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Issue 1, March 2001

Physical Sciences & Mathematics
Use of Spatial Averaging to Investigate Protein-Ligand Interactions: A Molecular Mechanics Study

Manuel J. Mora
University of Central Florida
Advisor: Harry L. Price, Ph.D.
Department of Chemistry, University of Central Florida

Abstract

In the work presented here, the HyperChem molecular modeling program was used to construct substrate and analog complexes between the folate-dependent enzymes dihydrofolate reductase (DHFR) and thymidylate synthase (TS). The flexible ligand-rigid binding site approach, together with molecular mechanics energy minimization, was used to investigate the stability of these complexes. Results of these calculations allowed for the categorization of key intermolecular interactions involved in complex formation. Superimposition of the optimized geometries of the ligands in the bound state yielded a collection (ensemble) of conformations and associated distributions of electronegative atoms (oxygen and nitrogen) that outlined the stereo-electronic characteristics within the DHFR and TS binding site.

Introduction

In biochemical research, the three-dimensional (3D) structure of a protein, or virtually any biomolecule, can be obtained from databases such as the Brookhaven National Laboratory Protein Data Bank (PDB). This public domain database has thousands of X-ray crystallographic and NMR structure files. Using a molecular modeling program such as HyperChem, a biomolecular structure (protein, nucleic acid, etc.) can be retrieved from a database and used to investigate the interactions between it and other molecules via a user interface.

Since there are a myriad of thermodynamically favorable conformations, the 3D structures obtained from a structural database represent a 'snap shot' or thermal average of a biologically functional conformation. In order to determine how well a molecule 'fits' into a binding site, molecular mechanics calculations are used to generate a potential energy matrix. This matrix describes the forces acting on every atom of the target molecule. An energy minimization operation is then executed to search for a stable bound conformation. By identifying the favorable and unfavorable interactions between the ligand and binding site, the structure of the ligand can be modified by addition or deletion of substituents, to maximize favorable interactions.

The degree of complementarity between the ligand and binding site is determined by treating the binding site as a fixed collection of atoms and allowing the docked ligand to adjust its conformation until an energetically favorable orientation, and hence, conformation is obtained. This approach, known as the flexible ligand-rigid binding site approach (Lorber and Shoichet 1998) has proved useful in the area of rational drug design. For example, the development of inhibitors targeting malarial proteases (Kuntz et al. 1993; Kuntz et al. 1996), HIV protease inhibitors (Lam et al. 1994), and influenza sialidase inhibitors (von Itzstein et al. 1993). The results obtained from molecular modeling programs allow for the construction of a detailed model that reveals key interactions between residues that make up the binding site and the bound ligand. Specifically, these interactions involve hydrophobic stacking between aromatic groups, hydrogen bonding, and ionic interactions.

Although there are hundreds of targets for modern chemotherapeutic agents, reactions involved in nucleic acid metabolism continue to draw a great deal of attention (Pratt et al. 1994). Compounds such as the plant derived drug, camptothecin, interfere with DNA function by inhibiting the enzyme topoisomerase I (Wang et al. 1998). Other agents such as mitomycin bind to and covalently modify DNA (Tomasz et al. 1987), inhibiting replication and transcription. Still other agents act as antimetabolites, that is to say they mimic a natural substrate or essential cofactor. One group of antimetabolites, the antifolates, has become a principal tool for the treatment of some types infectious diseases (Ouellette et al. 1998) and cancer (Allegra 1990). The effectiveness of antifolates stems from the absolute requirement by all organisms for folic acid. The 3D structures of five folate-dependent enzymes, these being, dihydrofolate reductase (DHFR) (Bystroff et al. 1990), glycine-N-methyltransferase (GNMT) (Huang et al. 2000), glycine ribonucleotide transformylase (GRTF) (Wang et al. 1998), serine hydroxymethyl transferase (SHMT) (Scarsdale et al. 1999), and thymidylate synthase (TS) (Montfort et al. 1990) have been determined and can be obtained from the Brookhaven Protein Databank.

