Shortly after the determination of the first protein x-ray crystal structures, researchers analyzed their cores and reported packing fractions ϕ ≈ 0.75, a value that is similar to close packing of equal-sized spheres. A limitation of these analyses was the use of extended atom models, rather than the more physically accurate explicit hydrogen model. The validity of the explicit hydrogen model was proved in our previous studies by its ability to predict the side chain dihedral angle distributions observed in proteins. In contrast, the extended atom model is not able to recapitulate the side chain dihedral angle distributions, and gives rise to large atomic clashes at side chain dihedral angle combinations that are highly probable in protein crystal structures. Here, we employ the explicit hydrogen model to calculate the packing fraction of the cores of over 200 high-resolution protein structures. We find that these protein cores have ϕ ≈ 0.56, which is similar to results obtained from simulations of random packings of individual amino acids. This result provides a deeper understanding of the physical basis of protein structure that will enable predictions of the effects of amino acid mutations to protein cores and interfaces of known structure.

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.

Protein core repacking is a standard test of protein modeling software. A recent study of six different modeling software packages showed that they are more successful at predicting side chain conformations of core compared to surface residues. All the modeling software tested have multicomponent energy functions, typically including contributions from solvation, electrostatics, hydrogen bonding and Lennard-Jones interactions in addition to statistical terms based on observed protein structures. We investigated to what extent a simplified energy function that includes only stereochemical constraints and repulsive hard-sphere interactions can correctly repack protein cores. For single residue and collective repacking, the hard-sphere model accurately recapitulates the observed side chain conformations for Ile, Leu, Phe, Thr, Trp, Tyr and Val. This result shows that there are no alternative, sterically allowed side chain conformations of core residues. Analysis of the same set of protein cores using the Rosetta software suite revealed that the hard-sphere model and Rosetta perform equally well on Ile, Leu, Phe, Thr and Val; the hard-sphere model performs better on Trp and Tyr and Rosetta performs better on Ser. We conclude that the high prediction accuracy in protein cores obtained by protein modeling software and our simplified hard-sphere approach reflects the high density of protein cores and dominance of steric repulsion.

We compare side chain prediction and packing of core and non-core regions of soluble proteins, protein-protein interfaces, and transmembrane proteins. We first identified or created comparable databases of high-resolution crystal structures of these 3 protein classes. We show that the solvent-inaccessible cores of the 3 classes of proteins are equally densely packed. As a result, the side chains of core residues at protein-protein interfaces and in the membrane-exposed regions of transmembrane proteins can be predicted by the hard-sphere plus stereochemical constraint model with the same high prediction accuracies (>90%) as core residues in soluble proteins. We also find that for all 3 classes of proteins, as one moves away from the solvent-inaccessible core, the packing fraction decreases as the solvent accessibility increases. However, the side chain predictability remains high (80% within 30°) up to a relative solvent accessibility, rSASA≲0.3, for all 3 protein classes. Our results show that ≈40% of the interface regions in protein complexes are "core", that is, densely packed with side chain conformations that can be accurately predicted using the hard-sphere model. We propose packing fraction as a metric that can be used to distinguish real protein-protein interactions from designed, non-binding, decoys. Our results also show that cores of membrane proteins are the same as cores of soluble proteins. Thus, the computational methods we are developing for the analysis of the effect of hydrophobic core mutations in soluble proteins will be equally applicable to analyses of mutations in membrane proteins.

The self-assembly of amyloid proteins into β-sheet rich assemblies is associated with human amyloidoses including Alzheimer's disease, Parkinson's disease, and type 2 diabetes. An attractive therapeutic strategy therefore is to develop small molecules that would inhibit protein self-assembly. Natural polyphenols are potential inhibitors of β-sheet formation. How these compounds affect the kinetics of self-assembly studied by thioflavin T (ThT) fluorescence is not understood primarily because their presence interferes with ThT fluorescence. Here, we show that by plotting peak intensities from nuclear magnetic resonance (NMR) against incubation time, kinetic profiles in the presence of the polyphenol can be obtained from which kinetic parameters of self-assembly can be easily determined. In applying this technique to the selfassembly of the islet amyloid polypeptide in the presence of curcumin, a biphenolic compound found in turmeric, we show that the kinetic profile is atypical in that it shows a prenucleation period during which there is no observable decrease in NMR peak intensities. KEYWORDS: amyloid, ThT fluorescence, curcumin, NMR A total of 27 proteins have been identified to form the extracellular β-sheet containing amyloid fibrils associated with human amyloidoses. 1 These include the amyloid-β protein (Aβ) in Alzheimer's disease, α-synuclein in Parkinson's disease, and the islet amyloid polypeptide (IAPP) in type 2 diabetes (T2D). In spite of the large differences in the primary structure of the precursor proteins, the mature fibrils possess common characteristics including unbranched, 10 nm wide morphology as determined by electron microscopy, the ability to bind Congo red and exhibit green birefringence, and X-ray diffraction patterns consistent with cross-β-sheet. 1 Mechanistic studies of fibril formation in hydro have shown that Aβ, α-synuclein, and IAPP undergo a random coil to β-sheet conformational transition. 2 IAPP is a 37-residue polypeptide ( Figure 1A) that is cosecreted with insulin by β-cells of the islets of Langerhans in the pancreas. Molecular biological, biophysical, and genetic evidence support a central role for IAPP in β-cell death and dysfunction associated with T2D. 3,4 The progressive formation of islet amyloid leads to a decrease in β-cell mass. 5 The toxicity of fibrillar IAPP was first demonstrated in the early 1990s, 6 but more recent studies suggest that oligomeric assemblies could be the proximate cytotoxic species in T2D. 3,7 A number of mechanisms behind the toxicity of IAPP oligomers have been proposed, 8 but recent biophysical studies have focused on the ability of IAPP to disrupt model membranes, as reviewed recently. 3 A missense mutation involving the substitution of serine at position 20 with glycine ( Figure 1A) has been linked to an early onset, more severe form of T2D. 9 The mutant polypeptide aggregates faster 10,11 and is more toxic than wildtype IAPP. 10 Together, these findings suggest that molecules that significantly delay or completely inhibit IAP...