Evidence for dynamics in proteins as a mechanism for ligand dissociation

Abstract

Signal transduction, regulatory processes and pharmaceutical responses are highly dependent upon ligand residence times. Gaining insight into how physical factors influence residence times (1/k_off) should enhance our ability to manipulate biological interactions. We report experiments that yield structural insight into k_off involving a series of eight 2,4-diaminopyrimidine inhibitors of dihydrofolate reductase whose binding affinities vary by six orders of magnitude. NMR relaxation-dispersion experiments revealed a common set of residues near the binding site that undergo a concerted millisecond-timescale switching event to a previously unidentified conformation. The rate of switching from ground to excited conformations correlates exponentially with the binding affinity K_i and k_off, suggesting that protein dynamics serves as a mechanical initiator of ligand dissociation within this series and potentially for other macromolecule-ligand systems. Although the forward rate of conformational exchange, k_conf,forward, is faster than k_off, the use of the ligand series allowed for connections to be drawn between kinetic events on different timescales.

Main

A long-sought goal in the biochemistry of receptor-ligand interactions is to gain an understanding of what molecular forces contribute to binding affinity and kinetics. A fundamental question is how dissociation occurs once a ligand (for example, a peptide or small molecule) is bound to its receptor. This is an important question as ligand residence times control the strength of regulatory processes^1,2. One model for dissociation is simple diffusion of ligand from the receptor. A more mechanistic line of reasoning would be that a specific event physically disrupts the interaction between ligand and receptor, leading to ligand release or ejection. Indeed, myoglobin requires structural deformations to bind and release oxygen^3,4; however, it can be viewed as a special case as its ligand is completely buried, making it inaccessible to solvent. We postulate that protein structural fluctuations could be a more generally used mechanism for weakening intermolecular interactions and effectively 'pushing' or shearing a ligand away from its receptor. Experimental studies directed at this question should benefit structure-based drug design and protein (enzyme) engineering. From a biological perspective, because signal transduction is driven by countless cycles of ligand binding and release⁵, insight into mechanisms of ligand release could also make it possible to draw fundamental connections between internal protein dynamics and cell signaling.

To probe the potential role of dynamics in small-molecule ligand dissociation, we took a 'medicinal chemistry' approach to observe how protein motions change in response to varying structural features within a ligand series. Enzymes are common pharmaceutical targets and show considerable dynamics that are amenable to characterization by NMR relaxation dispersion^{6,7,8,9,10,11}. Thus, to test our approach, we characterized relaxation dispersion in Escherichia coli dihydrofolate reductase (DHFR) in complex with eight different antifolate inhibitors spanning an affinity range of six orders of magnitude. Three of these were reported previously: methotrexate (MTX), trimethoprim (TMP) and 1 (5-((4-chlorophenyl)thio)quinazoline-2,4-diamine)^12,13 (Fig. 1a). This data set comprises a 'dynamics structure-activity relationship' (DSAR) series. In other words, this approach probes whether the dynamics of DHFR are sensitive to structural differences in small-molecule ligands. As part of this series, five tetrahydroquinazoline inhibitors were designed to bind with reduced affinity for the purpose of loosening the ligands to allow detection of rare motions related to ligand dissociation. Although the location and rate of microsecond to millisecond conformational switching in DHFR depends on specific ligand structure, a cluster of residues around the active site dynamically samples the same excited state in all eight of the complexes. Analysis of relaxation-dispersion curves showed that the kinetics of conformational switching in DHFR correlate with both K_i and k_off, though conformational switching is always faster than k_off. These data implicate a common dynamic mechanism for dissociation of ligands within this series and suggest that internal protein motion may be a critical event for ligand dissociation in general. The medicinal chemistry approach taken allows focused and methodical perturbations within the active site, which starkly contrasts with global systematic perturbations such as temperature variations or the addition of chemical denaturants. Recent studies have linked conformational dynamics with catalytic timescales through coincidental values of rate constants^8,14. We show here, through the use of a ligand series, that linkages can also be made between events on different timescales.

Figure 1: The series of reduced-affinity and previously characterized antifolates.

(a) Chemical structures of the previously characterized antifolates: methotrexate (MTX), trimethoprim (TMP) and 1. (b) Chemical structures of the reduced-affinity antifolates 2–6. (c) The relationship between k_off and K_i for the series of reduced-affinity antifolates (R = 0.99).

