and irreversible inhibition. The first is a covalent bond resulting from a specific interaction between a small molecule and protein. As illustrated in Figure 1A , this occurs in two steps. First, the inhibitor (I) binds to the target protein (P), and a reversible protein-inhibitor complex (P•I) is formed. The potency of this first step is defined by the binding constant K_I. The K_I term describes the concentration of inhibitor required for half of the maximum potential rate of covalent bond formation. This should not be confused with K_i describing the dissociation of the P•I complex, which is not affected by covalent bond formation. In the second step, the nucleophile reacts with the electrophile, forming a covalent protein-inhibitor complex (P-I). The rate of the second step will depend on the concentration of P•I. When all the target protein exists with reversibly bound inhibitor (P•I) and no free target protein remains (P), the observed rate of inactivation is the k_inact. The k_inact is a first-order rate constant describing the maximum potential rate of covalent bond formation. Taken together, the overall rate of covalent bond formation from free, unbound protein (P) to the covalent protein-inhibitor complex (P-I) is defined by the ratio of k_inact to K_I or k_inact/K_I. This bimolecular rate constant accounts for both the potency of the first step (K_I) and the maximum potential rate of covalent bond formation (k_inact). The k_inact/K_I can be determined in two steps. In a binding assay, the total occupancy is measured over time at different inhibitor concentrations. This is illustrated in Figure 2A at 1000 nM, 100 nM, and 10 nM of inhibitor E from Table 1 with a k_inact/K_I of 1.2 × 10³ M⁻¹s⁻¹. The observed occupancy over time at each inhibitor concentration is fit to equation (1).

$$\%\mathrm{Total\; Occupancy}=100(1-\exp (-{\mathrm{k}}_{\mathrm{obs}}+\mathrm{time})).$$

Figure 1.

(A) A two-step mechanism of inhibition where P reflects the target protein, I is the inhibitor, P•I is the reversibly bound protein inhibitor complex, and P-I reflects the formation of a covalent bond between the target protein and inhibitor. The potency of the first reversible binding event is defined by K_I, and the maximum potential rate of inactivation is defined by k_inact. Taken together, the k_inact/K_I is a second-order rate constant describing the efficiency of the overall conversion of free P to the covalent P-I complex. (B) A one-step mechanism of covalent inhibition expected for an inhibitor where there is no observed binding event. P reflects any cellular macromolecule (protein or small molecule).

Figure 2.

(A) The change in total occupancy over time for 1000 nM, 100 nM, and 10 nM inhibitor E in Table 1 used to determine the observed rate of inactivation (k_obs). (B) The k_inact/K_I relationship between inhibitor concentration and the observed rate of inactivation for inhibitor E with a K_I of 1000 nM and a k_inact of 0.0693 min⁻¹ ( $t_{1/2}^{\infty }$ of 10 min). (C) The k_inact/K_I relationship between inhibitor concentration and the observed rate of inactivation for inhibitor A with a K_I of 10 nM and a k_inact of 0.693 min⁻¹ ( $t_{1/2}^{\infty }$ of 1 min). The rapid observed rates may prevent an accurate determination of the K_I and k_inact ( $t_{1/2}^{\infty }$ ). The initial slope of this line is the k_inact/K_I. (D) The k_inact/K_I relationship between inhibitor concentration and the observed rate of inactivation for a nonspecific inhibitor with either no binding or a very high K_I. The slope of this line is the k_inact/K_I (12 M⁻¹s⁻¹). These plots were generated using the following equations: % Occupancy = Y_max(1 − exp(−1 * Rate * time)) + Y₀; Y_max = 100 − 100/(1 + K_I/[I]); Y₀ = 100/(1 + K_I/[I]); Rate = k_inact * [I]/(K_I + [I]).

Table 1.

Modeled In Vitro Potency and In Vivo Covalent Occupancy for Inhibitors with Different Covalent Kinetic Properties.

				Biochemical or Cellular IC50, nM a
				0.5-h Assay		4-h Assay		% Covalent Occupancy at 24 h b
Protein or Inhibitor	KI, nM	$t_{1/2}^{\infty }$ , min	kinact/KI, M−1s−1	No PreInc	2-h PreInc	No PreInc	2-h PreInc	10 mg/kg	1.0 mg/kg	Dose (mg/kg) Needed for >90% Occ. at 24 h b
A	10	1	1.2 × 106	0.30	0.034	0.038	0.019	100	100	0.008
B	10	10	1.2 × 105	2.7	0.35	0.38	0.19	100	100	0.08
C	10	100	1.2 × 104	8.2	3.5	3.2	1.9	100	89	1.1
D	1000	1	1.2 × 104	30	3.4	3.8	1.9	100	95	0.8
E	1000	10	1.2 × 103	267	35	37	19	94	26	8
F	1000	100	1.2 × 102	821	348	319	192	25	3	110

a

The % inhibition was calculated at a range of [inhibitor] by adding the reversibly bound inhibitor, defined by FreeProtein/(1 + K_I/[I]), to the covalently modified fraction ± preincubation using FreeProtein*(1 − exp(−1 * Rate * time)) where the preincubation contained 2×[inhibitor] and Rate = k_inact * [I]/(K_I + [I]). The FreeProtein term was corrected at each step to account for the fraction of covalently occupied protein. The % inhibition at each [inhibitor] was then fit to the four-parameter logistic equation to determine the IC₅₀.

b

The following pharmacokinetic (PK) parameters were used: 0.1 fraction bioavailable, 0.1 fraction unbound, k_a of 2h⁻¹, k_e of 0.09h⁻¹, and a clearance of 5 mL/min/kg with a molecular weight of 400 g/mol.

This yields the k_obs, an observed first-order rate constant with units of inverse time, at each inhibitor concentration. The k_obs values are then fit to equation (2) to determine the k_inact and K_I.

$${\mathrm{k}}_{\mathrm{obs}}=\frac{{\mathrm{k}}_{\mathrm{inact}}[\mathrm{Inhibitor}]}{{\mathrm{K}}_{\mathrm{I}}+[\mathrm{Inhibitor}]}.$$

This is illustrated in Figure 2B for inhibitor E. The maximum potential rate of inactivation, k_inact, is 0.0693 min⁻¹, which is only observed at inhibitor concentrations well above the K_I of 1000 nM. This rate can also be represented as a $t_{1/2}^{\infty }$ of 10 min. The $t_{1/2}^{\infty }$ is determined by dividing 0.693 by the k_inact. It describes the time required for half of the protein to be covalently modified at some theoretically infinite inhibitor concentration. The $t_{1/2}^{\infty }$ is often a more useful and practical term in discussions of the maximum potential rate of covalent bond formation. When the concentration of inhibitor presented to the protein decreases to the K_I levels, only 50% of the protein contains reversibly bound inhibitor, and the observed rate of inactivation is one-half k_inact. When the inhibitor concentration tested is 5-fold above the K_I, the observed rate of inactivation is approximately 83% of the k_inact. When inhibitor concentrations below the K_I are also tested, an accurate estimate of the individual k_inact and K_I values can be obtained. However, when the k_inact/K_I is very high, as true for the most efficient inhibitors, it may be difficult to determine each term accurately. This is illustrated in Figure 2C for an inhibitor with a k_inact/K_I of 1.2 × 10⁶ M⁻¹s⁻¹ (inhibitor A in Table 1 ). This inhibitor has a $t_{1/2}^{\infty }$ of 1 min. For biochemical assays with a low signal to background, high variability, or an inability to measure a sufficient number of early time points, this rate may be too rapid to accurately determine k_obs values above K_I and near the k_inact. The relationship between inhibitor concentration and the observed rate of inactivation is nearly linear ( Fig. 2C ). In this example, the individual k_inact and K_I terms are >0.12 min⁻¹ and >2.0 nM, respectively. The k_inact/K_I ratio can be determined accurately and is equal to the initial slope. Other methods, presented later, would need to be explored to estimate the k_inact and K_I.

