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Grigas AT, Fisher A, Shattuck MD, O'Hern CS. Connecting polymer collapse and the onset of jamming. Phys Rev E 2024; 109:034406. [PMID: 38632799 DOI: 10.1103/physreve.109.034406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2023] [Accepted: 02/13/2024] [Indexed: 04/19/2024]
Abstract
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.
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Affiliation(s)
- Alex T Grigas
- Graduate Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut 06520, USA
- Integrated Graduate Program in Physical and Engineering Biology, Yale University, New Haven, Connecticut 06520, USA
| | - Aliza Fisher
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Mark D Shattuck
- Benjamin Levich Institute and Physics Department, The City College of New York, New York, New York 10031, USA
| | - Corey S O'Hern
- Graduate Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut 06520, USA
- Integrated Graduate Program in Physical and Engineering Biology, Yale University, New Haven, Connecticut 06520, USA
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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2
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Grigas AT, Liu Z, Regan L, O'Hern CS. Core packing of well‐defined X‐ray and
NMR
structures is the same. Protein Sci 2022; 31:e4373. [PMID: 35900019 PMCID: PMC9277709 DOI: 10.1002/pro.4373] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2022] [Revised: 05/06/2022] [Accepted: 06/02/2022] [Indexed: 11/10/2022]
Abstract
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.
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Affiliation(s)
- Alex T. Grigas
- Graduate Program in Computational Biology and Bioinformatics Yale University New Haven Connecticut USA
- Integrated Graduate Program in Physical and Engineering Biology Yale University New Haven Connecticut USA
| | - Zhuoyi Liu
- Integrated Graduate Program in Physical and Engineering Biology Yale University New Haven Connecticut USA
- Department of Mechanical Engineering and Materials Science Yale University New Haven Connecticut USA
| | - Lynne Regan
- Institute of Quantitative Biology, Biochemistry and Biotechnology Centre for Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh Edinburgh UK
| | - Corey S. O'Hern
- Graduate Program in Computational Biology and Bioinformatics Yale University New Haven Connecticut USA
- Integrated Graduate Program in Physical and Engineering Biology Yale University New Haven Connecticut USA
- Department of Mechanical Engineering and Materials Science Yale University New Haven Connecticut USA
- Department of Physics Yale University New Haven Connecticut USA
- Department of Applied Physics Yale University New Haven Connecticut USA
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3
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Truzzolillo D. Mixing-demixing transition and void formation in quasi-2D binary mixtures on a sphere. J Chem Phys 2022; 156:034904. [DOI: 10.1063/5.0080352] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- D. Truzzolillo
- Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Universitè de Montpellier, F-34095 Montpellier, France
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4
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Klatt MA, Ziff RM, Torquato S. Critical pore radius and transport properties of disordered hard- and overlapping-sphere models. Phys Rev E 2021; 104:014127. [PMID: 34412300 DOI: 10.1103/physreve.104.014127] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2021] [Accepted: 06/29/2021] [Indexed: 02/01/2023]
Abstract
Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δ_{c}. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, quantizer sphere packings, and crystalline sphere packings. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. The critical pore radius δ_{c} is often used as the key characteristic length scale that determines the fluid permeability k. A recent study [Torquato, Adv. Wat. Resour. 140, 103565 (2020)10.1016/j.advwatres.2020.103565] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size 〈δ^{2}〉, which is easier to determine than δ_{c}. Here, we compare δ_{c} to the second moment of the pore size 〈δ^{2}〉, and indeed confirm that, for all porosities and all models considered, δ_{c}^{2} is to a good approximation proportional to 〈δ^{2}〉. However, unlike 〈δ^{2}〉, the permeability estimate based on δ_{c}^{2} does not predict the correct ranking of k for our models. Thus, we confirm 〈δ^{2}〉 to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the τ order metric. We find that (effectively) hyperuniform models tend to have lower values of k than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targeted pore statistics.
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Affiliation(s)
- Michael A Klatt
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.,Institut für Theoretische Physik, FAU Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
| | - Robert M Ziff
- Center for the Study of Complex Systems and Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Salvatore Torquato
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.,Department of Chemistry, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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5
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Biroli G, Charbonneau P, Corwin EI, Hu Y, Ikeda H, Szamel G, Zamponi F. Interplay between percolation and glassiness in the random Lorentz gas. Phys Rev E 2021; 103:L030104. [PMID: 33862778 DOI: 10.1103/physreve.103.l030104] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2020] [Accepted: 02/23/2021] [Indexed: 11/07/2022]
Abstract
The random Lorentz gas (RLG) is a minimal model of transport in heterogeneous media that exhibits a continuous localization transition controlled by void space percolation. The RLG also provides a toy model of particle caging, which is known to be relevant for describing the discontinuous dynamical transition of glasses. In order to clarify the interplay between the seemingly incompatible percolation and caging descriptions of the RLG, we consider its exact mean-field solution in the infinite-dimensional d→∞ limit and perform numerics in d=2...20. We find that for sufficiently high d the mean-field caging transition precedes and prevents the percolation transition, which only happens on timescales diverging with d. We further show that activated processes related to rare cage escapes destroy the glass transition in finite dimensions, leading to a rich interplay between glassiness and percolation physics. This advance suggests that the RLG can be used as a toy model to develop a first-principle description of particle hopping in structural glasses.
