Protein folding as a jamming transition.

Proteins fold to a specific functional conformation with a densely packed hydrophobic core that controls their stability. We develop a geometric, yet all-atom model for proteins that explains the universal core packing fraction of ϕc=0.55 found in experimental measurements. We show that as the hydrophobic interactions increase relative to the temperature, a novel jamming transition occurs when the core packing fraction exceeds ϕc. The model also recapitulates the global structure of proteins since it can accurately refold to native-like structures from partially unfolded states.

Identifying the minimal sets of distance restraints for FRET-assisted protein structural modeling.

Proteins naturally occur in crowded cellular environments and interact with other proteins, nucleic acids, and organelles. Since most previous experimental protein structure determination techniques require that proteins occur in idealized, non-physiological environments, the effects of realistic cellular environments on protein structure are largely unexplored. Recently, Förster resonance energy transfer (FRET) has been shown to be an effective experimental method for investigating protein structure in vivo. Inter-residue distances measured in vivo can be incorporated as restraints in molecular dynamics (MD) simulations to model protein structural dynamics in vivo. Since most FRET studies only obtain inter-residue separations for a small number of amino acid pairs, it is important to determine the minimum number of restraints in the MD simulations that are required to achieve a given root-mean-square deviation (RMSD) from the experimental structural ensemble. Further, what is the optimal method for selecting these inter-residue restraints? Here, we implement several methods for selecting the most important FRET pairs and determine the number of pairs Nr that are needed to induce conformational changes in proteins between two experimentally determined structures. We find that enforcing only a small fraction of restraints, Nr/N≲0.08, where N is the number of amino acids, can induce the conformational changes. These results establish the efficacy of FRET-assisted MD simulations for atomic scale structural modeling of proteins in vivo. Significance: Determining protein structure in vivo is essential for understanding protein function. Most protein structures have been studied in non-physiological conditions using x-ray crystallography, NMR spectroscopy, and cryo-electron microscopy. Thus, we do not know whether the cellular environment significantly affects protein structure. We emphasize the benefits of FRET-assisted molecular dynamics simulations in characterizing protein structure in vivo at the atomic scale. We identify the minimum number of FRET pairs that can induce conformational changes in several proteins, including one that has been characterized using in-cell NMR.

Connecting polymer collapse and the onset of jamming.

Previous studies have shown that the interiors of proteins are densely packed, reaching packing fractions that are as large as those found for static packings of individual amino-acid-shaped particles. How can the interiors of proteins take on such high packing fractions given that amino acids are connected by peptide bonds and many amino acids are hydrophobic with attractive interactions? We investigate this question by comparing the structural and mechanical properties of collapsed attractive disk-shaped bead-spring polymers to those of three reference systems: static packings of repulsive disks, of attractive disks, and of repulsive disk-shaped bead-spring polymers. We show that the attractive systems quenched to temperatures below the glass transition T≪T_{g} and static packings of both repulsive disks and bead-spring polymers possess similar interior packing fractions. Previous studies have shown that static packings of repulsive disks are isostatic at jamming onset, i.e., the number of interparticle contacts N_{c} matches the number of degrees of freedom, which strongly influences their mechanical properties. We find that repulsive polymer packings are hypostatic at jamming onset (i.e., with fewer contacts than degrees of freedom) but are effectively isostatic when including stabilizing quartic modes, which give rise to quartic scaling of the potential energy with displacements along these modes. While attractive disk and polymer packings are often considered hyperstatic with excess contacts over the isostatic number, we identify a definition for interparticle contacts for which they can also be considered as effectively isostatic. As a result, we show that the mechanical properties (e.g., scaling of the potential energy with excess contact number and low-frequency contribution to the density of vibrational modes) of weakly attractive disk and polymer packings are similar to those of isostatic repulsive disk and polymer packings. Our results demonstrate that static packings generated via attractive collapse or compression of repulsive particles possess similar structural and mechanical properties.

Core packing of well-defined X-ray and NMR structures is the same.

