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Register a new userVoid distributions reveal structural link between jammed packings and protein cores
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Dense packing of hydrophobic residues in the cores of globular proteins determines their stability. Recently, we have shown that protein cores possess packing fraction $phi approx 0.56$, which is the same as dense, random packing of amino acid-shaped particles. In this article, we compare the structural properties of protein cores and jammed packings of amino acid-shaped particles in much greater depth by measuring their local and connected void regions. We find that the distributions of surface Voronoi cell volumes and local porosities obey similar statistics in both systems. We also measure the probability that accessible, connected void regions percolate as a function of the size of a spherical probe particle and show that both systems possess the same critical probe size. By measuring the critical exponent $tau$ that characterizes the size distribution of connected void clusters at the onset of percolation, we show that void percolation in packings of amino acid-shaped particles and protein cores belong to the same universality class, which is different from that for void percolation in jammed sphere packings. We propose that the connected void regions of proteins are a defining feature of proteins and can be used to differentiate experimentally observed proteins from decoy structures that are generated using computational protein design software. This work emphasizes that jammed packings of amino acid-shaped particles can serve as structural and mechanical analogs of protein cores, and could therefore be useful in modeling the response of protein cores to cavity-expanding and -reducing mutations.
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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$_{alpha}$ atomic positions, identities of core amino acids, backbone and sidechain dihedral angles, and packing fraction of core residues. In contrast to prior studies, we identify the physical basis for these differences by modelling 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.
We consider multi-chain protein native structures and propose a criterion that determines whether two chains in the system are entangled or not. The criterion is based on the behavior observed by pulling at both temini of each chain simultaneously in the two chains. We have identified about 900 entangled systems in the Protein Data Bank and provided a more detailed analysis for several of them. We argue that entanglement enhances the thermodynamic stability of the system but it may have other functions: burying the hydrophobic residues at the interface, and increasing the DNA or RNA binding area. We also study the folding and stretching properties of the knotted dimeric proteins MJ0366, YibK and bacteriophytochrome. These proteins have been studied theoretically in their monomer
Normal mode analysis offers an efficient way of modeling the conformational flexibility of protein structures. Simple models defined by contact topology, known as elastic network models, have been used to model a variety of systems, but the validation is typically limited to individual modes for a single protein. We use anisotropic displacement parameters from crystallography to test the quality of prediction of both the magnitude and directionality of conformational variance. Normal modes from four simple elastic network model potentials and from the CHARMM forcefield are calculated for a data set of 83 diverse, ultrahigh resolution crystal structures. While all five potentials provide good predictions of the magnitude of flexibility, the methods that consider all atoms have a clear edge at prediction of directionality, and the CHARMM potential produces the best agreement. The low-frequency modes from different potentials are similar, but those computed from the CHARMM potential show the greatest difference from the elastic network models. This was illustrated by computing the dynamic correlation matrices from different potentials for a PDZ domain structure. Comparison of normal mode results with anisotropic temperature factors opens the possibility of using ultrahigh resolution crystallographic data as a quantitative measure of molecular flexibility. The comprehensive evaluation demonstrates the costs and benefits of using normal mode potentials of varying complexity. Comparison of the dynamic correlation matrices suggests that a combination of topological and chemical potentials may help identify residues in which chemical forces make large contributions to intramolecular coupling.
Many proteins carry out their biological functions by forming the characteristic tertiary structures. Therefore, the search of the stable states of proteins by molecular simulations is important to understand their functions and stabilities. However, getting the stable state by conformational search is difficult, because the energy landscape of the system is characterized by many local minima separated by high energy barriers. In order to overcome this difficulty, various sampling and optimization methods for conformations of proteins have been proposed. In this study, we propose a new conformational search method for proteins by using genetic crossover and Metropolis criterion. We applied this method to an $alpha$-helical protein. The conformations obtained from the simulations are in good agreement with the experimental results.
Inverse statistical approaches to determine protein structure and function from Multiple Sequence Alignments (MSA) are emerging as powerful tools in computational biology. However the underlying assumptions of the relationship between the inferred effective Potts Hamiltonian and real protein structure and energetics remain untested so far. Here we use lattice protein model (LP) to benchmark those inverse statistical approaches. We build MSA of highly stable sequences in target LP structures, and infer the effective pairwise Potts Hamiltonians from those MSA. We find that inferred Potts Hamiltonians reproduce many important aspects of true LP structures and energetics. Careful analysis reveals that effective pairwise couplings in inferred Potts Hamiltonians depend not only on the energetics of the native structure but also on competing folds; in particular, the coupling values reflect both positive design (stabilization of native conformation) and negative design (destabilization of competing folds). In addition to providing detailed structural information, the inferred Potts models used as protein Hamiltonian for design of new sequences are able to generate with high probability completely new sequences with the desired folds, which is not possible using independent-site models. Those are remarkable results as the effective LP Hamiltonians used to generate MSA are not simple pairwise models due to the competition between the folds. Our findings elucidate the reasons for the success of inverse approaches to the modelling of proteins from sequence data, and their limitations.
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