Analyzing GPCR-Ligand Interactions with the Fragment Molecular Orbital (FMO) Method

G-protein-coupled receptors (GPCRs) have enormous physiological and biomedical importance, and therefore it is not surprising that they are the targets of many prescribed drugs. Further progress in GPCR drug discovery is highly dependent on the availability of protein structural information. However, the ability of X-ray crystallography to guide the drug discovery process for GPCR targets is limited by the availability of accurate tools to explore receptor-ligand interactions. Visual inspection and molecular mechanics approaches cannot explain the full complexity of molecular interactions. Quantum mechanics (QM) approaches are often too computationally expensive to be of practical use in time-sensitive situations, but the fragment molecular orbital (FMO) method offers an excellent solution that combines accuracy, speed, and the ability to reveal key interactions that would otherwise be hard to detect. Integration of GPCR crystallography or homology modelling with FMO reveals atomistic details of the individual contributions of each residue and water molecule toward ligand binding, including an analysis of their chemical nature. Such information is essential for an efficient structure-based drug design (SBDD) process. In this chapter, we describe how to use FMO in the characterization of GPCR-ligand interactions

Computational Methods Used in Hit-to-Lead and Lead Optimization Stages of Structure-Based Drug Discovery

GPCR modeling approaches are widely used in the hit-to-lead (H2L) and lead optimization (LO) stages of drug discovery. The aims of these modeling approaches are to predict the 3D structures of the receptor-ligand complexes, to explore the key interactions between the receptor and the ligand and to utilize these insights in the design of new molecules with improved binding, selectivity or other pharmacological properties. In this book chapter, we present a brief survey of key computational approaches integrated with hierarchical GPCR modeling protocol (HGMP) used in hit-to-lead (H2L) and in lead optimization (LO) stages of structure-based drug discovery (SBDD). We outline the differences in modeling strategies used in H2L and LO of SBDD and illustrate how these tools have been applied in three drug discovery projects

The importance of tunneling in the first hydrogenation step in ammonia synthesis over a Ru(0001) surface.

The hydrogenation of nitrogen (N(ads)+H(ads)-->NH(ads)) on metal surfaces is an important step in ammonia catalysis. We investigate the reaction dynamics of this hydrogenation step by time independent scattering theory and variational transition state theory (VTST) including tunneling corrections. The potential energy surface is derived by hybrid density functional theory on a model cluster composed of 12 ruthenium atoms resembling a Ru(0001) surface. The scattering calculations are performed on a reduced dimensionality potential energy hypersurface, where two dimensions are treated explicitly and all others are included implicitly by the zero-point correction. The VTST calculations include quantum effects along the reaction coordinate by applying the small curvature tunneling scheme. Even at room temperature (where ruthenium already shows catalytic activity) we find rate enhancement by tunneling by a factor of approximately 70. Inspection of the reaction probabilities shows that the major contribution to reactivity comes from the vibrational ground state of the reactants into vibrationally excited product states. The reaction rates are higher than determined in previous studies, and are compatible with experimental overall rates for ammonia synthesis

Comparative study of cluster- and supercell-approaches for investigating heterogeneous catalysis by electronic structure methods: tunneling in the reaction N + H --> NH on Ru(0001).

Different ruthenium clusters of various sizes are constructed with the aim to model the Ru(0001) surface with a sufficient accuracy for predicting catalysis by hybrid density functional methods (B3LYP). As an example reaction the hydrogenation step N(ads) + H(ads) --> NH(ads) from the catalytic production cycle of ammonia is chosen. A cluster of 12 ruthenium atoms is found to reproduce experimental geometries and frequencies of the various reactants on the surface satisfyingly. To get the geometries of adsorbed hydrogen qualitatively correct it is shown that second layer atoms have to be included in the model cluster. Boundary effects are believed to have minor effects on optimized geometries, whereas the effects on reaction barriers are significant. A comparison of model cluster calculations to a periodic supercell approach employing plane waves and density functional methods (RPBE) reveals similar barriers for reaction. The influence of tunneling in this reaction is determined by the small curvature tunneling approach on the electronic surfaces

