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John M. Strelow, Lilly Research Laboratories, Eli Lilly and Company, Lilly Corporate Center, 355 E. Merrill St., Indianapolis, IN 46285, USA. Email: strelow_john_mark@lilly.com
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 kinact/KI. The kinact/KI is a rate constant describing the efficiency of covalent bond formation resulting from the potency (KI) of the first reversible binding event and the maximum potential rate (kinact) of inactivation. In this perspective, it is proposed that the kinact/KI 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 kinact/KI 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.
공유결합 의약품의 임상적 및 상업적 성공으로 의약품 발견 단계에서 공유결합 및 비가역적 기전을 새로 만들고 보다 계획적으로 추구하도록 요청되었습니다. 공유결합 기전으로 생화학, 세포 또는 생체내 환경에서 강력한 억제를 생성할 수 있습니다. 대부분의 경우, 팀에서는 IC50 값으로 정의된 공유결합 반응 결과에 중점을 두기를 원합니다. 생화학적 분석법에서, IC50은 분석법에서 단순히 표적 단백질 농도를 나타내는 것일 수 있습니다. kinact/KI로 정의된 공유결합 수정 비율의 중요성에 대한 관심은 적었습니다. kinact/KI는 첫 번째 가역적 결합 반응의 역가(KI) 및 불활성화 최대 전위 속도(kinact)로 인한공유결합 형성의 효율을 설명하는 속도 상수입니다. 이 관점에서, kinact/KI가 공유결합 억제제를 확인하고, 구조 활성 관계(SAR) 해석하며, 생화학적 분석법을 통한 세포 활성을 명백히 밝히고, 선택성을 보다 정확하게 정의하는 중요한 매개변수로 활용되어야 한다고 제안됩니다. 또한, 생리적으로 관련 있는 kinact/KI 및 표적 단백질에 대한 억제제의 직접적 노출을 나타내는 약동학 프로필에서 생성된 (비결합) AUC가 생체내 공유결합 점유율의 두 가지 중요한 결정 요인인 것으로 제시됩니다. 이 관련성을 정의하고 공유결합 및 비가역적 약력학의 해석을 개선하기 위해 단순한 방정식이 제시됩니다.
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.
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.
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.
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.
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.
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.
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).
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 kinact/KI during a structure-activity relationship (SAR) campaign is often recommended but infrequently applied. The kinact/KI 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 kinact/KI, 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 KI. The KI term describes the concentration of inhibitor required for half of the maximum potential rate of covalent bond formation. This should not be confused with Ki 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 kinact. The kinact 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 kinact to KI or kinact/KI. This bimolecular rate constant accounts for both the potency of the first step (KI) and the maximum potential rate of covalent bond formation (kinact). The kinact/KI 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 kinact/KI of 1.2 × 103 M–1s–1. The observed occupancy over time at each inhibitor concentration is fit to equation (1).
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 KI, and the maximum potential rate of inactivation is defined by kinact. Taken together, the kinact/KI 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 (kobs). (B) The kinact/KI relationship between inhibitor concentration and the observed rate of inactivation for inhibitor E with a KI of 1000 nM and a kinact of 0.0693 min–1 ( of 10 min). (C) The kinact/KI relationship between inhibitor concentration and the observed rate of inactivation for inhibitor A with a KI of 10 nM and a kinact of 0.693 min–1 ( of 1 min). The rapid observed rates may prevent an accurate determination of the KI and kinact (). The initial slope of this line is the kinact/KI. (D) The kinact/KI relationship between inhibitor concentration and the observed rate of inactivation for a nonspecific inhibitor with either no binding or a very high KI. The slope of this line is the kinact/KI (12 M–1s–1). These plots were generated using the following equations: % Occupancy = Ymax(1 – exp(–1 * Rate * time)) + Y0; Ymax = 100 – 100/(1 + KI/[I]); Y0 = 100/(1 + KI/[I]); Rate = kinact * [I]/(KI + [I]).
The % inhibition was calculated at a range of [inhibitor] by adding the reversibly bound inhibitor, defined by FreeProtein/(1 + KI/[I]), to the covalently modified fraction ± preincubation using FreeProtein*(1 – exp(–1 * Rate * time)) where the preincubation contained 2×[inhibitor] and Rate = kinact * [I]/(KI + [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.
