ARTICLE

Use of Calculated Cation-␲ Binding Energies to Predict Relative Strengths of Nicotinic Acetylcholine Receptor Agonists Mathew Tantama and Stuart Licht*

Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Building 16, Room 573B, Cambridge, Massachusetts 02139

N

icotinic acetylcholine receptors (nAChRs) are ion channels involved in a broad range of synaptic activities throughout the nervous system and are the targets of therapeutic drugs for a variety of conditions (1). These drugs are often agonists or competitive antagonists that bind the nAChR transmitter binding sites (TBSs) in a state-selective manner. A strong agonist exhibits a high affinity for the closed state and an even higher affinity for the open state, promoting the efficient conformational change from the closed state to the open state (i.e., gating). A strong competitive antagonist exhibits a high affinity for the closed state but not for the open state, making gating inefficient. Establishing chemical metrics that correlate with closed-state affinity and open-state affinity may be useful in the design of drugs that modulate nAChR activity. For example, structure⫺activity relationships (SARs) have been used to develop nAChR antagonists that can be used as muscle relaxants (2). However, SAR parameters such as molecular shape, charge, and hydrogen bonding ability have had limited utility in guiding the design of neuromuscular blocking agents. In the brain, nAChRs have been proposed to be targets for treating nicotine addiction, depression, and a variety of neurological disorders (3). SARs for these drug candidates are typically centered on derivatives of nAChR agonists or antagonists derived from natural sources, such as nicotine or epibatidine. However, the small molecule drugs that bind nAChRs are structurally very diverse, and the identification of simple, independent parameters that correlate with binding or gating would be useful for expanding the scope of SAR-guided drug design for these targets. Cation-␲ binding ability is a computationally accessible parameter that may be useful in this regard. Like

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A B S T R A C T Agonists and antagonists of the nicotinic acetylcholine receptor (nAChR) are used to treat nicotine addiction, neuromuscular disorders, and neurological diseases. In designing small molecule therapeutics with the nAChR as a target, it is useful to identify chemical parameters that correlate with ability to activate the receptor. Previous studies have shown that cation-␲ interactions at the transmitter binding sites of the nAChR are important for receptor activation by strong agonists such as acetylcholine. We hypothesized that a calculated estimate of cation-␲ binding ability could be used to predict the efficiency for channel opening (i.e., the gating efficiency) associated with activation of the acetylcholine receptor by a series of structurally related organic cations. We demonstrate that the calculated cation-␲ energy is strongly correlated with gating efficiency but only weakly correlated with closed-state binding affinity. Our results suggest that cation-␲ interactions contribute significantly to the open-state affinity of these cations and that the calculated cation-␲ energy will be a useful parameter for designing nAChR agonists and antagonists.

*Corresponding author, [email protected].

Received for review August 4, 2008 and accepted September 23, 2008. Published online November 21, 2008 10.1021/cb800189y CCC: $40.75 © 2008 American Chemical Society

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αTyr198

αTrp149 αTyr93

αTyr190 δTyr55

Figure 1. The binding site aromatic cage: green, the apoAChBP structure (PDB 2BYN); cyan, the epibatidine-bound AChBP structure (PDB 2BYQ). The bound epibatidine molecule has been removed for clarity. In the nAChR itself, ␦Trp55 takes the place of ␦Tyr55 in the AChBP structure.

hydrogen bonds and salt bridges, cation-␲ interactions are well-characterized noncovalent interactions that are strong enough (4−6) to drive a protein conformational change if that change alters the interaction strength. Cation-␲ interactions have been shown to be important for the function of nAChRs and other members of the Cys-loop superfamily (7, 8). Cation-␲ interactions between charged small molecules and the nAChR were originally proposed because of the large number of aromatics situated at the TBSs (9). The muscle-type nAChR, the archetype for the Cys-loop superfamily, is a pentameric ion channel consisting of two ␣ subunits, a ␤ subunit, a ␦ subunit, and either a ␥ or ␧ subunit. One TBS is situated at the ␣-␦ interface, and a second TBS is situated at the ␣-␥ interface (in fetal receptors) or the ␣-␧ interface (in adult receptors). Structural and biochemical studies of the nAChR and the acetylcholine binding protein (AChBP) have identified an “aromatic cage” at the two TBSs, consisting of residues ␣Tyr93, ␣Trp149, ␣Tyr190, ␣Tyr198, and ␦Trp55 (or ␥/␧Trp55) (10−17). When agonist is bound, the aromatic cage is contracted, increasing its favorable contacts with the agonist (Figure 1). Unnatural amino acid mutagenesis has allowed structure⫺activity studies analogous to those employed in classical physical organic chemistry to be carried out on the nAChR, providing evidence that cation-␲ interaction is important for binding of agonists (15−18). By using unnatural amino acid mutagenesis, ␣Trp149 was shown to form cation-␲ interactions with cholinergic agonists (18, 19). Substitution of fluorine on the indole ring of this residue increased the concentration necessary for half-maximal nAChR activation, the 694

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EC50, for epibatidine and acetylcholine. The observed increase in EC50 correlated with the calculated decrease in cation-␲ binding ability of the fluorinated analogs. A similar correlation was not observed for the other binding site aromatic residues, suggesting that ␣Trp149 is primarily responsible for the cation-␲ interaction between acetylcholine and the muscle-type nAChR (19−21). Analogously to KM in enzyme kinetics, EC50 reflects both binding and conformational or chemical equilibria. For an ion channel, the gating equilibrium can be a significant component of EC50. Therefore, the correlation between EC50 and cation-␲ binding energy is consistent with three possibilities. The cation-␲ energy might contribute entirely to binding/closed-state affinity, indicating that the interaction fully forms when agonist binds the closed state. Alternatively, the cation-␲ energy might contribute to both binding and gating, indicating that the interaction forms in the closed state and strengthens in the open state. Finally, the cation-␲ energy might contribute entirely to the open-state affinity (gating), indicating the interaction only exists in the open state. In all three cases, attenuation of the cation-␲ energy would increase the EC50. It has been hypothesized that the correlation between EC50 and cation-␲ energy primarily reflects contributions to binding (18). Both 5-hydroxytryptamine (5HT) and acetylcholine (ACh) are strong agonists for the serotonin receptor 5-HT3AR, an nAChR-related channel. For both 5-HT and ACh, channel activation is attenuated by fluorination of ␣Trp149, and EC50’s are linearly correlated with calculated cation-␲ binding energies for the fluorination series. For all combinations of agonists and mutated receptors, maximal currents of similar magnitude were observed when saturating concentrations of agonist were used, suggesting gating efficiency was not severely compromised (22). However, with the strong agonists used in these studies, changes in gating efficiency could lead to relatively small changes in channel maximal currents. The authors of the previous studies therefore did not rule out the possibility that the interaction between agonist and ␣Trp149 changes with gating (18, 19, 22). To test the hypothesis that cation-␲ interactions contribute mainly to closed-state binding affinity, we calculated cation-␲ interaction energies between benzene and a series of organic cations and measured closedstate agonist binding affinity (KD) and gating efficiency www.acschemicalbiology.org

