Comparison of atomic solvation parametric sets: applicability and limitations in protein folding and binding

Empirical free energy calculation: comparison to calorimetric data

An effective free energy potential, developed originally for binding free energy calculation, is compared to calorimetric data on protein unfolding, described by a linear combination of changes in polar and nonpolar surface areas. The potential consists of a molecular mechanics energy term calculated for a reference medium (vapor or nonpolar liquid), and empirical terms representing solvation and entropic effects. It is shown that, under suitable conditions, the free energy function agrees well with the calorimetric expression. An additional result of the comparison is an independent estimate of the side-chain entropy loss, which is shown to agree with a structure-based entropy scale. These findings confirm that simple functions can be used to estimate the free energy change in complex systems, and that a binding free energy evaluation model can describe the thermodynamics of protein unfolding correctly. Furthermore, it is shown that folding and binding leave the sum of solute-solute and solute-solvent van der Waals interactions nearly invariant and, due to this invariance, it may be advantageous to use a nonpolar liquid rather than vacuum as the reference medium.

SIMS: computation of a smooth invariant molecular surface

SIMS, a new method of calculating a smooth invariant molecular dot surface, is presented. The SIMS method generates the smooth molecular surface by rolling two probe spheres. A solvent probe sphere is rolled over the molecule and produces a Richards-Connolly molecular surface (MS), which envelops the solvent-excluded volume of the molecule. In deep crevices, Connolly's method of calculating the MS has two deficiencies. First, it produces self-intersecting parts of the molecular surface, which must be removed to obtain the correct MS. Second, the correct MS is not smooth, i.e., the direction of the normal vector of the MS is not continuous, and some points of the MS are singular. We present an exact method for removing self-intersecting parts and smoothing the singular regions of the MS. The singular MS is smoothed by rolling a smoothing probe sphere over the inward side of the singular MS. The MS in the vicinity of singularities is replaced with the reentrant surface of the smoothing probe sphere. The smoothing method does not disturb the topology of a singular MS, and the smooth MS is a better approximation of the dielectric border between high dielectric solvent and the low dielectric molecular interior. The SIMS method generates a smooth molecular dot surface, which has a quasi-uniform dot distribution in two orthogonal directions on the molecular surface, which is invariant with molecular rotation and stable under changes in the molecular conformation, and which can be used in a variety of implicit methods of modeling solvent effects. The SIMS program is faster than the Connolly MS program, and in a matter of seconds generates a smooth dot MS of a 200-residue protein. The program is available from the authors on request (see http:@femto.med.unc.edu/SIMS).

Simulations of nucleation and early growth stages of protein crystals

Analysis of known protein crystal structures reveals that interaction energies between monomer pairs alone are not sufficient to overcome entropy loss related to fixing monomers in the crystal lattice. Interactions with several neighbors in the crystal are required for stabilization of monomers in the lattice. A microscopic model of nucleation and early growth stages of protein crystals, based on the above observations, is presented. Anisotropy of protein molecules is taken into account by assigning free energies of association (proportional to the buried surface area) to individual monomer-monomer contacts in the lattice. Lattice simulations of the tetragonal lysozyme crystal based on the model correctly reproduce structural features of the movement of dislocation on the (110) crystal face. The dislocation shifts with the speed equal to the one determined experimentally if the geometric probability of correct orientation is set to 10(-5), in agreement with previously published estimates. At this value of orientational probability, the first nuclei, the critical size of which for lysozyme is four monomers, appear in 1 ml of supersaturated solution on a time scale of microseconds. Formation of the ordered phase proceeds through the growth of nuclei (rather then their association) and requires nucleations on the surface at certain stages.

