1
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Lipska A, Sieradzan AK, Atmaca S, Czaplewski C, Liwo A. Toward Consistent Physics-Based Modeling of Local Backbone Structures and Chirality Change of Proteins in Coarse-Grained Approaches. J Phys Chem Lett 2023; 14:9824-9833. [PMID: 37889895 PMCID: PMC10641867 DOI: 10.1021/acs.jpclett.3c01988] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Revised: 10/23/2023] [Accepted: 10/24/2023] [Indexed: 10/29/2023]
Abstract
A reliable representation of local interactions is critical for the accuracy of modeling protein structure and dynamics at both the all-atom and coarse-grained levels. The development of local (mainly torsional) potentials was focused on careful parametrization of the predetermined (usually Fourier) formulas rather than on their physics-based derivation. In this Perspective we discuss the state-of-the-art methods for modeling local interactions, including the scale-consistent theory developed in our laboratory, which implies that the coarse-grained torsional potentials inseparably depend on the virtual-bond angles adjacent to a given dihedral and that multitorsional terms should be considered. We extend the treatment to split the residue-based torsional potentials into the site-based regular and improper torsional potentials. These considerations are illustrated with the revised torsional potentials and improper-torsional potentials involving the l-alanine residue and the improper-torsional potential corresponding to serine-residue enantiomerization. Applications of the new approach in coarse-grained modeling and revising all-atom force fields are discussed.
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Affiliation(s)
- Agnieszka
G. Lipska
- Centre
of Informatics Tri-city Academic Supercomputer and Network (CI TASK), Gdańsk University of Technology, Fahrenheit
Union of Universities in Gdańsk, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland
| | - Adam K. Sieradzan
- Centre
of Informatics Tri-city Academic Supercomputer and Network (CI TASK), Gdańsk University of Technology, Fahrenheit
Union of Universities in Gdańsk, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland
- Faculty
of Chemistry, University of Gdańsk,
Fahrenheit Union of Universities, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland
| | - Sümeyye Atmaca
- Kocaeli
University, Institute of Science,
Umuttepe Yerleşkesi, 41001 İzmit/Kocaeli̇, Türkiye
| | - Cezary Czaplewski
- Centre
of Informatics Tri-city Academic Supercomputer and Network (CI TASK), Gdańsk University of Technology, Fahrenheit
Union of Universities in Gdańsk, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland
- Faculty
of Chemistry, University of Gdańsk,
Fahrenheit Union of Universities, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland
| | - Adam Liwo
- Centre
of Informatics Tri-city Academic Supercomputer and Network (CI TASK), Gdańsk University of Technology, Fahrenheit
Union of Universities in Gdańsk, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland
- Faculty
of Chemistry, University of Gdańsk,
Fahrenheit Union of Universities, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland
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2
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Mioduszewski Ł. Choosing the right density for a concentrated protein system like gluten in a coarse-grained model. EUROPEAN BIOPHYSICS JOURNAL : EBJ 2023; 52:583-591. [PMID: 37378869 PMCID: PMC10618313 DOI: 10.1007/s00249-023-01667-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Revised: 05/05/2023] [Accepted: 05/24/2023] [Indexed: 06/29/2023]
Abstract
Large coarse-grained simulations are often conducted with an implicit solvent, which makes it hard to assess the water content of the sample and the effective concentration of the system. Here the number and the size of cavities and entanglements in the system, together with density profiles, are used to asses the homogeneity and interconnectedness of gluten. This is a continuation of an earlier article, "Viscoelastic properties of wheat gluten in a molecular dynamics study" (Mioduszewski and Cieplak 2021b). It turns out there is a wide range of densities (between 1 residue per cubic nanometer and 3 residues/nm[Formula: see text]) where the system is interconnected, but not homogeneous: there are still large empty spaces, surrounded by an entangled protein network. Those findings should be of importance to any coarse-grained simulation of large protein systems.
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Affiliation(s)
- Łukasz Mioduszewski
- Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University, Wóycickiego 1/3, 01-938, Warsaw, Poland.
