Receptor–Ligand Interaction at 5-HT3 Serotonin Receptors: A Cluster

May 30, 2014 - A fundamental understanding of the interaction of ligands with biological receptors is important because many drugs exert their influen...
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Receptor−Ligand Interaction at 5‑HT3 Serotonin Receptors: A Cluster Approach Bijan K. Rao,† Devleena Samanta,‡ Shawn Joshi,†,§ Kinjal Basu,∥ Sheryl D. Baldwin,⊥ Amrita Jha,# Malgorzata Dukat,¶ Richard A. Glennon,¶ and Puru Jena*,† †

Department of Physics, §Department of Biomedical Engineering, ⊥Center for the Study of Biological Complexity, #Department of Chemistry, and ¶Department of Medicinal Chemistry, Virginia Commonwealth University, Richmond, Virginia 23284, United States ‡ Department of Chemistry and ∥Department of Statistics, Stanford University, Stanford, California 94305, United States S Supporting Information *

ABSTRACT: A fundamental understanding of the interaction of ligands with biological receptors is important because many drugs exert their influence via receptors. Using a cluster approach, we have studied the role of structural and electronic parameters on receptor−ligand binding by carrying out density functional theory based calculations. As model systems, we have studied substituted arylguanidines, which activate 5-HT3 receptors in a manner similar to that of serotonin. The geometries of the arylguanidine derivatives were fully optimized to obtain the lowest energy structures. Electronic properties such as binding energies, dipole moments, polarizabilities, and electron affinities, as well as geometric properties, such as molecular volume and dihedral angles were calculated, and their relationship with binding affinity was evaluated. Results obtained were compared to experimental ligand−receptor binding affinity data available. These fundamental studies show that though both electronic and geometric properties of the ligands are important for binding, the electron affinities of the substituent species play a dominant role. Potential new fundamental indices for ligand−receptor affinity are also discussed.

I. INTRODUCTION Design of drugs to effectively treat various disorders can be significantly improved if a fundamental understanding of biological processes at the atomic level can be achieved. In spite of tremendous progress made in the development of computer hardware and software as well as physical techniques, this understanding is difficult due to the complex architecture of biological molecules. Simple semiempirical methods have been traditionally used for this purpose as methods based on first-principles techniques cannot deal with molecules that contain thousands of atoms. Because for most of the reactions only the local environment of the reacting site of a molecule is of primary importance, it is possible to understand the key parameters that control the reactivity of biological systems by using a cluster approach that models the central reacting site surrounded by near neighbor atoms. We recall that atomic clusters are a new phase of matter intermediate between the atoms and bulk. At the dawn of this field, it was expected that a study of the structure and properties of atomic clusters can illustrate how bulk properties evolve, one atom at a time. In spite of considerable progress in this field1 an unambiguous answer to the question “when does a cluster becomes a crystal?” has been difficult to find because the answer depends not only on the chemistry of the clusters but also on the property being investigated. On the other hand, atomic clusters have been found to bridge many disciplines 2−4 often addressing fundamental questions in physics, chemistry, biology, medicine, © 2014 American Chemical Society

and the environment. In this paper we use the cluster approach to focus on the design of drugs used for the treatment of disorders in the central nervous system (CNS), and show that clusters can be used as a bridge between physics, chemistry, and medicine. An effective strategy in drug design for the CNS has been to identify specific receptors for important neurotransmitters. Serotonin (5-hydroxytryptamine or 5-HT) is one of the most basic neurotransmitters. There are seven different families of serotonin receptors,5−9 5-HT1 through 5-HT7. Serotonin (5HT) interacts with each receptor type7 and each receptor type can be related to different physiological or pharmacological functions.9 Thus, it would be very useful to have therapeutic agents that selectively activate one receptor population, but not the other 5-HT receptors. In some instances this has been achieved.10,11 The challenge is to develop agents that have selectivity as well as optimal binding properties with the receptor of interest. In spite of considerable work on many of these receptors7−11 an atomic level first-principles understanding of receptor−ligand is still lacking. Special Issue: A. W. Castleman, Jr. Festschrift Received: February 20, 2014 Revised: May 29, 2014 Published: May 30, 2014 8471