ARTICLE µM

TMA

ETMA

DEDMA

TEMA

TMP

1 pA 100 ms

1 pA 100 ms

1 pA 100 ms

1 pA 100 ms

1 pA 100 ms

10

50

200

1000

5000

Figure 2. Examples of clustered single-channel activity evoked by the organic cations TMA, ETMA, DEDMA, TEMA, and TMP at concentrations of 10 ␮M to 5 mM.

(⌰2) for activation of muscle-type nAChRs by these cations. Single-channel electrophysiology was used to measure microscopic rate constants directly, allowing discrimination of ⌰2 and KD in the measurements. Small organic cations were used so that the role of the aromatic cage in agonist binding and gating could be probed without having to deconvolve the effect of secondary elements such as the ester moiety of ACh. For the set of compounds tested, there is a strong correlation between the ab initio calculated cation-␲ binding energy and ⌰2, but there is only a weak correlation with KD. Our results provide evidence that cation-␲ interactions can be an important factor in determining open state affinity and that calculated cation-␲ interaction energies have the potential to be used as a parameter in predict-

ing whether small molecules will be nAChR agonists or competitive antagonists. RESULTS AND DISCUSSION Activation and Blockade by Organic Cations. To determine binding and gating equilibrium constants for agonists, single-channel activity was first measured as a function of agonist concentration. Single-channel currents from the ␣G153S nAChR (see Methods) (23) were measured using tetramethylammonium (TMA), ethyltrimethylammonium (ETMA), diethyldimethylammonium (DEDMA), triethylmethylammonium (TEMA), and tetramethylphosphonium (TMP) as agonists (Figure 2). Clusters of openings and closings were analyzed to ensure that the kinetics represent the activity of only one chan-

TABLE 1. DoseⴚResponse Parameters Agonist

TMA TMP ETMA DEDMA TEMAf

POMaxa

EC50a

na

KBb

␤2c

␣2d

KGape

0.8 ⫾ 0.03 0.77 ⫾ 0.04 0.6 ⫾ 0.04 0.3 ⫾ 0.03 0.03 ⫾ 0.01

50 ⫾ 7 310 ⫾ 50 80 ⫾ 10 230 ⫾ 60 400 ⫾ 200

1.2 ⫾ 0.1 1.6 ⫾ 0.1 1.7 ⫾ 0.2 1.6 ⫾ 0.2 1.5

7000 ⫾ 2000 2900 ⫾ 300 2000 ⫾ 100 1000 ⫾ 100 500 ⫾ 20

10300 ⫾ 500 5200 ⫾ 100 3400 ⫾ 200 380 ⫾ 30 60 ⫾ 40

700 ⫾ 70 900 ⫾ 40 1030 ⫾ 90 1400 ⫾ 100 2000 ⫾ 100

0.24 ⫾ 0.05 0.22 ⫾ 0.08 0.33 ⫾ 0.09 1.4 ⫾ 0.4 30

a From a Hill fit of intracluster open probability. EC50 in ␮M. bSee Figure 3, panel a. KB in ␮M. cSee Figure 3, panel b. ␤2 in s⫺1. dSee Figure 3, panel c. ␣2 in s⫺1. eSee Figure 3, panel d. KGap is unitless. fTo obtain POMax, EC50, and ␤2 for TEMA, n was constrained to 1.5. POMax was used to calculate KGap and constrain fitting in Figure 3, panel d to obtain a KD for TEMA.

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b

9

12,000

TMA ETMA DEDMA TEMA TMP

10,000

Effective β (s−1)

Single-channel current (pA)

a

6

3

0

TMA ETMA DEDMA TEMA TMP 10

8000 6000 4000 2000 0

100

10

1000

100

Agonist (µM) 6 5 4

d

TMA ETMA DEDMA TEMA TMP

Intracluster open probability

Mean intracluster open time (ms)

c

3 2 1 0

10

1000

Agonist (µM)

100

1.0 0.8

TMA ETMA DEDMA TEMA TMP

0.6 0.4 0.2 0.0 10

1000

100

Agonist (µM)

1000

Agonist (µM)

Figure 3. Analysis of single-channel clusters. a) Fast, unresolved open-channel block causes a decrease in apparent singlechannel current with increasing agonist concentration. b) The effective opening rate ␤2= approaches the true opening rate ␤2 as agonist saturates the receptor. c) The closing rate is inversely proportional to the unblocked mean open lifetime. d) Fitting the intracluster open probability using Scheme 1 provides estimates of the closed-state affinity, KD. TEMA data are also shown with independent scaling in Supporting Information.

nel (24). The agonist concentration dependence of the open probability within clusters (PO) was fitted to a Hill equation (eq 1), where EC50 is the concentration for halfmaximal open probability and n is the Hill coefficient (Table 1). PO ⫽ POMax ·

[Agonist]n EC ⫹ [Agonist] n 50

n

(1)

