Evaluation of the protein solvent-accessible surface using reduced representations in terms of critical points of the electron density

The aim of our study is the development of a method for calculating the interface of dimerization of protein-protein complexes based on simplified medium-resolution structures. In particular, we wished to evaluate if the existing concepts for the computation of the Solvent-Accessible Surface Area (SASA) of macromolecules could be applied to medium-resolution models. Therefore, we selected a set of 140 protein chains and computed their reduced representations by topological analysis of their electron density maps at 2.85 A crystallographic resolution. This procedure leads to a limited number of critical points (CPs) that can be identified and associated to backbone and side-chain parts. To evaluate the SASA and interfaces of dimerization of the reduced representations, we chose and modified two existing programs that calculate the SASA of atomic representations, and tested (1) several radii tables of amino acids, (2) the influence of the backbone and side-chain points, and (3) the radius of the solvent molecule, which rolls over the surface. The results are shown in terms of relative error compared to the values calculated on the corresponding atomic representations of the proteins.     

Atoms-in-molecules analysis for planewave DFT calculations--a numerical approach on a successively interpolated charge density grid

We used a successive charge interpolation scheme and Ridders method for differentiation, to acquire accurate charge densities and their higher derivatives in electronic structure calculations. This enables us to search bond critical points using arbitrary charge density grids. We applied the planewave-DFT code, VASP, to generate the charge density of selected benchmark molecules. The properties of bond critical points are in good agreement with those obtained by complementary implementations. We validated our GRID implementation by performing electronic structure calculations using the Gaussian 03 program package and various tools for analysis of the charge density provided by the AIMPAC package. In particular, we carefully investigate the influence of effective core potentials on the location of bond critical points, especially for a short chemical bond, which is crucial in the present pseudopotential-based planewave DFT calculations. We expect our generic implementation will not only be useful for the analysis of chemical bonding in molecules, but will particularly provide a microscopic understanding of extended systems including periodic boundary conditions.     

Representation of molecular structure using quantum topology with inductive logic programming in structure–activity relationships

The requirement of aligning each individual molecule in a data set severely limits the type of molecules which can be analysed with traditional structure activity relationship (SAR) methods. A method which solves this problem by using relations between objects is inductive logic programming (ILP). Another advantage of this methodology is its ability to include background knowledge as 1st-order logic. However, previous molecular ILP representations have not been effective in describing the electronic structure of molecules. We present a more unified and comprehensive representation based on Richard Bader's quantum topological atoms in molecules (AIM) theory where critical points in the electron density are connected through a network. AIM theory provides a wealth of chemical information about individual atoms and their bond connections enabling a more flexible and chemically relevant representation. To obtain even more relevant rules with higher coverage, we apply manual postprocessing and interpretation of ILP rules. We have tested the usefulness of the new representation in SAR modelling on classifying compounds of low/high mutagenicity and on a set of factor Xa inhibitors of high and low affinity.     

Geminal model chemistry II. Perturbative corrections

We introduce and investigate a chemical model based on perturbative corrections to the product of singlet-type strongly orthogonal geminals wave function. Two specific points are addressed (i) Overall chemical accuracy of such a model with perturbative corrections at a leading order; (ii) Quality of strong orthogonality approximation of geminals in diverse chemical systems. We use the Epstein-Nesbet form of perturbation theory and show that its known shortcomings disappear when it is used with the reference Hamiltonian based on strongly orthogonal geminals. Application of this model to various chemical systems reveals that strongly orthogonal geminals are well suited for chemical models, with dispersion interactions between the geminals being the dominant effect missing in the reference wave functions.     

Molecular model with quantum mechanical bonding information

The molecular structure can be defined quantum mechanically thanks to the theory of atoms in molecules. Here, we report a new molecular model that reflects quantum mechanical properties of the chemical bonds. This graphical representation of molecules is based on the topology of the electron density at the critical points. The eigenvalues of the Hessian are used for depicting the critical points three-dimensionally. The bond path linking two atoms has a thickness that is proportional to the electron density at the bond critical point. The nuclei are represented according to the experimentally determined atomic radii. The resulting molecular structures are similar to the traditional ball and stick ones, with the difference that in this model each object included in the plot provides topological information about the atoms and bonding interactions. As a result, the character and intensity of any given interatomic interaction can be identified by visual inspection, including the noncovalent ones. Because similar bonding interactions have similar plots, this tool permits the visualization of chemical bond transferability, revealing the presence of functional groups in large molecules.     