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3
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Anila MM, Ghosh R, Różycki B. Membrane curvature sensing by model biomolecular condensates. SOFT MATTER 2023; 19:3723-3732. [PMID: 37190858 DOI: 10.1039/d3sm00131h] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Biomolecular condensates (BCs) are fluid droplets that form in biological cells by liquid-liquid phase separation. Their major components are intrinsically disordered proteins. Vast attention has been given in recent years to BCs inside the cytosol and nucleus. BCs at the cell membrane have not been studied to the same extent so far. However, recent studies provide increasingly more examples of interfaces between BCs and membranes which function as platforms for diverse biomolecular processes. Galectin-3, for example, is known to mediate clathrin-independent endocytosis and has been recently shown to undergo liquid-liquid phase separation, but the function of BCs of galectin-3 in endocytic pit formation is unknown. Here, we use dissipative particle dynamics simulations to study a generic coarse-grained model for BCs interacting with lipid membranes. In analogy to galectin-3, we consider polymers comprising two segments - one of them mediates multivalent attractive interactions between the polymers, and the other one has affinity for association with specific lipid head groups. When these polymers are brought into contact with a multi-component membrane, they spontaneously assemble into droplets and, simultaneously, induce lateral separation of lipids within the membrane. Interestingly, we find that if the membrane is bent, the polymer droplets localize at membrane regions curved inward. Although the polymers have no particular shape or intrinsic curvature, they appear to sense membrane curvature when clustered at the membrane. Our results indicate toward a generic mechanism of membrane curvature sensing by BCs involved in such processes as endocytosis.
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Affiliation(s)
- Midhun Mohan Anila
- Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland.
| | - Rikhia Ghosh
- Icahn School of Medicine at Mount Sinai, 1 Gustave L. Levy Pl, New York, NY 10029, USA
| | - Bartosz Różycki
- Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland.
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4
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Sun B, Kekenes-Huskey PM. Myofilament-associated proteins with intrinsic disorder (MAPIDs) and their resolution by computational modeling. Q Rev Biophys 2023; 56:e2. [PMID: 36628457 PMCID: PMC11070111 DOI: 10.1017/s003358352300001x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
The cardiac sarcomere is a cellular structure in the heart that enables muscle cells to contract. Dozens of proteins belong to the cardiac sarcomere, which work in tandem to generate force and adapt to demands on cardiac output. Intriguingly, the majority of these proteins have significant intrinsic disorder that contributes to their functions, yet the biophysics of these intrinsically disordered regions (IDRs) have been characterized in limited detail. In this review, we first enumerate these myofilament-associated proteins with intrinsic disorder (MAPIDs) and recent biophysical studies to characterize their IDRs. We secondly summarize the biophysics governing IDR properties and the state-of-the-art in computational tools toward MAPID identification and characterization of their conformation ensembles. We conclude with an overview of future computational approaches toward broadening the understanding of intrinsic disorder in the cardiac sarcomere.
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Affiliation(s)
- Bin Sun
- Research Center for Pharmacoinformatics (The State-Province Key Laboratories of Biomedicine-Pharmaceutics of China), Department of Medicinal Chemistry and Natural Medicine Chemistry, College of Pharmacy, Harbin Medical University, Harbin 150081, China
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5
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Rizuan A, Jovic N, Phan TM, Kim YC, Mittal J. Developing Bonded Potentials for a Coarse-Grained Model of Intrinsically Disordered Proteins. J Chem Inf Model 2022; 62:4474-4485. [PMID: 36066390 PMCID: PMC10165611 DOI: 10.1021/acs.jcim.2c00450] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Recent advances in residue-level coarse-grained (CG) computational models have enabled molecular-level insights into biological condensates of intrinsically disordered proteins (IDPs), shedding light on the sequence determinants of their phase separation. The existing CG models that treat protein chains as flexible molecules connected via harmonic bonds cannot populate common secondary-structure elements. Here, we present a CG dihedral angle potential between four neighboring beads centered at Cα atoms to faithfully capture the transient helical structures of IDPs. In order to parameterize and validate our new model, we propose Cα-based helix assignment rules based on dihedral angles that succeed in reproducing the atomistic helicity results of a polyalanine peptide and folded proteins. We then introduce sequence-dependent dihedral angle potential parameters (εd) and use experimentally available helical propensities of naturally occurring 20 amino acids to find their optimal values. The single-chain helical propensities from the CG simulations for commonly studied prion-like IDPs are in excellent agreement with the NMR-based α-helix fraction, demonstrating that the new HPS-SS model can accurately produce structural features of IDPs. Furthermore, this model can be easily implemented for large-scale assembly simulations due to its simplicity.
