Matta, Boyd. The quantum theory of atoms in molecules

492 18 QTAIM in Drug Discovery and Protein Modeling

Fig. 18.7 The EP surface of the turkey egg-white lysozyme 135L, computed using RECON through hexadecapole order. The surface here is constructed as a simple union of atom-centered spheres at predetermined van der Waals radii for each atom.

proteins in chromatographic columns under a variety of experimental conditions [128–130]. TAE multipoles can also be used to generate more refined EP surfaces for proteins. As an example, Fig. 18.7 shows the EP surface of a small protein, turkey egg-white lysozyme 135L, computed using RECON through hexadecapole order. Computation of 3D RAD and PEST descriptors using the 3D protein structure and integrated atomic TAE properties entails a small computational overhead but is still accessible even when using very modest computational resources [131].

18.7 Conclusions

We have seen that the QTAIM is a powerful method for rapid generation of abinitio quality electron densities and electronic properties of large molecules, proteins, and entire of pharmaceutical databases, using TAE RECON technology. Electron-density-derived descriptors generated using the TAE RECON method have also been successfully used to predict diverse molecular properties. Such conformation-insensitive descriptors are valuable in their own right for several reasons:

For a molecule that has not yet been synthesized, conformational information is not available and can be theoretically computed only by energy minimization, which is often computation-intensive and sensitive to details of the

18.7 Conclusions 493

algorithm and the values used. It is desirable to have a set of theoretical descriptors that have uniquely defined values, irrespective of the details of minimization.

Even for naturally occurring biomolecules, the active conformation responsible for a certain physiological e ect is often unknown. For large fluxional molecules like proteins the minimum energy conformation, even if known, need not correlate with the physiologically active conformation. Further, no single conformation may be su cient to explain the observed activity.

RECON descriptors can be supplemented, with some increase in computation time, by hybrid shape–property descriptors from the PEST algorithm. PEST descriptors encode information about the molecular shape, without requiring an alignment procedure for their computation. The supplementary information available from PEST descriptors is useful when the shape of the molecule plays a determining role in binding.

RAD descriptors may be used, where necessary, to achieve an optimum compromise between conformation sensitivity and computation speed. Computation of RAD incorporates conformational information into the descriptors, while introducing a mere 3–5% CPU overhead.

In this respect and in terms of speed and high-throughput capability, RECON descriptors scale computationally in much the same way as topological descriptors [78, 82–91], with the added advantage that they contain information derived from the electron density distribution, well beyond that contained in indices derived from connectivity alone. The TAE RECON technology has promise for virtual high-throughput screening and design of focused libraries.

Several other electron-density-derived properties are amenable to computational evaluation in a QTAIM framework and are likely to be of value as molecular descriptors in di erent contexts. Electron-density-derived measures of molecular similarity provide a convenient and fundamental means of exploring chemistry space and assessing the similarities of molecules, the predictive capability of a QSAR model, or the diversity of a molecular library. The QTAIM is also, currently, one of the most computationally tractable methods for going beyond classical models for study of biological molecules and their interactions. CoLiBRI a ords rapid prefiltering of large chemical databases to eliminate compounds that have little chance of binding to a receptor active site. Knowledge of the receptor active site structure a ords straightforward and e cient identification of its complementary ligands with CoLiBRI; conversely, starting from the ligand chemical structure, one may also identify possible complementary receptor cavities. The QTAIM thus provides the basis for a versatile collection of promising techniques for drug-design applications.

494 18 QTAIM in Drug Discovery and Protein Modeling

References

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19

Fleshing-out Pharmacophores with Volume Rendering of the Laplacian of the Charge Density and Hyperwall Visualization Technology

Preston J. MacDougall and Christopher E. Henze

19.1 Introduction

‘‘When the distribution of charge over an atom is the same in two di erent molecules, i.e. when the atom or some functional grouping of atoms is the same in the real space of two systems, then it makes the same contribution to the total energy and other properties in both systems.’’ This quotation, from page 3 of Richard Bader’s classic monograph [1], displays at once his style and precision of writing, and his desire to get right to the crux of the matter at hand. In this chapter, we examine the charge densities of sets of functional groupings of atoms in drug molecules. These sets are referred to as the ‘‘pharmacophores’’ presumed to be responsible for the pharmacological activity of the drugs [2].

When two things are the same, it does not matter how you look at them. As long as you look at them in the same way, they will look the same. If two things are not the same, particularly if they are di erent in a subtle way, then their appearance can be quite dependent on how you look at them. For instance, the silhouette of one’s right hand, palm down, is nearly indistinguishable from the silhouette of one’s left hand, palm up.