The following pharmacokinetic (PK) parameters were used: 0.1 fraction bioavailable, 0.1 fraction unbound, ka of 2h–1, ke of 0.09h–1, and a clearance of 5 mL/min/kg with a molecular weight of 400 g/mol.
The following pharmacokinetic (PK) parameters were used: 0.1 fraction bioavailable, 0.1 fraction unbound, ka of 2h–1, ke of 0.09h–1, and a clearance of 5 mL/min/kg with a molecular weight of 400 g/mol.
0.5-h Assay
4-h Assay
No PreInc
2-h PreInc
No PreInc
2-h PreInc
10 mg/kg
1.0 mg/kg
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
aThe % inhibition was calculated at a range of [inhibitor] by adding the reversibly bound inhibitor, defined by FreeProtein/(1 + KI/[I]), to the covalently modified fraction ± preincubation using FreeProtein*(1 – exp(–1 * Rate * time)) where the preincubation contained 2×[inhibitor] and Rate = kinact * [I]/(KI + [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.
bThe following pharmacokinetic (PK) parameters were used: 0.1 fraction bioavailable, 0.1 fraction unbound, ka of 2h–1, ke of 0.09h–1, and a clearance of 5 mL/min/kg with a molecular weight of 400 g/mol.
This yields the kobs, an observed first-order rate constant with units of inverse time, at each inhibitor concentration. The kobs values are then fit to equation (2) to determine the kinact and KI.
(2)
This is illustrated in Figure 2B for inhibitor E. The maximum potential rate of inactivation, kinact, is 0.0693 min–1, which is only observed at inhibitor concentrations well above the KI of 1000 nM. This rate can also be represented as a of 10 min. The is determined by dividing 0.693 by the kinact. It describes the time required for half of the protein to be covalently modified at some theoretically infinite inhibitor concentration. The 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 KI levels, only 50% of the protein contains reversibly bound inhibitor, and the observed rate of inactivation is one-half kinact. When the inhibitor concentration tested is 5-fold above the KI, the observed rate of inactivation is approximately 83% of the kinact. When inhibitor concentrations below the KI are also tested, an accurate estimate of the individual kinact and KI values can be obtained. However, when the kinact/KI 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 kinact/KI of 1.2 × 106 M–1s–1 (inhibitor A in Table 1). This inhibitor has a 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 kobs values above KI and near the kinact. The relationship between inhibitor concentration and the observed rate of inactivation is nearly linear (Fig. 2C). In this example, the individual kinact and KI terms are >0.12 min–1 and >2.0 nM, respectively. The kinact/KI ratio can be determined accurately and is equal to the initial slope. Other methods, presented later, would need to be explored to estimate the kinact and KI.
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 kinact/KI 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 KI 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 kobs is linear with a slope that is equal to the kinact/KI. 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.
Kinetic Glutathione Chemoassay to Quantify Thiol Reactivity of Organic Electrophiles—Application to Alpha, Beta-Unsaturated Ketones, Acrylates, and Propiolates.
Estimates of nonspecific reactivity can also be made at a fixed concentration of inhibitor, often presented as a half-life (t1/2) 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.
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 KI 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 KI. This produces a much higher kinact/KI than a nonspecific inhibitor having a much higher KI and a smaller kinact/KI. This highlights a potential challenge in evaluating covalent fragments. Many of these could appear to be nonspecific in a kinetic study with KI values well above the highest concentration tested. As presented later, it is important to estimate the KI 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 kinact/KI 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).
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 kinact/KI of an inhibitor. The classical approaches, represented for enzyme activity assays and illustrated earlier for a binding assay, have been well documented.
A Critical Evaluation of the Experimental Design of Studies of Mechanism Based Enzyme Inhibition, with Implications for In Vitro–In Vivo Extrapolation.
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.
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 t1/2 offset of 23 h, which lacks a reactive electrophile.
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.
Covalent Inhibitors of Human Monoacylglycerol Lipase: Ligand-Assisted Characterization of the Catalytic Site by Mass Spectrometry and Mutational Analysis.