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Multiple receptor types can exist for a single neurotransmitter and, indeed, multiple receptors for serotonin have been identified.11,12 Further, there are different types of receptor families, e.g., G-protein coupled receptors (GPCRs) and ligand gated ion channel receptors (LGICRs).10,11 For these receptors, the neurotransmitter ligand binds to the receptor and elicits a response. Although neurotransmitters are the natural or endogenous ligands for these receptors, synthetic ligands can also bind to, and activate, the receptors.10 Receptors are traditionally viewed as “nano-locks” of specific three-dimensional structure. The ligands are considered as “nano-keys” that must be “docked”, fitting into the receptor, like a key in a lock.13−16 Further, there must be mechanisms that bind the “docked” ligand to the receptor. Conventional wisdom is that the most important factors relate to alteration of the protein receptors, and the achievement of a stable conformation for the “nano-lock/nano-key” complex. Such mechanisms arise from conformational changes in the receptor and the hydrophilic or lipophilic nature of the ligands, and from other electronic and physicochemical parameters. For drug design, it is essential to gain an understanding of how receptor−ligand binding can be modulated. The motivation of our work is that quantum mechanical studies based on firstprinciples cluster approach can, perhaps, shed light on the science underlying these interactions. This study involves a specific family of serotonin receptors, the 5-HT3 receptors, which are the only ion channel receptors in the 5-HT receptor family17,18 and are involved in pain perception, anxiety, and mental disorders. Dukat and Glennon have previously identified a set of synthetic ligands, arylguanidines, that show activity at this receptor.19−21 Arylguanidines (AG) have been shown to activate 5-HT3 receptors in a manner similar to that for serotonin. Therefore, arylguanidine derivatives have been synthesized and studied extensively for their binding with these receptors.19−21 It was found that with different substituents at different positions in the aryl ring, binding affinities vary over a very large range.19,21 Quantitative structure−activity relationship (QSAR) studies have indicated that affinity is dependent upon the electron withdrawing nature of the substituents at specific positions as well as a relationship to molecular polarizability.21 However, a striking inconsistency (to be discussed later) in binding data remained unexplained and no parameter or property had been identified to explain these apparent anomalies. In this work, we have conducted quantum mechanical calculations from first-principles using density functional theory to investigate both structural and electronic parameters on which the binding affinities of arylguanidine derivatives might depend.

receptor) are labeled with radioligand and the ability of agents to displace the radioligand is measured. The procedures used for these measurements and the synthesis of all arylguanidine (AG) compounds were detailed in an earlier work.19 A total of 14 molecules spanning a broad range of binding affinities were studied and the values are given in Table 1. Table 1. Binding Affinity Data for the Substituted Arylguanidines (AGs)21 1 2 3 4 5 6 7 8 9 10 11 12 13 14

AG compound (R)

Ki (nM)

pKi

3-CF3 H 3-OCH3 3-Cl 3-Cl, 5-OCH3 3,5-diCl 3,4,5-triCl 4-Cl 4-CF3 3-CF3, 4-Cl 3-NO2 3-CN 3-OH 3-CH3

2440 2340 1600 32 18 5 0.7 325 230 36 85 123 2020 6520

5.61 5.63 5.80 7.49 7.74 8.30 9.15 6.49 6.64 7.44 7.07 6.91 5.69 5.19

Figure 1 shows the structures of serotonin and the arylguanidines examined. The “R” indicates various substituents

Figure 1. Chemical structures of serotonin and the arylguanidines.