The second general category of covalent and irreversible inhibition is a nonspecific reaction between a nucleophile on a cellular macromolecule (e.g., a protein or glutathione) and an inhibitor bearing a reactive electrophile. When the cellular macromolecule is a protein, the efficiency of this reaction can be considered equivalent to the k_inact/K_I as depicted in Figure 1B . In this case, there is no evidence of a reversible binding event between the protein and electrophilic inhibitor, and this fact elicits the nonspecific description. In practice, it may be more accurate to conclude that the K_I is much higher than the top concentration of inhibitor included in the kinetic study. As illustrated in Figure 2D , the relationship between inhibitor concentration and k_obs is linear with a slope that is equal to the k_inact/K_I. A similar plot may be obtained when the cellular macromolecule is a small molecule and there is no potential for a reversible binding event. Estimates range from 0.005 M⁻¹s⁻¹ to 0.34 M⁻¹s⁻¹ for acrylamide toward cysteine, glutathione, or protein sulfhydryl groups.^26–28 Despite these small rate constants, many reactions were complete in less than 5 min. ²⁶ Estimates of the second-order rate constant of 26 Michael acceptors for glutathione spanned five orders of magnitude and were as high as 21 M⁻¹s⁻¹. ²⁹ Estimates of nonspecific reactivity can also be made at a fixed concentration of inhibitor, often presented as a half-life (t_1/2) of the inhibitor. An evaluation of almost 50 electrophiles that might be considered in drug discovery produced half-lives ranging from a few minutes to >60 min using millimolar concentrations of reactants. ³⁰ However, as illustrated in Figure 2D , these observed rates will change as a function of the inhibitor concentration.

There are two important points to remember when looking at the plots shown in Figure 2 . First, the most efficient specific inhibitor ( Fig. 2C ) can produce a plot very similar to a nonspecific inhibitor ( Fig. 2D ). Both can have nearly identical observed rates of inactivation that reflect a similar reactivity between the nucleophile and electrophile. Both also have K_I values greater than the top concentration of inhibitor included in the experiment. They differ in the concentration of inhibitor required to produce the observed rate of inactivation. A specific inhibitor will require far less inhibitor for covalent modification because it has a potent reversible binding component defined by K_I. This produces a much higher k_inact/K_I than a nonspecific inhibitor having a much higher K_I and a smaller k_inact/K_I. This highlights a potential challenge in evaluating covalent fragments. Many of these could appear to be nonspecific in a kinetic study with K_I values well above the highest concentration tested. As presented later, it is important to estimate the K_I using an alternative method (e.g., biophysical or direct binding). This might differentiate an interesting fragment active from an undesirable, nonspecific active. Second, the y-intercept of the k_inact/K_I plots in Figure 2B–D should be 0. In some cases, the electrophile can be chemically modified so that the covalent complex (P-I) can revert back to the reversible complex (P•I).^31,32 This would give y-intercepts that are >0. Although this is an intriguing type of covalent inhibitor that may allow one to achieve a specific residence time, this perspective will focus on completely irreversible inhibitors.

There are many methods to determine the k_inact/K_I of an inhibitor. The classical approaches, represented for enzyme activity assays and illustrated earlier for a binding assay, have been well documented.^33,34 However, these studies can be time-consuming, and the data analysis requires careful interpretations. ³⁵ Some biochemical assays measuring enzyme activity have nonlinear relationships between the product concentration and the measured signal, which affects how the data should be analyzed. ³⁶ In addition, it can be difficult to accurately estimate the y-intercept in Figure 2B , and inhibitors with a very slow off-rate can be mistaken for an irreversible inhibitor. This might not be an issue for inhibitors like Birb796, with a t_1/2 offset of 23 h, which lacks a reactive electrophile. ³⁷ However, the presence of a reactive group is insufficient to assume that the time-dependent inhibition observed ( Fig. 2A ) is due to a covalent event. Time-dependent inhibition can also result from a slow step prior to covalent bond formation. Kinetic studies should be complemented by mass spectrometry to confirm formation of a covalent protein-inhibitor adduct with the expected shift in the mass of the protein.^38–43 There have been numerous reports of higher throughput methods to estimate k_inact/K_I. These include evaluating the IC₅₀ versus time, calculating k_obs/[I], or measuring competition with an irreversible probe.^44–54 Many of these examples originate from studies of cytochrome P450 enzymes, where the k_inact/K_I is used to understand the potential for drug-drug interactions in the clinic. These methods can provide higher throughput alternatives, which offer significant improvements over an IC₅₀ measurement.

Identification of Covalent Inhibitors

There are primarily two strategies to identify a covalent inhibitor. They are rationally designed from a reversible scaffold or found in a screening campaign of electrophilic small molecules or fragments. In the first approach, a reversible inhibitor is identified and, if a reactive nucleophile is accessible in the binding pocket, an electrophile is designed into the inhibitor. If the electrophile is suitably positioned relative to the nucleophile, then a covalent bond is formed. Ibrutinib is a good example of a covalent inhibitor rationally designed from a reversible scaffold with an IC₅₀ of 8.2 nM. ⁵⁵ An optimally positioned acrylamide forms a covalent bond to Cys481 in Bruton’s tyrosine kinase (Btk). This produces an IC₅₀ of 0.72 nM, likely reflecting the concentration of Btk in the assay. Rational design from a reversible scaffold is often the preferred method to identify a covalent inhibitor. When this strategy is executed successfully, the chemical scaffold has been proven to make a productive and irreversible complex with the target protein. However, it can be very challenging to identify high-quality reversible inhibitors. The second approach to identify a covalent inhibitor could result from screening a collection of electrophilic compounds. This has been reported using mass spectrometry and applied to fragment-based drug discovery.^56,57 Surprisingly, covalent fragments may be more selective than expected. ⁵⁸ Once identified, the inhibitor would need to be evaluated in a biochemical format to confirm the covalent event has some functional consequence on the protein’s activity. In addition, relatively little quantitative information may be known about the potency of the first reversible step, and some actives may be nonspecific with no measurable binding event. Additional characterizations are critical to successfully select and advance the most promising starting points. This includes understanding the biochemical activity, the proper triage of nuisance inhibitors, and the incorporation of biophysical studies.