There have been numerous reports of higher throughput methods to estimate kinact/KI. These include evaluating the IC50 versus time, calculating kobs/[I], or measuring competition with an irreversible probe.
Discovery of 1-{(3R,4R)-3-[({5-Chloro-2-[(1-methyl-1H-pyrazol-4-yl)amino]-7H-pyrrolo[2,3-d]pyrimidin-4-yl}oxy)methyl]-4-methoxypyrrolidin-1-yl}prop-2-en-1-one (PF-06459988), a Potent, WT Sparing, Irreversible Inhibitor of T790M-Containing EGFR Mutants.
Many of these examples originate from studies of cytochrome P450 enzymes, where the kinact/KI 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.
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.
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 kinact and KI terms. This is illustrated in Table 1, where the IC50 values of six covalent inhibitors, with kinact/KI 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 kinact/KI. 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 kinact () and that could only be revealed in a kinact/KI determination.
Perhaps the greatest challenge in using a screening strategy to identify covalent inhibitors is the presence of nuisance inhibitors in many compound libraries.
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.
Identification of a Novel Class of Orally Active Pyrimido[5,4-3][1,2,4]Triazine-5,7-Diamine-Based Hypoglycemic Agents with Protein Tyrosine Phosphatase Inhibitory Activity.
Some of these false-positive redox actives have produced enticing isothermal calorimetry (ITC) results, albeit with poor-quality traces and a KD value that does not correlate to the biochemical potency.
PAINS represent a more diverse set of false-positive mechanisms that includes redox cyclers, covalent modifiers, metal complexers, and unstable compounds.
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.
Both 5-Arylidene-2-Thioxodihydropyrimidine-4,6(1H,5H)-Diones and 3-Thioxo-2,3-Dihydro-1H-imidazo[1,5-a]indol-1-Ones Are Light-Dependent Tumor Necrosis Factor–Alpha Antagonists.
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.
Many of these nuisance inhibitors will appear nonspecific in a kinact/KI 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.
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 KD 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.
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.
Covalent Inhibitors of Human Monoacylglycerol Lipase: Ligand-Assisted Characterization of the Catalytic Site by Mass Spectrometry and Mutational Analysis.
Unreactive mutants might also be used to determine or confirm the Ki for inhibitors with very high kinact/KI values (Fig. 2C). The kinact (or ) could then be estimated from the Ki and kinact/KI. 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 kinact. When considering these approaches, it is important to remember that a KI 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 (kinact) influences the binding of the inhibitor in the first step (KI). Examples illustrating this principle have been reported for the kinase activity of Csk and Btk.
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 kinact/KI was an important factor.
A subset of the human KAT II SAR showed significant changes in the kinact/KI 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 kinact/KI results demonstrated that improvements in the KI were critical to achieve optimal biochemical and cellular potency. Improvements in the KI should provide at least two benefits. First, inhibitors with a potent KI 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 KI is only one-half the maximum potential rate (kinact), an inhibitor with a lower KI will permit use of a lower drug concentration to rapidly modify the target protein. In addition to understanding on-target events, the kinact/KI is a critical parameter used to understand off-target events. In an evaluation of time-dependent cytochrome P450 3A4 inhibitors, kinact/KI values were a better predictor of drug-drug interactions in the clinic than IC50 studies.
The authors suggest IC50 studies should be restricted to preliminary investigations.
Despite examples showing the importance of the kinact/KI, there is still an overreliance on IC50 values to drive the SAR of covalent and irreversible inhibitors. As mentioned earlier, determining a kinact/KI 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 kinact/KI. In the discovery and SAR of transglutaminase (TG) 2 inhibitors, a good correlation (R
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 kinact/KI is expected. The correlation will improve as the kinact 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 KI, 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 KI. The IC50 will decrease over time as a function of the kinact and KI until there is a direct correlation between IC50 and the kinact/KI. At later time points, the IC50 of inhibitors C and D are equivalent because they have the same kinact/KI. An analysis of the shift in IC50 over time can even produce an estimate of the kinact and KI terms.
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 KI and 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 ~ KI 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 kinact/KI.
Figure 3In a biochemical and cellular assay, the IC50 of an irreversible inhibitor will shift from a value that approximates the KI (inhibitors D and E) to a value that correlates with the kinact/KI (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 kinact/KI. 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 kinact 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.