Results

Antifolate series spans a large range of K_i and k_off

A previous study of the dynamics of DHFR in the presence of the high-affinity (K_i ≤ 1 nM) inhibitors MTX and TMP (Fig. 1a and Supplementary Results, Supplementary Fig. 1a,b) showed that both inhibitors elicit the same pattern of slow motion in the enzyme¹². We wondered whether that same pattern of dynamics would be observed for any inhibitor bound to the same site, regardless of binding affinity or chemical structure. To address this question, we designed a series of substrate-competitive DHFR inhibitors, or antifolates, with K_i values greater than 1 nM. This series is composed of five tetrahydroquinazoline-2,4-diamine compounds (compounds 2–6; Fig. 1b). Compounds 2, 3, 4 and 6 are constitutional isomers and differ only in the placement of the methyl substituent on the tetrahydroquinazoline (THQ) ring. These compounds were prepared as racemic mixtures of methyl R and S forms. Inhibitor 5 lacks the methyl substituent and thus serves as a nonenantiomeric reference. Compounds 3 and 4 were previously identified as competitive inhibitors of DHFR from a high-throughput screen of 50,000 small molecules¹⁵. We postulated on the basis of structural similarity that 2, 5 and 6 would have K_i values similar to those published for 3 and 4. As with the three previously studied high-affinity inhibitors (MTX, TMP and 1)^12,13, binding, structural and dynamics properties were characterized for the THQ inhibitors in the presence of cofactor NADPH.

K_i values for the THQ inhibitors (K_i,app in the case of racemic mixtures) were determined to confirm previous measurements¹⁵ and to establish values for the new compounds. The K_i values cover a range spanning two orders of magnitude (0.3–43 μM; Table 1), and the THQ compounds, as well as 1, are named according to increasing K_i/K_i,app (that is, 1 is the strongest inhibitor and 6 is the weakest). Overall, the methyl substituent contributes positively to the binding affinity, as evidenced by 2–4 having an appreciably lower K_i,app than the K_i of 5. To our surprise, the methyl group at the C5 position of 6 increases K_i,app by greater than 40-fold relative to 2–4. The low apparent affinity of 6 relative to that of 2–5 is discussed in the Supplementary Methods. From this analysis of binding affinities, it is clear that DHFR is very sensitive to minor changes in bound ligand structure.

Table 1 Binding affinities, kinetic off rates and relaxation-dispersion group-fitted parameters for the series of antifolates

Next, the binding kinetics for the THQ series were determined. The off rate (k_off or k_off,app) for each inhibitor was determined using competitive stopped-flow fluorescence measurements. The series was found to span two orders of magnitude in k_off (0.2–20 s⁻¹), similar to the trend in K_i (Table 1). In fact, the relationship between K_i and k_off for these five antifolates is linear (Fig. 1c). The calculated kinetic on rates (k_on) for the THQ series are similar, in the range of 3 × 10⁵ M⁻¹ s⁻¹ to 3 × 10⁶ M⁻¹ s⁻¹. In the context of the entire antifolate series (MTX, TMP and 1–6), K_i spans a range of 10⁶ M, k_off spans 10⁵ s⁻¹ and k_on spans 10² M⁻¹ s⁻¹. Given that K_i = k_off / k_on and that k_on has relatively little variation within the ligand series, it therefore follows that binding affinity is determined largely by the rate of dissociation. Within the THQ series alone, the effect of k_off on K_i is larger than that of k_on, but k_off is less dominant than when considering all eight antifolates.

To test whether the precise R or S methyl orientation has a substantial influence on binding, we separated the enantiomeric forms of 3. We found that the two forms had k_off values that differed by 1.6-fold, suggesting that the R and S forms are essentially indistinguishable. This finding is further supported by the observation that the HSQC spectra of the complex formed from the racemic mixture did not show peak doublings, which would be expected if 3R and 3S have differential influence on DHFR.