Whether a covalent inhibitor is identified through rational design or in a screen, a biochemical assay is often used to identify inhibitors with covalent binding properties. This can be accomplished by preincubating the putative covalent inhibitor with protein prior to starting the assay. The resulting IC₅₀ can be compared to an assay lacking any preincubation. Those inhibitors showing a shift in IC₅₀ are time dependent. When the time dependence is due to covalent modification, the resulting IC₅₀ depends on the time points selected and the individual k_inact and K_I terms. This is illustrated in Table 1 , where the IC₅₀ values of six covalent inhibitors, with k_inact/K_I values ranging from 1.2 × 10² M⁻¹s⁻¹ to 1.2 × 10⁶ M⁻¹s⁻¹, are presented for different preincubation and assay times in a protein binding assay. The shifts in IC₅₀ range from only ~2- to 10-fold. IC₅₀ estimates in an enzyme activity assay are only slightly higher (up to 1.4- and 2.5-fold) with similar shifts in potency (unpublished observation). The greatest shift occurs when the preincubation time (2 h) exceeds the assay time (0.5 h). In this comparison, there is a relatively large difference in the total time (0.5–2.5 h). When the assay time increases to 4 h and the difference in the total time decreases (4–6 h), the IC₅₀ values ± preincubation become indistinguishable. Therefore, shifts in an IC₅₀ can be very misleading, and the kinetics should be evaluated to determine the potential for irreversible inhibition. In all four assay conditions simulated, the observed IC₅₀ is roughly proportional to the k_inact/K_I. This is particularly evident at the longer preincubation and assay times. However, these simulated IC₅₀ values do not account for the target protein concentration. The lowest measurable IC₅₀ in a biochemical assay is one-half the target protein concentration and typically ranges from high picomolar to tens of nanomolar. Assuming a biochemical assay uses 10 nM protein, all IC₅₀ values measured for inhibitors A and B are 5 nM, and any apparent shift in IC₅₀ has been eliminated. This creates an issue during SAR because these two inhibitors have a 10-fold difference in k_inact ( $t_{1/2}^{\infty }$ ) and that could only be revealed in a k_inact/K_I determination.

Perhaps the greatest challenge in using a screening strategy to identify covalent inhibitors is the presence of nuisance inhibitors in many compound libraries. ⁵⁹ Nuisance inhibitors represent a broad class of problematic mechanisms, including, at present, aggregation-based events, redox-based mechanisms, and Pan Assay Interference Compounds (PAINS). Of great concern is that many of these nuisance inhibitors produce time-dependent inhibition or react with proteins. Aggregation-based inhibitors were characterized, in part, based on their time-dependent inhibition and were initially thought to be covalent inhibitors.^60,61 Some compounds can inhibit enzyme activity by oxidizing cysteine residues or altering the redox state of metals or cofactors.^62,63 Some of these false-positive redox actives have produced enticing isothermal calorimetry (ITC) results, albeit with poor-quality traces and a K_D value that does not correlate to the biochemical potency. ⁶⁴ PAINS represent a more diverse set of false-positive mechanisms that includes redox cyclers, covalent modifiers, metal complexers, and unstable compounds.^65,66 As represented by a set of covalent inhibitors of the p53-HDMX complex, these can appear as attractive starting points that fail only after placed under greater scrutiny in a more in-depth mechanistic evaluation. ⁶⁷ Some PAINS are light dependent and react with otherwise unreactive amino acids like the main chain of alanine.^68,69 Compound stability in buffer can also produce misleading time-dependent behavior. ⁵⁹ It can be difficult to predict the sensitivity of a target protein to these nonspecific reactive events. While a screening campaign for a thiol protease produced only a small fraction of reactive false positives, most screening actives for a histone acetyltransferase were thiol reactive.^70,71 Fortunately, awareness of these nuisance events has dramatically increased along with publications of strategies for their identification and triage.^66,72–77 Many of these nuisance inhibitors will appear nonspecific in a k_inact/K_I study ( Fig. 2D ) and should produce unexpected protein-inhibitor adducts by mass spectrometry.

The growth of biophysical techniques in drug discovery, including surface plasmon resonance (SPR), thermal denaturation assays, and ITC, may greatly benefit the identification and characterization of covalent inhibitors.^78–84 While any individual technique can be misleading, the proper combination of biophysical and mechanistic studies can identify tractable scaffolds. In these applications, the reactive nucleophile in the target protein could be mutated to an unreactive amino acid (e.g., cysteine to serine or alanine), and the K_D of the first reversible step could be determined. When the compound originates from a screening library, this might provide a strategy to triage nuisance inhibitors and confirm the inhibitor is making a real, productive interaction with the protein. For example, a cysteine to alanine mutant of glucagon-like peptide-1 receptor (GLP-1R) was critical to identify positive allosteric modulators acting through a specific covalent mechanism. ⁸⁵ This was important given that many of the nonspecific electrophiles identified were not well predicted by computational methods. In addition, a combination of mutational studies and mass spectrometry was used to identify the amino acids responsible for covalent modification of human monoacylglycerol lipase. ³⁸ Unreactive mutants might also be used to determine or confirm the K_i for inhibitors with very high k_inact/K_I values ( Fig. 2C ). The k_inact (or $t_{1/2}^{\infty }$ ) could then be estimated from the K_i and k_inact/K_I. Proteins with mutated nucleophiles might also be useful in a biochemical binding assay or a mass spectrometry screen of covalent libraries. Larger shifts in IC₅₀ values might be expected between a wild-type and mutant protein. For mass spectrometry screens, use of a mutant protein may provide a relatively quick method to triage less selective covalent inhibitors. Last, the evaluation of nonreactive chemical analogues of an inhibitor can be used to estimate the potency of the initial reversible binding event and k_inact. When considering these approaches, it is important to remember that a K_I determined in a kinetic study ( Fig. 2B ) can disagree with a binding constant determined against a mutant protein or using an unreactive inhibitor analogue. This could occur when the second step (k_inact) influences the binding of the inhibitor in the first step (K_I). Examples illustrating this principle have been reported for the kinase activity of Csk and Btk.^86–88

Kinetic Perspective of SAR

After identification of a mechanistically confirmed specific covalent inhibitor, a drug discovery team can then initiate an optimization campaign to understand the SAR and improve inhibitor binding and covalent bond formation. In the optimization of fatty acid amide hydrolase (FAAH), kynurenine aminotransferase (KAT) II, and epidermal growth factor receptor (EGFR) inhibitors, understanding the k_inact/K_I was an important factor.^89–91 A subset of the human KAT II SAR showed significant changes in the k_inact/K_I with relatively no change in the IC₅₀. The IC₅₀ values were all nearly identical to the enzyme concentration (30 nM) used in the assay. For EGFR, the k_inact/K_I results demonstrated that improvements in the K_I were critical to achieve optimal biochemical and cellular potency. Improvements in the K_I should provide at least two benefits. First, inhibitors with a potent K_I may bind more specifically to the target protein and be more selective against a prospective off-target protein. Second, since the rate of inactivation at K_I is only one-half the maximum potential rate (k_inact), an inhibitor with a lower K_I will permit use of a lower drug concentration to rapidly modify the target protein. In addition to understanding on-target events, the k_inact/K_I is a critical parameter used to understand off-target events. In an evaluation of time-dependent cytochrome P450 3A4 inhibitors, k_inact/K_I values were a better predictor of drug-drug interactions in the clinic than IC₅₀ studies. ⁹² The authors suggest IC₅₀ studies should be restricted to preliminary investigations.