on the arylguanidine ring. The positions where the substitution of the H atom was made are marked by their ring position. The substituent, or R group, in each different molecule was varied to effect possible binding behavior toward the serotonin 5-HT3 receptor. Specifically, these compounds provided an ideal study for they were developed by substitution of a variety of R groups at the 3-, 4-, and/or 5-positions of the aryl ring. They were synthesized and experimentally evaluated for binding affinity at the 5-HT3 receptor using whole cell preparations and radioligand binding.19−21 Computational Procedure. Earlier studies have shown that, by itself, phenylguanidine (2 in Table 1) does not bind with high affinity to 5-HT3 receptors.19,21 However, on substitution, some substituents increased binding affinity whereas others decreased it. Although these affinities are traditionally understood from quantitative structure−activity relationship (QSAR) studies that are empirically based, there was an apparent inconsistency in the previous QSAR that remained unexplained. That is, high affinity could be (partially) explained by the presence of electron withdrawing substituents at the ring 3-position (e.g., −Cl) but it was difficult to account for the lower than expected affinity of the stronger electron withdrawing −CF3 analogues. This led to investigation of

II. METHODS Experimental Procedure. To assess the ability of a ligand to bind to a receptor, we focused on receptor “affinity”, which defines its ability to bind to a specific receptor. The measure of affinity, Ki, is the dissociation constant. Because Ki is an equilibrium dissociation constant, larger Ki values mean poorer binding and vice versa; e.g., a Ki = 1 nM represents high affinity, whereas a Ki = 10 000 nM represents 10 000-fold lower affinity. Using −log Ki or pKi (where Ki is in units of molarity), receptor affinity varies directly with pKi. It might be noted that it is customary to use the pKi for statistical correlation analysis. The affinity can be measured using radioligand binding techniques where receptors (in cell homogenates expressing the 5-HT3 8472

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molecular properties such as polarizability,21 but −CF3substituted analogues continued to appear as outliers. With a view to obtaining first-principles explanation of binding, calculations using density functional theory were performed on these substituted arylguanidines. The geometries of these were optimized to obtain the lowest energy structure for each compound. We used B3LYP22−24 hybrid functional for the exchange−correlation potential and 6-311++G**25,26 basis set for C, H, N, O, Cl, and F atoms. All structures were optimized without any symmetry constraint. No imaginary frequencies were found, indicating that the structures are dynamically stable. All calculations were performed using Gaussian 03 software.27 Several electronic and geometric properties of various substituted arylguanidines were investigated to determine the effects of the electronic structure as well as topology on receptor binding affinity (pKi). These included (1) dipole moments (DM), (2) polarization (dipole moment/volume), (3) molecular volume (intended to show the effect of steric hindrance), (4) dihedral angle between the guanidyl moiety and the benzene ring as the substituent was changed, (5) binding energy (atomization energy), (6) ionization potential (IP), (7) electron affinity (EA), (8) charge on the guanidyl moiety, (9) magnitude of exact polarizabilities, (10) total charge associated with the atom(s) and group(s) in positions 3, 4, and 5, (11) relative EA, (12) relative IP of the substituent (13) binding energy per atom, and (14) relative substituent binding energy. The relative EA (IP) was computed by taking the difference between the EA (IP) of the substituted species and the H atom they replace. Similarly, the relative substituent binding energy was computed by taking the difference between binding energy of the substituent to the phenylguanidine moiety and the binding energy of the H replaced. The charge on an atom was computed using the natural bond orbital (NBO) analysis. The calculations in this study did not include the structure of the receptor. Instead, the intent here was to discern which molecular attributes of the ligands themselves influence binding to the 5-HT3 receptor. That is, the structure of the receptor (although possibly existing in multiple conformations) was held constant. Routine QSAR studies have provided some information but have not yet adequately accounted for unexpected differences in receptor binding.21 Some of the problems were attributed to the possibility of rotameric binding,21 but a persistent problem was their inability to account for the binding of −CF3 arylguanidines. In our work, we took a cluster approach; i.e., we computed the electronic and geometric properties of arylguanidine molecules as opposed to bulk. In this way, we tried to discern molecular parameters that are important for the receptor−ligand binding. Because the chemical nature of the substituent and its substitution position are the principal changes from the basic arylguanidine structure, we looked at the problem from the perspective of the nature of these changes. Consequently, computing properties for the substituents themselves seemed logical and summing the changes in each position, we obtained the following results. We define the relative electron affinity (EA), ΔEA, as ΔEA =

