Measures of residue density in protein structures

A hierarchy of residue density assessments and packing properties in protein structures are contrasted, including a regular density, a variety of charge densities, a hydrophobic density, a polar density, and an aromatic density. These densities are investigated by alternative distance measures and also at the interface of multiunit structures. Amino acids are divided into nine structural categories according to three secondary structure states and three solvent accessibility levels. To take account of amino acid abundance differences across protein structures, we normalize the observed density by the expected density defining a density index. Solvent accessibility levels exert the predominant influence in determinations of the regular residue density. Explicitly, the regular density values vary approximately linearly with respect to solvent accessibility levels, the linearity parameters depending on the amino acid. The charge index reveals pronounced inequalities between lysine and arginine in their interactions with acidic residues. The aromatic density calculations in all structural categories parallel the regular density calculations, indicating that the aromatic residues are distributed as a random sample of all residues. Moreover, aromatic residues are found to be over-represented in the neighborhood of all amino acids. This result might be attributed to nucleation sites and protein stability being substantially associated with aromatic residues.

An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images

We describe an approach to the high-resolution three-dimensional structural determination of macromolecules that utilizes ultrashort, intense x-ray pulses to record diffraction data in combination with direct phase retrieval by the oversampling technique. It is shown that a simulated molecular diffraction pattern at 2.5-Å resolution accumulated from multiple copies of single rubisco biomolecules, each generated by a femtosecond-level x-ray free electron laser pulse, can be successfully phased and transformed into an accurate electron density map comparable to that obtained by more conventional methods. The phase problem is solved by using an iterative algorithm with a random phase set as an initial input. The convergence speed of the algorithm is reasonably fast, typically around a few hundred iterations. This approach and phasing method do not require any ab initio information about the molecule, do not require an extended ordered lattice array, and can tolerate high noise and some missing intensity data at the center of the diffraction pattern. With the prospects of the x-ray free electron lasers, this approach could provide a major new opportunity for the high-resolution three-dimensional structure determination of single biomolecules.

Evidence for nonrandom hydrophobicity structures in protein chains.

The question of whether proteins originate from random sequences of amino acids is addressed. A statistical analysis is performed in terms of blocked and random walk values formed by binary hydrophobic assignments of the amino acids along the protein chains. Theoretical expectations of these variables from random distributions of hydrophobicities are compared with those obtained from functional proteins. The results, which are based upon proteins in the SWISS-PROT data base, convincingly show that the amino acid sequences in proteins differ from what is expected from random sequences in a statistically significant way. By performing Fourier transforms on the random walks, one obtains additional evidence for nonrandomness of the distributions. We have also analyzed results from a synthetic model containing only two amino acid types, hydrophobic and hydrophilic. With reasonable criteria on good folding properties in terms of thermodynamical and kinetic behavior, sequences that fold well are isolated. Performing the same statistical analysis on the sequences that fold well indicates similar deviations from randomness as for the functional proteins. The deviations from randomness can be interpreted as originating from anticorrelations in terms of an Ising spin model for the hydrophobicities. Our results, which differ from some previous investigations using other methods, might have impact on how permissive with respect to sequence specificity protein folding process is-only sequences with nonrandom hydrophobicity distributions fold well. Other distributions give rise to energy landscapes with poor folding properties and hence did not survive the evolution.