Despite examples showing the importance of the k_inact/K_I, there is still an overreliance on IC₅₀ values to drive the SAR of covalent and irreversible inhibitors. As mentioned earlier, determining a k_inact/K_I can be more time-consuming and requires a more careful interpretation of the data. However, it is also true that some IC₅₀ measurements provide an estimate of the k_inact/K_I. In the discovery and SAR of transglutaminase (TG) 2 inhibitors, a good correlation (R ² = 0.95) between the biochemical IC₅₀ and k_inact/K_I was observed. ⁹³ In this case, most IC₅₀ values were at least 10-fold higher than the enzyme concentration (20 nM) used in the biochemical assay. When the IC₅₀ values are higher than the enzyme concentration, indicating that not all the protein has been covalently modified, a stronger correlation between the IC₅₀ and k_inact/K_I is expected. The correlation will improve as the k_inact decreases and the impact of the covalent event becomes less significant. The rationale for this observation is represented in Figure 3 , showing the decrease in IC₅₀ over time for inhibitors C, D, and E ( Table 1 ). When time to reach equilibrium for the first reversible P•I complex is rapid, relative to the measurement time, the IC₅₀ at a time approaching 0 is equivalent to the K_I, after accounting for the concentration of competing ligand in the assay. At the earliest time points, the IC₅₀ of inhibitors D and E approaches equivalence because they have the same K_I. The IC₅₀ will decrease over time as a function of the k_inact and K_I until there is a direct correlation between IC₅₀ and the k_inact/K_I. At later time points, the IC₅₀ of inhibitors C and D are equivalent because they have the same k_inact/K_I. An analysis of the shift in IC₅₀ over time can even produce an estimate of the k_inact and K_I terms.^47,48,50,51 However, at some later time point, the IC₅₀ measured in a biochemical assay will be one-half the target protein concentration in the assay. This is otherwise referred to as a “tight-binding” condition, and the IC₅₀ is always proportional to the target protein concentration. For example, if an assay uses 10 nM protein and a 2-h preincubation, then the IC₅₀ of inhibitors A to D would be 5 nM despite having dramatically different K_I and $t_{1/2}^{\infty }$ values. After accounting for assay variability, any IC₅₀ value within 5- to 10-fold of the target protein concentration should be viewed with caution. Of course, running assays with shorter incubation times so that IC₅₀ ~ K_I can require using higher target protein concentrations, which will exacerbate the tight-binding condition. Given the impact of protein concentration, preincubation time, and assay time on the observed IC₅₀, how should the best assay conditions be selected? Practical and mechanistic considerations (e.g., assay signal, stability, initial linear velocities) will often drive these choices. The best course of action is to be aware of the issues and determine the k_inact/K_I.

Figure 3.

In a biochemical and cellular assay, the IC₅₀ of an irreversible inhibitor will shift from a value that approximates the K_I (inhibitors D and E) to a value that correlates with the k_inact/K_I (inhibitors C and D). The rate of change over time will depend on the relationship between inhibitor concentration and rate of covalent modification defined by its k_inact/K_I. In a biochemical assay, the lower limit of the IC₅₀ is one-half of the enzyme concentration. In a cellular assay, the lower limit of the observed IC₅₀ may be well below the cellular concentration of target protein.

Perhaps the greatest risk of an overreliance on an IC₅₀ is that it does not inform whether the reactive electrophile selected is optimally positioned in the binding pocket. This is best confirmed by measuring the k_inact during SAR. For example, consider the nucleophilic attack of a π (double) bond. Not only must the electrophile be placed at the correct distance from the nucleophile, but there are two optimal angles to consider, defined as the Bürgi-Dunitz and Flippin-Lodge angles.^40,94 Collectively, these define the precise relative location of the nucleophile and electrophile in three-dimensional space required for an optimal rate of covalent bond formation. Modification of any part of the inhibitor could reposition the scaffold in the binding pocket, alter these angles and distances, and affect the rate of covalent bond formation. Some of these changes, designed to improve the rate of covalent bond formation, might affect binding to the target protein. As a result, improvements in the k_inact could be at the expense of the K_I (and vice versa). These trade-offs might be leveraged to design a more selective inhibitor. Figure 3 and Table 1 contain two inhibitors (C and D) that have similar IC₅₀ and k_inact/K_I values. This masks a 100-fold difference in their individual k_inact or K_I values. Inhibitor C has a longer $t_{1/2}^{\infty }$ of 100 min that might reflect a suboptimal placement of the electrophile. The optimization of this compound should focus on improving the k_inact to take full advantage of the reactivity of the chosen electrophile. Inhibitor D has a rapid $t_{1/2}^{\infty }$ of 1 min, perhaps due to more optimal placement or use of a more electrophilic reactive group. It has a relatively poor K_I of 1000 nM, and improvements in the K_I could permit the use of less electrophilic reactive groups. This becomes particularly important when considering the relative rate of a specific versus nonspecific covalent modification. When an inhibitor nonspecifically reacts with a cellular macromolecule, there may be no restriction on achieving an optimal angle or distance, and the observed rate of covalent modification can be very fast. In the design of a specific covalent inhibitor, teams need to balance the reactivity of the electrophile with its optimal placement in the pocket using measurements of the k_inact to design selective inhibitors that take full advantage of the electrophilicity of the reactive group. How does a team determine when they have appropriately balanced these factors and optimized the k_inact? As presented later, the desired or observed pharmacokinetic profile can be a useful benchmark. Otherwise, the team may need to consider the reactivity of the nucleophile and the contribution of its microenvironment on the maximum potential rate of inactivation. The pK_a of the cysteine side chain is 8 to 9 and would be protonated at a physiological pH. However, the pK_a and its nucleophilicity can be heavily influenced by the microenvironment. ⁹⁵ Many of the most biologically important cysteines are hyperreactive, and k_inact values greater than 0.0693 min⁻¹ ( $t_{1/2}^{\infty }$ ≤10 min) should be obtained. ⁹⁶ When the pH of a biochemical assay deviates from the physiological or disease-relevant pH, the impact of pH on the k_inact/K_I should be explored. An evaluation of the pH dependence could also provide an estimate of the pK_a of the nucleophile and its potential to react with an electrophilic inhibitor.^97,98