the substituent. Hence, we are taking into account the change in electron affinity of the substituent as we replace H by any other substituent group. Considering this change to be cumulative, we investigated the correlation between this quantity and pKi. For example, in the case of 3-Cl, 5-OCH3AG two hydrogen atoms have been replaced by substituents. Hence the total relative electron affinity is given by ΔEA = EA(Cl) + EA(OCH3) − 2EA(H)

Similarly, the relative IP is defined as ΔIP = ∑IP(S) − ∑IP(H) and the relative substituent binding energy is defined as RSBE = BE(S) − BE(H). To provide a basis for using relative electron affinities to quantify the binding affinity of substituent ligands, we note that in classical organic chemistry these substituents are designated, respectively, as electron donating or electron withdrawing groups. Here, however, we have actually computationally determined the fundamental physical factor involved in electron donating or electron withdrawing groups, namely, the ionization potential and electron affinity of those groups.

III. RESULTS AND DISCUSSION The optimized geometries of phenylguanidine and its substituted derivatives are given in Figure 2. It was previously suggested that both “substituent” parameters and “whole molecule” properties might account for the binding of AGs to 5-HT3 receptors.21 Here, we investigate both using firstprinciples techniques. Our task is to model the pKi (called Y hereafter) in terms of 14 different predictors, namely, DM, polarization, molecular volume, dihedral angle, binding energy, IP, EA, NBO charge on the guanidyl moiety, magnitude of exact polarizability, charge on 3,4,5 substituents, relative EA, relative IP, binding energy per atom, and relative substituent binding energy (called X1, X2, ..., X14 hereafter). A simple linear regression (SLR) between the Y of the 14 molecules and each of the predictors was performed. The correlation coefficients obtained using this basic approach, are given in Table 2. According to Table 2, relative electron affinity and total energy are the most important parameters that affect binding. We noticed an increase in binding with increased relative EA of the substituents. Figure 3 shows the variation of binding affinity with relative EA for all 14 molecules studied. Although this method is fairly simple, it does not provide an accurate description of the variation of Y with Xi. This is because it ignores the possibility of more than one predictor variable affecting Y. The low magnitude of the correlation coefficient (r) between Y and Xm attained through SLR does not necessarily imply that the variable Xm is insignificant. If multivariate regression analysis were to be done, Xm might be a significant predictor in conjunction with other variables. Moreover, correlation between the predictor variables (e.g., Xm and Xn) is neglected in SLR. Because our goal is to find which of the predictor variables are important and which are not, we have the problem of fitting predictors X on a variable Y to come up with the best model that not only gives a good theoretical interpretation but also helps in future predictions with minimum error. This necessitates multivariate regression analysis. To fit Y onto the data matrix X, it was required to find β such that

∑ EA(S) − ∑ EA(H)

where EA(S) is the electron affinity of the substituent and EA(H) is the electron affinity of the hydrogen atom replaced by 8473

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Table 2. Correlation Coefficients (r) for All the Parameters Investigated in Order of Increasing |r| parameter

r

dipole moment (DM) binding energy per atom polarization binding energy (atomization energy) relative ionization potential (ΔIP) of substituent ionization potential (IP) of molecule total nbo charge on substituents in 3,4,5-positions electron affinity (EA) of molecule dihedral angle molecular volume NBO charge on guanidyl moiety relative substituent binding energy exact polarizability relative electron affinity (ΔEA)

0.04 −0.19 −0.38 −0.40 0.45 0.50 −0.52 0.53 0.58 0.67 0.71 −0.77 0.84 0.93

Figure 3. Relationship between substituent relative electron affinity and 5-HT3 serotonin receptor affinity (pKi value) of 14 arylguanidines (r = 0.93).