On the suitability of strictly localized orbitals for hybrid QM/MM calculations

In the QM/MM method we have developed (LSCF/MM), the QM and the MM parts are held together by means of strictly localized bonding orbitals (SLBOs). Generally these SLBOs are derived from localized bond orbitals (LBOs) that undergo tails deletion, resulting in a nonpredictable change of their properties. An alternative set of SLBOs is provided by the extremely localized molecular orbitals (ELMOs) approach, where the orbitals are rigorously localized on some prefixed atoms without tails on the other atoms of the molecule. A comparative study of SLBOs arising from various localization schemes and ELMOs is presented to test the reliability and the transferability of these functions within the Local Self-Consistent Field (LSCF) framework. Two types of chemical bonds were considered: C--C and C--O single bonds. The localized functions are obtained on the ethane and the methanol molecules, and are tested on beta-alanine and diethyl ether molecules. Moreover, the various protonation forms of beta-alanine have been investigated to illustrate how well the polarity variation of the chemical bond can be handled throughout a chemical process. At last, rotation energy profiles around C--C and C--O bonds are reproduced for butane and fluoromethanol. Energetic, geometric, as well as electronic factors all indicate that ELMO functions are much more transferable from one molecule to another, leading to results closer to the usual SCF reference than any other calculations involving any other localized orbitals. When the shape of the orbital is the most important factor then ELMO functions will perform as well as any other localized orbital.     

Scaffold hopping using clique detection applied to reduced graphs

Similarity-based methods for virtual screening are widely used. However, conventional searching using 2D chemical fingerprints or 2D graphs may retrieve only compounds which are structurally very similar to the original target molecule. Of particular current interest then is scaffold hopping, that is, the ability to identify molecules that belong to different chemical series but which could form the same interactions with a receptor. Reduced graphs provide summary representations of chemical structures and, therefore, offer the potential to retrieve compounds that are similar in terms of their gross features rather than at the atom-bond level. Using only a fingerprint representation of such graphs, we have previously shown that actives retrieved were more diverse than those found using Daylight fingerprints. Maximum common substructures give an intuitively reasonable view of the similarity between two molecules. However, their calculation using graph-matching techniques is too time-consuming for use in practical similarity searching in larger data sets. In this work, we exploit the low cardinality of the reduced graph in graph-based similarity searching. We reinterpret the reduced graph as a fully connected graph using the bond-distance information of the original graph. We describe searches, using both the maximum common induced subgraph and maximum common edge subgraph formulations, on the fully connected reduced graphs and compare the results with those obtained using both conventional chemical and reduced graph fingerprints. We show that graph matching using fully connected reduced graphs is an effective retrieval method and that the actives retrieved are likely to be topologically different from those retrieved using conventional 2D methods.     

Lossless compression of chemical fingerprints using integer entropy codes improves storage and retrieval

Many modern chemoinformatics systems for small molecules rely on large fingerprint vector representations, where the components of the vector record the presence or number of occurrences in the molecular graphs of particular combinatorial features, such as labeled paths or labeled trees. These large fingerprint vectors are often compressed to much shorter fingerprint vectors using a lossy compression scheme based on a simple modulo procedure. Here, we combine statistical models of fingerprints with integer entropy codes, such as Golomb and Elias codes, to encode the indices or the run lengths of the fingerprints. After reordering the fingerprint components by decreasing frequency order, the indices are monotone-increasing and the run lengths are quasi-monotone-increasing, and both exhibit power-law distribution trends. We take advantage of these statistical properties to derive new efficient, lossless, compression algorithms for monotone integer sequences: monotone value (MOV) coding and monotone length (MOL) coding. In contrast to lossy systems that use 1024 or more bits of storage per molecule, we can achieve lossless compression of long chemical fingerprints based on circular substructures in slightly over 300 bits per molecule, close to the Shannon entropy limit, using a MOL Elias Gamma code for run lengths. The improvement in storage comes at a modest computational cost. Furthermore, because the compression is lossless, uncompressed similarity (e.g., Tanimoto) between molecules can be computed exactly from their compressed representations, leading to significant improvements in retrival performance, as shown on six benchmark data sets of druglike molecules.     