While all of these proteins are essential for the survival of an organism, DHFR and TS are the best characterized, and have been the focal point for the development of antifolates. DHFR is the enzyme responsible for maintaining folic acid in its biologically active reduced form. The DHFR reaction requires the biological reducing agent NADPH, and proceeds in two steps with conversion of folic acid to 7,8-dihydrofolate (DHF) and then to 5,6,7,8,-tetrahydrofolate (THF). The latter, fully reduced form is involved in various metabolic processes. The second enzyme, TS converts deoxyuracil monophosphate (dUMP) into thymidine, a reaction which results in the conversion of the folic acid derivative known as N5,N10-methylene tetrahydrofolate (methylene-THF) to 7,8-dihydrofolate. Agents that inhibit DHFR prevent the conversion of DHF to THF. One of the most effective antifolates is methotrexate (MTX). The primary biochemical effect of MTX is to inhibit DHFR. Once inhibition occurs, cellular stores of THF are consumed by the TS-catalyzed reaction and other reactions of nucleic acid metabolism. Depletion of cellular stores of reduced folic acid results in cell death. More recently, agents similar in structure to MTX have been developed as inhibitors of TS (Shoichet et al. 1993, Costi 1998). The interactivity of folate and thymidylate metabolism is accentuated by a new class of agents that can inhibit not only DHFR and TS, but also other folate-dependent enzymes (for a review of folic acid metabolism and pharmacological action of antifolates see Pratt et al. 1994). Using 3D structures of DHFR and TS as templates, it is our goal to systematically investigate, through use of molecular mechanics and the flexible ligand-rigid binding site approach, the interaction of a series of folate derivatives with these proteins. Ultimately, we hope to investigate the interaction of these compounds with GNMT, GRTF, and SHMT. The results of these studies will allow us to construct an "optimal" ligand or pharmacophore that possesses the average conformational, structural and electronic (stereo-electronic) elements required for binding to each of these enzymes. Design of such a compound, or compounds could lead to the development of a novel class of antifolates that simultaneously target all key folate-dependent enzymes, thereby, potentially leading to more effective treatments of diseases such as cancer.

Methods & Materials

Selection of Lead Compounds
The focus of the present work was to investigate the effect of replacing the bicyclic pterin ring system present in the DHFR substrate DHF and the TS substrate methylene-THF. To this end, all compounds studied contained the para-aminobenzoic acid-L-glutamic acid moiety. The molecular fragments selected to replace the pterin group were chosen based on the following criteria: 1) aromaticity (the presence of one, two, or three aromatic rings); 2) polarity (the presence of electronegative elements such as nitrogen and oxygen); 3) the presence of a polar functionality such as a carbonyl, or amino group; and 4) the ease with which a substituent could be attached to the para-aminobenzoic acid (PABA) group to form the complete analog. This last requirement is intended to facilitate the synthesis of these compounds in a laboratory setting. The initial search identified eight compounds that satisfied the aforementioned specification. The structures of these compounds are shown in Figure 1.


Three groups were evaluated. These are designated as: the bicyclics, guanine (5), xanthine (7) theophylline (8), and coumarin (11); the tricyclics, a derivative of folic acid (4) and a derivative of guanine (6); and lastly, the monocyclics, benzoyl (9), and N-benzoyloxy amine (10). This last group was selected for their reduced size and steric volume. As a primary control, the interaction of the natural DHFR and TS substrates DHF (1) and methylene-THF (2), respectively, were modeled to obtain baseline energies for the formation of complexes with these proteins. Additionally, L-amethopterin, also known as MTX (3), which inhibits both DHFR and TS, served as a secondary control to model the interaction of a known drug with each enzyme. The strategy for generating and evaluating folate analogs is outlined in Scheme 1.


Scheme 1
Construction of Molecules
All calculations were performed using HyperChem (version 4.5) running on a Silicon Graphics Indigo 2 workstation. Three-dimensional representations were created using 2D structures obtained from the Aldrich and Sigma Chemical Co. catalogs. Once the molecules were created, the 3D coordinates of DHFR and TS were retrieved from the PDB using their respective identification codes (DHFR = 7dfr and TS = 2tsc). Both DHFR (Bystroff et al. 1990) and TS (Montfort et al. 1990) structures correspond to the Escherichia coli enzymes.

Docking and Geometry Optimization
The substrate contained within the crystal structure of DHFR was copied and inserted into a new workspace and used as a template. The angles, torsions and 3D positions of the atoms in each analog were adjusted until its structure was maximally superimposed on that of the substrate. Once this was accomplished, the analog was docked into the binding site within DHFR. Docking was performed with the natural substrate present. In this way, the position of the analog within the binding site could be adjusted with a greater degree of precision. Upon successful docking, the original substrate was deleted. At this point the coordinates of the protein were held fixed (rigid binding site), and the potential energy of the analog minimized (flexible ligand) utilizing the general purpose MM+ force field (Allinger 1977). The above procedure was also used when docking analogs into TS.

