Van der Waals sphere

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). 

The acce.ssible surface is also widely used. As originally defined by Lee and Richards [Lee and Richai ds 1971] this is the surface that is traced by the centre of the probe molecule as it rolls on the van der Waals surface of the molecule (Figure 1.6). The centre of the probe molecule can thus be placed at any point on the accessible surface and not penetrate the van der Waals spheres of any of the atoms in the molecule. 

The PCM algorithm is as follows. First, the cavity siuface is determined from the van der Waals radii of the atoms. That fraction of each atom s van der Waals sphere which contributes to the cavity is then divided into a nmnber of small surface elements of calculable surface area. The simplest way to to this is to define a local polar coordinate frame at tlie centre of each atom s van der Waals sphere and to use fixed increments of AO and A(p to give rectangular surface elements (Figure 11.22). The surface can also be divided using tessellation methods [Paschual-Ahuir d al. 1987]. An initial value of the point charge for each surface element is then calculated from the electric field gradient due to the solute alone ... 

Lonally, the templates were chosen by trial and error or exhaustive enumeration. A itafional method named ZEBEDDE (ZEolites By Evolutionary De novo DEsign) en developed to try to introduce some rationale into the selection of templates et al. 1996 Willock et al. 1997]. The templates are grown within the zeolite by an iterative inside-out approach, starting from a seed molecule. At each jn an action is randomly selected from a list that includes the addition of new (from a library of fragments), random translation or rotation, random bond rota-ing formation or energy minimisation of the template. A cost function based on erlap of van der Waals spheres is used to control the growth of the template ale ... 

Figure 16.7 On a surface generated by overlapping van der Waals spheres there will be areas (hatch) which are inaccessible to a solvent molecule (dotted sphere)...

The 21//,22//-tautomer 2 with hydrogens at adjacent pyrrole rings is less stable because of penetration of each hydrogen into the van der Waals sphere of the other. However, NMR studies with unsymmetrically substituted porphyrins at low temperature have allowed the observation of both tautomers 1 and 2. The kinetic parameters of tautomerism investigated by NMR measurements at different temperatures are consistent with a two-step process forming 3 from 1 via 2 rather than a concerted two-hydrogen shift which could form 3 from 1 directly. 

Figure 10-5. Representative conformations of the (5 amyloid peptide (10-42) under different pH conditions. The conformations were obtained as centroids of the most populated clusters from the replica-exchange CPHMD folding simulations [43, 44]. The N-terminal residues 10-28 are shown in blue the C-terminal residues 29-42 are shown in red. In the most aggregation-prone state (pH 6), the side chains of the central hydrophobic cluster Leu-17, Val-18, Phe-19, Phe-20 and Ala-21 are shown as van der Waals spheres in pink, grey, cyan, purple and green, respectively...

Fig. 6. Comparative projections along the c axis of the diol molecules and the canals they enclose in 1, 2,3,8 and 9. The bond thickening signifies depth in individual molecules only, because the helical characteristic is absent from these projections of the lattice. The canal boundaries are marked as the intersecting projected van der Waals spheres of the hydrogen atoms which line the canals. All five diagrams are presented on the same scale. Significant hydrogen atoms are marked as filled circles, and the spines are circled...

Fig. 3.2 The structure of myoglobin (deoxy form, PDB entry 1AGN, at 1.15 A resolution [3f]). The heme active center is highlighted (van der Waals spheres), as are the proximal and distal histidines (His93 and His64, respectively, shown as sticks).

Fig. 11. Overlap (cross-striped part) of van der Waals spheres neglected in estimation of the van der Waals volume according to Bondi72)...

Figure 11 Details of the calculation of the maximum semicone angle, 6/2. The point of contact of the cone-generating vector M - X from the metal, with the van der Waals sphere of the hydrogen atom, is coplanar with the metal, phosphorus and...

Figure 9.43 Single crystal X-ray structures of IRMOF-n (n = 1 — 7,8,10,12,14, and 16), labelled respectively. MOF-5 is re-designated IRMOF-1 as part of this series. IRMOFs 9,11,13, and 15 are doubly interpenetrated. Zn (II) tetrahedral shown as polyhedra. The large spheres represent the largest van der Waals spheres that fit in the cavities without touching the frameworks (reprinted from [47] with permission from AAAS).

Fig. 4 is a drawing of an all-valence-shell-electron-domain model of ethane superimposed on the molecule s conventional graphic formula. Not shown are the electron-domains of the carbon atoms Is electrons. In Fig. 4, each valence-stroke, i.e. each valence-shell electron-pair of ethane, protonated ("C—H") or unprotonated ( C—C"), is represented by a van der Waals sphere. 

Fig. 3.5 Two substrate oxidation sites in VP left, Oxidation site for high redox-potential substrates (such as VA, RB5, and lignin) by a LRET pathway (dotted arrow) from a tryptophan residue forming a catalytic neutral radical (W164-) to a heme methyl group via a leucine residue [57-59] right, Oxidation site for Mn2+, at the internal propionate of heme, involving three acidic amino acid residues [10]. Axial view of the heme region (a water molecule, represented as van der Waals spheres, is seen at the top position on the heme iron)...

Fig. 3.6 Solvent access surfaces (colors represent electrostatic potentials) showing the exposed tryptophan residue (as yellow van der Waals spheres) involved in oxidation of lignin and other high redox-potential substrates by VP (a) and LiP (b). Lignin can be directly oxidized by VP at the tryptophan radical, while LiP requires the simultaneous presence of VA (synthesized by the fungus) acting as an enzyme-bound mediator [74]. Based on VP and LiP crystal structures (PDB 2BOQ and 1LLP, respectively)...

Let us imagine the charges e of the dipole at the positions of the nuclei of the atoms such that s d = fx. The minimum distance for the negative pole of the C—Cl dipole is then determined by the Van der Waals radius of the chlorine atom (Table 17) this is 1.8 A. With the OH group the Van der Waals radius measured from the nucleus of the oxygen atom is 1.40 A. Since the O—H distance is 0.97 A, however, the shortest distance for the (positive) pole to the edge of the Van der Waals sphere is now 0.43 A. 

More specific to low-dimensional organic conductors is the approach of Chasseau [69]. The conductivity was assumed to be directly related to the efficiency of the molecular overlap between adjacent moieties within TCNQ stacks. This overlap efficiency was quantized on the basis of the total intersection volume between van der Waals spheres attached to each atom. This method, although very approximate, gave good results for ammonium... 

A QSAR approach based on a set of methods that combines molecular shape similarity and commonality measures with other - molecular descriptors both to search for similarities among molecules and to build QSAR models [Hopfinger, 1980 Burke and Hopfinger, 1993], The term molecular shape similarity refers to molecular similarity on the basis of a comparison of three-dimensional molecular shapes represented by some property of the atoms composing the molecule, such as the van der Waals spheres. TTie molecular shape commonality is the measure of molecular similarity when conformational energy and molecular shape are simultaneously considered [Hopfinger and Burke, 1990]. 

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