Structural differences induced by the series are minimal

Any structural differences must be considered in characterizing the protein dynamics of a series of receptor–small molecule complexes, as large changes can underlie differences in observed dynamics. Large structural changes in DHFR were not expected, given the chemical similarity of the antifolates. High-resolution crystal structures were determined for E–NADPH–3, E–NADPH–4 and E–NADPH–5 in the P2₁2₁2₁ space group (Fig. 2a and Supplementary Table 1). As expected, the overall structures are highly similar (largest backbone r.m.s. deviation = 0.28 Å). The THQs bind in the folate-binding pocket of DHFR, which forms a small crevice in the structure but is not closed off by the protein. We note that electron density in the C6 methyl substituent of 3 is apparent for only one enantiomer (R) (Supplementary Fig. 2a), which could be caused by a number of factors, such as the subtle difference in off rate (described above). It is also possible that the S form also crystallized and that R and S methyls are not resolvable given the resolution of this structure (2.09 Å), although we view this as unlikely. In contrast to E–NADPH–3, electron density for both R and S forms in the E–NADPH–4 structure were observed (Supplementary Fig. 2b). The slight differences in sugar puckers resulted in the R and S methyl groups occupying the same space (Supplementary Fig. 2b). Regardless of the enantiomers present, the THQs overlay very closely with one another (Fig. 2a). In addition, the 2,4-diamine moieties of 3–5 overlay closely to that of MTX^16,17, although the orientation is slightly tilted such that the saturated ring of the THQs shifts ∼1 Å toward the side chain of Phe31.

Figure 2: High-resolution crystal structures for the series.

(a) Overlay of the crystal structures for E–NADPH–3 (blue), E–NADPH–4 (teal) and E–NADPH–5 (maroon). NADPH is shown in cyan, and bound antifolate is shown in the colors designated for each complex. The Met20, FG and GH loops are shown. (b) Expansion of the C-helix, now overlaying five inhibitor-bound complexes (E–NADPH–1 in dark gray and E–NADPH–MTX in light gray). PDB codes are listed parenthetically. (c) Differential puckering of the saturated ring in the bound inhibitors, colored as in a.

Subtle differences in the protein structure are observable in helix C above the antifolate binding site, in the loop that follows helix C and at N23 in the Met20 loop. The orientation of helix C is particularly noteworthy because the plasticity of this helix seems to accommodate the binding of various ligands, as noted previously¹⁷. The tilt of the C terminus of this helix away from the antifolate binding site was identified previously in the presence of 1 (and NADPH), which contains a bulky and flexible side chain¹³. When the current three structures (Protein Data Bank (PDB) codes 3R33, 3QYL and 3QYO) were overlaid with previously determined inhibitor complexes E–NADPH–1 and E–NADPH–MTX (PDB codes 3KFY and 1RX3, respectively), we found that the C terminus of helix C is tilted away from the antifolate binding site in E–NADPH–3 and E–NADPH–1, whereas it is positioned closer to the antifolate binding site in E–NADPH–4 and E–NADPH–5 (Fig. 2b). In the case of 3, the R methyl substituent at C6 is oriented toward the helix, forcing it away. In contrast, the methyl substituents at C7 in 4 are directed away from the helix, and the absence of a methyl in 5 allows the C helix to move closer to these antifolates. The position of helix C in E–NADPH–MTX is intermediate between the tilted-away position (observed in complexes involving 1 and 3) and the closed position (observed in complexes involving 4 and 5)(Fig. 2b). Though this helix orientation appears to be sensitive to bound antifolate structure, it does not correlate with the K_i of the bound antifolate.

Unlike the structure of E–NADPH–1 determined previously¹³, the ternary complexes with 3, 4 and 5 show strong electron density within the Met20 loop. The loop was modeled in the closed conformation, similar to that observed in the presence of MTX. NMR chemical shift perturbations also suggest that the Met20 loop is closed in solution (Supplementary Fig. 2c). In all three crystal structures, strong electron density is observed for NADPH and bound antifolates (Fig. 2a and Supplementary Fig. 2a,b). Ligand orientations were also confirmed to be identical in solution, as assessed by chemical shift perturbations (Supplementary Fig. 2d,e). With these and the above considerations in mind, no substantial differences in structure are observed among these five ternary complexes. A straightforward comparison of the differential dynamics of complexes in this series is therefore possible.

Slow timescale dynamics structure-activity relationships

DSARs are obtained by registering changes in DHFR's dynamics as inhibitor structure is varied. For each of the five THQ complexes, microsecond-millisecond motion was detected by ¹⁵N Carr-Purcell-Meiboom-Gill (CPMG)-relaxation-dispersion experiments¹⁸. The dynamics of DHFR on this timescale have been shown to occur as a sequence of loop motions that are important to catalytic function when DHFR is bound to endogenous ligands⁸. In addition, notable differences in slow motions are observed in binary complexes that are off the enzyme's catalytic cycle (E–folate, E–dihydrofolate) as opposed to the 'on-cycle' binary product complex (E–tetrahydrofolate), confirming the enzyme's innate sensitivity to different ligands¹⁹. Relaxation-dispersion experiments allow for the determination of the transverse relaxation rate due to conformational exchange (R_ex), which is a component of the overall rate of transverse relaxation (R₂):

where is the intrinsic transverse relaxation rate in the absence of exchange. Assuming a two-state exchange process, these experiments provide kinetic, thermodynamic and structural information about the transition: R_ex depends on the exchange rate constant (k_ex), the populations of ground state A and excited state B (p_A and p_B) and the difference in chemical shift between states A and B (Δω)²⁰.