The potential energy of the analog was minimized using a smooth switching function. This type of function is typically used when determination of the interaction energies of large numbers of atoms over long distances would unnecessarily increase the calculation time. When used in this type of calculation, a switching function causes the force-field algorithm to increasingly neglect interactions between atoms beginning at a minimum distance, in this instance 10 Å, obtaining complete neglect beyond a maximum distance, which in this case is 14 Å. A combination of optimization methods was used to search the potential energy surface for energy minima (Hypercube, Inc. 1994). These algorithms calculate a potential energy matrix based on contributions of stretch, bending, dihedrals, van der Waals and electrostatic interactions to the molecular energy. The Newton-Raphson block-diagonal method (NRBD) was chosen as the first in the series, because it allows for a more efficient determination of energies, and as a result, the energy converges toward a minimum more quickly. Typically, after ten iterations using the NRBD method, a second search method known as the method of steepest descent was used to achieve optimal convergence within a local minimum. Steepest descent was chosen as the second method because of its ability to locate the greatest (steepest) descent out of a collection of local minima. Lastly, conjugate-gradient methods were used to achieve final convergence. Two algorithms are available in HyperChem: Fletcher-Reeves, and Polak-Ribiere. Both methods gave similar results and were used during the minimization process. A successful minimization was achieved when the variation in the energy gradient was no more than 0.25 Kcal/mole-Å. Once a minimum potential energy was obtained, the binding site was isolated making sure to include all cofactor atoms and any solvent. The analog was then repositioned inside this cavity to alter its potential energy and the energy minimization process repeated. Once a new minimum energy was obtained it was compared to the initial minimum energy conformer. This process was repeated minimum of 10-30 times, with the most stable conformer selected. This 'shaking' procedure was followed for all enzyme-analog complexes.

Data Analysis

The results of these molecular mechanics calculations were recorded as a single-point calculation 'log file' in HyperChem. Log files contain the individual contributions to the total potential energy, also referred to as the energy of minimization (Etotal). These component energies are expressed as Ebond, Eangle, Edihedral, Evan der Waals, Estretch-bend interactions, and Eelectrostatic energies. The components used to evaluate docking were Evan der Waals, Eelectrostatic, Etotal, and the energy of binding (DEbinding). This last term was derived from a single point calculation of the ligand by itself (Eligand), the protein without ligand (Eprotein), and the ligand/protein complex (Ecomplex). The DEbinding provides an indication of the stability gained by the ligand as a result of complex formation, and is given by the following expression: DEbinding = Ecomplex - (Eprotein + Eligand). The numerical results for all systems were tabulated using Microsoft Excel 97. Once optimized, structures in their bound conformation were copied and inserted into a new workspace. Three carbons forming a triangle within the benzene ring of the PABA group of each analog were selected as reference points for the superimposition. These carbons were in turn translated to the coordinates occupied by these reference carbons in the PABA group of the natural substrate (Figure 1) as obtained from the X-ray crystal structure for both DHFR and TS. Lastly, since biological activity is often coupled to molecular conformation, in particular, to one or more dihedral angles, a single dihedral angle (a) was selected to examine the relationship between it and Etotal for analogs bound to DHFR and TS. Rotation about the dihedral angle a determines the orientation of the substituent attached to the PABA nitrogen.

Results & Discussion

All compounds shown in Figure 1 were docked into DHFR and TS with the exception of theophylline (8). This compound, which carries sterically bulky N-methyl groups could not be docked into DHFR, and only with the greatest of difficulty docked into TS (Etotal = 81.3 Kcal/mole). As a result, theophylline complexes are not included in the discussion. It is important to note that the dimensions of theophylline thus serve as an upper-limit of the capacity of the DHFR and TS binding sites. The value of Etotal for DHF bound to DHFR and methylene-THF bound to TS was determined to be -37.7 and -9.3 Kcal/mole, respectively (Figure 2).


In terms of binding affinity, these values parallel the known affinities for each ligand to its respective enzyme, with DHFR exhibiting greater affinity for DHF (Km = 0.44 mM) (Poe 1972) than TS for its cofactor methylene-THF (Km = 14 mM) (Haertle et al. 1979).