Numerous studies have investigated the differences and similarities between protein structures determined by solution NMR spectroscopy and those determined by X-ray crystallography. A fundamental question is whether any observed differences are due to differing methodologies or to differences in the behavior of proteins in solution versus in the crystalline state. Here, we compare the properties of the hydrophobic cores of high-resolution protein crystal structures and those in NMR structures, determined using increasing numbers and types of restraints. Prior studies have reported that many NMR structures have denser cores compared with those of high-resolution X-ray crystal structures. Our current work investigates this result in more detail and finds that these NMR structures tend to violate basic features of protein stereochemistry, such as small non-bonded atomic overlaps and few Ramachandran and sidechain dihedral angle outliers. We find that NMR structures solved with more restraints, and which do not significantly violate stereochemistry, have hydrophobic cores that have a similar size and packing fraction as their counterparts determined by X-ray crystallography at high resolution. These results lead us to conclude that, at least regarding the core packing properties, high-quality structures determined by NMR and X-ray crystallography are the same, and the differences reported earlier are most likely a consequence of methodology, rather than fundamental differences between the protein in the two different environments.

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

The ability to consistently distinguish real protein structures from computationally generated model decoys is not yet a solved problem. One route to distinguish real protein structures from decoys is to delineate the important physical features that specify a real protein. For example, it has long been appreciated that the hydrophobic cores of proteins contribute significantly to their stability. We used two sources to obtain datasets of decoys to compare with real protein structures: submissions to the biennial Critical Assessment of protein Structure Prediction competition, in which researchers attempt to predict the structure of a protein only knowing its amino acid sequence, and also decoys generated by 3DRobot, which have user-specified global root-mean-squared deviations from experimentally determined structures. Our analysis revealed that both sets of decoys possess cores that do not recapitulate the key features that define real protein cores. In particular, the model structures appear more densely packed (because of energetically unfavorable atomic overlaps), contain too few residues in the core, and have improper distributions of hydrophobic residues throughout the structure. Based on these observations, we developed a feed-forward neural network, which incorporates key physical features of protein cores, to predict how well a computational model recapitulates the real protein structure without knowledge of the structure of the target sequence. By identifying the important features of protein structure, our method is able to rank decoy structures with similar accuracy to that obtained by state-of-the-art methods that incorporate many additional features. The small number of physical features makes our model interpretable, emphasizing the importance of protein packing and hydrophobicity in protein structure prediction.

Analyses of protein cores reveal fundamental differences between solution and crystal structures.

There have been several studies suggesting that protein structures solved by NMR spectroscopy and X-ray crystallography show significant differences. To understand the origin of these differences, we assembled a database of high-quality protein structures solved by both methods. We also find significant differences between NMR and crystal structures-in the root-mean-square deviations of the C α atomic positions, identities of core amino acids, backbone, and side-chain dihedral angles, and packing fraction of core residues. In contrast to prior studies, we identify the physical basis for these differences by modeling protein cores as jammed packings of amino acid-shaped particles. We find that we can tune the jammed packing fraction by varying the degree of thermalization used to generate the packings. For an athermal protocol, we find that the average jammed packing fraction is identical to that observed in the cores of protein structures solved by X-ray crystallography. In contrast, highly thermalized packing-generation protocols yield jammed packing fractions that are even higher than those observed in NMR structures. These results indicate that thermalized systems can pack more densely than athermal systems, which suggests a physical basis for the structural differences between protein structures solved by NMR and X-ray crystallography.

Lipid Vesicle-Coated Complex Coacervates.

Compartmentalization by complex coacervation is important across a range of different fields including subcellular and prebiotic organization, biomedicine, food science, and personal care products. Often, lipid self-assemblies such as vesicles are also present intracellularly or in commercial formulations. A systematic understanding of how phospholipid vesicles interact with different complex coacervates could provide insight and improve control over these systems. In this manuscript, anionic phospholipid vesicles were added to a series of different complex coacervate samples in which coacervates were formed by mixing one of five polycations with one of three (poly)anions that varied in chemical structure and length. Vesicles were found to assemble at the coacervate/continuous phase interface and/or form aggregates. We report how factors such as the charge density of polyelectrolytes and the charge ratio of cationic-to-anionic moieties impact the vesicle distribution in coacervate samples. Our findings emphasize the importance of interactions between vesicles and polycations in the dilute supernatant phase for determining whether the vesicles aggregate prior to assembly at the liquid-liquid interface. The uptake of an RNA oligonucleotide (A15) was also investigated to understand the effect of these liposome coatings on diffusion into coacervate droplets. Systems in which uniform vesicle coronas assemble around coacervate droplets without restricting the entry of biomolecules such as RNAs could be of interest as bioreactors.