Solvent accessible surfaces

Only a part of the van der Waals surface is accessible to solvent molecules because, as a rule, the solvent doesn t access the cavities of the analyzed molecule. The mathematical definition of a cavity, and then the identification and calculation of the surface of molecular cavities are not simple tasks (Pascual-Ahuir and Silla 1990 Rinaldi et al. 1992 Ulmscheider and Penigault 1999a Ulmscheider and Penigault 1999b). As a rule, the solvent-accessible surface is the locus of the center of a probe sphere rolling over the van der Waals surface. It was found that some biochemical properties correlate acceptably with the surface accessible to the solvent (Lee and Richards 1971 Shrake and Rupley 1973) and with the surface not accessible to the solvent (Connolly 1992). 

The COnductor-like Screening MOdel (COSMO) is a method that computes the electrostatic interaction of the analyzed molecule with a certain solvent by considering the dielectric continuum surrounding the solute molecule outside of molecular cavities (Klamt and Schuiirmann 1993). The COSMO method can be used by all methods that compute the net atomic charges in analyzed molecules, for example, the semiempirical quantum mechanics method PM6. 

The approximated surface calculation (ASC) procedure calculates partial atomic van der Waals surface areas through an analytical method (Ulmscheider and Penigault 1999a) and then the Gibbs free energy of hydration is calculated by considering it to be an additive property. The ASC procedure considers the hybridization state of the atoms. 

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. 

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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... 

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... 

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... 

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). 

AGg (X) can be removed by assuming that it is equivalent to the polar contribution to the free energy of solution of solute X in a nonpolar hydrocarbon solvent, such as squalane. A second reason for using a reference hydrocarbon solvent is to correct, at least partially, for the fact that the hardcore van der Haals volume is a poor estimate of the size of the cavity and its accessible surface for solvent interactions for aromatic and cyclic solutes. The solvent accessible surface area would logically be the preferred parameter for the cavity term but is very difficult to calculate while the van der Haals volume is readily accessible. With the above approximations the solvent interaction term for... 

If this hypothesis is true, one could expect the solvent-accessible surface area (ASA) of the polypeptide backbone in the PPII conformation to be correlated with measured PPII helix-forming propensities. In order to test this, Monte Carlo computer simulations of short peptides Ac-Ala-Xaa-Ala-NMe (Xaa = Ala, Asn, Gin, Gly, lie, Leu, Met, Pro, Ser, Thr, and Val) were run. These particular residues were examined because their... 

PPII helix-forming propensities have been measured by Kelly et al. (2001) and A. L. Rucker, M. N. Campbell, and T. P. Creamer (unpublished results). In the simulations the peptide backbone was constrained to be in the PPII conformation, defined as (0,VO = ( — 75 25°, +145 25°), using constraint potentials described previously (Yun and Hermans, 1991 Creamer and Rose, 1994). The AMBER/ OPLS potential (Jorgensen and Tirado-Rives, 1988 Jorgensen and Severance, 1990) was employed at a temperature of 298° K, with solvent treated as a dielectric continuum of s = 78. After an initial equilibration period of 1 x 104 cycles, simulations were run for 2 x 106 cycles. Each cycle consisted of a number of attempted rotations about dihedrals equal to the total number of rotatable bonds in the peptide. Conformations were saved for analysis every 100 cycles. Solvent-accessible surface areas were calculated using the method of Richmond (1984) and a probe of 1.40 A radius. 

The sum of the estimated average solvent-accessible surface areas, (ASA), for the peptide units (—CO—NH—) on either side of residue Xaa, plus the Ca of Xaa, in each peptide simulated are given in Table II. Also shown are the estimated PPII helix-forming propensities for each residue measured by Kelly et al. (2001) and A. L. Rucker, M. N. Campbell, and... 

Fig. 2.3 The solvent accessible surface (SAS) area corresponds to that mapped out by the center of a sphere representing the solvent molecule (gray) as it is rolled over the van der Waals surface of the solute (light gray). In the COSMO model, the SAS is then divided into a series of segments of area S and charge density cr, centered at a position R(j. ...

In (2.105), the assumption of the proportionality of solvent-accessible surface and cavity energy is explicitly shown, and therefore ak depends on the type of the k-atom interacting with the solvent. Ak(p ) is the complex function describing the solvent accessible surface area, and depends on p, which is defined by the following expression ... 

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