In contrast to the high similarity of microsecond-millisecond dynamics that result from MTX or TMP binding¹² (Supplementary Fig. 1a,b), the THQ inhibitors elicit a more heterogeneous distribution of sites showing nonzero R_ex (the majority of residues in DHFR have R_ex = 0 s⁻¹, as determined from CPMG relaxation dispersion) (Fig. 3 and Supplementary Fig. 3). However, among the 8 complexes there are 12 consensus residues with slow motions (discussed below). Thus, the pattern of slow motion elicited by MTX and TMP is not restricted to high-affinity antifolates. In addition to the consensus 'antifolate sites', new motions are detected near the hinge region (residues 38 and 88) and in α-helices C and F as K_i increases. Although within the THQ series there is no obvious correlation between K_i and the number of sites with a nonzero R_ex, as a whole this series has a greater amount of nonzero R_ex than MTX and TMP. None of the motions in the series are suspected to be the result of association-dissociation cycle effects, as k_off values are slow (Table 1) and complexes are saturated to ≥99.5%.

Figure 3: Slow timescale dynamics for the reduced-affinity inhibitor series.

Sites along the backbone with detectable microsecond-millisecond motion are highlighted in colored spheres for each complex, ordered from left to right by increasing K_i value. The number of residues with nonzero R_ex values is given parenthetically.

As highlighted in previous NMR studies of the enzyme, the chemical shifts of a group of ∼20 residues report directly on the conformation of the Met20 loop²¹. These 'marker' residues have distinct chemical shifts when the loop samples either the closed or occluded conformation. In the E–NADPH–6 complex, the numerous nonzero R_ex values observed at Met20 loop-switching markers suggest a functional conformational switch from a closed to occluded state²¹. However, only five residues show a correlation between chemical shift difference values (Δω) fitted from relaxation dispersion and the chemical shift difference between the two stable ground states (Δδ) for closed-to-occluded motion of the loop (Supplementary Fig. 4i; residues 12, 115, 118, 120 and 149). Although the loop appears to be mobile, its motion is not as clear and coherent as observed previously in the presence of 1 (13 residues in the correlation)¹³. We believe that this Met20 loop motion is the result of steric clash between the nicotinamide of NADPH and the C5 methyl group of 6 within the active site (Supplementary Methods). Residues within the F-G and G-H loops, not those within the Met20 loop itself, are the best ¹⁵N markers of Met20 loop switching (for example, residues 115, 116, 118, 119, 120, 121, 122, 149 and 150). It should be noted that the ¹⁵N Met20 loop marker residues within the F-G and G-H loops are not generally observed to undergo microsecond-millisecond motion in the presence of compounds 2–5 of the series (Supplementary Tables 2 and 4) and that even the best examples of closed complexes (with bound MTX or TMP) show broadening of some of the marker residue peaks because of conformational exchange. Further supporting that E–NADPH–6 is different from the other complexes in terms of its Met20 loop mobility, Gly121 is severely broadened in the presence of 6 but not in the presence of the remaining compounds of the series.