Activation by TEMA was weak, and the Hill coefficient was constrained to a value of 1.5 to produce a reliable fit. Hill coefficients have been generally observed to be 1⫺2 for nAChR agonists (25). In this range, the maximal open probability (POMax) varied from 0.028 to 0.053 (see Supporting Information), and the standard deviation of this range of values was used to estimate the uncertainty in POMax. It is important to measure the magnitude of unresolved open-channel blockade because fast blockade will cause an overestimation of open probabilities. Cationic agonists can block the open channel by binding the open pore and interrupting current flow (26). When blockade kinetics are sufficiently fast, the current interruptions are unresolved because of limited recording bandwidth, and a reduction in open-channel current at high concentrations is observed (Figure 3). The apparent current amplitude in the presence of unresolved open696

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channel block is a function of the maximal current in the absence of blocker, i0, and the blocking dissociation constant, KB (27) (eq 2). The agonist concentration dependence of current amplitude was fitted to obtain KB (Table 1). i ⫽ i0 ·

KB KB ⫹ [Blocker]

(2)

Measurement of Diliganded Gating Rate Constants and ⌰2. The diliganded opening rate constant, ␤2, can be measured from the dose⫺response relationship of the intracluster closed times (Figure 3, Table 1). The ef-

Scheme 1. nAChR model for conformational transitions: C, closed states; O, open states; G, gap states; B, blocked state; A, bound agonist; kⴙ, association rate constant; kⴚ, dissociation rate constant; KD ⴝ kⴚ/kⴙ, dissociation constant; ␤2, diliganded opening rate constant; ␣2, closing rate constant; ⌰2, gating equilibrium constant; KB ⴝ kⴚB/kⴙB, blocking dissociation constant; KG ⴝ kⴙGap/ kⴚGap, gap equilibrium constant. www.acschemicalbiology.org

ARTICLE TABLE 2. Calculated cation-␲ energy and measured gating and binding equilibria Agonist

TMA TMP ETMA DEDMA TEMAd

Cation-␲a

⌰2 (sⴚ1)

ⴚR·T·ln(⌰2)b

KDc

ⴙR·T·ln(KD)d

⫺28.45 ⫾ 0.01 ⫺26.97 ⫾ 0.05 ⫺27.19 ⫾ 0.19 ⫺26.28 ⫾ 1.80 ⫺23.31 ⫾ 1.62

15 ⫾ 2 5.8 ⫾ 0.3 3.3 ⫾ 0.4 0.27 ⫾ 0.03 0.03 ⫾ 0.02

⫺6.7 ⫾ 0.3 ⫺4.4 ⫾ 0.1 ⫺2.9 ⫾ 0.3 3.3 ⫾ 0.3 9⫾2

120 ⫾20 530 ⫾ 50 120 ⫾ 10 110 ⫾ 20 200 ⫾ 200

⫺22.3 ⫾ 0.4 ⫺18.7 ⫾ 0.2 ⫺22.4 ⫾ 0.3 ⫺22.7 ⫾ 0.3 ⫺21 ⫾ 3

a Cation-␲ energies are reported as the mean ⫾ SD for three repeated HF6-31g(d,p)//HF6-31g(d,p) geometry optimizations. bEnergies in kJ/mol. R is the gas constant. T ⫽ 298.15 K. cDissociation constants in ␮M. dFor TEMA, n was constrained to 1.5 to obtain an diliganded opening rate constant used to estimate ⌰2, and KGap was constrained to 30 to obtain and estimate of KD.

fective opening rate, ␤2=, reflects gating and agonist binding transitions and is inversely proportional to the major intracluster closed time component, which scales with agonist concentration (28). As the agonist concentration increases, the receptor saturates so that ␤2= approaches the true opening rate ␤2 (eq 3) (28). Estimation of ␤2 in this manner (29, 30) does not require assumption of a specific model. ␤2' ⫽ ␤2 ·

[Agonist]n n KApparent ⫹ [Agonist]n

(3)

For TEMA, constraining the Hill coefficient n to 1.5 also affects the estimate of ␤2. The estimate of ␤2 is fairly sensitive to n, and the uncertainty in this rate constant was estimated as the standard deviation of values obtained from fits where n was constrained to values ranging from 1.0 to 2.0 (see Supporting Information). This procedure gives an estimate of ␤2 ⫽ 60 ⫾ 40 s⫺1 for activation of the ␣G153S nAChR by TEMA. The diliganded closing rate constant ␣2 can be estimated from the mean length of single-channel openings. Open lifetimes increased with agonist concentration (Figure 3), consistent with the presence of fast, unresolved open-channel blockade as described above. The increase in mean open lifetime, ⬍tO⬎, is linearly related to concentration (eq 4). The value of ⬍tO⬎ in the limit of low blocker concentration represents the unblocked open lifetime and is inversely proportional to the diliganded closing rate constant ␣2 (Table 1). Measurement of both the closing and opening rate constants allows determination of the gating equilibrium constant: ⌰2 ⫽ ␤2/␣2 (Table 2). www.acschemicalbiology.org

⬍tO⬎ ⫽

1 ␣2

⫹

1 [Blocker] · ␣2 KB

(4)

Estimation of KD From the PO DoseⴚResponse Curve. The closed state affinities, KD, were estimated by fitting the PO dose⫺response relationships using Scheme 1, with the values of KB and ⌰2 measured above used as constraints (Figure 3) (30, 31). PO equals the total steady-state occupancy of all open states within the cluster (eq 5) and is a function of the agonist concentration, A.

