Accessible surface areas as a measure of the thermodynamic parameters of hydration of peptides.

Abstract

A method is described for the inclusion of the effects of hydration in empirical conformational energy computations on polypeptides. The free energy of hydration is composed of additive contributions of various functional groups. The hydration of each group is assumed to be proportional to the accessible surface area of the group. The constants of proportionality, representing the free energy of hydration per unit area of accessible surface, have been evaluated for seven classes of groups (occurring in peptides) by least-squares fitting to experimental free energies of solution of small monofunctional aliphatic and aromatic molecules. The same method has also been applied to the modeling of the enthalpy and heat capacity ofhydration, each of which is computed from the accessible surface area.The free energy of folding of a protein consists of the sum of contributions from the energy of its intramolecular interactions (1, 2) and from the free energy of interaction of the molecule with the surrounding solvent water. Exact computation of the latter contribution still poses problems (3). As a practical approach, hydration-shell models have been used. In these models, the free energy of interaction of water molecules with the solute is expressed in the form of an averaged effective potential of interaction of atoms (and functional groups) of a solute molecule with a layer of solvent around each atom (4-10)-i.e., in terms ofa potential ofmean force (3). An empirical free energy of hydration is assigned to every atom and group. When the conformation of the protein changes, some water is eliminated from the hydration shell whenever groups on the protein approach each other. The free energy change accompanying this process depends on the total free energy of hydration of the groups and on the amount of water being eliminated from the hydration shells. This amount, in turn, depends on the size and distance of separation of the groups that approach each other, and it can be computed by geometrical methods from the volumes of overlapping spheres (4-6, 10, 11).The hydration-shell model contains several approximations, which may be sources of error and also reduce the speed of computer-based numerical computations (8), such as the thickness of the shell, the apportioning of the free energy between overlapping hydration shells of covalently connected atoms, and the calculation of the volume of overlap of three or more hydration spheres that belong to nearby atoms. The latter problem can be overcome, however, by modifying the computing procedures (10, 11).We have initiated an alternative approach, in order to avoid these problems. We assume that the extent of interaction of any functional group i of a solute with the solvent is proportional to the solvent-accessible surface area Ai of group i (12-14) because the group can interact directly only with the water molecules that are in contact with the group at this surface. Thus, the total free energy of hydration of a solute molecule is given by Eq. 1: AGh = E Ai [1] where...

Using multi-objective computational design to extend protein promiscuity

“…free energies of the different models are calculated with the CHARMM force-field [26] and a free-energy solvation term proportional to the surface area [27]. Calculations on a reference state (taken to represent the unfolded state) allow a quantity akin to the unfolding free energy to be computed for each model.…”

Hydrophobic regions on protein surfaces. Derivation of the solvation energy from their area distribution in crystallographic protein structures

“…In this case, the parameter for hydrophobic atoms may be influenced seriously by side effects as a result of polar interactions with solvent that contribute the major share to the transfer energy of polar compounds. This happened obviously in the case of the parameter for carbonyl carbons in the set of Ooi et al (1987), which is 427 cal/ (mol.A2), compared with only 8 cal/(mol.A2) for any apolar carbon (S6 in Table 3A). Similarly, optimization of the surface energy parameters within the CHARMm force field (Schiffer et al, 1993) results in a large hydrophobic energy (S9 in Table 3A).…”

“…To summarize, the interpretation of small organic molecule experimental data is consistent with a specific hydrophobic surface energy in the ranges of 19.5-33 cal/(mol,A2) (hydrocarbon solubility), 16.6-20.1 and 17-33 cal/(mol.A2) (solubility of alkanes with functional groups and succinic crystal geometry, respectively), and 12-18 cal/(mol.A2) (carbon in atomic solva- Solubility of series of alkyl derivatives (transfer pure organic compound +water), Solubility of series of alkyl derivatives (transfer pure organic compound + water), Solubility of series of alkyl derivatives (transfer pure organic compound + water), Interfacial free energy between pure hydrocarbon and water (Tanford, 1979) Amino acid transfer energies octanol + water (Eisenberg & McLachlan, 1986) Transfer of small organic solutes gas phase + water (Ooi et al, 1987) Amino acid transfer energies octanol +water (Eisenberg et al, 1989) Amino acid transfer energies vacuum -+ water, correction for entropy of mixing Combined structure optimization with CHARMm and surface energy (Schiffer Geometry of succinic acid crystal (Rees & Wolfe, 1993) Amino acid transfer energies octanol + water, correction for entropy of mixing probe radius 1.5 A (Herrmann, 1972(Herrmann, , 1977 probe radius 1.5 A (Reynolds et al, 1974) probe radius 1.5 A (Amidon et al, 1975;Valvani et al, 1976) (Wesson & Eisenberg, 1992) et al, 1993) (Koehl & Delarue, 1994) B. Derivation from protein data PI 20 (+lO)C Protein stability change due to cavity-creating mutation in T4 lysozyme (Eriksson et al, 1992(Eriksson et al, , 1993 lysozyme (Blaber et al, 1993(Blaber et al, , 1994 myoglobin (Pinker et al, 1993) The range is 4 -8 0 cal/(mol .Az) for the molecular surface and has been converted to that for solvent-accessible surface with factor 2.4" (Rees & Wolfe, 1993).…”

“…The atomic solvation parameters (ASP) for hydrophobic atoms have been derived almost exclusively from experimental data on small organic compounds by: (1) using transfer energies from a hydrophobic environment to water (Herrmann, 1972(Herrmann, , 1977Reynolds et al, 1974;Amidon et al, 1975;Valvani et al, 1976;Eisenberg & McLachlan, 1986;Ooi et al, 1987;Wesson & Eisenberg, 1992); (2) measuring surface tension at hydrocarbon-water interfaces (Tanford, 1979); or (3) relying on small molecule crystal geometry [succinic acid crystals (Rees & Wolfe, 1993)]. The transferability of the latter parameters to biological macromolecules was assumed but not proven, The derivation of an atomic solvation parameter for hydrophobic atoms was also attempted with site-directed protein mutation studies (Eriksson et al, 1992;Blaber et al, 1993;Pinker et al, 1993) and with a neural network trained to distinguish native and nonnative protein conformations (Wang et al, 1999, albeit with considerably less confidence than in the case of small organic molecules (see the Discussion).…”

Fundamentals of drug design from a biophysical viewpoint

“…In this type of mean solvation model the local solvent contribution to the potential of mean force for solute atoms is taken to be proportional to the area of the solute atom or group of atoms that is accessible to solvent molecules (Ooi et al 1987;Still et al 1990;Schiffer et al 1992;Wesson & Eisenberg, 1992 Other local quantities, such as the hydration volume (Kang et al 1988;Vila et al 1991), or the number of solute-solvent contacts (Stouten et al 1993) can be used too. The expression for the accessible surface area of a solute atom generally depends on the coordinates of the solute atom itself and those of its nearest neighbour solute atoms.…”