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 kinact could be at the expense of the KI (and vice versa). These trade-offs might be leveraged to design a more selective inhibitor. Figure 3andTable 1 contain two inhibitors (C and D) that have similar IC50 and kinact/KI values. This masks a 100-fold difference in their individual kinact or KI values. Inhibitor C has a longer of 100 min that might reflect a suboptimal placement of the electrophile. The optimization of this compound should focus on improving the kinact to take full advantage of the reactivity of the chosen electrophile. Inhibitor D has a rapid of 1 min, perhaps due to more optimal placement or use of a more electrophilic reactive group. It has a relatively poor KI of 1000 nM, and improvements in the KI 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 kinact 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 kinact? 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 pKa of the cysteine side chain is 8 to 9 and would be protonated at a physiological pH. However, the pKa and its nucleophilicity can be heavily influenced by the microenvironment.
When the pH of a biochemical assay deviates from the physiological or disease-relevant pH, the impact of pH on the kinact/KI should be explored. An evaluation of the pH dependence could also provide an estimate of the pKa of the nucleophile and its potential to react with an electrophilic inhibitor.
The application of kinact/KI 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 kinact/KI values, the inhibitor would appear to be 1000-fold selective, resulting from a 100-fold shift in KI and 10-fold shift in . 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 kinact/KI 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 KI values, the differences in kinact/KI will drive the observed selectivity. At 10 µM inhibitor, the selectivity decreases to only 11-fold and approximates the 10-fold difference in their kinact () values. At these higher concentrations, any selectivity afforded by the difference in their KI is eliminated. Teams that determine kinact/KI 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 4The kinact/KI relationship is illustrated for an inhibitor with an apparent 1000-fold selectivity for protein B over protein F (Table 1). The kinact/KI for protein B is 1.2 × 105 M–1s–1 with a KI of 10 nM and a kinact of 0.0693 min–1 ( of 10 min). The kinact/KI for protein F is 1.2 × 102 M–1s–1 with a KI of 1000 nM and a kinact of 0.00693 min–1 ( 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 KI, the kinact/KI will drive the observed selectivity. At inhibitor concentrations above KI, the kinact will drive the observed selectivity.
Perhaps the greatest risk of relying on a biochemical kinact/KI is that they are determined using purified proteins. As presented earlier for EGFR, it is important to understand the correlation between the biochemical kinact/KI and the cell-based potency.
In addition, a good correlation between KI, determined from the kinact/KI, and cell death was used to implicate caspase 8 in a cell model of apoptosis.
When a good correlation does not exist, the incorrect protein or protein complex may have been selected for the biochemical kinact/KI study. As a result, it is always most appropriate, when possible, to use physiologically relevant proteins and reagents in biochemical assays.
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 kinact/KI study.
When the objective of the kinact/KI 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.
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 kinact/KI. 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 kinact/KI. 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 kinact/KI. 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.
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.
Biochemical Mechanisms of New Molecular Entities (NMEs) Approved by United States FDA during 2001–2004: Mechanisms Leading to Optimal Efficacy and Safety.
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.
Characterization of the Fatty Acid Amide Hydrolase Inhibitor Cyclohexyl Carbamic Acid 3′-Carbamoyl-Biphenyl-3-yl Ester (URB597): Effects on Anandamide and oleoylethanolamide deactivation.
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 KM of ATP.
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 KM 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 KI measured in a mechanistically balanced biochemical assay will shift to some higher value in cells (appKI) as a function of the concentration of competing ligand relative to its binding constant. When this occurs, the cellular kinact/KI will be proportionally lower than the biochemical kinact/KI. 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 kinact/KI.
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.
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 t1/2 >6.93 h).
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.
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.
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 kinact/KI 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.
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.
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.
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.
When differences are observed in the potency of an irreversible inhibitor, it may reflect differences in the cellular kinact/KI.
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.
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.
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.
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.
More recently, the cellular kinact/KI 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 kinact/KI of 76 M–1s–1.
Last, the discovery and characterization of FAAH inhibitors offer a workflow for evaluating the cellular pharmacology and proteomic profile of a covalent inhibitor.
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 kinact/KI 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.