关 共 兲 共 兲兴 关 共 兲 共兲共 兲共 兲共 兲 共 兲兴

PO ⫽

⫹

A2

A2

KD

2 D

· ⌰2 ⫹ 2

A2

KD2

⫹

K

· ⌰2 ·

A

KB

⁄ 1⫹

A2

A2

A

KD

KD

KB

· ⌰2 ⫹ 2

· ⌰2 · 2 ⫹

A2

KD2

⫹

2·A KD

A2

KD2

· ⌰2 ·

· ⌰2 · KG

A

KB

· KG

(5)

We used the model-independent measurements of KB and ⌰2 obtained above to constrain the modeldependent analyses, an approach often used to produce physically relevant fitted solutions (23, 25, 29, 30). These constraints prevent overparameterization and prevent optimization to values inconsistent with the observed data (Table 2). Because TEMA is a weak agonist, channel closures were long enough that short-lived desensitization was frequently observed within clusters. An additional constraint was placed on KG (the equilibrium constant for the short-lived desensitized state) to obtain an estimate of KD for TEMA. KG can be set so that the fitted curve saturates at the observed POMax (eq 6). From our estiVOL.3 NO.11 • 693–702 • 2008

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Figure 4. Correlations between calculated cation-␲ binding energy, gating, and closed-state affinity; red lines represent linear fits. a) Cation-␲ binding energy is strongly correlated with gating and therefore open-state affinity. b) Cation-␲ binding energy does not correlate well with closed-state binding affinity.

mate of POMax for TEMA, KG was constrained to a value of 30. POMax ⫽ lim PO ⫽

1 1 ⫹ KG

(6)

Because we obtained estimates of POMax and ⌰2 for TEMA by constraining the Hill coefficient to n ⫽ 1.5, we examined the sensitivity of KD estimation to the values of POMax and KG. Sensitivity analysis of POMax and ⌰2 produced a range of 11 values for each parameter (see Supporting Information). We estimated KD for the 121 possible combinations, and the standard deviation of these 121 values was used to estimate the uncertainty in the dissociation constant for TEMA, KD ⫽ 200 ⫾ 200 ␮M. Calculation of Cation-␲ Interaction Energies. Ab initio calculations of benzene⫺cation complexes were carried out using the Gaussian 03 program (32). Geometries were optimized and Hartree⫺Fock energies were calculated in the gas phase, using the 6-31g(d,p) basis set. The cation-␲ energies calculated for TMA, ETMA, DEDMA, and TMP were similar, and the calculated energy for TEMA was obviously lower (Table 2). As shown in previous computational studies (5, 6, 33, 34), calculated energies for cation-␲ interactions were comparable to observed gas-phase dissociation energies (4). The distance between the cation heteroatom and the 698

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benzene ring ranged from 4.8 to 5.0 Å, in agreement with other calculations for quaternary ammoniums (33, 34). For all optimized complexes, three ␣ carbons are oriented with protons facing the benzene ␲ system in a facial conformation, as has been previously observed (see Supporting Information) (33). Calculated Cation-␲ Energy Correlates Strongly with Gating Energy. The calculated cation-␲ binding energies are linearly correlated with the diliganded gating energies for simple organic cations (Figure 4). Singlechannel recording allowed us to experimentally measure the diliganded rate constants ␣2 and ␤2 for TMA, ETMA, DEDMA, TEMA, and TMP, and the diliganded gating equilibrium, ⌰2, was calculated from these microscopic rate constants. There is a clear linear correlation between cation-␲ energy and the diliganded gating energy, ⫺R·T·ln(⌰2). A slope of m⌰ ⫽ 3.1 ⫾ 0.6 (R2 ⫽ 0.87) was measured. Although the slope m⌰ cannot be directly interpreted as a measurement of cation-␲ interaction energy, it might be expected to be less than unity, since the predicted gas-phase cation-␲ interaction energy is a reasonable upper limit for the expected interaction energy of a cation solvated by the aqueous/protein environment. The slope m⌰ ⬎ 1 suggests that either the calculated cation-␲ binding energy underestimates the strength of the interaction in the nAChR binding site or multiple cation-␲ interactions are important to openstate affinity. We used a simple model system to perform ab initio calculations of cation-␲ binding energies between the cations and benzene. In reality, the aromatic cage of the nAChR TBSs contains both tyrosine and tryptophan residues. The cation-␲ binding ability of benzene and phenol have been calculated to be nearly equal, but an indole has significantly greater cation-␲ binding potential (35, 36). Thus, if the cations are primarily interacting with the indoles of tryptophan residues, our calculations may underestimate the true cation-␲ binding energy, leading to a slope greater than unity. It is also reasonable to expect that the cation can form cation-␲ interactions with the multiple aromatic residues when the aromatic cage is compactly arranged in the open state. Although previous studies using unnatural amino acids suggested that the aromatic cage residues other than ␣Trp149 do not make cation-␲ interactions with acetylcholine in the muscle-type nAChR (19, 21), other studies have shown that different agonists can bind with different favorable contacts (12, 13, www.acschemicalbiology.org

ARTICLE 18, 22, 37). Notably, residues ␣Tyr190 and ␣Tyr198 appear to be in significantly greater contact with the agonist molecule in bound AChBP structures (12, 13). NMR studies also suggest that the cationic head of acetylcholine comes within 3.9 Å of all five aromatic cage residues when bound to the nAChR (38). Calculated Cation-␲ Energy Correlates Weakly with Close-State Affinity. The calculated cation-␲ binding energies exhibit only a weak correlation with the closedstate affinity (Figure 4). When the binding energies, ⫹R·T·ln(KD), are plotted versus the calculated cation-␲ binding energies, TMP is a clear outlier. Even when TMP data are excluded, the correlation is weak (slope mK ⫽ 0.3 ⫾ 0.1, R2 ⫽ 0.50; see Supporting Information). The slope mK is significantly smaller than the slope m⌰, suggesting that gating is more sensitive than binding to differences in the abilities of simple agonists to form cation-␲ interactions. These results suggest that the cation-␲ binding interactions make a relatively small contribution to the total closed-state binding affinity of simple organic cations to the nAChR. However, they do not rule out a role for cation-␲ interactions in the closed state. The lack of a strong correlation may be due to other factors, such as hydrophobicity (see Supporting Information), having a stronger influence on affinity than the cation-␲ interaction does. Implications for the nAChR Binding and Activation Mechanism. The strong linear correlation between calculated cation-␲ energy and gating energy suggests that cation-␲ interactions are important for open-state affinity of organic cations to the nAChR TBSs. There is a weak linear correlation between closed-state binding affinities and calculated cation-␲ energies with a near-zero slope, suggesting other agonist-channel interactions are more important than cation-␲ interactions in the closed state. Simple organic cations are not positioned for a strong closed-state cation-␲ interaction by any mechanisms other than partitioning to the binding site and conformational sampling. In contrast, agonist-bound AChBP structures suggest the TBS aromatic cage can assume a compact arrangement around an organic cat-

