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MM/CG approach applied to receptors

Ligand-protein docking is currently an important tool in drug discovery efforts; indeed, in the last years, structure-based drug design protocols have been the subject of important developments in general, and in particular in neurobiology. Despite the high levels of accuracy of computational tools, there are still important challenges if we want to deeply characterize the mechanism of interaction between neuronal receptors and their cognate ligands. Undertaking these challenges is of fundamental importance on protein classes of the upmost neurobiological relevance like G-protein coupled receptors (GPCRs). Combining modeling techniques with extensive MD simulations helps understanding the mechanisms underlying the interaction of the receptors with their agonists/inhibitors/drugs. Still this approach can be very CPU intensive. A possible strategy to address this issue is to combine atomistic with coarse-grained modelling, through a hybrid "Molecular Mechanics/Coarse-Grained" (MM/CG) scheme. In this approach, a region of interest (the binding site) is treated at molecular mechanics (MM) level using an atomistic force field while the rest of the system is described at coarse grained (CG) level. This MM/CG hybrid scheme allows the simulation of complex biological systems on length-scales and timescales that are inaccessible for all-atoms molecular dynamics simulations and can provide the atomic description of the intermolecular ligand/protein interactions. Moreover, by restricting the atomistic representation to a limited region of interest, we allow the side chains to relax much more quickly than in an all-atom simulation. We have adapted a hybrid molecular mechanics/coarse-grained (MM/CG) approach, applied previously to enzymes [1], to GPCR/ligand complexes.

Regions of different resolution in the MM/CG modelFigure 1 – Regions of different resolution in the MM/CG model.

In our scheme (Figure 1), the potential energy function reads:

V = EMM +EI + EMM/I +ECG + ECG/I+ ESD

EMM is the potential describing at atomistic resolution the residues in the binding site using the GROMOS96 43a1 force field and a droplet of water molecules using the SPC model. ECG describes the part of the receptor far from the binding site in terms of a Go-like potential between beads centred on the Cα atoms. Specifically, the bonded interactions are represented by a quartic potential, while the non-bonded interactions are represented by a Morse potential. EI refers to the interface region (I), located between the MM and the CG parts, which is treated with the MM potential. The terms EMM/I and ECG/I represent cross-terms interactions. EMM/I has the same form of the potential used in the MM region, while ECG/I has the form of the potential used for the CG region, where the bonded interactions act now between the beads of the CG region and the Cα atoms of the I region and the non-bonded interactions act between the CG beads and either the Cα or the Cβ atoms of the I region. This term ensures the protein backbone integrity. ESD mimics the stochastic and frictional forces acting on the system. Five virtual walls are built around the receptor (Figure 2) in order to mimic the presence of the membrane and prevent solvent evaporation. Correspondingly, five boundary potentials, defined as functions of the distance from the relevant walls, are added to the MM/CG potential energy function. Specifically, ϕ5 is expressed by a softened Lennard-Jones-like potential (2-1), which mimics the protein-membrane interaction, while ϕ1,2,3,4 are described by a repulsive potential (∝1/d, where d is the distance from the corresponding walls), which prevents solvent permeation through the membrane (ϕ1,2) and solvent evaporation (ϕ3,4). More details on the methodology can be found in [2].

MM/CG potentials to mimic the presence of lipid bilayerFigure 2 – Five walls around the GPCR are used to mimic the presence of lipid bilayer and prevent water evaporation: the planar walls (?1,2) are located at the height of the membrane lipids head, the outer walls (?3,4) are the two hemispheres, the membrane wall (?5) is the surface around the protein. Close-up: Final simulated system. MM and I regions are emphasized by licorice.

In order to improve the description of the solvation shell and avoid possible artifacts due to the boundary conditions imposed by the water droplet, we are currently working on the implementation of an adaptive resolution scheme in collaboration with Dr. Raffaello Potestio (Max-Planck Institute, Mainz). This scheme allows water molecules to freely diffuse across the regions at different resolutions (Fig. 3). Water molecules change on the fly their resolution while their density is maintained uniform and the temperature balanced between the two regions.

MM/CG model combined with an adaptive resolution scheme for the solventFigure 3 – MM/CG model combined with an adaptive resolution scheme for the solvent. Water molecules freely diffuse across the MM and CG regions changing on the fly their resolution. Dashed lines include the transition region (I solvent) for water molecules, where high- and low-resolution regimes are smoothly coupled.

References

[1] Neri M, Baaden M, Carnevale V, Anselmi C, Maritan A, et al. (2008) Microseconds Dynamics Simulations of the Outer-Membrane Protease T. Biophysical Journal. 94: 71–78. doi: 10.1529/biophysj.107.116301

[2] Leguebe M, Nguyen C, Capece L, Hoang Z, Giorgetti A, et al. (2012) Hybrid molecular mechanics/coarse-grained simulations for structural prediction of G-protein coupled receptor/ligand complexes. PLoS ONE 7: e47332. doi: 10.1371/journal.pone.0047332


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