Packing in protein cores

Abstract

Proteins are biological polymers that underlie all cellular functions. The first high-resolution protein structures were determined by x-ray crystallography in the 1960s. Since then, there has been continued interest in understanding and predicting protein structure and stability. It is well-established that a large contribution to protein stability originates from the sequestration from solvent of hydrophobic residues in the protein core. How are such hydrophobic residues arranged in the core; how can one best model the packing of these residues, and are residues loosely packed with multiple allowed side chain conformations or densely packed with a single allowed side chain conformation? Here we show that to properly model the packing of residues in protein cores it is essential that amino acids are represented by appropriately calibrated atom sizes, and that hydrogen atoms are explicitly included. We show that protein cores possess a packing fraction of [Formula: see text], which is significantly less than the typically quoted value of 0.74 obtained using the extended atom representation. We also compare the results for the packing of amino acids in protein cores to results obtained for jammed packings from discrete element simulations of spheres, elongated particles, and composite particles with bumpy surfaces. We show that amino acids in protein cores pack as densely as disordered jammed packings of particles with similar values for the aspect ratio and bumpiness as found for amino acids. Knowing the structural properties of protein cores is of both fundamental and practical importance. Practically, it enables the assessment of changes in the structure and stability of proteins arising from amino acid mutations (such as those identified as a result of the massive human genome sequencing efforts) and the design of new folded, stable proteins and protein-protein interactions with tunable specificity and affinity.

Comparing side chain packing in soluble proteins, protein‐protein interfaces, and transmembrane proteins

“…Figure A clearly shows that the distributions of packing fractions of core residues in the Dun1.0, PPI, and TM datasets are all very similar with mean values, , 0.56 ±0.02, and 0.55 ±0.01, respectively. In prior studies, we showed that this packing fraction matches the value for random close packing of elongated, bumpy particles that match the aspect ratio and surface roughness of core amino acids …”

“…In this study, we investigate whether the same approach can predict the conformations of amino acid side‐chains at protein‐protein interfaces and in transmembrane proteins. The reason the hard‐sphere model can accurately predict side‐chain conformations in protein cores is because they are densely packed . We therefore first calculated the packing fraction of the cores of protein‐protein interfaces and transmembrane proteins, and compared these values with the packing fraction of the cores of soluble proteins.…”

“…We have also found that protein cores are as densely packed as jammed packings of residue‐shaped particles with explicit hydrogens, which possess a packing fraction . With these data as background, we now seek to investigate to what extent the hard‐sphere modeling approach can be applied to contexts other than the cores of soluble proteins—namely non‐core residues, protein‐protein interfaces, and membrane‐embedded regions of transmembrane proteins.…”

Using physical features of protein core packing to distinguish real proteins from decoys

“…The distribution of packing fraction ϕ of core residues in proteins whose structures are determined by X-ray crystallography occur over a relatively narrow range, with a mean of 0.55 and an SD of 0.02. 46,48,51 We define core residues as those with small values of the relative solvent accessible surface area, rSASA ≤ 10 −3 (see Section 4 for a description of the database of high-resolution protein X-ray crystal structures and definition of rSASA). In contrast, we find that many of the CASP submissions and 3DRobot decoys possess core residues with packing fractions that are much higher than those in experimentally determined proteins structures.…”

“…[37][38][39][40][41][42][43][44][45] Additionally, in our previous work, we have found that several features of core packing are universal among well-folded experimental structures, such as the repacking predictability of core residue side chain placement, core packing fraction, and distribution of core void space. [46][47][48][49][50][51] This work suggests that analysis of core residue placement and packing in proteins more generally should be effective in determining the accuracy of protein decoys. Indeed, software to assess X-ray crystal structure model quality often calculates interatomic overlaps, 53,54 the RosettaHoles software uses defects in interior void space to differentiate between high-resolution X-ray crystal structures and protein decoys, 52 VoroMQA scores protein decoys using a statistical potential based on Voronoi contact areas, 34 and many other decoy detection methods attempt to incorporate predictions of solvent accessibility.…”