The problem of a self-consistent description of the equilibrium distribution of particles in three states of aggregation

The possibility of unified self-consistent calculations of equilibrium distributions of molecules in three states of aggregation within the framework of the lattice gas model is considered. The corresponding approach was generalized to arbitrary pressures with including the compressibility of lattice structures. Closed equations were obtained for calculating thermodynamic functions (including an equation for the chemical potential of mixture components) in the continuum quasi-chemical approximation. Their use ensures equally accurate calculations of interphase equilibria in gas-liquid-solid systems and the determination of the triple and critical points. Possibilities for simplifying the equations by passing to the effective pair interaction potential, which takes into account averaged vibrations and volume accessible to the translational motion of molecules of commensurate sizes, are considered.     

Students’ Microscopic, Macroscopic, and Symbolic Representations of Chemical Reactions

This study examined the mental representations of chemical reactions used by six students (three male, three female) who achieved above-average grades in a college freshman chemistry class at a large midwestern university. The representations expressed by the students in structured interviews were categorized as microscopic, macroscopic, or symbolic representations of chemical reactions. The study revealed that the participants did make at least some use of each of the three representations; however, there were wide variations among participants in the sophistication of the various representations they used and in their understanding of the relationships between representations. Also, participants receiving very similar course grades sometimes demonstrated very different conceptual understandings of chemical reactions.     

Topography of approximate molecular electrostatic potentials

A new method is described for the approximation of the molecular electrostatic potential (MESP). This method is used for the study of the topography of small molecules. The critical points of the approximate and the exact MESP are compared. It is found that most of the critical points of the exact MESP are retained, but in regions where the exact MESP changes slowly near critical points the number of critical points of the approximate MESP can be reduced.     

Diversity‐Oriented Approach for Chemical Biology

Synthetic molecules that modulate and probe biological events are critical tools in chemical biology. Utilizing combinatorial and diversity‐oriented synthetic strategies, access to large numbers of small molecules is becoming more and more feasible, and research groups in this field can take advantage of the power of chemical diversity. Since the majority of early studies were focused on the discovery of compounds that perturb protein functions, diversity‐based approaches are often considered as therapeutic lead discovery tactics. However, the diversity‐oriented approach can also be applied to advance distinct aims, such as target protein identification, or the development of imaging probes and sensors. This review provides a personal perspective of the chemical‐diversity‐based approach and how this principle can be adapted to various chemical biology studies.     

Spatial hydration maps and dynamics of naphthalene in ambient and supercritical water

The hydration structures and dynamics of naphthalene in aqueous solution are examined using molecular-dynamics simulations. The simulations are performed at several state points along the coexistence curve of water up to the critical point, and above the critical point with the density fixed at 0.3 g/cm(3). Spatial maps of local atomic pair-density are presented which show a detailed picture of the hydration shell around a bicyclic aromatic structure. The self-diffusion coefficient of naphthalene is also calculated. It is shown that water molecules tend to form pi-type complexes with the two aromatic regions of naphthalene, where water acts as the H-bond donor. At ambient conditions, the hydration shell of naphthalene is comprised, on average, of about 39 water molecules. Within this shell, two water molecules can be identified as pi-coordinating, forming close to one H-bond to the aromatic rings. With increasing temperature, the hydration of naphthalene changes dramatically, leading to the disappearance of the pi-coordination near the critical point.     

Application of multiresolution analyses to electron density maps of small molecules: Critical point representations for molecular superposition

Three different methods are applied to generate low resolution molecular electron density (ED) distribution functions: a crystallography-based formalism, an analytical approach which allows the calculation of a promolecular ED distribution in terms of a weighted summation over atomic ED distributions, and a wavelet-based multiresolution analysis approach. Critical point graph representations of the molecular ED distributions are then generated by locating points where the gradient of the density is equal to zero, and further considered for pairwise molecular superpositions of thrombin inhibitors using a Monte Carlo/Simulated Annealing technique.     

Critical point representations of electron density maps for the comparison of benzodiazepine-type ligands

A procedure for the comparison of three-dimensional electron density distributions is proposed for similarity searches between pharmacological ligands at various levels of crystallographic resolution. First, a graph representation of molecular electron density distributions is generated using a critical point analysis approach. Pairwise as well as multiple comparisons between the obtained graphs of critical points are then carried out using a Monte Carlo/simulated annealing technique, and results are compared with genetic algorithm solutions.