The application of k_inact/K_I during SAR can also directly influence how to define selectivity. For example, consider an inhibitor targeting protein B and selective for protein F. The kinetic constants and simulated IC₅₀ values are shown in Table 1 . Based on their k_inact/K_I values, the inhibitor would appear to be 1000-fold selective, resulting from a 100-fold shift in K_I and 10-fold shift in $t_{1/2}^{\infty }$ . Based on the IC₅₀ values and using a relatively low protein concentration, the inhibitor would appear ~300- to 1000-fold selective. However, if 10 nM protein is used in the assay, then the observed selectivity is only ~40- to 160-fold. Similar to our view of SAR, the observed selectivity in an IC₅₀ assay is driven by how much protein is present. So it would appear that k_inact/K_I provides the most accurate view of selectivity. It is a more detailed parameter defining a relationship between inhibitor concentration and the observed rate of covalent bond formation at that concentration. In Figure 4 , this full relationship is overlaid for proteins B and F. If selectivity is interpreted as the difference in the observed rate of inactivation and consequently the fraction of proteins B and F covalently occupied by an inhibitor, then the selectivity decreases at higher inhibitor concentrations. At 10 nM inhibitor, a 505-fold difference in the observed rate of inactivation is expected. In this region, where the inhibitor concentration is near or below their K_I values, the differences in k_inact/K_I will drive the observed selectivity. At 10 µM inhibitor, the selectivity decreases to only 11-fold and approximates the 10-fold difference in their k_inact ( $t_{1/2}^{\infty }$ ) values. At these higher concentrations, any selectivity afforded by the difference in their K_I is eliminated. Teams that determine k_inact/K_I for their on- and off-target proteins during SAR can better understand these relationships and more accurately define selectivity at a particular inhibitor concentration.

Figure 4.

The k_inact/K_I relationship is illustrated for an inhibitor with an apparent 1000-fold selectivity for protein B over protein F ( Table 1 ). The k_inact/K_I for protein B is 1.2 × 10⁵ M⁻¹s⁻¹ with a K_I of 10 nM and a k_inact of 0.0693 min⁻¹ ( $t_{1/2}^{\infty }$ of 10 min). The k_inact/K_I for protein F is 1.2 × 10² M⁻¹s⁻¹ with a K_I of 1000 nM and a k_inact of 0.00693 min⁻¹ ( $t_{1/2}^{\infty }$ of 100 min). An overlay of the rate of inactivation at each inhibitor concentration reveals that the observed selectivity, ranging from 10- to 1000-fold, depends on the inhibitor concentration presented to the two proteins. At inhibitor concentrations below K_I, the k_inact/K_I will drive the observed selectivity. At inhibitor concentrations above K_I, the k_inact will drive the observed selectivity.

Translation of Kinetics to the Cell

Perhaps the greatest risk of relying on a biochemical k_inact/K_I is that they are determined using purified proteins. As presented earlier for EGFR, it is important to understand the correlation between the biochemical k_inact/K_I and the cell-based potency. ⁹¹ In addition, a good correlation between K_I, determined from the k_inact/K_I, and cell death was used to implicate caspase 8 in a cell model of apoptosis. ⁹⁹ When a good correlation does not exist, the incorrect protein or protein complex may have been selected for the biochemical k_inact/K_I study. As a result, it is always most appropriate, when possible, to use physiologically relevant proteins and reagents in biochemical assays. ¹⁰⁰ When the target protein is an enzyme and the objective is to identify a new chemical scaffold, it is important that the biochemical assay is mechanistically balanced so that all potential forms of the enzyme are present in the k_inact/K_I study. ¹⁰⁰ When the objective of the k_inact/K_I study is to better understand the cellular activity, more physiologically or disease-relevant conditions should be considered (e.g., high concentrations of ATP for a kinase target). When the reactive nucleophile is cysteine, its oxidation state will also affect the biochemical correlation to cells. In a biochemical assay, mild reducing agents that do not react with the electrophilic inhibitor may be needed to ensure the cysteine remains reduced over time. In a cell-based assay, cysteine can undergo posttranslational modifications that can be important for a wide range of biological functions, including metal binding, structural integrity, nucleophilic and redox catalysis, and other regulatory roles. ¹⁰¹ There are 200 kinases with a cysteine near the ATP pocket, and their activities may be regulated by the oxidation state of the cysteine.^102–104 For example, epidermal growth factor (EGF) stimulation of cells leads to oxidation of Cys797 in EGFR and increased tyrosine kinase activity. ¹⁰⁵ The same cysteine is targeted by several covalent inhibitors. ¹⁰⁶ The additional steric bulk of an oxidized cysteine increases the K_I of covalent inhibitors. ⁹¹ This might also prevent covalent bond formation in cells. When these oxidation events are in equilibrium with a reducing event, this might only decrease their cellular k_inact/K_I. The presence of other posttranslational modifications or binding partners in a cell could produce a similar effect and result in a poor correlation to the biochemical k_inact/K_I. It is important to continue monitoring this correlation throughout an SAR because it may identify an inhibitor whose cellular activity is poorly predicted by the biochemical k_inact/K_I. Some of these observations could be leveraged to design or identify more physiologically relevant inhibitors. A poor correlation may also indicate that an off-target event is affecting the cellular response.

It has been well established that competition with high concentrations of ligands, substrates, and accessory proteins in a cell will decrease the observed potency of a rapid equilibrium reversible inhibitor. ¹⁰⁷ This is an issue for a majority of drugs, as 80% of Food and Drug Administration (FDA)–approved drugs from 2001 to 2004 compete with a substrate or ligand for binding to a target protein. ¹⁰⁸ This competition may also result from enzyme inhibition that produces higher transient substrate levels, and irreversible inhibitors can provide a strategy to overcome this competition.^109,110 Substrate competition can also have a significant impact on our view of cellular selectivity. This has been reviewed for kinase inhibitors that have large variations in the K_M of ATP. ¹¹¹ The observed biochemical potency and selectivity of an ATP competitive inhibitor will shift in cells as a function of the cellular concentration of ATP and the K_M for each kinase. For an irreversible inhibitor, the formation of the first reversible P•I complex will be governed by the same rules. The observed K_I measured in a mechanistically balanced biochemical assay will shift to some higher value in cells (_appK_I) as a function of the concentration of competing ligand relative to its binding constant. When this occurs, the cellular k_inact/K_I will be proportionally lower than the biochemical k_inact/K_I. When the target protein is a multisubstrate enzyme, it may also be important to understand both the enzyme reaction mechanism and which form of the enzyme is bound best by inhibitor. This might provide a mechanistic rationalization for a difference between a biochemical and cellular k_inact/K_I.

The translation of biochemical potency to the cell is also complicated by differences in incubation times and protein resynthesis. For example, the effect of epigenetic inhibitors in cell-based assays can take days to see changes in a mark or gene and perhaps weeks to see a phenotypic response. ¹¹² In these cases, the inhibitor is given a relatively long time to covalently modify the target, and this would lower the observed IC₅₀. This can significantly affect correlations to a biochemical IC₅₀ that may have resulted from a shorter incubation time. Longer cell-based assays also increase the risk of protein resynthesis. In the human A549 adenocarcinoma cell line, roughly 500 of 600 proteins have a rate of degradation <0.1 h⁻¹ (or t_1/2 >6.93 h). ¹¹³ So while most proteins appear to be very stable, a small yet significant fraction has higher rates of degradation and perhaps resynthesis. Proteins in yeast can be synthesized just in time to meet the demands of the cell cycle. ¹¹⁴ The expression of GFP in K562 cells occurs only 4 h after transfection. ¹¹⁵ Protein resynthesis may also be triggered by a stimulant. Following sugar uptake in Escherichia coli, proteins in the arabinose utilization system are resynthesized in less than 20 min. ¹¹⁶ Covalent modification of the target protein may also affect the protein turnover. ¹¹⁷ For example, the turnover of interleukin-2 inducible T-cell kinase (Itk) in resting primary T cells is approximately 2 h. Following covalent modification of Itk, the related pathway is silenced for more than 24 h to suggest Itk has not yet been resynthesized. Finally, the rate of resynthesis might be affected by the rate of cell proliferation. Inhibitors that alter cell growth might be expected to alter protein resynthesis rates. Taken together, these factors could affect the observed cellular IC₅₀ and k_inact/K_I of a covalent inhibitor.