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Affiliation(s)
- Giulio Biroli
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.,Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Eric I Corwin
- Department of Physics and Material Science Institute, University of Oregon, Eugene, Oregon 97403, USA
| | - Yi Hu
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Harukuni Ikeda
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
| | - Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Francesco Zamponi
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
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Mei Z, Treado JD, Grigas AT, Levine ZA, Regan L, O'Hern CS. Analyses of protein cores reveal fundamental differences between solution and crystal structures. Proteins 2020; 88:1154-1161. [PMID: 32105366 PMCID: PMC7415476 DOI: 10.1002/prot.25884] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2019] [Revised: 02/05/2020] [Accepted: 02/23/2020] [Indexed: 12/20/2022]
Abstract
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.
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Affiliation(s)
- Zhe Mei
- Integrated Graduate Program in Physical & Engineering Biology, Yale University, New Haven, Connecticut
- Department of Chemistry, Yale University, New Haven, Connecticut
| | - John D Treado
- Integrated Graduate Program in Physical & Engineering Biology, Yale University, New Haven, Connecticut
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut
| | - Alex T Grigas
- Integrated Graduate Program in Physical & Engineering Biology, Yale University, New Haven, Connecticut
- Graduate Program in Computational Biology & Bioinformatics, Yale University, New Haven, Connecticut
| | - Zachary A Levine
- Department of Pathology, Yale University, New Haven, Connecticut
- Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, Connecticut
| | - Lynne Regan
- Institute of Quantitative Biology, Biochemistry and Biotechnology, Center for Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh, Edinburgh, UK
| | - Corey S O'Hern
- Integrated Graduate Program in Physical & Engineering Biology, Yale University, New Haven, Connecticut
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut
- Department of Physics, Yale University, New Haven, Connecticut
- Department of Applied Physics, Yale University, New Haven, Connecticut
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Grigas AT, Mei Z, Treado JD, Levine ZA, Regan L, O'Hern CS. Using physical features of protein core packing to distinguish real proteins from decoys. Protein Sci 2020; 29:1931-1944. [PMID: 32710566 PMCID: PMC7454528 DOI: 10.1002/pro.3914] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2020] [Revised: 07/10/2020] [Accepted: 07/20/2020] [Indexed: 01/06/2023]
Abstract
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.
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Affiliation(s)
- Alex T. Grigas
- Graduate Program in Computational Biology and BioinformaticsYale UniversityNew HavenConnecticutUSA
- Integrated Graduate Program in Physical and Engineering BiologyYale UniversityNew HavenConnecticutUSA
| | - Zhe Mei
- Integrated Graduate Program in Physical and Engineering BiologyYale UniversityNew HavenConnecticutUSA
- Department of ChemistryYale UniversityNew HavenConnecticutUSA
| | - John D. Treado
- Integrated Graduate Program in Physical and Engineering BiologyYale UniversityNew HavenConnecticutUSA
- Department of Mechanical Engineering and Materials ScienceYale UniversityNew HavenConnecticutUSA
| | - Zachary A. Levine
- Department of PathologyYale UniversityNew HavenConnecticutUSA
- Department of Molecular Biophysics and BiochemistryYale UniversityNew HavenConnecticutUSA
| | - Lynne Regan
- Institute of Quantitative Biology, Biochemistry and Biotechnology, Centre for Synthetic and Systems Biology, School of Biological SciencesUniversity of EdinburghEdinburghUK
| | - Corey S. O'Hern
- Graduate Program in Computational Biology and BioinformaticsYale UniversityNew HavenConnecticutUSA
- Integrated Graduate Program in Physical and Engineering BiologyYale UniversityNew HavenConnecticutUSA
- Department of Mechanical Engineering and Materials ScienceYale UniversityNew HavenConnecticutUSA
- Department of PhysicsYale UniversityNew HavenConnecticutUSA
- Department of Applied PhysicsYale UniversityNew HavenConnecticutUSA
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