Rate of conformational switching correlates with K_i and k_off

Residue-grouped fitting of relaxation-dispersion data can indicate which sites move together in a single concerted exchange process²². Residues that are included in a group fit are forced to share single k_ex and p_A values, but they retain their individual Δω values. To probe whether the observed R_ex values reflect concerted conformational exchange processes, group fits were carried out for all of the ternary THQ complexes. For complexes involving 3, 5 and 6, group-fitted k_ex values were found to range from 1,000–1,500 s⁻¹, values greater than those for the higher-affinity antifolates (400–800 s⁻¹), and p_B remained fixed at approximately 2% (Table 1). It follows that the forward rate of conformational exchange (k_conf,forward) ranges from 20–35 s⁻¹ for these three complexes. Initial plots of k_conf,forward versus K_i suggested a correlation for these three protein-inhibitor complexes. To further test this correlation, the k_conf,forward and K_i values for MTX, TMP and 1 were added to the plot (Table 1)^12,13,23. For these six complexes, whose binding affinities cover six orders of magnitude, we find that k_conf,forward correlates exponentially with K_i (Fig. 4a). As binding affinity decreases (larger K_i), k_conf,forward increases (Table 1). Unfortunately, single-group fitting for complexes 2 and 4 did not converge and thus does not further support this trend, although an alternative fit for 4 was obtained (described in Methods). On the basis of the exponential relationship between k_conf,forward and K_i and the linear correlation between K_i and k_off (Fig. 1c), we plotted k_conf,forward versus k_off and found that they correlate exponentially (Fig. 4b). We note that k_conf,forward is always greater than k_off by at least a factor of two for each complex, providing further evidence against the notion that k_ex results from association-dissociation cycles. Thus, this correlation of k_conf,forward and k_off, with k_conf,forward > k_off, is highly suggestive of a mechanistic role for the conformational change from ground to excited state in ligand release. Because k_off values for TMP and 1 are too slow to be detected via the assay we used (Fig. 4b), they were calculated from K_i and their approximate k_on values for the series. The k_off value for MTX was taken from the literature²⁴. The best fitted k_conf,forward for 4 has been included in Figure 4b, even though group fitting was more challenging in this case; when plotted, its position off the main correlation line suggests that additional factors may contribute to release for a particular ligand, even if it is part of a structurally constrained series. Nevertheless, the fact that the remaining ligands fall on the line suggests that the millisecond structural fluctuations potentiate dissociation over the entire ligand series, including MTX and TMP.

Figure 4: Internal motions vary with K_i and k_off.

(a) The forward rate of motion (k_conf,forward) fit from relaxation-dispersion data for each complex varies exponentially with the K_i value for the bound inhibitor (R = 0.97). The open circle represents the best fit for E–NADPH–4. (b) An exponential correlation is also seen between k_conf,forward and k_off (R = 0.97). Data points in red have predicted k_off values, as described in the text. k_off for TMP and 1 were calculated on the basis of estimated values for k_on. For 1, the average k_on for the THQ series was used. Because of its greater similarity to MTX, TMP's k_on was taken to be intermediate between MTX and the average value for the THQ series. The data point for E–NADPH–4 (unfilled circle) does not fall along this exponential correlation, suggesting that this correlation may not always be predictive. The dashed curve represents what would be expected if the correlation were linear. Error bars represent s.d. (originating from Monte Carlo simulations in the case of k_conf,forward).

Antifolate complexes sample the same excited state

Relaxation-dispersion experiments can also provide structural information about the excited state. As mentioned previously, data on the eight drug-inhibitor complexes show that there are ∼12 consensus residues undergoing microsecond-millisecond motion (Fig. 5a). We define a residue as a consensus site if slow motion is detected at that position (when assignable) in ≥ 66% of the eight complexes (residues 8–11, 14, 29, 31, 111–113) or in ≥ 50% of the complexes when the other 50% has an R_ex that is nonzero but is just below our stringent requirement of 2 s⁻¹ (residues 7 and 30)¹². A number of these sites were initially identified from the least dynamic complexes, those with MTX or TMP bound¹². The dynamic changes in chemical shift values (Δω) at these consensus sites, which were fitted from relaxation dispersions for each complex, were analyzed. The fitted Δω parameter for each individual residue clusters around the same value, despite changes in chemical structure and binding affinity for the different inhibitors (Fig. 5b). This clustering of Δω values indicates that the same excited state is sampled by the consensus residues in each of the eight antifolate complexes. This pattern of Δω values does not correlate with Δω fitted from previous studies of DHFR bound to physiological folate-derived ligands (Supplementary Fig. 4j)⁸ and hence is unique to the antifolates studied here. In addition, because poor correlations between Δω fitted from the dispersion data and Δδ from chemical shift changes (E–NADPH to E–NADPH–antifolate) were observed for the consensus sites (Supplementary Fig. 4a–h), the antifolates seem to be bound in the excited state. We propose that these residues, which sample a new excited state, mediate the dissociation of antifolate ligand. This state is sampled at somewhat different rates, but the concerted motion of the consensus residues is conserved across these antifolate complexes.

Figure 5: Antifolate consensus sites sample a structurally similar excited state.

