Surfaces - molecular

Ramsay-Shields equation An equation relating the molecular surface energy of a liquid with its temperature... 

The experimental study of detergency ranges from the very practical to the molecular surface-sensitive approaches discussed in this book. In more practical studies, model... 

Overney R, Howald L, Frommer J, Meyer E and Guntherodt H 1991 Molecular surface structure of tetracene mapped by the atomic force microscope J. Chem. Phys. 94 8441... 

Extraction of a ligand from the binding pocket of a protein. The force (represented by an arrow) applied to the ligand (shown in van der Waals spheres) leads to its dissociation from the binding pocket of the protein (a slice of the protein represented as a molecular surface is shown). 

Connolly, M. L. Analytical molecular surface calculation. J. Appl. Crystallogr. 16 (1983) 548-558... 

To be introduced to molecular surfaces and to different models for visualization... 

The representation of molecular surfaces, including the display of molecular surface properties, can be regarded as the next level of this hierarchy, but will be addressed in Sections 2,10 and 2,11 in this volume. 

Figure2-116. Graphical representations of molecular surfaces of phenylalanine a) dots b) mesh or chicken-wire c) solid d) semi-transparent,...

Depending on the application, models of molecular surfaces arc used to express molecular orbitals, clcaronic densities, van dor Waals radii, or other forms of display. An important definition of a molecular surface was laid down by Richards [182] with the solvent-accessible envelope. Normally the representation is a cloud of points, reticules (meshes or chicken-wire), or solid envelopes. The transparency of solid surfaces may also be indicated (Figure 2-116). 

The following models describe those definitions of molecular surfaces that are most widely used. The van dcr Waals surface, the solvent-accessible surface, and the Connolly surface (sec below) based on Richards definitions play a major role [182],... 

The interpretation of molecular surfaces is particularly important wherever molecular interactions, reactions, and properties play a dominant role, such as in drug design or in docking c.xpcrimcnts. 

The van der Waals surface (or the hard sphere model, also known as the scale model or the corresponding space-filling model) is the simplest representation of a molecular surface. It can be determined from the van dcr Waals radii of all... 

Whereas the contact region is the basis in the Connolly method, the center of the solvent-sphere determines the shape of the molecular. surface in the SAS method. In this case, the resulting surface is larger and the transition between the different atoms is more significant. 

Figure 2-120. The center ofthe rolling probe sphere defines the solvent-accessible surface during movement of the probe over the van der Waals surface. Thus, the molecular surface is expanded by the radius of the solvent molecule,...

The molecular surface of receptor site regions cannot be derived from the structure infoi mation of the molecule, bth represents the form ofthe active site of a protein surrounded by a ligand. This surface representation is employed in drug design in order to illustrate the volume of the pocket region or the molecular interaction layers [186. ... 

Besides the expressions for a surface derived from the van der Waals surface (see also the CPK model in Section 2.11.2.4), another model has been established to generate molecular surfaces. It is based on the molecular distribution of electronic density. The definition of a Limiting value of the electronic density, the so-called isovalue, results in a boundary layer (isoplane) [187]. Each point on this surface has an identical electronic density value. A typical standard value is about 0.002 au (atomic unit) to represent electronic density surfaces. 

A completely new method of determining siufaces arises from the enormous developments in electron microscopy. In contrast to the above-mentioned methods where the surfaces were calculated, molecular surfaces can be determined experimentally through new technologies such as electron cryomicroscopy [188]. Here, the molecular surface is limited by the resolution of the experimental instruments. Current methods can reach resolutions down to about 10 A, which allows the visualization of protein structures and secondary structure elements [189]. The advantage of this method is that it can be apphed to derive molecular structures of maaomolecules in the native state. 

As the graphical capabilities of the computer systems became more powerful simultaneously the number of visualized structures increased. With the introduction of raster graphics (1974) and colored raster graphics displays (1979), other forms of molecular representations were possible [197]. CPK models could be represented and colored bonds or molecular surfaces could be visualized. 

To display properties on molecular surfaces, two different approaches are applied. One method assigns color codes to each grid point of the surface. The grid points are connected to lines chicken-wire) or to surfaces (solid sphere) and then the color values are interpolated onto a color gradient [200]. The second method projects colored textures onto the surface [202, 203] and is mostly used to display such properties as electrostatic potentials, polarizability, hydrophobidty, and spin density. 

The representation of molecular properties on molecular surfaces is only possible with values based on scalar fields. If vector fields, such as the electric fields of molecules, or potential directions of hydrogen bridge bonding, need to be visualized, other methods of representation must be applied. Generally, directed properties are displayed by spatially oriented cones or by field lines. 

