New determinations and simplified representations of macromolecular surfaces

Description of hydration free energy density as a function of molecular physical properties

A method to calculate the solvation free energy density (SFED) at any point in the cavity surface or solvent volume surrounding a solute is proposed. In the special case in which the solvent is water, the SFED is referred to as the hydration free energy density (HFED). The HFED is described as a function of some physical properties of the molecules. These properties are represented by simple basis functions. The hydration free energy of a solute was obtained by integrating the HFED over the solvent volume surrounding the solute, using a grid model. Of 34 basis functions that were introduced to describe the HFED, only six contribute significantly to the HFED. These functions are representations of the surface area and volume of the solute, of the polarization and dispersion of the solute, and of two types of electrostatic interactions between the solute and its environment. The HFED is described as a linear combination of these basis functions, evaluated by summing the interaction energy between each atom of the solute with a grid point in the solvent, where each grid point is a representation of a finite volume of the solvent. The linear combination coefficients were determined by minimizing the error between the calculated and experimental hydration free energies of 81 neutral organic molecules that have a variety of functional groups. The calculated hydration free energies agree well with the experimental results. The hydration free energy of any other solute molecule can then be calculated by summing the product of the linear combination coefficients and the basis functions for the solute.

Monte-Carlo calculations of the solvent effects on the conformation of angiotensin II

An efficient Metropolis Monte-Carlo (MMC) procedure is proposed in order to calculate averages of the energy of conformation and structural properties of a polypeptide chain in interaction with a solvent. The contribution of hydration to the free energy of conformation of the macromolecule is calculated using the accessible surface area method. This algorithm, performed with different sets of atomic solvation parameters (ASP), is applied to the peptidic hormone angiotensin II. Different situations of solvation of that molecule are described when the ASP of the polar atoms are fixed to 0, whereas those of the apolar atoms are given values varying from -1.0 to 1.0. From results thus obtained, transitions from extended to collapsed conformations of the polypeptide chain can be simulated. Such changes of conformation could be related to a possible mechanism of binding of this hormone on a membrane surface.

SMART: a solvent-accessible triangulated surface generator for molecular graphics and boundary element applications

An algorithm is presented for generating a representation of the solvent-accessible molecular surface as a smooth triangulated manifold. The algorithm, called SMART (SMooth moleculAR surface Triangulator), divides the contact and reentrant portions of the solvent-accessible molecular surface into curvilinear three-sided elements. In contrast to the author's earlier implementation of this general approach [Zauhar, R.J. and Morgan, R.S., J. Comput. Chem., 11 (1990) 603], the SMART algorithm defines elements directly on the appropriate geometric surface types (rather than using interpolation over cubic elements), and has special features to handle highly distorted regions which often appear in deep crevices and internal cavities. While the method is designed for use with boundary element techniques in continuum electrostatics, it can also be applied to the accurate computation of molecular surface areas and volumes, and the generation of shaded surfaces for display with interactive computer graphics.

The molecular surface package

The Molecular Surface Package is a reimplementation, in C, of a set of earlier FORTRAN programs for computing analytical molecular surfaces, areas, volumes, polyhedral molecular surfaces, and surface curvatures. The software does not do interactive molecular graphics, but it will produce pixel maps of smooth molecular surfaces. The polyhedral molecular surfaces are suited to display on graphics systems with real-time rendering of polyhedra.

Empirical solvation models in the context of conformational energy searches: application to bovine pancreatic trypsin inhibitor

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.

Shape distributions of protein topography

A method is presented for measuring protein surface shape. It is an improvement of an earlier method that intersects a sphere with the solvent-excluded volume of a protein molecule. The new method, called a shape distribution, produces a more sophisticated description of the region of the sphere inside the protein than is provided by simply measuring the region's area or solid angle. This method is applied to the prediction of molecular complexes in three systems: the hemoglobin nonallosteric interface, trypsin and trypsin inhibitor, and heme and apomyoglobin. It does not uniquely predict the correct structure, even though the individual structures are taken from the experimentally determined complex structure. However, it does provide a list of several hundred predicted complexes, one of which is correct, and from which the correct complex might be extracted by a subsequent chemical filter.

Program for the visualization of inorganic crystals

A program has been developed to manipulate images of inorganic structures and organic molecules on ALLIANT VFX/40 using the PHIGS + standard. This article reviews algorithms for representing spheres, ellipsoids and various polyhedrons involved in inorganic chemistry. The program also supports the display and manipulation of animated frames from dynamics simulations. Many graphical facilities have been implemented and we discuss their interest in the field of molecular graphics.