(a) The twelve antifolate consensus sites are highlighted in yellow colored spheres. (b) Dynamic Δω values fitted from relaxation-dispersion data for these twelve sites cluster for each residue. The eight complexes are colored by the bound inhibitor, as indicated in the legend. Averages were calculated only from residues that have the dominant sign. No bar is shown if that residue did not exhibit significant slow motion while bound to a particular inhibitor. Error bars represent s.d. derived from Monte Carlo simulations.

We note that although these complexes share this common dynamic sampling, differences in slow motions remain among the complexes^12,13 (Fig. 3 and Supplementary Table 2). Thus, this shared motion seems to be able to exist in the context of additional motions (or lack thereof) in other regions of the enzyme.

Discussion

Binding and dissociation are the two fundamental processes that determine a ligand's affinity for its receptor. Mechanistic insight into these processes is therefore expected to facilitate the rational design of drugs and macromolecules with desired ligand-binding properties. To evaluate whether conformational dynamics should be considered relevant to ligand dissociation, we monitored the dynamics of the classic drug target DHFR, which is known to undergo extensive motions on the microsecond-millisecond timescale. The wide range of affinities of the eight inhibitor complexes studied elicited a variety of dynamic behaviors in the enzyme and therefore constitutes a dynamics structure-activity relationship. This is distinct from, yet complementary to, flexibility-activity relationships, which focus on the dynamics of the bound ligand, as shown previously for peptide ligands of Pin1 (ref. 25). Our results underscore the benefits of using a series of ligands to extract a kinetic relationship between internal motion and dissociation. A similar benefit arising from the use of a ligand series was demonstrated recently for correlating picosecond-nanosecond dynamics with conformational entropy in the case of calmodulin²⁶.

Here we show that, for a series of homologous antifolates binding to DHFR, K_i is determined largely by k_off. We also demonstrate from CPMG relaxation-dispersion measurements that k_conf,forward is related to both binding affinity and k_off for the series. Specifically, the correlation of k_conf,forward to k_off provides evidence that internal protein motion is a mechanical initiator of ligand dissociation. Analysis of chemical shifts suggests that DHFR samples an identical excited state in solution regardless of which particular antifolate is bound and that this state is unique because it differs from the excited states observed in the absence of ligand and in physiological complexes (Supplementary Fig. 4j). It is also worth noting that the THQ complexes undergo switching approximately three times faster than the physiological complexes. Because ligand is bound in the excited state and the rates of internal motion correlate with k_off, we propose that this excited state occurs en route to inhibitor dissociation and that k_conf,forward provides an upper limit to k_off.

In previous work, connections between internal motions and protein activity have been drawn when an internal switching rate precisely matches a macroscopic rate constant^8,14. We show here, through the use of a homologous ligand series, that such matching is not required to mechanistically connect two functional events. Ligand dissociation is fundamental in macromolecular interactions, and insights into what stimulates dissociation have potentially broad implications for manipulating biological systems. The main insight revealed here is that dissociation can be driven by defined protein internal motion (presumably at the interface) rather than by a fully stochastic process. The inference that motions drive dissociation would seem to be expected for a buried binding site in which a 'lid' must open for release; however, in this particular case, the ligand binding site is exposed, yet dissociation does not seem to be stochastic.

At what point during the conformational sampling does release actually occur? The simplest model consistent with our data is the following conformational gating model:

Upon transitioning to the excited state (state B), the ligand initially remains bound but is subject to release while the gate is open, with rate constant k_off,B. In this model, release might depend on sub-millisecond motions that essentially kick out the ligand or break noncovalent interactions through shearing motions. Release from the open gate could also occur in a stochastic manner that would be dependent on the overall strength of interactions (described below). Equation (2) is formally equivalent to the Linderstrom-Lang model for amide H-D exchange²⁷. Hence, the overall rate constant for dissociation can be expressed²⁸ as k_off = (k_conf,forward × k_off,B) / (k_conf,forward + k_conf,reverse + k_off,B), which can be rearranged to

in which K_conf = k_conf,forward / k_conf,reverse and k_off is the bulk dissociation rate constant. The use of equation (3) yields values of k_off,B ∼25–100 times that of k_off, indicating much faster dissociation from the excited state (Supplementary Table 5) compared to the rate obtained when assuming simple dissociation from the ground state. We note that this gating model excludes ligand rebinding and hence is consistent with kinetic decay experiments. Rebinding may occur via different structures or mechanisms as the antifolate excited state is not observed in the holoenzyme (DHFR–NADPH; Supplementary Fig. 4j).