Molecular surfaces can express various chemical and physical properties, such as electrostatic potential, atomic charges or hydrophobicity, using colored mapping. 

P.G. Mezey, Molecular surfaces, in Reviews in Computational Chemistry, K. Lipko-witz, D. Boyd (Eds.), VCH, Weinheim, 1990, pp. 265-294. 

The MEP at the molecular surface has been used for many QSAR and QSPR applications. Quantum mechanically calculated MEPs are more detailed and accurate at the important areas of the surface than those derived from net atomic charges and are therefore usually preferable [Ij. However, any of the techniques based on MEPs calculated from net atomic charges can be used for full quantum mechanical calculations, and vice versa. The best-known descriptors based on the statistics of the MEP at the molecular surface are those introduced by Murray and Politzer [44]. These were originally formulated for DFT calculations using an isodensity surface. They have also been used very extensively with semi-empirical MO techniques and solvent-accessible surfaces [1, 2]. The charged polar surface area (CPSA) descriptors proposed by Stanton and Jurs [45] are also based on charges derived from semi-empirical MO calculations. 

The calculation of autocorrelation vectors of surface properties [25] is similar (Eq. (21), with the distance d XiXj) between two points and Xj on the molecular surface within the interval between d[ and d a certain property p, e.g., the electrostatic potential (ESP) at a point on the molecular surface and the number of distance intervals 1). 

The component of the autocorrelation vector for a certain distance interval between the boundaries 4 and du is the sum of the products of the property p x,) at a point Xi on the molecular surface with the same property p Xj) at a point Xj within a certain distance d Xj,Xj) normalized by the number of distance intervals 1. All pairs of points on the surface are considered only once. 

The representation of molecules by molecular surface properties was introduced in Section 2.10. Different properties such as the electrostatic potential, hydrogen bonding potential, or hydrophobicity potential can be mapped to this surface and seiwe for shape analysis [44] or the calculation of surface autocorrelation vectors (refer to Section 8.4.2). 

The possibilities for the application for neural networks in chemistry arc huge [10. They can be used for various tasks for the classification of structures or reactions, for establishing spcctra-strncturc correlations, for modeling and predicting biological activities, or to map the electrostatic potential on molecular surfaces. 

D descriptors), the 3D structure, or the molecular surface (3D descriptors) of a structure. Which kind of descriptors should or can be used is primarily dependent on the si2e of the data set to be studied and the required accuracy for example, if a QSPR model is intended to be used for hundreds of thousands of compounds, a somehow reduced accuracy will probably be acceptable for the benefit of short processing times. Chapter 8 gives a detailed introduction to the calculation methods for molecular descriptors. 

Methods of analyzing the diversity of the selected subset ensure that an appropriate chemical space is covered. Descriptors such as fingerprints, and 2D, and 3D descriptors, as well as molecular surface properties, which can be... 

Fig. l.fi. The van tier Waals (vdw) surface of a molecule corresponds to the outward-facing surfaces of the van der Waak spheres of the atoms. The molecular surface is generated hy rolling a spherical probe (usually of radius 1.4 A to represent a mater molecule) on the van der Wools surface. The molecular surface is consiructed from contact and re-entrant surface elements. The centre of the probe traces out the accessible surface. 

C/jnnolly M L 1983b. Analytical Molecular Surface Calculation. Journal of Applied Crystallography 16 548-558. 

Non-covalent interactions between molecules often occur at separations where the van der Waals radii of the atoms are just touching and so it is often most useful to examine the electrostatic potential in this region. For this reason, the electrostatic potential is often calculated at the molecular surface (defined in Section 1.5) or the equivalent isodensity surface as shown in Figure 2.18 (colour plate section). Such pictorial representations... 

Ire boundary element method of Kashin is similar in spirit to the polarisable continuum model, lut the surface of the cavity is taken to be the molecular surface of the solute [Kashin and lamboodiri 1987 Kashin 1990]. This cavity surface is divided into small boimdary elements, he solute is modelled as a set of atoms with point polarisabilities. The electric field induces 1 dipole proportional to its polarisability. The electric field at an atom has contributions from lipoles on other atoms in the molecule, from polarisation charges on the boundary, and where appropriate) from the charges of electrolytes in the solution. The charge density is issumed to be constant within each boundary element but is not reduced to a single )oint as in the PCM model. A set of linear equations can be set up to describe the electrostatic nteractions within the system. The solutions to these equations give the boundary element harge distribution and the induced dipoles, from which thermodynamic quantities can be letermined. 

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