Increased Molecular Flexibility Widens the Gap between K_i and K_d values in Screening for Retinoid X Receptor Modulators

Abstract

Screening for small-molecule modulators targeting a particular receptor is frequently based on measurement of K_d, i.e., the binding constant between the receptor and the compound of interest. However, K_d values also reflect binding at receptor protein sites other than the modulatory site. We designed derivatives of retinoid X receptor (RXR) antagonist CBTF-EE (1) with modifications that altered their conformational flexibility. Compounds 6a,b and 7a,b showed quite similar K_d values, but 7a,b exhibited 10-fold higher K_i values than those of 6a,b. Further, 6a,b showed potent RXR-antagonistic activity, while 7a,b were inactive. These results suggest that increased conformational flexibility promotes binding at nontarget receptor sites. In this situation, conventional determination of K_d is less effective for screening purposes than the determination of K_i using a ligand that binds specifically to the site regulating transcriptional activity. Thus, the use of K_i values for orthosteric ligands may increase the hit rate in screening active regulatory molecules.

Small-molecule drug candidates, including natural products, have been screened using two main approaches: phenotype-based drug discovery and target-based drug discovery.¹ The target-based approach has various advantages, including (1) easy to perform, (2) provides information on molecular mechanisms, (3) low cost, (4) enables efficient structure–activity relationship (SAR) development.² For example, fluorescence quenching assay (FQA), surface plasmon resonance (SPR) measurements, and nuclear magnetic resonance (NMR) spectroscopy can be used to screen modulators targeting nuclear receptors based on direct interaction between the purified protein and test compounds.³⁻⁷ In the case of a simple system in which there is only one agonist-binding site (the orthosteric site), the dissociation constant, K_d, can be determined by FQA, SPR, or NMR and reflects the affinity of the ligand for the receptor. But, if the protein has multiple binding sites for a ligand, K_d would reflect binding to not only the orthosteric site but also other site(s). In other words, K_d does not necessarily reflect specific binding to the site that modulates the activity. In contrast, K_i can be used to compare test compounds across multiple assay conditions, because it is independent of the assay conditions.⁸ Therefore, it is preferable in principle to evaluate the agonist or antagonist activity of test compounds based on K_i toward orthosteric ligands, but not K_d.

We have reported methods to screen for modulators targeting retinoid X receptors (RXRs), which are multifunctional nuclear receptors.^9,10 Lifestyle-related diseases such as cancer and type 2 diabetes are thought to be associated with “metaflammation,” which is the result of metabolic imbalance in the body.¹¹ Metabolic homeostasis is maintained by the function of nuclear receptors (NRs).¹² Among them, RXRs function as homodimers or heterodimers with other nuclear receptors, such as peroxisome proliferator-activated receptors (PPARs) and liver X receptors (LXRs), and are involved in regulation of sugar and lipid metabolism.¹³ RXR agonists can activate RXR heterodimers such as PPAR/RXR and RXR/LXR,¹⁴ which called permissive heterodimers, and show therapeutic effects in a variety of disease models, including cancer, metabolic disease, neurodegenerative diseases, and autoimmune diseases.¹⁵ RXR antagonists have also been reported to show efficacy in type 2 diabetes models.¹⁶ Thus, RXRs are considered an interesting therapeutic target for lifestyle-related diseases.

In RXR research, FQA is widely used in the analysis of interactions between RXRs and their ligands and in screening for natural or synthetic RXR modulators.^9,10,17−31 FQA evaluates the ligand-binding ability (K_d) based on quenching of the fluorescence around 330 nm due to Trp282 and Trp305 in the RXR-ligand binding domain (LBD).¹⁷ There are at least 17 reports that have discussed RXR-modulating activity in terms of K_d evaluated by FQA.^9,10,17−31 However, as mentioned above, this may lead to erroneous conclusions. Here, to exemplify the importance of this issue, we describe modifications of the RXR antagonist CBTF-EE (1, Figure 1A)³¹ to alter its binding characteristics to RXR, and we show that the modulator activities of the synthesized derivatives differ dramatically, and correlate with K_i, but not with K_d.

Figure 1.

(A) Chemical structures of RXR antagonists. (B) Molecular design strategy of new RXR antagonists.