Rates of the reaction C2H3+H-2 -> C2H4+H

The reaction C2H3 + H2 → C 2H4 + H has been studied by different direct ab initio approaches. Accurate rate constants in the temperature range 200-1200 K have been derived by time-independent scattering theory, employing R-matrix propagation on a 2D reduced dimensional G3B3 potential energy surface. Reported experimental reaction rates at room temperature vary over 3 orders of magnitude as they have to be determined indirectly. The computed room temperature rate of 2.1 × 10-18 cm3 molecule-1 s-1 in this study should remove this ambiguity. At higher temperatures the calculated rates meet experimental rates from direct measurements very well. The use of a reduced dimensionality model is justified by comparing full-dimensional semiclassical tunnelling contributions to those derived on a 2D potential with the same method. The employed semiclassical approach (small curvature tunnelling) yields very similar rates to the scattering approach, thus showing that small curvature tunnelling is a very reliable method to describe reactions like these

Rates of the reaction C2H3+H-2 -> C2H4+H

The reaction C2H3 + H2 → C 2H4 + H has been studied by different direct ab initio approaches. Accurate rate constants in the temperature range 200-1200 K have been derived by time-independent scattering theory, employing R-matrix propagation on a 2D reduced dimensional G3B3 potential energy surface. Reported experimental reaction rates at room temperature vary over 3 orders of magnitude as they have to be determined indirectly. The computed room temperature rate of 2.1 × 10-18 cm3 molecule-1 s-1 in this study should remove this ambiguity. At higher temperatures the calculated rates meet experimental rates from direct measurements very well. The use of a reduced dimensionality model is justified by comparing full-dimensional semiclassical tunnelling contributions to those derived on a 2D potential with the same method. The employed semiclassical approach (small curvature tunnelling) yields very similar rates to the scattering approach, thus showing that small curvature tunnelling is a very reliable method to describe reactions like these

Reaction rates of all hydrogenation steps in ammonia synthesis over a Ru(0001) surface

The hydrogenation reactions of nitrogen (NH n, (ads) + H (ads) → NH n + 1, (ads), n = 0, 1, 2) on metal surfaces are important elementary steps in the catalytic formation of ammonia. We investigate the reaction dynamics of these hydrogenations on a Ru(0001) surface using transition state theory, including small curvature tunneling corrections. Potential energy surfaces are derived by density functional theory (RPBE) in two or three dimensions. Tunneling is shown to enhance rates significantly for the first two hydrogenation steps at low and ambient temperatures, doubling reaction rates even at temperatures of 400 K. However, tunneling plays no significant role at current synthesis temperatures. © 2006 Elsevier Inc. All rights reserved

The thermodesorption mechanism of ammonia from Ru(0001)

Thermodesorption rates for the desorption of ammonia from Ru(0 0 0 1) are calculated by Transition State Theory including small curvature tunneling corrections. The potential energy surface is derived on a model cluster employing hybrid density functional theory (B3LYP). Two desorption pathways can be identified, just distinguished by the orientation of the leaving ammonia entity. It is found that the rate dominating mechanism comprises an umbrella-like flipping movement of the hydrogen atoms during the desorption. Nevertheless tunneling does not play any significant role in the reaction as the hydrogen movements are shown to occur at the low energy regions of the barrier. © 2006 Elsevier B.V. All rights reserved

An improved treatment of spectator mode vibrations in reduced dimensional quantum dynamics: application to the hydrogen abstraction reactions mu + CH4, H + CH4, D + CH4, and CH3 + CH4.

A method for projecting chemical reaction surface coordinates from a Hessian in curvilinear internal coordinates has recently been developed. Here we introduce a modification to this approach which allows for analytical evaluation of the necessary coordinate derivatives, thus reducing the number of ab initio calculations required. We apply this method to the determination of spectator mode frequencies and zero-point energies for the series of hydrogen abstraction reactions X + CH(4) --> XH + CH(3), X = muonium (mu), H, D, CH(3). Comparison of these frequencies with those obtained using rectilinear coordinates allows us to examine how the mass of X affects the coordinate sensitivity of the spectator modes. We carry out two-dimensional quantum reactive scattering calculations for these reactions to highlight instances where the choice of coordinates may have a significant impact on the evaluated thermal rate constants