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Affiliation(s)
- Azamat Rizuan
- Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, United States
| | - Nina Jovic
- Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, United States
| | - Tien M Phan
- Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, United States
| | - Young C Kim
- Center for Materials Physics and Technology, Naval Research Laboratory, Washington, District of Columbia 20375, United States
| | - Jeetain Mittal
- Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, United States
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6
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Stelzl L, Pietrek LM, Holla A, Oroz J, Sikora M, Köfinger J, Schuler B, Zweckstetter M, Hummer G. Global Structure of the Intrinsically Disordered Protein Tau Emerges from Its Local Structure. JACS AU 2022; 2:673-686. [PMID: 35373198 PMCID: PMC8970000 DOI: 10.1021/jacsau.1c00536] [Citation(s) in RCA: 33] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Indexed: 05/13/2023]
Abstract
The paradigmatic disordered protein tau plays an important role in neuronal function and neurodegenerative diseases. To disentangle the factors controlling the balance between functional and disease-associated conformational states, we build a structural ensemble of the tau K18 fragment containing the four pseudorepeat domains involved in both microtubule binding and amyloid fibril formation. We assemble 129-residue-long tau K18 chains with atomic detail from an extensive fragment library constructed with molecular dynamics simulations. We introduce a reweighted hierarchical chain growth (RHCG) algorithm that integrates experimental data reporting on the local structure into the assembly process in a systematic manner. By combining Bayesian ensemble refinement with importance sampling, we obtain well-defined ensembles and overcome the problem of exponentially varying weights in the integrative modeling of long-chain polymeric molecules. The resulting tau K18 ensembles capture nuclear magnetic resonance (NMR) chemical shift and J-coupling measurements. Without further fitting, we achieve very good agreement with measurements of NMR residual dipolar couplings. The good agreement with experimental measures of global structure such as single-molecule Förster resonance energy transfer (FRET) efficiencies is improved further by ensemble refinement. By comparing wild-type and mutant ensembles, we show that pathogenic single-point P301L, P301S, and P301T mutations shift the population from the turn-like conformations of the functional microtubule-bound state to the extended conformations of disease-associated tau fibrils. RHCG thus provides us with an atomically detailed view of the population equilibrium between functional and aggregation-prone states of tau K18, and demonstrates that global structural characteristics of this intrinsically disordered protein emerge from its local structure.
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Affiliation(s)
- Lukas
S. Stelzl
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
- Faculty
of Biology, Johannes Gutenberg University
Mainz, Gresemundweg 2, 55128 Mainz, Germany
- KOMET 1, Institute of Physics, Johannes
Gutenberg University Mainz, 55099 Mainz, Germany
- Institute of Molecular Biology (IMB), 55128 Mainz, Germany
| | - Lisa M. Pietrek
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
| | - Andrea Holla
- Department
of Biochemistry, University of Zurich, 8057 Zurich, Switzerland
| | - Javier Oroz
- German
Center for Neurodegenerative Diseases (DZNE), von-Siebold-Str. 3a, 37075 Göttingen, Germany
- Rocasolano
Institute for Physical Chemistry, CSIC, Serrano 119, 28006 Madrid, Spain
| | - Mateusz Sikora
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
- Faculty
of Physics, University of Vienna, Kolingasse 14-16, 1090 Vienna, Austria
| | - Jürgen Köfinger
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
| | - Benjamin Schuler
- Department
of Biochemistry, University of Zurich, 8057 Zurich, Switzerland
- Department
of Physics, University of Zurich, 8057 Zurich, Switzerland
| | - Markus Zweckstetter
- German
Center for Neurodegenerative Diseases (DZNE), von-Siebold-Str. 3a, 37075 Göttingen, Germany
- Department
for NMR-based Structural Biology, Max Planck
Institute for Multidisciplinary Sciences, Am Faßberg 11, 37077 Göttingen, Germany
| | - Gerhard Hummer
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
- Institute
for Biophysics, Goethe University Frankfurt, Max-von-Laue-Straße 9, 60438 Frankfurt am Main, Germany
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7