ion in the open state (12, 13). The increase in favorable contacts between the cation and aromatics improve positioning for cation-␲ interactions in the open state. This mode of binding may differ with other agonists, and the different contributions cation-␲ energies make to closed-state or open-state affinities for different agonist can be tested. For example, 5-HT and ACh are both more complex than the organic cations investigated here, and cation-␲ interactions for these strong agonists are hypothesized to contribute primarily to binding rather than channel gating (18). For more complex agonists, the structural components separate from the cationic center may help position the molecule for a cation-␲ interaction in the closed state. For example, the backbone carbonyl of ␣Trp149 affects activation, an effect that may be due to hydrogen-bonding interactions between the agonist and the carbonyl group (18). For 5-HT and ACh, the noncationic moieties might position the cationic center optimally for a strong cation-␲ interaction. In that case, the strength of the closed-state interaction would be nearly maximal, and the interaction would not strengthen in the open state to a large extent. Cation-␲ Interaction Energy as a Parameter for SARs. These results suggest that the calculated cation-␲ binding energy between a charged agonist and an aromatic ring will be a useful parameter for SARs that distinguish agonists from antagonists. For simple organic cations, we have shown that the cation-␲ energy is strongly correlated with gating. Thus, similar small molecules that can bind the closed state well but do not form cation-␲ interactions are likely to be good candidates for activity as antagonists, whereas those that do form such interactions are more likely to be agonists. Cation-␲ interactions have been shown to impact the function of a broad array of ion channels, both ligandgated and voltage-gated, and enzymes (39). The results of this work thus suggest that calculated cation-␲ binding energies may be a useful parameter for predicting agonist versus antagonist activity of a variety of drug candidates.

METHODS

vided by Professor Anthony Auerbach at SUNY Buffalo (40). The gain-of-function ␣G153S mutation was engineered using sitedirected mutagenesis (Quickchange Kit, Qiagen) and verified by sequencing (MIT Biopolymers Laboratory). Justification for Use of the ␣G153S Mutant. The organic cations assayed in this work are weak agonists and cause fast

Materials. TMA chloride, TEMA chloride, and TMP bromide were from Aldrich. ETMA iodide was from TCI. DEDMA hydroxide from Fluka was neutralized with hydrochloric acid. Cell culture reagents were from Invitrogen. Plasmids for expression of the adult mouse ␣, ␤, ␦, and ␧ subunits were generously pro-

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open-channel block of the wild-type nAChR at high concentrations. The advantage of using the ␣G153S mutant is that it enables clustered single-channel activity to be recorded and analyzed at lower agonist concentrations, where open-channel block is not as severe and can be compensated for in the analysis. The ␣G153S mutation primarily increases agonist affinity (23) by influencing the allosteric transduction mechanism (41). Although this mutation occurs at the binding site, it is not part of the aromatic cage. The ␣G153S mutation is not likely to directly impair the cation-␲ interaction between ␣Trp149 and the agonist, and ␣Trp149 has been shown to be primarily stabilized by ␣D89 and a redundant hydrogen-bonding network (42, 43). Furthermore, the cation-␲ interaction has been shown to be robust to variations in TBS sequence and structure, existing in several different Cys-loop receptors (37). We therefore use this mutant assuming that its effects are equivalent for the series of agonists used here. As a control to demonstrate that the mutation affects the series of cations equivalently, a rate-equilibrium free energy relationship (REFER) was shown to be linear with a slope of approximately 1, as has been observed previously for energetic changes at the TBSs due to mutation or ligand variation (see Supporting Information) (44, 45). Single-Channel Recordings. Adult mouse, muscle-type receptors containing the ␣G153S mutation were heterologously expressed in HEK-293 cells as previously described (30), and single-channel recording was performed in the cell-attached mode (46). The bath solution was Dulbecco’s phosphate buffered saline (DPBS) containing (in mM): 137 NaCl, 0.9 CaCl2, 0.5 MgCl2, 2.7 KCl, 1.5 KH2PO4, 8.1 Na2PO4, pH 7.3. Pipette solutions were DPBS supplemented with agonist. Cell membrane potentials were typically ⫺30 to ⫺40 mV, and a command voltage of ⫺70 mV was used during recording. Single-channel currents were amplified with an Axopatch 200B patch-clamp amplifier (Axon Instruments) and recorded through a low-pass Bessel filter at 10 kHz. Data were digitized at a sampling rate of 20 kHz using a NI 6040 E Data Acquisition Board (National Instruments). Data was recorded using QuB software (www.qub. buffalo.edu) (47−51). The baselines of single-channel records were adjusted manually using QuB. A 5 kHz Gaussian digital filter was applied, and records were idealized using either the segmental k-means or half amplitude algorithms in QuB (47). All records were examined visually in their entirety, and misidealizations were corrected manually. Analysis of Single-Channel Clusters. Single-channel analysis was carried out on clusters of openings as previously described (see Supporting Information) (30, 31). At high agonist concentrations, clusters of openings represent activity from one nAChR. Each cluster is a series of openings flanked by long closed durations in which all channels are desensitized. Clusters are defined as those series of openings for which these flanking closed durations are longer than a critical time (␶crit). The value of ␶crit is assigned as the intersection of the predominant closed component of the single-channel closed-time distribution and the succeeding component of longer duration. The predominant component scales with agonist concentration and reflects transitions between nAChR closed and open conformations, including binding and gating steps. The value of ␶crit was chosen to minimize the percentage of misclassified events, and the fraction of misclassified events was typically less than 5%. Clusters with multiple-conductance levels (more than one channel) or fewer than five events were excluded. Analysis of clustered activity at the single-channel level allows measurement of microscopic rate constants and distinction of binding and gating steps. To estimate the diliganded closing rate constant ␣2, the diliganded opening rate constant ␤2, and the diliganded gating equilibrium constant ⌰2 ⫽ ␤2/␣2, the intracluster closed and open dwell-time distributions were