We have reported 1 as a nonallosteric RXR antagonist, which does not show allosteric inhibition in permissive RXR heterodimers.³¹ Compound 1 was designed to suppress free rotation at the bond between the hydrophobic moiety and acidic pharmacophore by introducing the benzimidazole skeleton, which is present in the RXR partial agonist CBTF-PMN (4, Figure 1B). X-ray cocrystallography of 1/hRXRα-LBD revealed that this targets the binding of 1 toward the orthosteric site (the ligand-binding pocket, LBP) and contributes to the nonallosteric character of the RXR antagonistic activity of 1. Furthermore, the trifluoromethyl group of 1 is not involved in the interaction with RXRα-LBD, supporting the idea that it may instead play a role in suppressing free rotation at the bond between the hydrophobic moiety and the acidic pharmacophore. We also reported a structurally flexible RXR partial agonist CBt-PMN (5, Figure 1B), which contains a benzotriazole skeleton, binds to RXR, and induces conformational changes of RXR into active and inactive forms.³² We hypothesized that replacing the benzimidazole of 1 with a benzotriazole moiety would yield a compound that would bind to the orthosteric site and also other site(s) and that its antagonistic activity would be decreased as a result of decreased specificity for the LBP, even though its K_d toward RXR would be maintained.

Compound 1 contains an ethoxy ethyl group that was introduced to increase its water solubility, and this is also thought to contribute to the nonallosteric antagonism. RXR antagonists are generally designed by introducing an alkyl side chain into the skeleton of RXR agonists.¹⁶ For example, Nahoum et al. reported that the introduction of an alkoxy chain with five or more carbons into an RXR agonist makes it function as an RXR antagonist.³³ Compounds 6a and 6b, in which the ethoxy ethyl group of 1 is replaced with n-pentyl and n-hexyl, respectively, as in UVI3003 (2)³³ and PA452 (3),³⁴ were therefore expected to show enhanced RXR antagonist activity compared to 1. Compounds 7a and 7b (Figure 1B), in which the benzimidazole in 1 is replaced with benzotriazole as in 5, were expected to show decreased RXR antagonist activity.

To examine whether the free rotation of 7a is suppressed compared to that of 6a, we calculated the rotational barrier energy at the N12–C17 bond using semiempirical molecular orbital calculation (MOPAC, PM3, Figure 2).³⁵ The dihedral angles between C17–N12 and C17–C18 in the most stable conformations of 6a and 7a were 80.44° and 84.04°, and the values of heat of formation were −68.76 and −261.91 kcal, respectively (Figure 2A, B). The rotational barrier at the N12- C17 bond was calculated by determining the heat of formation under the condition that the dihedral angle between C7–N12 and C17–C18 was set to 70–290°. Compound 7a showed a smaller value of Δheat of formation, which is the difference in heat of formation between the calculated dihedral angle and that of the most stable conformation, as compared with 6a (Figure 2C).

Figure 2.

Values of rotational barrier energy at the N12–C17 bond of 6a and 7a. (A) The most stable conformations of 6a and 7a. (B) Dihedral angle between C17–N12 and C17–C18 and the heat of formation for the most stable conformation. (C) The difference in heat of formation (ΔHf) of 6a (blue) and 7a (green) at the indicated dihedral angle and that of the most stable conformation.

Next, compounds 6a,b and 7a,b were synthesized according to Scheme S1.³¹ The RXR-antagonistic activity of 6a,b and 7a,b toward transactivation by NEt-TMN (15)³⁶ was compared with that of 1 and 3 by means of luciferase reporter gene assay (RGA) using COS-1 cells (Figure 3). The dose–response curve of 15 was shifted to a higher concentration in the presence of 1 μM 1 or 3 (Figure 3B) as well as in the presence of 1 μM 6a or 6b. The values of pA₂, a measure of competitive antagonist activity, of 6a and 6b calculated from a Schild plot³⁷ were 7.58 and 6.90, respectively (Table 1, Figure S1). Compounds 6a and 6b also showed antagonistic activity (pA₂ = 8.06, 8.17) toward the RXR full agonist bexarotene (16), which is used to treat cutaneous T cell lymphoma (CTCL)³⁸ (Table 1, Figure S2). On the other hand, the dose–response curve of 15 was not shifted in the presence of 1 μM 7a or 7b (Figure 3C). Here, 10 μM 7a and 7b showed weaker RXR antagonistic activity than 1 μM 6a or 6b (Figure 3B,C). Compounds 6a, 6b, 7a, and 7b did not show RXR agonist activity (Figure S3).

Figure 3.

