On the use of the experimentally determined enzyme inhibition constant as a measure of absolute binding affinity

Defined as a state function representing an inhibitor’s absolute affinity for its target enzyme, the experimentally determined enzyme inhibition constant (Ki) is widely used to rank order binding affinities of different inhibitors for a common enzyme or different enzymes for a common inhibitor and to benchmark computational approaches to predicting binding affinity. Herein, we report that adsorption of bis(7)-tacrine to the glass container surface increased its Ki against Electrophorus electricus acetylcholinesterase (eeAChE) to 3.2 ± 0.1 nM (n = 5) compared to 2.9 ± 0.4 pM (n = 5) that was determined using plastic containers with other assay conditions kept the same. We also report that, due to binding or “adsorption” of bis(7)-tacrine to the inactive eeAChE, the bis(7)-tacrine Ki increased from 2.9 ± 0.4 pM (n = 5) to 734 ± 70 pM (n = 5) as the specific eeAChE activity decreased from 342 U/mg to 26 U/mg while other assay conditions were kept the same. These results caution against using Kis to rank order binding potencies, define selectivity, or benchmark computational methods without knowing detailed assay conditions. Abbreviations Ki enzyme inhibition constant AChE acetylcholinesterase eeAChE Electrophorus electricus AChE ATCh acetylthiocholine chloride bis(7)-tacrine 1,7-N-heptylene-bis-9,9'-amino-1,2,3,4-tetrahydro-acridinium dihydrochloride DTNB 5,5’-dithiobis(2-nitrobenzoic acid) SEA specific enzyme activity tacrine 9-amino-1,2,3,4-tetrahydroacridinium monohydrochloride.


Introduction
Enzyme inhibition constant (K i ), also known as inhibitor dissociation constant, is an equilibrium constant of a reversible inhibitor for complexation with its target enzyme. Unless otherwise specified all inhibitors described hereafter are reversible inhibitors. K i is associated with thermodynamic parameters in that ΔG = RTln(K i ), where ΔG, R, and T are the absolute binding free energy, the gas constant, and the absolute temperature, respectively [1]. Here K i should not be confused with K I of an irreversible inhibitor, which is the irreversible inhibitor concentration that causes a rate of inactivation equal to a half of pseudo-unimolecular inhibition rate constant. Nor should K i be confused with k i of an irreversible inhibitor that is a bimolecular inhibition rate constant [2][3][4][5]. Unlike the inhibitor concentration that causes 50% enzyme inhibition (IC 50 ), K i is a state function that is independent of the concentration of enzyme used to determine the K i . Therefore, K i represents the absolute affinity of an inhibitor for its target enzyme, and one can theoretically use K i to rank order binding affinities of different inhibitors for a common enzyme, define selectivity of an inhibitor for different enzymes, and benchmark in silico approaches to prediction of inhibitor binding affinities. 3 However, a cursory literature search showed a wide range of experimentally determined K i s for 9-amino-1,2,3,4-tetrahydroacridinium monohydrochloride (tacrine, a withdrawn Alzheimer's drug [6]) against acetylcholinesterase (AChE) [7][8][9][10][11][12][13] from the same species using the same spectrophotometric Ellman assay [14] under the same assay conditions (temperature, pH, and ionic strength). For example, the K i of tacrine was reported to be 20.2 ± 0.1 nM by one group and yet 340 ± 97 nM by another group for inhibiting Electrophorus electricus AChE (eeAChE) under the same Ellman assay conditions [15,16]. For another example, the K i of tacrine was reported to be 36 ± 1 nM by one group and later 137 nM by the same group for inhibiting recombinant human AChE under the same Ellman assay conditions [17,18]. These results raised concerns on the use of the experimentally determined K i as a measure of absolute binding affinity.
In this article we report our enzyme kinetics studies using a model system of eeAChE and its water-soluble inhibitors tacrine and 1,7-N-heptylene-bis-9,9'-amino-1,2,3,4-tetrahydroacridinium dihydrochloride, an analog of tacrine known as bis (7)-tacrine [19], to evaluate the suitability of using the experimentally determined K i as a measure of absolute binding affinity.
The advantages of this model system are that AChE is a well-studied one-substrate enzyme and that preparation of the inhibitor solution for tacrine and bis(7)-tacrine does not require use of any co-solvent such as dimethyl sulfoxide, a mild oxidation reagent [20] that has an inhibitory effect on AChE [21].  250 pg); 1U is defined as converting 1 µmol of substrate to its product in a minute [23]. K i was obtained from 1/v, 1/[ATCh], and [tacrine] or [bis(7)-tacrine] using Prism 4 with the Lineweaver-Burk plot [24] (see Supplementary information for details).