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Latham AP, Zhang B. Unifying coarse-grained force fields for folded and disordered proteins. Curr Opin Struct Biol 2022; 72:63-70. [PMID: 34536913 PMCID: PMC9057422 DOI: 10.1016/j.sbi.2021.08.006] [Citation(s) in RCA: 21] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2021] [Revised: 08/08/2021] [Accepted: 08/17/2021] [Indexed: 12/22/2022]
Abstract
Liquid-liquid phase separation drives the formation of biological condensates that play essential roles in transcriptional regulation and signal sensing. Computational modeling could provide high-resolution structural characterizations of these condensates and help uncover physicochemical interactions that dictate their stability. However, many protein molecules involved in phase separation often contain multiple ordered domains connected with flexible, structureless linkers. Simulating such proteins necessitates force fields with consistent accuracy for both folded and disordered proteins. We provide a critical review of existing coarse-grained force fields for disordered proteins and highlight the challenges in their application to folded proteins. After discussing existing algorithms for force field parameterization, we propose an optimization strategy that should lead to computer models with improved transferability across protein types.
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Affiliation(s)
- Andrew P Latham
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Bin Zhang
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, USA.
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8
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Co NT, Li MS, Krupa P. Computational Models for the Study of Protein Aggregation. Methods Mol Biol 2022; 2340:51-78. [PMID: 35167070 DOI: 10.1007/978-1-0716-1546-1_4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Protein aggregation has been studied by many groups around the world for many years because it can be the cause of a number of neurodegenerative diseases that have no effective treatment. Obtaining the structure of related fibrils and toxic oligomers, as well as describing the pathways and main factors that govern the self-organization process, is of paramount importance, but it is also very difficult. To solve this problem, experimental and computational methods are often combined to get the most out of each method. The effectiveness of the computational approach largely depends on the construction of a reasonable molecular model. Here we discussed different versions of the four most popular all-atom force fields AMBER, CHARMM, GROMOS, and OPLS, which have been developed for folded and intrinsically disordered proteins, or both. Continuous and discrete coarse-grained models, which were mainly used to study the kinetics of aggregation, are also summarized.
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Affiliation(s)
- Nguyen Truong Co
- Institute of Physics, Polish Academy of Sciences, Warsaw, Poland
| | - Mai Suan Li
- Institute of Physics, Polish Academy of Sciences, Warsaw, Poland
- Institute for Computational Science and Technology, Ho Chi Minh City, Vietnam
| | - Pawel Krupa
- Institute of Physics, Polish Academy of Sciences, Warsaw, Poland.
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9
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Nguyen PH, Derreumaux P. Computer Simulations Aimed at Exploring Protein Aggregation and Dissociation. Methods Mol Biol 2022; 2340:175-196. [PMID: 35167075 DOI: 10.1007/978-1-0716-1546-1_9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Protein aggregation can lead to well-defined structures that are functional, but is also the cause of the death of neuron cells in many neurodegenerative diseases. The complexity of the molecular events involved in the aggregation kinetics of amyloid proteins and the transient and heterogeneous characters of all oligomers prevent high-resolution structural experiments. As a result, computer simulations have been used to determine the atomic structures of amyloid proteins at different association stages as well as to understand fibril dissociation. In this chapter, we first review the current computer simulation methods used for aggregation with some atomistic and coarse-grained results aimed at better characterizing the early formed oligomers and amyloid fibril formation. Then we present the applications of non-equilibrium molecular dynamics simulations to comprehend the dissociation of protein assemblies.
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Affiliation(s)
- Phuong H Nguyen
- Laboratoire de Biochimie Théorique, UPR 9080, CNRS, Université de Paris, Paris, France
- Institut de Biologie Physico-Chimique, Fondation Edmond de Rothschild, PSL Research University, Paris, France
| | - Philippe Derreumaux
- Laboratoire de Biochimie Théorique, UPR 9080, CNRS, Université de Paris, Paris, France.