Interestingly, Etotal for the complexes formed with DHFR exhibit a greater variability compared to complexes formed with TS, with analogs 3-6 exhibiting a more favorable Etotal when bound to DHFR (Figure 2). When DHFR and TS methotrexate complexes (3) are compared, the DHFR complex (-17.1 Kcal/mole) is 9.0 Kcal/mole higher in energy than the corresponding TS complex (-26.1 Kcal/mole). This is interesting, since DHFR is significantly more sensitive to methotrexate than TS (Baccanari and Joyner 1981). This discrepancy can be reconciled by considering the importance of bound water (Shoichet et al. 1999). In the case of this work, water was not removed from the binding site of either protein. It is possible, however, that the difference in Etotal is due to the absence of one or more bound water molecules. Exclusion of water from the binding site could reduce stabilizing contributions made by hydrogen bonds, which contribute approximately 3-4 Kcal/mole of energy per bond. It is also interesting to note that substitution of the bicyclic pterin ring with a tricyclic ring (Figure 1, analogs 4 and 6) did not adversely affect the docking of these molecules to either DHFR or TS. The greatest difference in Etotal between DHFR and TS was observed with analog 5, which exhibited nearly two-fold more negative Etotal when bound to DHFR (-26.7 Kcal/mole) than to TS (-13.2 Kcal/mole). As would be expected, the replacement of the pterin ring with a small aromatic group, such as a benzoyl or benzoyloxy amine fragment (analogs 9 and 10, respectively), resulted in the formation of complexes with the smallest values of Etotal. This result is not surprising given that these enzymes have evolved to preferentially bind larger, more substituted ligands. Thus, it is reasonable to conclude that values of Etotal obtained for these small aromatic derivatives reflect the characteristics of a loose-fitting complex.

It is important to recall that while Etotal provides a primary indication of the goodness-of-fit between a ligand and its binding site, a second indicator of the stability of a complex is provided by the binding energy, DEbinding. This term provides an indication of the amount of stabilization that a binding site confers to a ligand upon binding. The DEBinding for DHFR and TS ligand complexes are shown in Figure 3.



Most notably, all ligands exhibit significant DEbinding, with the least negative DEbinding being observed for DHFR and TS coumarin complexes. The greatly reduced DEBinding for this analog is reflected in the positive Etotal observed for the DHFR complex (15.1 Kcal/mole), and the marginally favorable Etotal obtained for the TS complex (-7.1 Kcal/mole). Taken together these results indicate that complex formation is associated, as one would expect, with stabilizing interactions that are not present when the ligand is free in solution. Moreover, these results indicate an overall similar degree of stereo-electronic complementarity to the binding sites within DHFR and TS.

Comparison of the electrostatic energy term (Eelectrostatic) for DHFR and TS complexes revealed a marked difference in the contribution of this term to the overall energy of the bound ligand (Figure 4).



Most notably, the benzoyl and benzoyloxy amine analogs exhibited a negligible Eelectrostatic contribution. This characteristic is consistent with the lack of heteroatoms (nitrogen, oxygen) and further confirms the importance of polarity in the binding of folates and antifolates to these proteins. Also of potential significance is the observation that DHFR displayed an overall greater sensitivity to Eelectrostatic than TS. Such a difference is most likely due to the types of amino acids present, and the polarity in folate binding site. In fact, it is known that the folate binding site in DHFR possesses a positive electrostatic potential (Bajorath et al. 1991). When considering electrostatic potentials, the orientation of the bound ligand becomes very important. With this in mind, it is reasonable to conclude that the trends observed in Eelectrostatic for both DHFR and TS reflect not only the amino acid composition of each binding site, but equally as important, reflect the orientation of the bound analog. Comparison of the van der Waals energy term (Evan der Waals) for DHFR and TS complexes revealed a uniform contribution of this intermolecular interaction term to complex formation (Figure 5).



Most notably, the coumarin analog (10), which yielded a positive Etotal, demonstrated a positive Evan der Waals term (10.6 Kcal/mole) for binding to DHFR and a marginal contribution (-8.9 Kcal/mole) for binding to TS. These results are consistent with the unfavorable steric profile of this analog.

Figures 6 and 7 show a representative drug complex formed between analog 5 and DHFR and TS, respectively.