RXR-antagonistic activity of 6a, 6b, 7a, and 7b. (A) Chemical structure of RXR full agonist NEt-TMN (15).³⁶ (B) Dose-dependent RXRα agonistic activities of 15 in the absence (open circle) or presence of 1 μM 1 (orange circle), 3 (green circle), 6a (pink circle), and 6b (purple circle). (C) Dose-dependent RXRα agonistic activities of 15 in the absence (open circle) or presence of 1 μM 1 (orange circle), 3 (green circle), 7a (red tilted square), and 7b (blue tilted square) and 10 μM 7a (red tilted square, dashed line) or 7b (blue tilted square, dashed line). Values are mean ± SD (n = 3).

Table 1. pA₂ Values of 6a and 6b in RXR Homodimer.

	compd
	1	3	6a	6b
pA2 (vs 15)a	7.06	7.11b	7.58	6.90
pA2 (vs 16)a	6.74c	7.20c	8.06	8.17

^aCalculated using Prism 9.

^bCited from ref (39).

^cCited from ref (31).

In order to determine the cause of the marked difference in RXR-antagonistic activity between 6a,b and 7a,b, the interactions between these compounds and the RXR-LBD were analyzed. The binding affinity to human RXRα-LBD (hRXRα-LBD) was evaluated by FQA (Figure 4A, Table 2). The fluorescence around 330 nm due to tryptophan residues in the hRXRα-LBD is observed when excited by UV at 280–290 nm and is quenched by ligand binding.¹⁷ The binding ratio was calculated as [1– F_obs/F₀] (Ex 290 nm/Em 330 nm), where F₀ is the fluorescence intensity in the absence of test compounds and F_obs is the observed fluorescence intensity. The K_d values toward hRXRα-LBD of 6a,b and 7a,b were determined to be 0.277, 0.281 μM and 0.764, 0.705 μM, respectively (Figure 4A, Table 2), and are of the same order of magnitude.

Figure 4.

Binding assay data of 6a, 6b, 6c, and 6d to hRXRα-LBD. (A) Fluorescence quenching assay. Binding ratio of 6a (pink circle, solid line), 6b (purple circle, solid line), 7a (red tilted square), and 7b (blue tilted square) to hRXRα-LBD was calculated as [1 – F_obs/F₀] (Ex 290 nm, Em 330 nm). F₀ is the fluorescence intensity in the absence of test compounds, and F_obs is the observed fluorescence intensity in the presence of test compounds. Values are mean ± SD (n = 3). (B) Competitive binding assay using fluorescent RXR antagonist NEt-C343 (17)⁹ at λEx = 430 nm/λEm = 535 nm. Fluorescence intensity curves in the presence of 6a (pink circle, solid line), 6b (purple circle, solid line), 7a (red tilted square), and 7b (blue tilted square). Values are mean ± SD (n = 3). (C) Chemical structure of 17.

Table 2. Binding Affinity of 6a,b and 7a,b toward hRXRα-LBD^a.

	compd
	6a	6b	7a	7b
FQA (Kd, μM)	0.277 ± 0.038	0.281 ± 0.070	0.764 ± 0.129	0.705 ± 0.096
competitive binding assay (Ki, μM)	0.384 ± 0.072	0.391 ± 0.047	3.541 ± 0.858	3.157 ± 0.449
Ki/Kd	1.39	1.39	4.63	4.48

^aThese values were calculated using Prism 9. Values are mean ± SD (n = 3).

Next, competitive binding assay was performed (Figure 4B, Table 2). We have reported a competitive binding assay using the fluorescent RXR antagonist NEt-C343 (17, Figure 4C).⁹ Compound 17 emits strong fluorescence only when bound to the hRXRα-LBD (λEx and λEm of 430 and 535 nm, respectively), and the fluorescence is reduced in the presence of a competitive ligand.⁹ We found that the fluorescence intensity of compound 17 in the presence of hRXRα-LBD was reduced depending on the concentration of 6a,b and 7a,b (Figure 4B). Competitive binding of these compounds to the LBP in hRXRα-LBD with respect to 17 was confirmed. The K_i values of 6a,b and 7a,b were determined to be 0.384, 0.391 μM and 3.541, and 3.157 μM, respectively (Table 2). The K_i/K_d ratios of 6a and 6b were 1.39 and 1.39, while those of 7a and 7b were 4.63 and 4.48, respectively (Table 2).