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 kinact/KI relationship, and it provides a useful guide.
Physiologically relevant kinact (or ) and KI (or appKI) values of an inhibitor can be used to estimate the PK profile necessary for covalent bond formation in vivo. If the 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 appKI. At lower inhibitor concentrations, the rate of covalent bond formation is slower than estimated by the , and more exposure time would be required. The PK profile observed for an inhibitor can be used to estimate the required covalent kinetic parameters ( and KI). If the target protein is exposed to 100 nM inhibitor for 120 min, then in vivo appKI and 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 kinact/KI 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 Cmax 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 kinact/KI relationship defined for protein B in Table 1. The biochemical, cellular, and in vivo kinact/KI values were assumed to be equivalent. This inhibitor has a kinact/KI of 1.2 × 105 M–1s–1 with a KI of 10 nM and a 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 kinact/KI, 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 5A model of the covalent kinetic (CK) and pharmacokinetic (PK) profiles where the kinact/KI, dose, and clearance were varied. The percent covalent target occupancy of an inhibitor was modeled using the kinact/KI 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, ka of 2 h–1, ke 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 = kinact[I]/(KI + [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 Cmax 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 kinact/KI. The higher unbound Cmax 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 Cmax 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.
(3)
This equation defines a direct relationship between the kinact/KI 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 kinact/KI 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 KI. 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 2BandFigure 4, inhibitor concentrations at and above KI 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 kinact/KI less than 10-fold would be expected to improve the in vivo covalent occupancy. Likewise, improvements in the kinact/KI 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.
In these instances, the kinact, KI, and Ki terms were critical factors used to model drug-drug interactions. In fact, the FDA and European Medicines Agency recommend kinact/KI studies to assess the risk of drug-drug interactions.
U.S. Department of Health and Human Services, Food and Drug Administration, Center for Drug Evaluation and Research (CDER) Guidance for Industry, Drug Interaction Studies—Study Design, Data Analysis, Implications for Dosing, and Labeling Recommendations.
European Medicine Agency (EMA), Committee for Human Medicinal Products (CHMP). Guideline on the Investigation of Drug Interactions. 2012. www.ema.europa.eu/ema
The relationship defined by equation (3) was then used to understand the profiles in Figure 5. Protein B has a kinact/KI 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 kinact/KI 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 KI. The challenge in applying equation (3) to predict in vivo covalent occupancy is estimating the in vivo kinact/KI. The best estimate may be obtained from a time-dependent evaluation of a relevant cell-based assay.
An estimate might also be obtained from a biochemical kinact/KI after accounting for a shift in KI due to competing ligands in the cell or from a cellular kinact/KI determined using an IC50 shift assay.
In some cases, the in vivo or cellular kinact/KI 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 appKI 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 2Covalent Kinetic and Pharmacokinetic Parameters Modeled in Figure 5.
With an understanding now that the kinact/KI 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 kinact/KI 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 Cmax-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 kinact/KI values, would still be predicted to achieve full target occupancy. Inhibitor E in Table 1 has a relatively poor kinact/KI of 1.2 × 103 M–1s–1 resulting from a KI of 1000 nM and 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 kinact/KI 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 kinact/KI and the minimum dose needed was observed. Inhibitor A from Table 1, with a very efficient kinact/KI 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 kinact/KI 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.
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 kinact/KI, should be a key component of the drug discovery effort. The kinact/KI 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 KI and kinact values are as important as the kinact/KI 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 kinact/KI values could be expected to produce full in vivo covalent occupancy. Teams striving for a low clinical dose should continue improving the kinact/KI. 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 Cmax 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 kinact/KI, 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.
Acknowledgments
I thank John Schindler and my colleagues in ADME, Jeffrey Cramer and Brian Mattioni, and Medicinal Chemistry, Steve Kuklish and Zoran Rankovic, for many helpful conversations and their feedback on this article. I also thank Art Wittwer at Confluence Discovery Technologies for helpful discussions in using DynaFit to confirm the modeling work presented in this article.
Supplementary material for this article is available on the Journal of Biomolecular Screening Web site at http://jbx.sagepub.com/supplemental.
Declaration of Conflicting Interests
The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author received no financial support for the research, authorship, and/or publication of this article.
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