Especially evident in both models is the close proximity and orientation between the guanine ring and the NADPH cofactor in DHFR (4.3 Å), and the uracil substrate in TS (4.0 Å). In both complexes, the space occupied by this analog would normally be occupied by DHF in the case of DHFR, and methylene-THF in the case of TS. Similar results were obtained for all compounds exhibiting favorable interactions. More importantly, the results of this modeling study make it possible to map out the stereo-electronic features of each binding site. This is accomplished by superimposition of the analogs as they exist in the bound state (Lemmen et al. 1998). With the exception of analog 8, Figure 8 shows the superimposed structures of analogs 1, 3-11 for DHFR complexes (A), and 2-11 for TS complexes (B).



The ensembles of bound conformations also make it possible to estimate the volume available for occupation. Molecular volumes were calculated based on the observation that each ensemble occupied an approximate pyramidal volume (Figure 8C). The superimposed DHFR-bound analogs indicate that the binding site occupied by these substituents enclosed a volume of approximately 48.4 Å. Li kewise, superimposition of TS-bound analogs reveals an approximate binding site volume of 49.6 Å. When compared, both sets of ensembles reveal conformationally flexible L-glutamate groups, rigidly held PABA groups, and conformationally distributed substituents attached to the PABA nitrogen. Further examination of the DHFR and TS ensembles reveals the spatial distribution of nitrogen (purple) and oxygen (red) atoms within each group of substituents. The observed spatial distribution of these heteroatoms is undoubtedly a reflection of the steric and electronic interactions that allow for nominal stabilization of the substituent. Biological activity is often coupled to molecular conformation, in particular, to one or more dihedral angles. In this study, a single dihedral angle (a) was selected and the relationship between it and Etotal examined. Rotation of a determines the orientation of the substituent attached to the PABA nitrogen. Figure 9 shows the dependence of Etotal on a for both DHFR (upper panel) and TS (lower panel) complexes.


Complexes formed with DHFR span a range of approximately 95o (-75o to -170o). Within this range appear two clusters of a that yield favorable interactions. One cluster falls between approximately -75o and -90o and the second cluster falls between -135o and -170o. The value of a assumed by coumarin (-110o), which did not bind favorably, falls in the region between these two clusters. Complexes formed with TS span a range of approximately 75o (-65o to -140o). Unlike the hypoxanthine-DHFR complex, the hypoxanthine-TS complex falls well outside of this range (+5o) yet represents an energetically favorable conformation. Closer examination of the hypoxanthine (7) molecular structure reveals the presence of increased flexibility resulting from an N-ethyl linker. It is reasonable to conclude that differences in the topology of the binding sites in these two proteins are responsible for the conformation assumed by this analog when bound to DHFR or TS. When compared to DHFR, TS complexes span a more restricted range of Etotal (approximately 19.1 Kcal/mole) than DHFR (33.0 Kcal/mole, exclusive of coumarin). Taken together these results indicate a more rigid binding site in TS than in DHFR. A property that could be exploited when searching for novel inhibitors.

In summary, the flexible ligand-rigid binding site approach was used to investigate the binding of a series of compounds carrying different PABA-linked substituents to the folate-dependent enzymes DHFR and TS. Comparison of Etotal, Eelectrostatic, Evan der Waals and DEbinding obtained from molecular mechanics calculations allowed for the dissection of determinants involved in complex formation. Superimposition of folate analogs made it possible to estimate the average volume available for occupancy, and to visualize en masse the spatial distribution of heteroatoms. Lastly, the relationship between a key dihedral angle (a) and Etotal was investigated. Comparison of DHFR and TS complexes revealed distinct differences in the range of a and Etotal. The results of this study provide the foundation for continued investigation into the interaction of these and other analogs with the following folate-requiring enzymes, glycine-N-methyltransferase, glycine ribonucleotide transformylase, and serine hydroxymethyl transferase. When results from these future studies are combined with these data, a pharmacophore search will be carried out in an effort to identify, and ultimately construct, an optimal ligand possessing the average conformational, structural and electronic (stereo-electronic) elements required for binding to each of these enzymes. Design of such a compound, or compounds could lead to the development of a novel class of antifolates that simultaneously target all key folate-dependent enzymes, thereby, potentially leading to more effective treatments of diseases such as cancer.


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Journal of Young Investigators. 2001. Volume Three.
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