In a biochemical setting, the most potent IC₅₀ that can be obtained is simply one-half of the purified, functional target protein added in the assay. The lowest potential concentration of target protein in a cell can be estimated using the volume of the cell. For example, one protein molecule placed in E. coli would have a concentration of 1 nM. ¹¹⁸ This may be ~500-fold lower in larger human HeLa and U2O2 cells. ¹¹⁹ An analysis of the global protein expression profile in Saccharomyces cerevisiae revealed as few as 50 to more than one million individual copies of a protein per cell. ¹²⁰ This reflects protein concentrations ranging from 1 nM to over 20 µM and correlates well to estimates of 10 nM and higher.^118,121 Regardless, IC₅₀ values far below these concentrations can be obtained in cells. The target protein concentration in cells reflects the number of protein molecules in the relatively small volume of a cell. Significantly lower concentrations of inhibitor present in the much larger media volume would often still provide a stoichiometric excess of inhibitor to covalently modify all the target protein. ¹¹¹ This does not mean that the cellular potency is independent of the target protein concentration or expression levels in cells. For example, the expression of Bcr-Abl protein decreases in cells with short-interfering RNA (siRNA) treatment, and this increases the sensitivity to imatinib. ¹²² When differences are observed in the potency of an irreversible inhibitor, it may reflect differences in the cellular k_inact/K_I.

In addition to these issues, compound permeability, choice of cell line, and proximity of the measured response relative to the target protein are important factors to consider. Collectively, these potential issues highlight the importance of demonstrating covalent bond formation in cells and understanding the cellular kinetics. There are several tools available to interrogate this in cells. Measuring the cellular activity of an inhibitor after washing out unbound and reversibly bound inhibitor can be a simple method to demonstrate irreversible behavior. ¹²³ In addition, irreversible fluorescent probes can be useful tools to determine the fraction of unbound target protein in cells. ¹²⁴ This was used in the clinical development of ibrutinib and may have applications much earlier in drug discovery. While this can be a powerful method to show target engagement in cells, it is important to remember that even minor modifications of a covalent inhibitor or probe can have a dramatic impact on its cellular pharmacology. ¹²⁵ Therefore, potential probes should be well characterized. Occupancy assays should be complemented by functional cell-based assays to understand the consequence of covalent occupancy. When possible, a more in-depth evaluation of the cellular kinetics can be performed. For regulator of G-protein signaling (RGS) 4, covalent modification in cells was confirmed using a combination of Western blots and mass spectrometry. ¹²⁶ For Kelch-like ECH-associated protein (Keap) 1, the kinetic rate constants for an irreversible inhibitor were measured against different cysteines on Keap1 in HEK293 cells. ¹²⁷ More recently, the cellular k_inact/K_I for a covalent inhibitor (ARS-853) of GDP-bound KRAS(G12C) was determined to be 140 M⁻¹s⁻¹ in H358 cells. This correlated well to the biochemical k_inact/K_I of 76 M⁻¹s⁻¹. ¹²⁸ Last, the discovery and characterization of FAAH inhibitors offer a workflow for evaluating the cellular pharmacology and proteomic profile of a covalent inhibitor.^129,130 With any of these studies, increasing either inhibitor concentration or incubation time will improve covalent modification of the target protein and identify more specific and nonspecific off-target activities. Each of these events will be driven by a k_inact/K_I relationship. When armed with that information, what are the most relevant time points and concentrations to test? The cell-based assay conditions may be the most appropriate consideration when that assay is the object of the investigation. For the most advanced inhibitors, it is best to consider the pharmacokinetic profile.

Covalent Kinetic and Pharmacokinetic (CK/PK) Relationship

For a rapidly reversible inhibitor, the observed pharmacodynamic (PD) effect should be directly linked to the observed pharmacokinetic (PK) profile. As a result, the target is inhibited only when the in vivo exposure of the inhibitor to the target protein is higher than its binding constant in that setting, often estimated by a relevant cell-based assay. This ratio drives whether the target will be occupied with inhibitor. As the drug is cleared from the body and the concentration of inhibitor decreases below that binding constant, the target’s functional activity is restored. In contrast, irreversible inhibitors (or inhibitors with a very slow off-rate) have a pharmacodynamic response that extends beyond what the pharmacokinetic profile would predict. Once all the target protein has been covalently modified in vivo, the inhibitor may be cleared from the body and the target protein’s functional activity would only return when new protein is synthesized. This has been referred to as the “ultimate physiological goal” of an inhibitor. ¹³¹ In fact, the target protein in vivo would only need to be exposed to a sufficient concentration of inhibitor for a specific time necessary to form the covalent bond. How should the concentration and time required be determined? As illustrated earlier in Figure 2 , the relationship between concentration of inhibitor, time, and rate of covalent bond formation is defined by the k_inact/K_I relationship, and it provides a useful guide.

Physiologically relevant k_inact (or $t_{1/2}^{\infty }$ ) and K_I (or _appK_I) values of an inhibitor can be used to estimate the PK profile necessary for covalent bond formation in vivo. If the $t_{1/2}^{\infty }$ of an inhibitor is 20 min, then 100 min (or 5 half-lives) of exposure would be required to achieve >95% occupancy. However, this rate of inactivation is only attained at inhibitor concentrations above the in vivo _appK_I. At lower inhibitor concentrations, the rate of covalent bond formation is slower than estimated by the $t_{1/2}^{\infty }$ , and more exposure time would be required. The PK profile observed for an inhibitor can be used to estimate the required covalent kinetic parameters ( $t_{1/2}^{\infty }$ and K_I). If the target protein is exposed to 100 nM inhibitor for 120 min, then in vivo _appK_I and $t_{1/2}^{\infty }$ values approaching 100 nM for ≤12 min, respectively, may be needed. While these comparisons can provide some qualitative guidelines, they are imprecise and neglect to account for the changing inhibitor concentrations observed in vivo. As illustrated in Figure 2 , changes in the inhibitor concentration will change the observed rate of covalent bond formation. Despite this challenge, the covalent kinetic (CK) profile, defined by the k_inact/K_I relationship, and the PK profile can be modeled to estimate the in vivo covalent occupancy expected over time. In Figure 5A , a PK profile is modeled for an inhibitor. At a dose of 10 mg/kg, it achieves an unbound C_max of 19.6 nM and an unbound AUC of 20.8 nM*h. It has a high clearance of 200 mL/min/kg, and consequently very little inhibitor is present after 4 h (33 pM). The percent covalent occupancy was then estimated over time using the k_inact/K_I relationship defined for protein B in Table 1 . The biochemical, cellular, and in vivo k_inact/K_I values were assumed to be equivalent. This inhibitor has a k_inact/K_I of 1.2 × 10⁵ M⁻¹s⁻¹ with a K_I of 10 nM and a $t_{1/2}^{\infty }$ of 10 min. This profile results in rapid ~100% covalent occupancy of protein B. The same PK profile was used to estimate the covalent occupancy for a prospective off-target (protein F from Table 1 ). It has a 1000-fold lower k_inact/K_I, and the model shows virtually no occupancy after 24 h. The rate of protein resynthesis was assumed to be negligible for both proteins. A covalent and irreversible inhibitor with fast clearance, rapid on-target inactivation that is maintained after the drug is cleared, and lack of off-target occupancy might be considered an ideal profile.