Protein thermal stability, hydrogen bonds, and ion pairs

Researchers in both academia and industry have expressed strong interest in comprehending the mechanisms responsible for enhancing the thermostability of proteins. Many and different structural principles have been postulated for the increased stability. Here, 16 families of proteins with different thermal stability were theoretically examined by comparing their respective fractional polar atom surface areas and the number and type of hydrogen bonds and salt links between explicit protein atoms. In over 80% of the families, correlations were found between the thermostability of the familial members and an increase in the number of hydrogen bonds as well as an increase in the fractional polar surface which results in added hydrogen bonding density to water. Thus increased hydrogen bonding may provide the most general explanation for thermal stability in proteins. The number of ion pairs was also found to increase with thermal stability in two-thirds of the families tested; however, their rate of addition was only about one-sixth that for internal hydrogen bonds amongst the protein atoms. The preferred residue exchanges and surface atom types useful in engineering enhanced stability were also examined.

Hydrophobicity regained

A widespread practice is to use free energies of transfer between organic solvents and water (delta G0transfer to define hydrophobicity scales for the amino acid side chains. A comparison of four delta G0transfer scales reveals that the values for hydrogen-bonding side chains are highly dependent on the non-aqueous environment. This property of polar side chains violates the assumptions underlying the paradigm of equating delta G0transfer with hydrophobicity or even with a generic solvation energy that is directly relevant to protein stability and ligand binding energetics. This simple regaining of the original concept of hydrophobicity reveals a flaw in approaches that use delta G0transfer values to derive generic estimates of the energetics of the burial of polar groups, and allows the introduction of a "pure" hydrophobicity scale for the amino acid residues.

Empirical potentials and functions for protein folding and binding

Simplified models and empirical potentials are being increasingly used for the analysis of proteins, frequently augmenting or replacing molecular mechanics approaches. Recent folding simulations have employed potentials that, in addition to terms assuring proper polypeptide geometry, include only two noncovalent effects-hydrogen bonding and hydrophobicity, with extremely simple approximations to the latter. The potentials that have been used in the free-energy ranking of protein-ligand complexes have generally been more involved. These potentials have more detailed solvation models and account for both local (hydrophobic and polar) solute-solvent phenomena and long range electrostatic solvation effects. The models of solvation that have been used most frequently are surface area related atomic parameters, knowledge-based models extracted from protein-structure data, and continum electrostatics with an additional area-related parameter. The knowledge-based approaches to solvation, although convenient and accurate enough, are suspect of double counting certain free-energy terms.

Structure-based drug design: computational advances

Structure-based computational methods continue to enhance progress in the discovery and refinement of therapeutic agents. Several such methods and their applications are described. These include molecular visualization and molecular modeling, docking, fragment methods, 3-D database techniques, and free-energy perturbation. Related issues that are discussed include the use of simplified potential energy functions and the determination of the positions of tightly bound waters. Strengths and weaknesses of the various methods are described.

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

For the first time, a direct approach for the derivation of an atomic solvation parameter from macromolecular structural data alone is presented. The specific free energy of solvation for hydrophobic surface regions of proteins is delineated from the area distribution of hydrophobic surface patches. The resulting value is 18 cal/(mol.A2), with a statistical uncertainty of +/-2 cal/mol.A2) at the 5% significance level. It compares favorably with the parameters for carbon obtained by other authors who use the the crystal geometry of succinic acid or energies of transfer from hydrophobic solvent to water for small organic compounds. Thus, the transferability of atomic solvation parameters for hydrophobic atoms to macromolecules has been directly demonstrated. A careful statistical analysis demonstrates that surface energy parameters derived from thermodynamic data of protein mutation experiments are clearly less confident.

Hydrophobic patches on the surfaces of protein structures

A survey of hydrophobic patches on the surface of 112 soluble, monomeric proteins is presented. The largest patch on each individual protein averages around 400 A2 but can range from 200 to 1,200 A2. These areas are not correlated to the sizes of the proteins and only weakly to their apolar surface fraction. Ala, Lys, and Pro have dominating contributions to the apolar surface for smaller patches, while those of the hydrophobic amino acids become more important as the patch size increases. The hydrophilic amino acids expose an approximately constant fraction of their apolar area independent of patch size; the hydrophobic residue types reach similar exposure only in the larger patches. Though the mobility of residues on the surface is generally higher, it decreases for hydrophilic residues with increasing patch size. Several characteristics of hydrophobic patches catalogued here should prove useful in the design and engineering of proteins.