What is somewhat surprising from the correlation of k_conf,forward to K_i and k_off is that the relationship is log-linear. It follows that DHFR does not release inhibitors each time it reaches the excited state, as k_conf,forward is always greater than k_off. Thus, the enzyme seems to become more efficient at release as the rate of internal motion increases. Within the gating model, this may be explained by a loss of substituents. Adding substituents to the ring beyond the 2,4-diaminopyrimidine scaffold (for example, methyls in THQ series, methoxy groups in TMP, and so on) could have a dual effect on the steps shown in equation (2): as observed, these groups could serve to slow switching owing to the stabilization of both ground and excited states and provide additional contacts to protein, reducing the probability of stochastic release from the excited state (Fig. 4b and Table 1). Overall, the lack of a true linear relationship indicates that an additional process (beyond the conformational change detected here) is associated with the final release of ligand.

An important caveat is that any ligand bearing resemblance to those in the series (or that binds to the same active site) should not necessarily follow the correlation in Figure 4b. Indeed, 2 and 4 do not (Table 1 and Supplementary Table 2). It is reasonable to expect that numerous mechanisms for ligand release could compete with one another and that some ligands may trigger specific mechanisms over others owing to their chemical structure. We have been fortunate that the mechanism of dissociation is shared by our panel of ligands and, additionally, is distinct from the mechanism of release of folate-derived ligands. Although observation of dynamics-induced dissociation in the case of DHFR suggests that this mechanism will be used for other protein-ligand complexes, it will be important to test other ligand series against different proteins to determine how widely this mechanism is used by natural and therapeutic ligands.

Gaining an understanding of the molecular basis of k_off has implications for structure-based drug design. If protein dynamics are found to correlate with k_off in other systems, this type of analysis may be useful in optimizing ligand residence times to meet the desired pharmaceutical modulation of disease states. The DSAR methodology provides more than just a correlation between the rate of internal motions and k_off—it also potentially provides structural information on residues sampling multiple conformations and even on what the structure of the excited state (or states) may be^29,30. This combined information would be useful in directing medicinal chemistry efforts toward modulating the stability of excited states that promote efficient ejection of inhibitors.

Methods

Synthesis of (6-methyl-5,6,7,8-tetrahydroquinazoline-2,4-diamine, 3).

Compound 3 was prepared by a one-step condensation reaction, similar to that described previously³¹. Briefly, dicyandiamide (10.19 g, 0.12 mol) and 4-methylcyclohexanone (11.33 g, 0.10 mol) were combined in a round-bottom flask fitted with a Dean-Stark trap and a condenser. The reaction was heated in an oil bath at 180 °C for 3 h. Boiling water was added to the reaction as it was transferred to a separatory funnel for extraction. The desired compound was extracted from the aqueous layer with hot chloroform. The chloroform washes were dried over anhydrous magnesium sulfate before solvent was removed via rotary evaporation. A golden yellow liquid with white precipitate remained. Additional white solid was precipitated via addition of hexanes to the yellow liquid. The solid was isolated via filtration.

Synthetic procedures for 2 and 4–6 follow from those described above (Supplementary Methods). Spectroscopic data for all five compounds is summarized in Supplementary Methods. The enantiomers of 3 were separated on a Thar Investigator analytical/semi-preparative supercritical fluid chromatography system. Purification was carried out using 20% isopropyl alcohol (0.1% diethylamine) in CO₂ with a CHIRALPAK IC column from Chiral Technologies.

K_i determination.

As described previously, biochemical competition assays using a 96-well-plate reader were used to determine the inhibition constant (K_i) for 2–6 (refs. 13,15). The decrease in absorbance at 340 nm was monitored over time in a two-dimensional titration of inhibitor and substrate.

Protein expression and purification.

Isotopically labeled wild-type E. coli DHFR was overexpressed and purified as described previously¹². Purified apoDHFR was flash frozen, lyophilized and stored in a dessicator at 4 °C until use.

NMR spectroscopy.

