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Grigas AT, Liu Z, Logan JA, Shattuck MD, O'Hern CS. Protein folding as a jamming transition. ARXIV 2024:arXiv:2405.09646v1. [PMID: 38800654 PMCID: PMC11118678] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Subscribe] [Scholar Register] [Indexed: 05/29/2024]
Abstract
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 ϕ c = 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 ϕ c . The model also recapitulates the global structure of proteins since it can accurately refold to native-like structures from partially unfolded states.
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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
| | - Zhuoyi Liu
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut, 06520, USA
- Integrated Graduate Program in Physical and Engineering Biology, Yale University, New Haven, Connecticut, 06520, USA
| | - Jack A Logan
- 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
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut, 06520, USA
- 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 Physics, Yale University, New Haven, Connecticut, 06520, USA
- Department of Applied Physics, Yale University, New Haven, Connecticut, 06520, USA
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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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Nakagawa H, Yamamoto N. Incoherent Neutron Scattering and Terahertz Time-Domain Spectroscopy on Protein and Hydration Water. Life (Basel) 2023; 13:life13020318. [PMID: 36836676 PMCID: PMC9961865 DOI: 10.3390/life13020318] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2022] [Accepted: 01/20/2023] [Indexed: 01/24/2023] Open
Abstract
Incoherent inelastic and quasi-elastic neutron scattering (INS) and terahertz time-domain spectroscopy (THz-TDS) are spectroscopy methods that directly detect molecular dynamics, with an overlap in the measured energy regions of each method. Due to the different characteristics of their probes (i.e., neutron and light), the information obtained and the sample conditions suitable for each method differ. In this review, we introduce the differences in the quantum beam properties of the two methods and their associated advantages and disadvantages in molecular spectroscopy. Neutrons are scattered via interaction with nuclei; one characteristic of neutron scattering is a large incoherent scattering cross-section of a hydrogen atom. INS records the auto-correlation functions of atomic positions. By using the difference in neutron scattering cross-sections of isotopes in multi-component systems, some molecules can be selectively observed. In contrast, THz-TDS observes the cross-correlation function of dipole moments. In water-containing biomolecular samples, the absorption of water molecules is particularly large. While INS requires large-scale experimental facilities, such as accelerators and nuclear reactors, THz-TDS can be performed at the laboratory level. In the analysis of water molecule dynamics, INS is primarily sensitive to translational diffusion motion, while THz-TDS observes rotational motion in the spectrum. The two techniques are complementary in many respects, and a combination of the two is very useful in analyzing the dynamics of biomolecules and hydration water.
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Affiliation(s)
- Hiroshi Nakagawa
- Materials Sciences Research Center, Japan Atomic Energy Agency, Tokai-mura 319-1195, Ibaraki, Japan
- J-PARC Center, Japan Atomic Energy Agency, Tokai-mura 319-1195, Ibaraki, Japan
- Correspondence: (H.N.); (N.Y.)
| | - Naoki Yamamoto
- Division of Biophysics, Department of Physiology, Jichi Medical University, Shimotsuke 329-0498, Tochigi, Japan
- Correspondence: (H.N.); (N.Y.)
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Bose Majumdar A, Kim IJ, Na H. Effect of solvent on protein structure and dynamics. Phys Biol 2020; 17:036006. [DOI: 10.1088/1478-3975/ab74b3] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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