technique (least absolute shrinkage and selection operator), we obtained the equation of best fit to be Y = 7.418083 + 19.144761X8 + 0.001978X 9 + 0.304841 X11 − 0.176612X14

The adjusted R2 of the fit is 0.8813. Writing in terms of variable names, we have pK i = 7.418083 + 19.144461 × charge on guanidyl moiety + 0.001978 × polarizability + 0.304841 × relative EA Figure 2. Optimized geometries of phenylguanidine and its derivatives. Gray represents C, blue represents N, red represents O, yellow represents F, white represents H, and green represents Cl.

− 0.176612 × relative substituent binding energy

Therefore, we find that among the 14 parameters, the charge on the guanidyl moiety, polarizability, relative electron affinity, and relative substituent binding energy are the best variables in the linear model. After knowing this, we tested the level of significance of each of these three variables. The variable X11, or relative EA, is the most significant variable at level 0.01. This means there is a 1% chance that the coefficient of X11 in the regression equation is zero. The binding affinity increases with an increase in the charge on the guanidyl moiety, polarizability, and relative EA and decreases as the relative substituent binding energy increases. We can now explain the apparent discrepancy of why the −CF3-substituted arylguanidines have lower binding affinity than −Cl-substituted arylguanidines, in spite of being more

n

∑ (Yi − Xi′β)2 = ||Y − Xβ||2 2 i=1

is minimized, where β is the coefficient of the predictor variables. Because all the variables are being used in such a simple model, we are clearly overfitting the data, and this model will surely have a huge variance for future predictions. Known literature tells us how to select the important predictor variables through a procedure as generalized model selection, which is done automatically by LASSO28 (see Supporting Information for more details). Using the LASSO 8474

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affinity of substituent) as well as geometric or topological factors (such as position of substituent on the phenyl ring) are responsible for binding affinity for this set of arylguanidine ligands for the serotonin 5-HT3 receptor. A method to computationally include the positional dependence needs to be developed for ligand binding, such as that done by Parr and Yang for chemical reactivity.29,30

electron withdrawing in nature. This is because though CF3 is more electron withdrawing than Cl, it has a lower relative EA (Table S2 in Supporting Information). The significance of the relative EA shows that more electron deficient substituents help arylguanidines to bind more strongly to the receptor. Although we have identified four variables as being important in predicting the variable pKi, we cannot claim that these are the only important variables. It should be noted that the data matrix, X, had columns that were highly correlated. The correlation matrix (in absolute values) is given in Table S3 (Supporting Information). We find that there is strong absolute correlation between X8 and X4 and between X8 and X6. So, there is a chance that variables X4 and X6, viz, dihedral angle and ionization potential, might also be important in predicting the Y values. But because of high absolute correlation between these variables, it is enough to include just one in the model. We should mention that traditionally, for developing such regression models, the molecules are randomly divided into two groups called the training set and the test set, respectively. The training set is used to develop the regression equation. Using this equation, the Y values of the test set of molecules are determined. The goodness of the fit is determined by looking at the errors between the predicted and actual Y values of the test set. Our approach using the LASSO method is superior to this technique. In our method, we assigned the 14 molecules to 5 groups at random. We chose four of the groups as the training set and calculated the error in predicting Y of the remaining group, the test set. Out of the 5C4 ways of choosing the training set and the test set, we chose the model that minimizes the test error. This process is repeated, starting from the initial randomization, 200 times to develop a robust model. The parameters listed above correspond to the optimized structures presented in Figure 2. We recognize that several rotational isomers are possible for each of the structures, which may influence the dipole moment, molecular volume, polarization, dihedral angle, polarizability, etc. To accurately calculate these values, the relative abundance of the rotamers at a particular temperature needs to be known. However, because most rotational isomers are within 0.2 eV of each other, which is within the accuracy of the DFT calculations, they can be considered to be energetically degenerate in this case. Therefore, correlation between the total energy and pKi or relative electron affinity and pKi is not expected to change. In general, we can conclude that the most important parameters that affect binding are the electronic properties. At this stage, we cannot model the influence of the position of the substituent on binding. However, we observed that when Cl, a substituent with higher EA, is moved from the 3- to the 4position, the binding affinity decreases whereas in the case of CF3, a substituent with lower EA, the opposite effect is observed. We further noted from the literature that the pKi’s of 4-OCH3 phenylguanidine (EA of OCH3 is 0.68 eV) and 4-CH3 phenylguanidine (EA of CH3 is −1.27 eV) are 6.00 and 6.35, respectively.21 In this case also, as the electron affinity of the ligand decreases, the binding affinity increases when the ligand is moved from the 3- to the 4-position. We should emphasize that the calculations are carried out on free-standing molecules (i.e., clusters) whereas the affinity measurements are performed in real samples where the environment may play a role. Thus, it is important to recognize trends and overall agreement rather than focusing solely on quantitative agreement. Clearly, we have found that both electronic factors (charge on the guanidyl moiety, polarizability, and relative electron