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analyzed in QuB. To estimate the closed-state affinity KD, intracluster open probabilities were analyzed according to the equivalent binding sites model shown in Scheme 1. A gap state is included as previously described (30). The gap state encompasses short-lived desensitized states that has a lifetime on the order of 1⫺10 ms (30). The gap state is accessible from both the unblocked and blocked open state. The resting and desensitization gates have been shown to be distinct entities (52, 53), and it has also been shown that the desensitization gate can close while the open pore is blocked (54). Fitting was performed in Origin (OriginLab, Northhampton, MA). Computations. Ab initio calculations were carried out using the Gaussian 03 program package (32). Gas phase calculations have previously been used for investigating the trends in a cation-␲ perturbation series (18, 19, 22, 33, 35, 36). Geometry optimization and Hartree⫺Fock energies were calculated in the gas phase using the 6-31g(d,p) basis set. As a simple model system, we examined the binding energy trends between benzene and the cations experimentally investigated in this work (33−36). The binding energy was estimated as the difference in energies of benzene and the cation optimized separately versus the energy of the pair optimized in complex. The cation was initially placed 4.5 Å above the benzene ring in at least three different orientations; for example, TMA was placed with one, two, or three methyl groups facing the benzene ring. The conformations of the benzene-cation complexes optimized to approximately the same final conformation in each case, and the mean and standard deviation of the calculated binding energies were used throughout the work. No constraints were placed on the conformation of the benzene ring or the benzene-cation distance. The calculated TMA-benzene interaction energy and conformation agreed with the previously published value using this method and basis set (33). Acknowledgment: We thank S. Difley for help with the Gaussian 03 software. This work was supported by the Beckman Foundation and the MIT Department of Chemistry. Supporting Information Available: This material is free of charge via the Internet.

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Use of Calculated Cation- Binding Energies to Predict Relative Strengths of Nicotinic Acetylcholine Receptor Agonists

Mathew Tantama Stuart Licht* Department of Chemistry Massachusetts Institutes of Technology 77 Massachusetts Avenue, Building 16, Room 573B Cambridge, Massachusetts 02139 Telephone: (617) 452-3525 Fax: (617) 258-7847 E-mail: [email protected]

Supporting Information 1. Indentifying single-channel clusters 2. Example Single-Channel Activity and Intracluster Dwell-Time Distributions 3. Error Analysis of Fitting Constraints and Sensitivity of TEMA KD to , n, and KGap 4. Linear Rate-Equilibrium Free Energy Relationship: Diliganded Gating -Value 5. Ab Initio Geometry Optimizations 6. Correlation Between Experimentally Measured KD and Calculated Cation- Energy 7. Correlation Between KD and Log P

1. Identifying Single-Channel Clusters. At high agonist concentrations, single-channel events have a characteristic clustered appearance. Most channels are desensitized, resulting in the long closed sojourns between clusters. If only one open conductance level is observed in the cluster, the clusters themselves likely represent activity from one channel. As the “intracluster” open probability increases, the probability that the cluster represents activity from exactly one channel becomes very high. Therefore, analysis of intracluster events permits estimation of microscopic rate constants without the problem of ensemble averaging. The data presented in this study are derived from intracluster events and the durations, or dwells, of these events. The baselines of single-channel records were adjusted manually using QuB. A 5 kHz Gaussian digital filter was applied, and records were idealized using either the segmental kmeans or half-amplitude algorithms in QuB (1). All records were examined visually in their entirety, and misidealizations were corrected manually. To identify clusters, the desensitized and non-desensitized closed dwells are classified and separated by analyzing exponential time constants that describe the close dwell-time distribution. There are several non-desensitized and desensitized closed states, and the lifetime of each of these states is exponentially distributed. Each state contributes an exponential time component, or time constant, to the observed closed dwell-time distribution. For each idealized dwell-time record, these time constants and their fractional contribution to the distribution, or amplitude, were determined in QuB using a maximum-interval likelihood (MIL) algorithm (2). MIL fitting in QuB requires the use of a kinetic model. The fitted time constants depend on the number of states included in the model but not the topology of the model. Thus, an arbitrary, uncoupled star model was used to obtain time constants, ignoring the fitted rate constants (3). Closed and open states were added successively until the negative log-likelihood score increased by less than the ln(N)/2, the Schwarz threshold for nested model selection for N events (3, 4). This procedure results in a set of time constants and associated fractional amplitudes, (i, ai), that describe the observed closed dwell-time distribution By inspecting the closed dwell-time distribution and time constants determined above, a critical time, tcrit, was chosen to separate non-desensitized dwells and desensitized dwells. Typically, non-desensitized closed dwells make the largest contribution to the distribution at shorter times. In contrast, desensitized dwells contributed longer closed dwells. To choose a tcrit,

the closed-dwell time was visually inspected, and an initial cutoff was subjectively chosen to separate non-desensitized and desensitized components. The non-desensitized components (i, ai) are shorter than the cutoff, and the desensitized components (j, aj) are longer than the cutoff. The critical time was chosen to minimize the percentage of misclassified events by solving Equation 1, and the fraction of misclassified events, , is given by Equation 2. An example is given in Supporting Figure 1. The fraction of misclassified events was typically less than 5%. m

ai

 i 1

m

e

 tcrit

i



 t crit

i



i 1

aj



j  m 1

i

   ai  e

n

e

 tcrit

j

(1)

j

n

 a j  (1  e

 t crit

j

)

(2)

j  m 1

Once the tcrit is determined, clusters were defined as successive open and closed events separated by closed dwells of length greater than the tcrit. Clusters with fewer than five events and multiple-conductance levels (more than one channel) were excluded. Clusters were visually examined to ensure tcrit was properly chosen.