Considering the differences in hydrophobicity of 6a,b and 7a,b, we next evaluated the cellular uptake of each compound. The intracellular concentrations of 6b and 7b, which have an n-hexyl chain, tended to be higher than those of 6a and 7a, which have an n-pentyl chain. There was no correlation between intracellular concentration and RXR-antagonistic activity (Table 3).

Table 3. Intracellular Concentrations of 6a,b and 7a,b.

	compd
	6a	6b	7a	7b
compds in living cells (pg/1 × 104 cells)a	14.8 ± 1.6	55.1 ± 16.9	10.2 ± 3.9	81.6 ± 12.1
clogPb	9.67	10.23	8.71	9.24

^aValues are mean ± SD (n = 3).

^bThese values were calculated using ChemDraw 20.1 software.

To examine differences in the binding energy of 6 and 7 to the RXRα-LBD, docking simulation for 6a or 7a using AutoDock vina⁴⁰ was tried, using the cocrystal structures of the RXRα-LBD bound with the RXR antagonist CBTF-EE (1) from our group (PDB ID: 7CFO)³¹ and that of RXRα-LBD bound with the RXR antagonist LG100754 (PDB ID: 3A9E).⁴¹ However, this approach was unsuccessful, possibly because of the conformational distortion of the ligands upon binding. To examine this, we focused on the internal strain energy generated by the binding of both compounds to the RXRα-LBD. Estimated binding structures of 7a to 6a were constructed based on the binding structure of 1 to RXRα-LBD (PDB ID: 7CFO).³¹ The bound conformation energies and the most stable structure energies were calculated using the semiempirical molecular orbital method, and the difference between the bound conformation energy and the most stable conformation energy was obtained as the internal strain energy (Figures 5 and S4).⁴² However, we found no significant difference between 7a and 6a. The binding conformation of 1 to the RXR-LBD was examined carefully, but the trifluoro group did not show any significant interaction with RXR. Therefore, the difference in binding strength between 6a and 7a to RXR appears to be based not on enthalpy but rather on entropy. 7a, which has a higher degree of freedom than 6a (Figure 2), is expected to have a large reduction in the degree of freedom due to binding to RXR, i.e., an entropy penalty.⁴³ Thus, the reason for the reduced binding ability of 7 to RXR compared to 6 seems likely to be the entropy penalty.

Figure 5.

Comparison of internal strain energy of each compound for binding to the RXRα-LBD. (A) Bound conformation in the RXRα-LBD (PDB ID: 7CFO) and global minimum conformation of 1. B) (a) Bound conformation energy, (b) global minimum energy, and (a–b) internal strain (energy between the global minimum and bound conformation) of 1, 6a, and 7a.

The aim of this research is to highlight the need to discuss RXR modulator activity in terms of K_i at the orthosteric site, rather than K_d. To illustrate this, we focused on the reported RXR antagonist CBTF-EE (1), which was designed to show low structural flexibility and to bind preferentially to the orthosteric site. Based on the idea that increasing the lipophilicity of 1 would enhance the RXR-antagonistic activity, we designed CBTF-C5 (6a) and CBTF-C6 (6b) (Figure 1B). In addition, we designed CBt-C5 (7a) and CBt-C6 (7b) based on the idea that increasing the structural flexibility of 6a and 6b would decrease the RXR-antagonistic activity (Figure 1B). To evaluate the ease of free rotation of the N12–C17 bond of the designed molecules, the rotational barrier energy of each was calculated (Figure 2). The finding that Δheat of formation of 7a was smaller than that of 6a suggests that 7a is more likely to rotate freely than 6a; in other words, 7a can readily form various conformations. Thus, 7a and 7b may be expected to bind more easily at sites other than the orthosteric site and consequently should show reduced RXR-antagonistic activity. Indeed, 6a and 6b showed potent RXR-antagonistic activities at 1 μM compared to the lead compound 1, while 7a and 7b showed weaker activities even at 10 μM (Figure 3, Table 1). Evaluation of the binding affinity for RXR by means of the FQA method demonstrated that 6a,b and 7a,b have K_d values of the same order of magnitude (several hundred μM) (Figure 4A, Table 2). In contrast, competitive binding assay versus the fluorescent RXR antagonist revealed that 6a and 6b showed K_i values similar to the K_d values, while 7a and 7b showed K_i values 4.5-fold higher than K_d (Figure 4B, Table 2). These K_i values are consistent with the weak RXR-antagonistic activity of 7a,b. The difference between K_d determined by FQA and K_i determined by competitive assay confirms that FQA detects binding not only to the orthosteric site, but also to other site(s). When a flexible ligand binds to a receptor, there is an entropy penalty.⁴³ Since 6a and 6b have reduced flexibility compared to 7a and 7b, they are expected to incur a lower entropy penalty upon binding to the RXR-LBD and therefore should bind more stably. Since the cell permeability of 6a,b and 7a,b showed no correlation with RXR-antagonistic activity (Table 3), the above results support our contention that K_i values for orthosteric ligands should be used instead of K_d values in the search for active regulatory molecules. An additional advantage of K_i is that it is independent of assay conditions.⁸ Furthermore, it has already been pointed out that it is important to confirm normal competitive behavior against a target in the screening of drug candidates.⁴⁴ It should be noted that K_i can also be determined in target-based screening of RXR ligands by performing competitive binding assays with tritium-labeled compounds or fluorescent ligands such as NEt-C343 (17)⁶ and CBTF-EE-BODIPY⁷ that bind to the orthosteric site.

