Resolution is a crucial parameter to consider in doing surface comparisons. A method is presented here for the rapid, objective, and automatic comparison of selected parts of protein surfaces as a function of resolution using differences and correlations of Fourier coefficients. A test-case application of this procedure to the surfaces of five immunoglobulin antigen-combining sites allowed them to be partitioned into two categories.
In the preceding paper[1], the structure of water around a model protein a-helix (made from polyalanine) was investigated using two-dimensional projections of the molecular distribution function. Here an attempt is made to assess the relative importance of packing, protein-water hydrogen-bonding, and water-water hydrogen-bonding in creating this water structure. To isolate the effect of protein-water hydrogen bonding, simulations with the helix charges 'switched' on and off were compared. Likewise, these 'normal' water simulations were compared to ones done with the water charges switched off to assess the relative contributions of packing and hydrogen-bonding. The energy of water molecules around the helix was also investigated. The results show that water-water hydrogen bonding, which underlies hydrophobicity, is the dominant interaction. On average it moves water molecules back from hydrophobic parts of the helix surface as compared to water molecules around hydrophilic parts. Furthermore, completely disrupting this interaction by switching off the water charges moves the solvent molecules in towards the helix, making narrow crevices more accessible to solvent. A function that synthesizes this energetic information with that from the molecular distribution function is used to characterize the hydrophobicity of the helix.
We have determined the variations in volume that occur during evolution in the buried core of 3 different families of proteins. The variation of the whole core is very small (~2.5 %) compared to the variation at individual sites (~13 %). However, by comparing our results to those expected from random sequence changes with no correlations between sites, we show that the small variation observed may simply be a manifestation of the statistical "law of large numbers" and not reflect any compensating changes in, or global constraints upon, protein sequences.
We have also analyzed in detail the volume variations at individual sites, both in the core and on the surface, and compared these variations with those expected from random sequences. Individual sites on the surface have nearly the same variation as random sequences (24 % vs. 28% variation). However, individual sites in the core have on average about half the variation of random sequences (13% vs. 30%). Roughly, half of these core sites strongly conserve their volume (0-10 % variation); one quarter have moderate variation (10-20%); and the remaining quarter vary randomly (20-40%).
Our results have clear implications for the relationship between protein sequence and structure. For our analysis, we have developed a new and simple method for weighting protein sequences to correct for unequal representation, which we describe in an appendix.
We survey all the known instances of domain movements in proteins for which there is crystallographic evidence for the movement. We explain these domain movements in terms of the repertoire of low-energy conformation changes that are known to occur in proteins. We first describe the basic elements of this repertoire, hinge and shear motions, and then show how the elements of the repertoire can be combined to produce domain movements. We emphasize that the elements used in particular proteins are determined mainly by the structure of the domain interfaces.
We analyze the volume of atoms on the protein surface during a molecular-dynamics simulation of one small protein (pancreatic trypsin inhibitor). To calculate the volumes, we use a particular geometric construction, called Voronoi polyhedra, that divides the total volume of the simulation box amongst the atoms, rendering them relatively larger or smaller depending on how tightly they are packed. We find that most of the atoms on the protein surface are larger than those buried in the core (by ~6%), except for the charged atoms, which decrease in size, presumably due to electroconstriction. We also find that water molecules are larger near apolar atoms on the protein surface and smaller near charged atoms, in comparison to "bulk" water molecules far from the protein. Taken together, these findings necessarily imply that apolar atoms on the protein sur face and their associated water molecules are less tightly packed (than corresponding atoms in the protein core and bulk water) and the opposite is the case for charged atoms. This looser apolar packing and tighter charged packing fundamentally reflects protein-water distances that are larger or smaller than those expected from van der Waals radii. In addition to the calculation of mean volumes, simulations allow us to investigate the volume fluctuations and hence compressibilities of the protein and solvent atoms. The relatively large volume fluctuations of atoms at the protein-water interface indicates that they have a more variable packing than corresponding atoms in the protein core or in bulk water. We try to adhere to traditional conventions throughout our calculations. Nevertheless, we are aware of and discuss three complexities that significantly qualify our calculations: the positioning of the dividing plane between atoms, the problem of vertex error, and the choice of atom radii. In particular, our results highlight how poor a "compromise" the commonly accepted value of 1.4 Angstroms is for the radius of a water molecule.
27 January 1995 / mbg@hyper.stanford.edu