For ternary inhibitor complexes, samples contained 1 mM DHFR in NMR buffer (70 mM HEPES, 20 mM KCl, 1 mM EDTA, 1 mM DTT, pH 7.6), 15 mM NADPH, 2.5–10 mM antifolate (10 mM E–NADPH–2; 2.5 mM E–NADPH–3, 8–10 mM E–NADPH–4, 10 mM E–NADPH–5, 10 mM E–NADPH–6), 10 mM glucose-6-phosphate, 10 U glucose-6-phosphate dehydrogenase and 10% D₂O for spectrometer locking purposes. All samples were protected from light and air exposure by containment in amber NMR tubes flame-sealed under argon. Stock solutions of 2–6 were prepared in 10% D₂O/H₂O, and PULCON was used to determine the concentration of each stock relative to either valine or trimethoprim standards³². NMR experiments were performed as described previously, using both room temperature (500 MHz, 600 MHz and 700 MHz) and cryogenic (500 MHz and 700 MHz) probes^12,13. NMRPipe was used to process NMR data, and data visualization was accomplished with the combination of NMRDraw and NMRView^33,34. Further experimental details on assignment and relaxation experiments are in Supplementary Methods.

CPMG relaxation dispersion.

¹⁵N CPMG relaxation-dispersion experiments were conducted on highly deuterated (>80%) DHFR for the E–NADPH–2, –4, –5 and –6 complexes whereas protonated DHFR was used for E–NADPH–3. Complexes with bound 2–4 were examined using a TROSY relaxation-dispersion experiment at 700 MHz with a room temperature probe. Data collection at 700 MHz for complexes with bound 5 or 6 used a cold probe and the regular non-TROSY experiment. Collection and analysis of the data was completed as described previously^12,13.

For group fits, all residues in a particular complex showing relaxation-dispersion profiles determined to reflect substantial microsecond-millisecond motion¹² (excluding the C-terminal residues; Supplementary Table 3) were grouped together, following the method outlined in ref. 22. Single k_ex and p_A values were fit for a group, whereas Δω values were fit in a residue-specific manner. Residues found to have a substantially improved local fit relative to the group fit (that is, having a χ²_group / χ²_local ratio of > 2) are reported with Δω values from the local fit instead of the group fit. Although it is possible that multiple groups with slightly different exchange parameters exist for individual complexes, the simplest case of a single group was used because the differences are small in most complexes and cannot be easily resolved. In the case of E–NADPH–2 and E–NADPH–4, single-group fits of all residues together would not converge. Upon removal of four residues with increased local k_ex values (residues 37, 50, 54 and 58), group fitting for E–NADPH–4 converged, and the residues seemed to fit together on the basis of χ² ratios. Using this same approach for E–NADPH–2 resulted in convergence (residues 40, 44, 48, 50, 54, 57, 98, 115 and 119 removed); however, the residues did not group well together on the basis of χ² ratios. Group fits for complexes with bound 2 and 4 are reported, but it should be noted that the fits were not conducted in the same fashion as for the rest of the series. One noteworthy point is that E–NADPH–2 and E–NADPH–4 resulted in similar group fitting for both the 'slow'- and 'fast'-moving sets of residues. We speculate that the similar placement of the methyl substituent in these two inhibitors may underlie why they appear to cause faster switching motions in DHFR. Also, for inhibitors 2 and 4, the possibility that both R and S enantiomers bind could also result in different switching compared to the remainder of the series, although this seems not to be the case for 6.

The sign of Δω was determined from peak positions in HSQC and HMQC spectra³⁵. Sign determination for Δω was completed on six of the eight ternary complexes (E–NADPH–2 and E–NADPH–4 excluded). Given the strong pattern of Δω sign observed for the antifolate consensus residues (Fig. 5b), the signs for the complexes with 2 and 4 were assumed to follow the pattern. Additionally, the sign of Δω determined for the three other THQ compounds (3, 5 and 6) should be representative of 2 and 4. Fitted parameters and the sign of Δω are summarized for each complex in Supplementary Results.

Protein crystallization and structure determination.

Crystals of E–NADPH–3, E–NADPH–4 and E–NADPH–5 were grown using similar conditions as described previously^13,17,36. Details of crystallization, data collection and structure refinement are in Supplementary Methods and Supplementary Results.

Determination of k_off.

A fluorescence competitive binding assay, as described previously, was used to determine k_off for 2–6 from the E–NADPH holoenzyme^13,37. A detailed methods description is provided in Supplementary Methods.

Accession codes.

Protein Data Bank: the newly acquired crystal structures for E–NADPH–3, E–NADPH–4 and E–NADPH-5 are deposited under accession codes 3R33, 3QYL and 3QYO, respectively. The previous published crystal structures for E–NADPH–1 and E–NADPH–MTX are deposited under accession codes 3KFY and 1RX3, respectively.