UV absorptions of inhibitor solutions that were prepared using glass or plastic vials
Briefly, to a single quartz cuvette that was washed with distilled water and dried by blowing N 2 gas, 3.0 mL of a tacrine or bis (7)

Container surface as nontarget binding site
To evaluate the suitability of using the experimentally determined K i as a measure of absolute binding affinity, we first turned our attention to a seemingly trivial detail-the arbitrary use of either glass or plastic containers for stock solutions of AChE inhibitors in our enzyme inhibition studies. Adsorption of peptides or proteins to container surfaces and its effect on 6 enzyme inactivation had been documented [3,25,26]. Additives leaching from laboratory plasticware had also been reported [27]. However, we did not find a report on adsorption of small-molecule inhibitors to container surfaces and its effect on K i . This led us to determine whether there was a difference in K i for two inhibitor stock solutions that were prepared using a 7.4-mL general-purpose borosilicate glass threaded vial (the glass vial) and a widely-used 2.0-mL microcentrifuge tube (the plastic vial). Unexpectedly, we found the mean and standard error of K i for bis (7)-tacrine against eeAChE to be 3.2 ± 0.1 nM (n = 5) or 2.9 ± 0.4 pM (n = 5) when the inhibition constant was determined using the glass or the plastic vials, respectively, while all other assay conditions were kept the same (Table 1). We also observed that the specific eeAChE activity resulting from short-exposure to the plastic vial (342 ± 10 U/mg; Table 1) was similar to the activity from the glass vial (334 ± 11 U/mg; Table 1). Rather than effects of possible additives leaching from the plastic vial, the 1000-fold difference in K i indicated that substantially more adsorption of bis(7)-tacrine to the glass than plastic surface occurred during the inhibitor solution preparation process. This adsorption was confirmed by the differential UV absorptions of two bis(7)-tacrine solutions that were prepared using the glass and plastic vials (Fig. 1). It was further confirmed by the reduction of the difference in UV absorption that was caused by adding 0.4% (v/v) Polysorbate 20, a nonionic surfactant that was routinely used to prevent analytes from adsorption to the microfluidic system in Biacore-based surface plasmon resonance studies (Fig. 1). It is worth noting that complete desorption of bis(7)-tacrine is impossible because increasing the concentration of Polysorbate 20 reduces the water solubility of bis(7)tacrine. Repeating the adsorption experiments using tacrine showed only slight differences in K i and UV adsorption (Table 1 and Fig. 1). These results demonstrate that container surface can serve as a nontarget binding site for a test inhibitor during the inhibitor solution preparation process. The results also explain that the 1000-fold change for the K i of bis(7)-tacrine against eeAChE was due to the adsorption-caused reduction of the actual inhibitor concentration that was available to eeAChE relative to the nominal inhibitor concentration.