Supporting Figure 1. Choice of tcrit for 1 mM TMA. At 1 mM TMA, there is typically a large peak centered at less than 1 ms, representing the bulk of non-desensitized dwells. Desensitized dwells are apparent at greater than 100 ms. For this record, the closed-time distribution was best fit to 7 components: (0.11 ms, 49%); (0.75 ms, 19%); (4.08 ms, 10%); (25.22 ms, 5%); (317.76 ms, 5%); (2461.89 ms, 9%); and (17645.30 ms, 2%). A critical time of approximated 50 ms is calculated (red arrow). Use of this critical time produces clustering that is visually verified (Figure 3). It causes misclassification of 1.7% of events.

2. Example Single-Channel Activity and Intracluster Dwell-Time Distributions

Supporting Figure 2. Single-channel activation of G153S2 AChR receptors by TMA. Examples of single-channel clusters are shown on the left. Openings are upward deflections. An example of a gap sojourn contaminating a high open probability cluster is indicated by the star. The intracluster closed and open dwell-time distributions are shown on the right.

Supporting Figure 3. Single-channel activation of G153S2 AChR receptors by ETMA.

Supporting Figure 4. Single-channel activation of G153S2 AChR receptors by DEDMA.

40 20 0 10

100

M Agonist

1000

0.10

2.0

Open Probability

Mean Open Time (ms)

-1

Effective  (s )

60

1.5

0.05

1.0

0.00

0.5 0.0

-0.05 10

100

M Agonist

1000

10

100 µM Agonist

1000

Supporting Figure 5. Single-channel activation of G153S2 AChR receptors by TEMA. Current amplitudes were too low for analysis at 5000 µM TEMA. TEMA activation doseresponse curves (Figure 3 of the main text) are shown in the lower panel: left, effective opening rate constant; center, mean open time; right, open probability within a cluster.

Supporting Figure 6. Single-channel activation of G153S2 AChR receptors by TMP.

3. Error Analysis of Fitting Constraints Estimation of 2 for ETMA: For ETMA, the unconstrained fit converged to values of 2 = 3400 ± 200 s-1 and a Hill coefficient of n = 5.7. The Hill coefficient fell far outside the expected range of 1.0 to 2.0 for AChR agonists (5). Constraining the Hill coefficient to 1.5 produced a good fit, and the opening rate constant was 2 = 3500 ± 200 s-1. We tested the sensitivity of the estimate of 2 to variation in n, and it varied from 3800 ± 400 s-1 (n=1) to 3500 ± 200 s-1 (n=2) with a coefficient of variation of 3%. Therefore, the estimate of 2 is insensitive to n and is robust and reliable. Supporting Table 1. Sensitivity of TEMA Dose-Response Estimates to the Hill Coefficient n n 1 1.1 1.2 1.3 1.4 1.5* 1.6 1.7 1.8 1.9 2 n

POMax 0.05 0.04 0.04 0.04 0.03 0.03 0.031 0.030 0.030 0.029 0.028

± 0.03 ± 0.02 ± 0.01 ± 0.01 ± 0.01 ± 0.01* ± 0.005 ± 0.004 ± 0.004 ± 0.004 ± 0.003

2 (s-1)

EC50 (µM) 1100 800 600 500 500 400 400 400 400 300 330

± 900 ± 500 ± 400 ± 300 ± 200 ± 200* ± 100 ± 100 ± 100 ± 00 ± 90

KApparent (µM)

1 200 ± 300 3000 ± 9000 1.1 100 ± 100 2000 ± 2000 1.2 80 ± 60 1000 ± 100 1.3 70 ± 40 800 ± 700 1.4 60 ± 30 700 ± 500 1.5* 60 ± 20* 600 ± 400* 1.6 50 ± 10 500 ± 300 1.7 50 ± 10 500 ± 300 1.8 50 ± 10 400 ± 200 1.9 47 ± 8 400 ± 200 2 45 ± 7 400 ± 200 * For TEMA, n was constrained to 1.5 to obtain estimates. Standard deviations of the ranges of values obtained in sensitivity analysis were used as the estimated errors for the respective parameters.

Supporting Table 2. Sensitivity of KD For TEMA Due to Constraints on the Hill Coefficient n Constraints on POMax KGap 

17.850 1

21.341 4

24.10 67

26.33 73

28.16 30

29.66 54

30.91 83

31.98 15

Constraints on 

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 n a 1 1280 1016 769 621 545 504 479 459 1.1 782 571 440 377 342 320 305 293 1.2 551 394 316 277 254 238 226 217 1.3 422 341 251 222 204 191 181 174 1.4 343 252 211 187 171 160 152 145 1.5 291 218 183 163 149 139 132 126 1.6 256 194 164 146 133 124 117 112 1.7 231 176 149 132 121 113 106 102 1.8 212 163 138 122 112 104 98 94 1.9 198 153 129 115 105 97 92 88 2 186 145 122 109 99 92 87 83 a Values reported in the main table section are KD in µM calculated by fitting.  0.08681 0.05433 0.04191 0.03541 0.03144 0.02879 0.02691 0.02551 0.02445 0.02362 0.02296

32.87 53

33.62 60

34.27 337

1.8 445 284 210 168 140 121 108 98 90 84 80

1.9 435 277 205 163 136 117 104 95 87 82 77

2 426 271 200 159 132 114 101 92 85 79 75

4. Linear Rate-Equilibrium Free Energy Relationship: Diliganded Gating -Value The diliganded gating rate constants and equilibria were measured in a modelindependent manner, and the slope, , of the linear rate-equilibrium free energy relationship (REFER) is consistent with previously measured values (6, 7) (Figure II.9). For the AChR allosteric gating mechanism, the -value is a measure of transition state structure and relative timing in the conformational reaction (8).

To measure , perturbations are applied to the

AChR at a specific location, such as a series of mutations at a single residue or a series of agonists at the transmitter binding site. For the series, the diliganded opening rate constant 2 is plotted as a function of the gating equilibrium 2 on a log-log scale. The -value is the slope of the linear REFER. A -value close to 1 indicates the change in gating equilibrium is due mostly to a change in 2. For the transmitter binding sites,  ~ 0.9 has been measured (6, 7). For the agonists examined here,  = 0.84 ± 0.01 (R2 = 0.9992) was observed. We conclude that in our

- R·T·ln(2) in kJ/mol

system, the mutant TBSs exhibit characteristics consistent with wild-type TBSs.

