John L. Finney

Volume occupation, environment and accessibility in proteins. The problem of the protein surface.

Abstract The volumes occupied by atoms or groups of atoms in ribonuclease S are calculated, using a new treatment of the surface, and considering buried and exposed atoms separately. The volumes occupied by particular atom types fall within a narrow range, with standard deviations between 10% and 15% of the mean. Summation of volumes over main and side-chain groups removes inaccuracies in the single atom data, and results in even narrower distributions. Comparison of the volume spreads with those found in model glasses suggests that the remaining variation is unlikely to be much reduced by improving further either the space-subdivision method or the surface treatment. These improved volume distributions might be used as more stringent criteria against which to test trial tertiary structures. The computer program used produces additional information that could be used to investigate quantitatively the possible freedom of movement in different parts of the molecule. It also provides complementary data on environment and surface exposure.

Calculation of protein volumes: an alternative to the Voronoi procedure.

Abstract All the methods that have been applied to assessing local volume occupation or packing in proteins have particular defects. For example, the Voronoi method used by Richards (method A) and by Finney misallocates both non-bonded and covalent contacts in a geometrically rigorous, though chemically inconsistent, manner. Richards method B, in which covalent and non-bonded contacts are partitioned in chemically sensible ways, is unfortunately not completely rigorous, in that every polyhedron vertex has associated with it a small vertex-error polyhedron, which is not allocated to any atom. We present here a generalization of the Voronoi method that is particularly suited to multicomponent assemblies such as proteins. This radical plane partitioning of volume is completely rigorous; it gives rise to no vertex error, and handles the more numerous non-bonded contacts realistically. Its application to RNAase-S is described and the results compared with both Voronois method and Richards method B. A particular advantage of both the radical plane and Richards methods is a relative insensitivity to the treatment of the surface, a problem that has plagued other approaches to describing packing in proteins. Although the radical plane is seen to misallocate volume chemically between covalently-bonded neighbours, this problem vanishes when groups of atoms in side-chain residues are considered.

Description of molecular surface shape using Fourier descriptors

Abstract We have developed a method for describing the three-dimensional (3D) shape of molecules based on the Fourier shape descriptor technique. Our method has proven valuable in two-dimensional (2D) shape description and recognition in a number of important areas. In this paper, we discuss the 2D method briefly and explain how we adapted it to the 3D description of molecular surfaces. Our method is based on representing a molecular surface in terms of spherical harmonics, and some results on the accuracy of such a representation are shown. We discuss the use of this representation for two interacting molecules for quantifying the goodness of fit based on the topography of the relevant interfaces.

AN ANALYSIS OF CRYSTALLIZATION BY HOMOGENEOUS NUCLEATION IN A 4000-ATOM SOFT-SPHERE MODEL

A molecular dynamics simulation of crystallization by the process of spontaneous homogeneous nucleation for a model of 4000 soft spheres with periodic boundary conditions is reported. When the amorphous system in the metastable state, at a point for which classical homogeneous nucleation theory predicts a vanishing of the free energy barrier, is annealed, many crystallites with variable symmetries are formed in the system. The nature and structures of the growing crystallites are analyzed by examination of the primary Voronoi polyhedra. The results support the qualitative correctness of the classical theory. Comparisons are made with previous nucleation studies for the Lennard‐Jones model at low temperatures and supercooled liquid metals as studied recently by Raman and co‐workers.

Inelastic neutron scattering analysis of picosecond internal protein dynamics: Comparison of harmonic theory with experiment☆

The experimental inelastic neutron scattering spectrum of a protein, the bovine pancreatic trypsin inhibitor (BPTI), in a powder sample is presented together with the generalized density of states, G(omega), as a function of the frequency, omega, derived from the scattering data. The experimental results are compared with calculations from two different normal mode analyses of BPTI. One of these, based on an improved model, gives a calculated spectrum and density of states in general agreement with those obtained experimentally; the other, based on an earlier model, shows considerable disagreement. The important improvements in the newer normal mode analysis are the explicit treatment of all atoms (non-polar as well as polar hydrogens are included) and a modified truncation scheme for the long-range electrostatic interactions. The fact that the inelastic neutron scattering measurements can distinguish between the two theoretical models makes clear their utility for the analysis of protein dynamics.