Figure 5.

A model of the covalent kinetic (CK) and pharmacokinetic (PK) profiles where the k_inact/K_I, dose, and clearance were varied. The percent covalent target occupancy of an inhibitor was modeled using the k_inact/K_I for proteins B and F in Table 1 . (A) An inhibitor with rapid clearance was modeled at a dose of 10 mg/kg (0.1 fraction bioavailable, 0.1 fraction unbound, k_a of 2 h⁻¹, k_e of 3.43 h⁻¹, and a clearance of 200 mL/min/kg). Rapid occupancy of protein B is observed with virtually no occupancy of protein F. The unbound AUC^(0–∞) equaled the unbound AUC^(0–24h) and was 20.8 nM*h. (B) The clearance of the inhibitor was reduced to 5 mL/min/kg while holding all other variables constant. This maintained excellent occupancy for protein B and increased occupancy for protein F to 25.0% at 24 h. The unbound AUC^(0–∞) increased to 833 nM*h. The unbound AUC^(0–24h) was 722 nM*h. (C) While maintaining the slow clearance, the dose was lowered to 0.25 mg/kg. The unbound AUC^(0–∞) was 20.8 nM*h, and unbound AUC^(0–24h) was 18.1 nM*h. This produces occupancies of proteins B and F nearly identical to those modeled in (A) when the dose was 10 mg/kg, the clearance was 200 mL/min/kg, and the unbound AUC was also 20.8 nM*h. (D) When the clearance was increased back to 200 mL/min/kg at a dose of 0.25 mg/kg, only 18.9% occupancy of protein B and nearly 0% occupancy of protein F was observed. The unbound AUC^(0–∞) equaled the unbound AUC^(0–24h) and was 0.52 nM*h. In (A), (C), and (D), the occupancy of protein F was nearly 0% at each time point. The pharmacokinetic (PK) profile was built using a single-compartment model. The occupancy was determined at 0.05-h intervals using the following equation: % Occupancy = OPT + (100 − OPT)(1 − exp(−0.05*Rate)), where Rate = k_inact[I]/(K_I + [I]) and OPT = occupancy at the previous time point.

In Figure 5B , the same relationship from Figure 5A is modeled except the clearance was reduced to 5 mL/min/kg. As a result, a dose of 10 mg/kg achieves an unbound C_max of 62 nM and an unbound AUC^(0–∞) of 833 nM*h. After 24 h, 10 nM of inhibitor is still present, and the unbound AUC^(0–24h) is 722 nM*h. This profile quickly produces 100% covalent occupancy of protein B. The improved exposure over time also results in increased occupancy of the off-target (25.0% occupancy of protein F). This is despite the 1000-fold difference in their k_inact/K_I. The higher unbound C_max produced here could decrease the observed selectivity, as illustrated in Figure 4 . This would appear to justify the rationale for advancing covalent inhibitors with a faster clearance. However, in Figure 5C , the dose was lowered 40-fold from 10 mg/kg to 0.25 mg/kg. This produces an unbound C_max of 1.6 nM, an unbound AUC^(0–∞) of 20.8 nM*h, and an unbound AUC^(0–24h) of 18.1 nM*h. Interestingly, the modeled covalent occupancy at 24 h was ~100% and ~0% for proteins B and F, respectively. This matches the modeled occupancy in Figure 5A at 10 mg/kg with a more rapid clearance. When the modeled dose in Figure 5A is reduced 40-fold to 0.25 mg/kg in Figure 5D , only 18.9% covalent occupancy of protein B is achieved at 24 h. Therefore, the simulations in Figure 5A , C produce nearly identical covalent occupancies for the on-target (protein B) and off-target (protein F). Despite having different PK profiles, they require very different doses and share a common unbound AUC.

The covalent kinetic and pharmacokinetic profiles modeled in Figure 5 suggest that the unbound AUC may be the dominant pharmacokinetic parameter. In an effort to rationalize this observation, equation (3) was derived (Suppl. Fig. S1) from a set of common equations routinely used to describe covalent kinetic (CK) and pharmacokinetic (PK) events.

$$\%\mathrm{Covalent\; Occupancy}=100(1-\exp (-({\mathrm{k}}_{\mathrm{inact}}/{\mathrm{K}}_{\mathrm{I}})({\mathrm{AUC}}_{\mathrm{u}}))).$$

This equation defines a direct relationship between the k_inact/K_I and the unbound AUC in the estimation of covalent occupancy. In this context, the unbound AUC reflects the area under the curve in a PK plot showing the concentration of drug exposed over time to the target protein. Armed with an understanding of the relationship between dose and unbound AUC, a physiologically relevant k_inact/K_I can now be used to estimate the dose needed to achieve a specific covalent occupancy. The primary assumption in the derivation of equation (3) is that the concentration of inhibitor is below K_I. This assumption essentially excludes any contribution of reversible inhibition (P•I) and the % Covalent Occupancy term reflects only covalent bond formation. As illustrated in Figure 2B and Figure 4 , inhibitor concentrations at and above K_I provide little improvement in the observed rate of covalent bond formation and may prevent selective inhibition.

Equation (3) might serve as a useful tool for drug discovery teams to quantify the PK/PD disconnect observed for covalent and irreversible inhibitors. This might be helpful at the earliest stages of drug discovery where trade-offs are consistently made between in vitro inhibition and PK properties. For example, a 10-fold increase in the unbound AUC and any decrease in k_inact/K_I less than 10-fold would be expected to improve the in vivo covalent occupancy. Likewise, improvements in the k_inact/K_I at the expense of the unbound AUC might improve in vivo covalent occupancy. However, it is important to consider that equation (3) is an oversimplification of a much more complex system. It does not account for many other important factors, including protein resynthesis rates. As a covalent inhibitor effort matures, the team will need to build a more complete model incorporating all relevant factors. Many excellent examples of this can be found for the time-dependent inhibition of cytochrome P450 enzymes.^132–138 In these instances, the k_inact, K_I, and K_i terms were critical factors used to model drug-drug interactions. In fact, the FDA and European Medicines Agency recommend k_inact/K_I studies to assess the risk of drug-drug interactions.^139,140