-10

TEMA

DEDMA

-15

-20

-25 -10

ETMA TMP TMA

-5

0

5

10

15

- R·T·ln(2) in kJ/mol Supporting Figure 7. The rate-equilibrium free energy relationship is linear. The slope is  = 0.84 ± 0.01 (R2 = 0.9992).

5. Ab Initio Geometry Optimizations

A

B

D

E

C

Supporting Figure 8. HF 6-31g(d,p)//HF 6-31g(d,p) gas-phase optimized geometries of (A) TMA, (B) TMP, (C) ETMA, (D) DEDMA, and (E) TEMA.

A

B

C

Supporting Figure 9. Overlay of the apo- (grey) and epibatidine-bound (cyan) aromatic box. X-ray structure of the epibatidine-bound AChBP (2BYQ) aromatic box with epibatidine hidden (A) or shown (B). (C) Optimized benzene-TMA complex manually positioned in the aromatic box. The benzene ring was overlaid with the Trp149. Hydrogens are not shown, except for TMA.

6. Correlation Between Experimentally Measured KD and Calculated Cation- Energy The measured closed-state affinities, KD, do not correlate well with the calculated cation energy. Considering the tetraalkylammonium series, there is possibly a weak linear correlation between the two parameters. The uncertainty in the slope of this correlation is affected by the uncertainty in the measured KD for TEMA; however, even considering the extreme cases, our conclusions are not affected. We can measure the slopes of the linear correlation using the upper and lower limits for the values of the TEMA KD (Supporting Figure 10). Through the entire range of possible slopes, the correlation between cation- energy and KD is weaker than between cation- energy and gating.

+ R·T·ln(KD) in kJ/mol

-18 TMP

-20 TEMA

-22

TMA

-24 -30

ETMA DEDMA

-27

-24

-21

Cation- Energy in kJ/mol Supporting Figure 10. Weak correlation between closed-state affinity and cation- energy. Range in slopes due to error in the KD for TEMA: maximum slope, red, slope 0.8 ± 0.3, R2 = 0.67; best fit slope, green, slope 0.3 ± 0.1, R2 = 0.50; minimum slope, blue, slope -0.28 ± 0.05, R2 = 0.92276.

7. Correlation Between KD and Log P The KDs for the ammonium series are very similar to each other, but TMP is an outlier, having a higher Kd than the other cations. TMP is a monovalent cation of approximately the same molecular size as ETMA or DEDMA, suggesting that simple electrostatics do not account for TMP’s anomalous behavior. The difference in hydrophobicity between TMP and the ammonium compounds may explain the difference in affinities. The hydrophobicity of small drugs is often estimated by the calculated octanol-water partition coefficient, Log P (9, 10). TMP is significantly more hydrophobic than the ammonium compounds. The relationship

between Log P and closed-state binding energy is approximately linear (Supporting Figure 11) (11, 12), and the slope is mKLogP = 0.7 ± 0.1 kJ/mol (R2 = 0.88), indicating that TMP’s greater hydrophobicity may account for its higher Kd.

+ R·T·ln(KD) in kJ/mol

-18 TMP

-20 TEMA

-22

TMA ETMA DEDMA

-24 -6

-3

0

3

Log P Supporting Figure 11. Correlation between closed-state binding energies and hydrophobicity. Log P correlates with closed-state binding affinity: mKLogP = 0.7 ± 0.1 kJ/mol (R2 = 0.88).

Supporting References 1.

Qin, F. (2004) Restoration of single-channel currents using the segmental k-means method based on hidden Markov modeling, Biophys. J. 86, 1488-1501.

2.

Qin, F., Auerbach, A., and Sachs, F. (1996) Estimating single-channel kinetic parameters from idealized patch-clamp data containing missed events, Biophys. J. 70, 264-280.

3.

Purohit, Y., and Grosman, C. (2006) Estimating binding affinities of the nicotinic receptor for low-efficacy ligands using mixtures of agonists and two-dimensional concentration-response relationships, J. Gen. Physiol. 127, 719-735.

4.

Schwarz, G. (1978) Estimating dimension of a model, Ann. Stat. 6, 461-464.

5.

Akk, G., and Auerbach, A. (1999) Activation of muscle nicotinic acetylcholine receptor channels by nicotinic and muscarinic agonists, Br. J. Pharmacol. 128, 1467-1476.

6.

Grosman, C., Zhou, M., and Auerbach, A. (2000) Mapping the conformational wave of acetylcholine receptor channel gating, Nature 403, 773-776.

7.

Purohit, P., Mitra, A., and Auerbach, A. (2007) A stepwise mechanism for acetylcholine receptor channel gating, Nature 446, 930-933.

8.

Auerbach, A. (2007) How to turn the reaction coordinate into time, J. Gen. Physiol. 130, 543-546.

9.

Chou, J. T., and Jurs, P. C. (1979) Computer-assisted computation of partition coefficients from molecular structures using fragment constants, J. Chem. Inf. Comp. Sci. 19, 172-178.

10.

Viswanadhan, V. N., Ghose, A. K., Revankar, G. R., and Robins, R. K. (1989) Atomic physicochemical parameters for 3-dimensional structure directed quantitative structure activity relationships .4. Additional parameters for hydrophobic and dispersive interactions and their application for an automated superposition of certain naturallyoccurring nucleoside antibiotics, J. Chem. Inf. Comp. Sci. 29, 163-172.

11.

Plaizier-Vercammen, J. A. (1987) Interaction of povidone with aromatic compounds. VI: Use of partition coefficients (log Kd) to correlate with log P values and apparent Kd values to express the binding as a function of pH and pKa, J. Pharm. Sci. 76, 817-820.

12.

Brown, M. L., Brown, G. B., and Brouillette, W. J. (1997) Effects of log P and phenyl ring conformation on the binding of 5-phenylhydantoins to the voltage-dependent sodium channel, J. Med. Chem. 40, 602-607.