IV. CONCLUSION We have studied a total of 14 substituted arylguanidine molecules using a cluster approach with a broad range of binding affinities for 5-HT3 receptors. We have calculated structure and electronic properties from first-principles and analyzed the results using a multivariate-regression method to explain the experimentally observed binding affinity. Our results have led to the following conclusions: (1) Both electronic and geometric properties of the ligands guide binding. Binding affinity increases as the polarizability of the ligand increases. The charge on the guanidyl moiety as well as the relative binding energy of the substituent to the arylguanidine backbone also influences the binding. However, the most important factor guiding the binding is the relative electron af f inity of the substituents in the ligand. Substituents with higher electron affinity favor stronger binding. We also note prior studies on local reactivity indices21 to help explain the dependence of binding of these compounds with the 5-HT3 receptors. (2) Multivariate regression analysis reveals that there is substantial correlation between the predictor variables. For example, the dihedral angle between the guanidyl moiety and the benzene ring shows high correlation with the charge on the guanidyl moiety. Therefore, either of the parameters can be used to determine strong binding. (3) Another important factor that guides the binding is the position of the substituent. Though the present study cannot fully account for change in binding with change in substituent position, we have observed that when Cl (high EA) is moved from the 3-position to the 4position, the binding affinity decreases. However, the binding affinity increases when CF3 (low EA) is moved from the 3- to the 4-position. Due to limited data we are unable to make any generalization, except that in each case, the lower energy structure binds more strongly. We hope that with more data, this model can be further improved. Our results show that the electron affinity of the substituent group does explain some apparent anomalous results in the experimental findings for the complete set of substituted arylguanidine compounds. This work also provides a more fundamental understanding of the basic science underlying receptor−ligand interactions for the 5-HT3 serotonin receptor. Both electronic and geometric parameters are important, in a manner not previously understood. The relative electron affinity suggests the importance of the chemical potential for these ligands in their interaction with the 5-HT3 receptor. Further, beyond this set of ligands, this may be a general principle driving binding in other ligand−receptor interactions. Thus, a computationally-derived binding index developed from first-principles, similar in nature to the local reactivity index of Parr and Yang,29,30 may be possible to explain receptor binding. Future work will involve additional investigation into this concept. In summary, we believe that the results of these studies provide a broader illumination on the basic science underlying the ligand−receptor interactions for the serotonin 5HT3 receptors, and potentially beyond. Further, a cluster model may help to explain reactivity of complex biological systems. 8475

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ASSOCIATED CONTENT

S Supporting Information *

Electron affinity and total relative electron affinity of substituents, relative substituent binding energies and values of pKi and relative electron affinity for all the molecules, and details of the LASSO method are presented in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*P. Jena: e-mail, [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This was supported in part by a grant from the Department of Energy and used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. In memory of B. K. Rao who initiated this study.

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REFERENCES

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