The relationship defined by equation (3) was then used to understand the profiles in Figure 5 . Protein B has a k_inact/K_I of 1.2 × 10⁵ M⁻¹s⁻¹, and equation (3) would predict that an unbound AUC^(0–24h) of 6.93 nM*h is needed to achieve 95% occupancy. In the four PK profiles modeled in Figure 5 , the unbound AUC^(0–24h) exceeds 6.93 nM*h in the three situations where >95% occupancy was modeled. Only in Figure 5D , where the unbound AUC was 0.52 nM*h, was the modeled occupancy <95%. Using an unbound AUC of 0.52 nM*h and a k_inact/K_I of 1.2 × 10⁵ M⁻¹s⁻¹ for protein B in equation (3) yields an expected occupancy of 19.4%, which correlates well to 18.9% in the full model. A summary of the PK parameters and occupancies modeled in Figure 5 can be found in Table 2 . As expected, equation (3) overestimates the modeled occupancy as the inhibitor concentration approaches or exceeds the K_I. The challenge in applying equation (3) to predict in vivo covalent occupancy is estimating the in vivo k_inact/K_I. The best estimate may be obtained from a time-dependent evaluation of a relevant cell-based assay.^33,34 An estimate might also be obtained from a biochemical k_inact/K_I after accounting for a shift in K_I due to competing ligands in the cell or from a cellular k_inact/K_I determined using an IC₅₀ shift assay.^{47,48,50,51,111} In some cases, the in vivo or cellular k_inact/K_I might be estimated in equation (3) using the unbound AUC or the concentration of inhibitor presented to the cells over time as an approximation of the AUC, respectively. Of course, this requires evidence of covalent bond formation, concentrations of inhibitor below the _appK_I in cells, and insignificant rates of protein resynthesis. Collectively, equation (3) may facilitate a more direct correlation of covalent inhibition in a biochemical, cellular, and in vivo setting.

Table 2.

Covalent Kinetic and Pharmacokinetic Parameters Modeled in Figure 5 .

	Modeled Pharmacokinetics a					Modeled % Covalent Occupancy at 24 h
Figure	Dose, mg/kg	Clearance, mL/min/kg	uCmax, nM	uAUC(0-∞), nM*h	uAUC(0-24 h), nM*h	Full Model		CK/PK Equation
						Protein B	Protein F	Protein B	Protein F
A	10	200	19.6	20.8	20.8	98.3	0.85	100.0	0.86
B	10	5	62	833	722	100.0	25.0	100.0	25.9
C	0.25	5	1.6	20.8	18.1	99.9	0.75	99.9	0.75
D	0.25	200	0.49	0.52	0.52	18.9	0.022	19.4	0.022

AUC, area under the curve; CK, covalent kinetic; PK, pharmacokinetic; u, unbound.

a

In each case, the bioavailability = 0.1, fraction unbound = 0.1, volume of distribution = 3.5 L/kg, k_a = 2 h⁻¹, and molecular weight = 400 g/mol.

With an understanding now that the k_inact/K_I is a critical factor to estimate in vivo covalent occupancy, the CK and PK profiles of proteins A to F in Table 1 were fully modeled in the manner depicted in Figure 5 . Using the PK profile from Figure 5B , C , a 10-mg/kg dose is expected to achieve >94% covalent occupancy at 24 h for five (proteins A–E) of the six proteins. Modeling a 1-mg/kg dose would produce >89% occupancy for four (proteins A–D) of the six proteins. In these situations, up to 100-fold selectivity in k_inact/K_I may not translate to selective in vivo covalent occupancy. Inhibitors showing 1000-fold or higher selectivity may be required. In cases where the PK resembles Figure 5A , D with a more C_max-driven AUC, the selectivity becomes a greater concern, as depicted in Figure 4 . This relationship also illustrates that inhibitors with good PK profiles, yet relatively slow k_inact/K_I values, would still be predicted to achieve full target occupancy. Inhibitor E in Table 1 has a relatively poor k_inact/K_I of 1.2 × 10³ M⁻¹s⁻¹ resulting from a K_I of 1000 nM and $t_{1/2}^{\infty }$ of 10 min. At a 10-mg/kg dose, it would be expected to achieve 94% occupancy after 24 h. This might be sufficient to observe efficacy in a prospective animal model. However, improvements in the k_inact/K_I could lower the dose (unbound AUC) needed to achieve full occupancy. This may be particularly important for compounds that already have an optimal PK profile. To illustrate this point, the minimum dose needed to produce >90% covalent occupancy for inhibitors A to F in Table 1 was determined in the full CK/PK model. As expected, a strong correlation between the k_inact/K_I and the minimum dose needed was observed. Inhibitor A from Table 1 , with a very efficient k_inact/K_I of 1.2 × 10⁶ M⁻¹s⁻¹, should require only 0.008 mg/kg for full target occupancy. In addition, inhibitors A to D may have completely indistinguishable IC₅₀ values in the biochemical assay and very potent cell-based activities. Similar trends would be expected for inhibitors with faster clearance, as modeled in Figure 5A , D (or given any fixed PK profile). In summary, teams that optimize their covalent inhibitors based on a physiologically relevant k_inact/K_I and an (unbound) AUC reflecting direct exposure of the inhibitor to the target protein could significantly lower the minimum dose needed for >90% covalent occupancy. This could translate to lower doses in the clinic, which should improve the safety and success of covalent inhibitors.^15,16,141

In conclusion, the discovery and optimization of a covalent, irreversible inhibitor introduces unique opportunities and risks that teams must balance to deliver a safe and efficacious drug. These inhibitors will produce potent biochemical and cellular activities that will only improve with longer assay times. For a target protein, this is a great benefit and can quickly produce promising in vitro results. For a prospective selectivity protein or macromolecule, this is a problem. In some cases, these selectivity issues may not surface until in vivo studies are performed or, worse yet, in the clinic. While there is a long list of factors that must be considered, the kinetics of covalent bond formation, defined by the k_inact/K_I, should be a key component of the drug discovery effort. The k_inact/K_I value defines a relationship between the concentration of drug and the rate of covalent bond formation. That relationship will determine the observed potencies across the biochemical, cellular, and in vivo studies used to identify, optimize, and advance the best and most selective inhibitors. In biochemical and cellular assays, where inhibitors are first identified and the SAR is determined, the individual K_I and k_inact values are as important as the k_inact/K_I ratio. Optimization using these measurements will facilitate the identification of a drug that makes a strong, specific interaction and enable the formation of a selective covalent bond to the target protein. For an in vivo study, the optimal CK profile will depend on the desired dose and the PK profile. Inhibitors with relatively weak k_inact/K_I values could be expected to produce full in vivo covalent occupancy. Teams striving for a low clinical dose should continue improving the k_inact/K_I. In addition, the (unbound) AUC reflecting drug exposure to the target protein is a critical PK parameter that might be used to estimate in vivo covalent occupancy. Optimization based simply on improving the C_max may eliminate any apparent selectivity. The relationship between optimal CK and PK profiles is reflected in a simple equation showing a direct relationship between a physiologically relevant k_inact/K_I, the (unbound) AUC presented directly to the target protein, and covalent occupancy. This might serve as a useful guide for biochemists to provide teams an estimate of in vivo covalent occupancy and selectivity at the earliest stages of drug discovery. The application of this and other recommendations in this perspective might aid in the discovery and development of new drugs with a covalent and irreversible mechanism.