Solvent accessibility

In Equation 10.7, is in units of h, and T is the temperature in degrees Celsius at which the hydrogen exchange reaction is performed. 

The earlier strategy was used to evaluate the PF values associated with five histidine residues in the DHFR enzyme system when the enzyme was in its apo form and when the enzyme was conplexed with folate and NADP-t (see Table 10.2) [28]. The measured PF values ranged from 1.1 to 31.5. The three-dimensional structures of apo-DHFR and DHFR-folate-NADP-t complex have been solved by X-ray crystallography [31]. Therefore, it was possible to determine the solvent-accessible surface area at the 

Residue Protection factor Solvent-accessible surface area (A )  

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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],... 

Tn general, the. solvent-accessible surface (SAS) represents a specific class of surfaces, including the Connolly surface. Specifically, the SAS stands for a quite discrete model of a surface, which is based on the work of Lee and Richards [182. They were interested in the interactions between protein and solvent molecules that determine the hydrophobicity and the folding of the proteins. In order to obtain the surface of the molecule, which the solvent can access, a probe sphere rolls over the van der Waals surface (equivalent to the Connolly surface). The trace of the center of the probe sphere determines the solvent-accessible surjace, often called the accessible swface or the Lee and Richards surface (Figure 2-120). Simultaneously, the trajectory generated between the probe and the van der Waals surface is defined as the molecular or Connolly surface. 

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 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. 

SASA Solvent-Accessible Surface Area Q . Average of absolule alomic charges... 

SAVOL Solvent-Accessible Volume Maximum positive charge on hydrogen atom... 

Connolly M L 1983a. Solvent-accessible Surfaces of Proteins and Nucleic Acids. Science 221 709-713. 

Richmond T J 1984. Solvent Accessible Surface Area and Excluded Volume in Proteins. Journal oj Molecular Biology 178 63-88. 

Breslow studied the dimerisation of cyclopentadiene and the reaction between substituted maleimides and 9-(hydroxymethyl)anthracene in alcohol-water mixtures. He successfully correlated the rate constant with the solubility of the starting materials for each Diels-Alder reaction. From these relations he estimated the change in solvent accessible surface between initial state and activated complex " . Again, Breslow completely neglects hydrogen bonding interactions, but since he only studied alcohol-water mixtures, the enforced hydrophobic interactions will dominate the behaviour. Recently, also Diels-Alder reactions in dilute salt solutions in aqueous ethanol have been studied and minor rate increases have been observed Lubineau has demonstrated that addition of sugars can induce an extra acceleration of the aqueous Diels-Alder reaction . Also the effect of surfactants on Diels-Alder reactions has been studied. This topic will be extensively reviewed in Chapter 4. 

We conclude that the beneficial effects of water are not necessarily limited to reactions that are characterised by a negative volume of activation. We infer that, apart from the retro Diels-Alder reaction also other reactions, in which no significant reduction or perhaps even an increase of solvent accessible surface area takes place, can be accelerated by water. A reduction of the nonpolar nature during the activation process is a prerequisite in these cases. 

The solvent accessible surface area (SASA) method is built around the assumption that the greatest amount of interaction with the solvent is in the area very close to the solute molecule. This is accounted for by determining a surface area for each atom or group of atoms that is in contact with the solvent. The free energy of solvation AG° is then computed by... 

The conductor-like screening model (COSMO) is a continuum method designed to be fast and robust. This method uses a simpler, more approximate equation for the electrostatic interaction between the solvent and solute. Line the SMx methods, it is based on a solvent accessible surface. Because of this, COSMO calculations require less CPU time than PCM calculations and are less likely to fail to converge. COSMO can be used with a variety of semiempirical, ah initio, and DFT methods. There is also some loss of accuracy as a result of this approximation. 

SAMI (semi-nh initio method one) a semiempirical method SASA (solvent-accessible surface area) algorithm for computing solvation elfects... 

Fig. 5. A representation of ranitidine displaying four layers of the Connolly solvent-accessible dot surface normally color-coded in this process to correspond with the energies of electrostatic potential (color not shown here). Thus, the highest charge density would be indicated by red dots representing points where the attraction to an atom is strongest, and conversely, purple points would signify regions of maximal positive charge.

In the following sections, we describe an implicit solvent model based on this free energy decomposition that is widely used in biophysics. It consists in representing the nonpolar free energy contributions on the basis of the solvent-accessible surface area... 

In Section III we described an approximation to the nonpolar free energy contribution based on the concept of the solvent-accessible surface area (SASA) [see Eq. (15)]. In the SASA/PB implicit solvent model, the nonpolar free energy contribution is complemented by a macroscopic continuum electrostatic calculation based on the PB equation, thus yielding an approximation to the total free energy, AVP = A different implicit... 

Figure 4 Sample spatial restraint m Modeller. A restraint on a given C -C , distance, d, is expressed as a conditional probability density function that depends on two other equivalent distances (d = 17.0 and d" = 23.5) p(dld, d"). The restraint (continuous line) is obtained by least-squares fitting a sum of two Gaussian functions to the histogram, which in turn is derived from many triple alignments of protein structures. In practice, more complicated restraints are used that depend on additional information such as similarity between the proteins, solvent accessibility, and distance from a gap m the alignment.

JU Bowie, ND Clarke, CO Paho, RT Sauer. Identification of protein folds Matching hydro-phohicity patterns of sequence sets with solvent accessibility patterns of known structures. Proteins Struct Func Genet 7 257-264, 1990. 

MJ Thompson, RA Goldstein. Predicting solvent accessibility Higher accuracy using Bayesian statistics and optimized residue substitution classes. Proteins Struct Funct Genet 25 38-47, 1996. 

The simplest shape for the cavity is a sphere or possibly an ellipsoid. This has the advantage that the electrostatic interaction between M and the dielectric medium may be calculated analytically. More realistic models employ moleculai shaped cavities, generated for example by interlocking spheres located on each nuclei. Taking the atomic radius as a suitable factor (typical value is 1.2) times a van der Waals radius defines a van der Waals surface. Such a surface may have small pockets where no solvent molecules can enter, and a more appropriate descriptor may be defined as the surface traced out by a spherical particle of a given radius rolling on the van der Waals surface. This is denoted the Solvent Accessible Surface (SAS) and illustrated in Figm e 16.7. 

The cavity/dispersion terms are parameterized according to the solvent accessible surface, as in eq. (16.43). 

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