Volume occupation, environment, and accessibility in proteins. Environment and molecular area of RNase-S

Abstract Using the same Voronoi polyhedron approach as has been used successfully to examine the internal volume occupation and packing efficiency in proteins (Richards, 1974; Finney, 1975), data on the molecular area and internal environment of protein molecules can be obtained. With small modifications, contact areas, surface roughness and solvent accessibility can be estimated, thus providing a single procedure for quantifying many related aspects of protein structure. Data for RNase-S are presented and discussed, in particular the nature and extent of internal and surface interactions. Although energy estimates have suggested that hydrogen-bonded polar groups within the protein can be treated as “hydrophobic units”, problems associated with the concept at the molecular level are discussed. Within the limitations of the X-ray co-ordinates, significant interactions between polar and apolar groups are implied, presumably of a dipoleinduced dipole nature. Comparison with simple clathrate hydrates suggests these interactions are stronger than those expected in proposed prototype structures thought to be associated with the hydrophobic interaction.

Direct Measurement of Hydration-Related Dynamic Changes in Lysozyme using Inelastic Neutron Scattering Spectroscopy

Inelastic neutron scattering spectroscopy is used to investigate dynamic changes in lysozyme powder at two different low D2O hydrations (0.07g D2O/g protein and 0.20 g D2O/g protein). In the higher hydration sample, the inelastic scattering between 0.8 and 4.0 cm-1 energy transfer is increased and the elastic scattering is decreased. The decreased elastic scattering suggests increased atomic amplitudes of motion and the increased 0.8 to 4.0 cm-1 scattering suggests increased motions in this frequency range. Comparison with normal mode models of lysozyme dynamics shows that the inelastic difference occurs in the frequency region predicted for the lowest frequency, largest amplitude, global modes of the molecular [M. Levitt, C. Sander and P.S. Stern, J. Mol. Biol. 181, 423 (1985). B. Brooks and M. Karplus, Proc. Natl. Acad. Sci (U.S.A) 82, 4995 (1985), R.E. Bruccoleri, M. Karplus and J.A. McCammon, Biopolymers 25 1767 (1986)]. Our results are consistent with a model in which an increased number of low frequency global modes are present in the higher hydrated sample.

Monte Carlo Studies on Water in the dCpG/Proflavin Crystal Hydrate

The extensive water network identified in the crystallographic studies of the dCpG/Proflavin hydrate by Neidle, Berman and Shieh (Nature 288, 129, 1980) forms an ideal test case for a) assessing the accuracy of theoretical calculations on nucleic acid--water systems based on statistical thermodynamic computer simulation, and b) the possible use of computer simulation in predicting the water positions in crystal hydrates for use in the further refinement and interpretation of diffraction data. Monte Carlo studies have been carried out on water molecules in the unit cell of dCpG/proflavin, with the nucleic acid complex fixed and the condensed phase environment of the system treated by means of periodic boundary conditions. Intermolecular interactions are described by potential functions representative of quantum mechanical calculations developed by Clementi and coworkers, and widely used in recent studies of the aqueous hydration of various forms of DNA fragments. The results are analyzed in terms of hydrogen bond topology, hydrogen bond distances and energies, mean water positions, and water crystal probability density maps. Detailed comparison of calculated and experimentally observed results are given, and the sensitivity of results to choice of potential is determined by comparison with simulation results based on a set of empirical potentials.

In-situ crystal growth and neutron four-circle diffractometry under high pressure

Abstract Pressure cells designed for work on four-circle diffractometers equipped with an Eulerian cradle and pressures up to 2.5 GPa are described. Single crystalline sapphire anvils allow the optical inspection of the sample crystals, e.g., during in-situ crystal growth and the pressure measurement with the ruby fluorescence technique. Experiments on normal and deuterated ice VI are reported.

The Structure and Dynamics of Water in Globular Proteins

Water plays more than a passive role in biomolecular processes that occur in aqueous media. Much of its involvement is often assigned to the so-called “hydrophobic interaction”, a process which, although well-characterised thermodynamically1, is poorly understood at the molecular level. In addition, there are other potentially large contributions to free energy changes accompanying such processes as protein-substrate binding or protein folding. These relate to hydrogen-bonding and entropic changes involving the solvent region2 and are similarly poorly understood.