Inactive enzyme as nontarget binding site
In performing the study described above, we also observed a correlation for both tacrine and bis (7)-tacrine between the experimentally determined K i and the amount of eeAChE required for the K i determination assay ( Table 2). In theory, K i is independent of the amount of the enzyme used in the assay. However, the correlation indicated that in practice K i depended on the amount of the enzyme used in the assay. The observed dependence of K i on the amount of enzyme suggested that a test inhibitor might bind to not only the active enzyme but also the inactive enzyme caused by dilution denaturation and/or thermal inactivation during the process of the enzyme inhibition assay. For simplicity we do not consider herein the minor binding of the inhibitor to nonactive-site regions of the active enzyme and nontarget proteins that coexist with eeAChE. The binding to the inactive enzyme might consequently reduce the actual inhibitor concentration available to the active enzyme causing an overestimation of the experimentally determined K i (viz., underestimation of the binding affinity). One way to confirm the inhibitor binding with the inactive enzyme was to confirm that the actual specific enzyme activity [23], a measure of the percentage of the active enzyme, was inversely proportional to K i . So we tested tacrine and bis(7)-tacrine using different batches of eeAChEeach of which had a unique specific enzyme activity that was determined at the time when the assay was performed-under the following three specific conditions. First, because loss of enzyme activity can occur while measuring reactions for extended periods [3] and each K i determination took about 30 minutes to complete, we performed five independent K i determinations for each batch of eeAChE in an effort to avoid a substantial change of the specific enzyme activity during the entire course of multiple K i determinations. Second, 8 because nonspecific binding of a test inhibitor to microsomes, phospholipid, and albumin can affect the IC 50 and K i of the inhibitor [28-30], we excluded albumin, glycerol, gelatin, or any other enzyme stabilizers in all of our enzyme inhibition assays reported in this article to minimize nonspecific binding of a test inhibitor. Third, according to our adsorption studies above, we also excluded the use of glass containers for inhibitor stock solutions to avoid the adsorption-caused deviation of the actual inhibitor concentration from the nominal inhibitor concentration. Reassuringly, Table 2 shows that the increase of K i of tacrine or bis(7)-tacrine is indeed inversely proportional to the increase of the specific enzyme activity at the time when the assay was performed. This inverse correlation shows that inactive enzyme can serve as a nontarget binding site for a test inhibitor during the process of the enzyme inhibition assay. It explains that the K i variations for both tacrine and bis(7)-tacrine were due to the reduction of the actual inhibitor concentration caused by the inhibitor binding to the inactive enzyme relative to the nominal inhibitor concentration. It also suggests that the reported K i variations for tacrine [15][16][17][18] were caused likely by the inhibitor binding to the inactive enzyme.

Caveat of using the experimental K i as an absolute affinity indicator
The above studies offer the first set of experimental evidence for container surfaces and inactive enzymes to serve as nontarget binding sites for test inhibitors. These studies demonstrate the profound but long-overlooked effects of these nontarget sites on the experimentally determined K i . Because the binding of a test inhibitor to the container surface during the inhibitor solution preparation process and/or to the inactive enzyme during the enzyme inhibition assay process is not factored in conventional experimental determination of K i , we caution against using the experimentally determined K i as a measure of absolute binding affinity to rank order binding potencies, define selectivity, or benchmark computational methods without knowing detailed assay conditions. To facilitate the use of the experimentally 9 determined K i as an "absolute" binding affinity indicator, we suggest greater evaluation and optimization of assay conditions to minimize inhibitor binding to nontarget sites as well as reporting, in online supplementary documents, all experimental details including specific enzyme activities at times when assays are performed (see Ref. [31] for an excellent example of reporting specific AChE activity associated with the reported K i of tacrine).

Conflict of interest
The listed authors have no conflict of interests.

Author contributions
Y.-P.P. conceived, designed, and supervised the project. Y.-P.P. and F.H.D. designed the UV absorption protocol and revised the enzyme inhibition assay protocol described in Ref.   Table S1 at pH = 8.0, 50 mM sodium phosphate buffer, temperature of 26 ± 2 °C, and acetylthiocholine concentration of 2.0 mM. b SE: standard error of five independent experiments. c K i was determined using the data in Table S1 and Fig. S1 employing glass or plastic vials for inhibitor stock solutions. b SEA: specific enzyme activity of EeAChE that was determined using the data in Table S1 at pH = 8.0, 50 mM sodium phosphate buffer, temperature of 26 ± 2 °C, and acetylthiocholine concentration of 2.0 mM. c SE: standard error of five independent experiments. d K i was determined from the data in Table S1 and Fig. S1 using plastic vials for inhibitor stock solutions. vials, and Polysorbate 20 are abbreviated as GV, PV, and P20, respectively. The relative absorbance was the absorbance of an inhibitor in distilled water with or without P20 subtracted by the absorbance of distilled water with or without P20, respectively. All UV absorptions were measured using a single quartz cuvette. The data for this figure are listed in Table S2.