An extremely coarse description of pharmacophores is required for rapid screening of a large number of possible drug molecules for variously defined measures of ‘‘fitness’’ with regard to their interaction with a known active site on an enzyme, or some other biological target. Typically, formless spheres are used to represent either inclusion or exclusion volumes, where hydrophobic groups should, or should not be, respectively. Similar, but alternatively labeled, spheres are also used to position hydrophilic groups. Other groups that may be included in a pharmacophore are, but are not limited to:

positive or negative formal, or partial, charges;

aromatic rings;

hydrogen-bond acceptors; and

hydrogen-bond donors.

500 19 Fleshing-out Pharmacophores with Volume Rendering of the Laplacian of the Charge Density

Fig. 19.1 A pharmacophore model for penamecillin. Only those features near the reactive site are included in the model. The green arrows indicate hydrogen bond-acceptor features and the lone mauve arrow indicates the hydrogen bond-donor feature. The gray spheres are hydrophobic exclusion volumes, and the yellow sphere marks the sulfur atom. Created by ‘‘Discovery Studio Visualizer’’, Accelrys Software, 2005.

For the last three there may be directional constraints in addition to positional constraints. This reflects the empirical observation that the most stable p–p interactions are face-on, and XaH Y hydrogen bonds are most frequently linear, or very close to being linear. An illustrative example of a pharmacophore is given in Fig. 19.1, in this case matched by penamecillin, a penicillin derivative.

To draw an anatomical analogy to a pharmacophore, a zoologist does not need to recover all of the bones of an animal to identify the species, its gender, and approximate age, even without doing any genetic testing. Just a finite number of key skeletal components will su ce. Just as there are millions of 75-year-old men but only one R.F.W. Bader (who hopefully still has a long life ahead of him), much more detail is needed in the pharmacophore to winnow from the billions of drug-like molecules those that will have a beneficial e ect (let alone the single most e ective drug possible).

A common approach in drug design is to start with a ‘‘hit or miss’’ approach with regard to the pharmacophore – does a molecule have all the required features within an acceptable distance or not? For most binding sites there will still be a very large number of hits, and from that point di erent researchers may use di erent, but almost always proprietary, algorithms to calculate the overall binding energy. There may be an optimum range for this result, and other factors must also be considered, for example solubility in water and fat, conformational flexibility, and permeability through barriers in vivo. Irrespective of which binding algorithm is used, the pharmacophore is obsolete at this point. The entire molecule is fed into a fitting algorithm, all of which are highly approximate by necessity, incapable of accurately describing the weak van der Waals interactions that are key to biomolecular interactions.

19.2 Computational and Visualization Methods 501

By ‘‘fleshing-out’’ pharmacophores with their highly accurate charge-density distributions, we hope to provide insight into which secondary factors, for example ring size or substituent electronegativity, are most likely to impart subtle but important di erences in the reactivities of key functional groups. The long-term plan is that more detail could be added to pharmacophores, but that these would be minimal, and would be informed by model-independent, physical characteristics of the functional groups that they are meant to represent. These refined pharmacophores would yield far fewer ‘‘hits’’ on initial screening, potentially enabling high-fidelity quantum mechanical modeling of the binding of all ‘‘first cut’’ molecules to the targeted active site, thus yielding a ‘‘final cut’’ of much higher quality.

To flesh-out the reactive sites of pharmacophores we have used volume rendering of the Laplacian of the charge density. We previously demonstrated that this graphical technique is very e ective for identifying physical features associated with hydrogen-bond-donor sites of di erent strength, and plainly apparent discrimination between hydrophilic and hydrophobic regions, all without the benefit of ‘‘rules’’ [3]. To best identify subtle di erences between corresponding functional groups of similar, but not identical, molecules we have explored the use of the recently developed hyperwall at NASA Ames [4].

These visualization technologies, and several insights into how pharmacophores might be most e ciently augmented, are discussed in greater detail below.

19.2

Computational and Visualization Methods

19.2.1

Computational Details

All the electron densities discussed here are obtained from ab initio electronicstructure calculations. With the exception of cisplatin, they are all at the Hartree– Fock level, with all-electron basis sets of high-quality (double-zeta plus polarization, or better). The cisplatin charge density was derived from an MP2 calculation employing an e ective core potential [5]. All computational details, for example software packages used, basis sets, geometric data, and any optimization constraints, can be found in the references cited.

19.2.2

Volume Rendering of the Laplacian of the Charge Density

It has been amply demonstrated, for large and small molecules and for crystals, and with representation from di erent regions of the periodic table, that sites of chemical reactivity can be related to the subtle and subatomic ‘‘lumps and holes’’