In conclusion, the RXR ligands 6a,b and 7a,b created in this study showed similar K_d values, but 7a,b showed considerably higher K_i values than 6a,b. Further, compounds 6a,b showed RXR-antagonistic activity, while 7a,b did not. Our findings suggest that the K_i values for orthosteric ligands should be used instead of K_d values in screening for RXR modulators.

Glossary

Abbreviations

BODIPY

boron-dipyrromethene

CTCL

cutaneous T cell lymphoma

DMF

N,N-dimethylformamide

DMSO

dimethyl sulfoxide

DTT

dithiothreitol

Em

emission

EtOAc

ethyl acetate

Ex

excitation

FAB

fast atom bombardment

FQA

fluorescence quenching assay

HPLC

high-performance liquid chromatography

HRMS

high-resolution mass spectrometry

hRXR

human RXR

LBD

ligand-binding domain

LBP

ligand-binding pocket

LXR

liver X receptor

MeOH

methanol

MOPAC

molecular orbital PACkage

Mp

melting point

MS

mass spectrometry

NMR

nuclear magnetic resonance

NR

nuclear receptor

PBS

phosphate-buffered saline

PPAR

peroxisome proliferator-activated receptor

qy

quantitative yield

rt

room temperature

RGA

reporter gene assay

Rt

retention time

RXR

retinoid X receptor

SAR

structure–activity relationship

SD

standard deviation

SPR

surface plasmon resonance

TFA

trifluoroacetic acid

TFAA

trifluoroacetic anhydride

THF

tetrahydrofuran

TLC

thin layer chromatography

UV

ultraviolet

UV–vis

ultraviolet–visible

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsmedchemlett.1c00575.

• Experimental section, chemistry (preparation of 6a, 6b, 7a, and 7b, compound data), computational chemistry (estimation of rotational barriers, estimation of internal strain of each compound for binding to the RXRα-LBD, coordinate for estimated bound conformation of 6a and 7a), in vitro assay (luciferase reporter gene assay, cloning, expression, and purification of ligand-binding domain of RXRα, fluorescence quenching assay, competitive ligand-binding assay with fluorescent RXR antagonist, confirmation of cell uptake), dose–response relationships for RXRα antagonist activity of test compounds toward NEt-TMN (15) or bexarotene (16)), dose–response relationships for RXRα agonist activity of test compounds, comparison of estimated bound and global minimum conformation of 6a and 7a, NMR charts, HPLC charts (PDF)

Author Contributions

^# M.W. and M.N.-N. contributed equally. M.W. and H.K. conceived and designed the project. M.W. and M.N.-N. synthesized compounds. M.W. performed the computational chemistry. M.F. performed reporter gene assays. M.K. and S.N. produced hRXRα-LBD. M.W. and M.F. performed binding assays. M.W. measured cell uptake of test compounds. The manuscript was written by M.W. and H.K. All authors have given approval to the final version of the manuscript.

This work was partially supported by grants from the Okayama Foundation for Science and Technology (to H.K.), The Tokyo Biochemical Research Foundation (TBRF) (to H.K.), and the Kobayashi Foundation (to H.K.). This research was partially performed in collaboration with AIBIOS K.K. The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article or the decision to submit it for publication.

M.F. was an employee of AIBOS.

The authors declare no competing financial interest.