- Institut de Biologie Physico-Chimique, Fondation Edmond de Rothschild, PSL Research University, Paris, France.
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10
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Latham AP, Zhang B. Consistent Force Field Captures Homologue-Resolved HP1 Phase Separation. J Chem Theory Comput 2021; 17:3134-3144. [PMID: 33826337 PMCID: PMC8119372 DOI: 10.1021/acs.jctc.0c01220] [Citation(s) in RCA: 38] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Many proteins have been shown to function via liquid-liquid phase separation. Computational modeling could offer much needed structural details of protein condensates and reveal the set of molecular interactions that dictate their stability. However, the presence of both ordered and disordered domains in these proteins places a high demand on the model accuracy. Here, we present an algorithm to derive a coarse-grained force field, MOFF, which can model both ordered and disordered proteins with consistent accuracy. It combines maximum entropy biasing, least-squares fitting, and basic principles of energy landscape theory to ensure that MOFF recreates experimental radii of gyration while predicting the folded structures for globular proteins with lower energy. The theta temperature determined from MOFF separates ordered and disordered proteins at 300 K and exhibits a strikingly linear relationship with amino acid sequence composition. We further applied MOFF to study the phase behavior of HP1, an essential protein for post-translational modification and spatial organization of chromatin. The force field successfully resolved the structural difference of two HP1 homologues despite their high sequence similarity. We carried out large-scale simulations with hundreds of proteins to determine the critical temperature of phase separation and uncover multivalent interactions that stabilize higher-order assemblies. In all, our work makes significant methodological strides to connect theories of ordered and disordered proteins and provides a powerful tool for studying liquid-liquid phase separation with near-atomistic details.
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Affiliation(s)
- Andrew P Latham
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Bin Zhang
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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11
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Mioduszewski Ł, Cieplak M. Viscoelastic properties of wheat gluten in a molecular dynamics study. PLoS Comput Biol 2021; 17:e1008840. [PMID: 33760823 PMCID: PMC8021197 DOI: 10.1371/journal.pcbi.1008840] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Revised: 04/05/2021] [Accepted: 02/28/2021] [Indexed: 11/19/2022] Open
Abstract
Wheat (Triticum spp.) gluten consists mainly of intrinsincally disordered storage proteins (glutenins and gliadins) that can form megadalton-sized networks. These networks are responsible for the unique viscoelastic properties of wheat dough and affect the quality of bread. These properties have not yet been studied by molecular level simulations. Here, we use a newly developed α-C-based coarse-grained model to study ∼ 4000-residue systems. The corresponding time-dependent properties are studied through shear and axial deformations. We measure the response force to the deformation, the number of entanglements and cavities, the mobility of residues, the number of the inter-chain bonds, etc. Glutenins are shown to influence the mechanics of gluten much more than gliadins. Our simulations are consistent with the existing ideas about gluten elasticity and emphasize the role of entanglements and hydrogen bonding. We also demonstrate that the storage proteins in maize and rice lead to weaker elasticity which points to the unique properties of wheat gluten. During the breadmaking process, expanding gas bubbles cause the dough to increase volume. Gluten proteins act as an elastic scaffold in that process, allowing the wheat dough to grow more than other kinds of dough. Thus, explaining the unique viscoelastic properties of gluten at the molecular level may be of great interest to the baking industry. Assessing the structural properties of gluten is difficult because its proteins are disordered. We provide the first molecular dynamics model of gluten elasticity, that is able to distinguish gluten and proteins from different plants, like maize and rice. Our model shows the structural changes the gluten proteins undergo during their deformation, which mimics the mixing of dough during kneading. It also allows for a determination of the force required to extend gluten proteins, as during baking. The data confirms existing theories about gluten, but it also provides molecular-level information about the extraordinary elasticity of gluten.
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Affiliation(s)
| | - Marek Cieplak
- Institute of Physics, Polish Academy of Sciences, Warsaw, Poland
- * E-mail:
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12
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Benayad Z, von Bülow S, Stelzl LS, Hummer G. Simulation of FUS Protein Condensates with an Adapted Coarse-Grained Model. J Chem Theory Comput 2021; 17:525-537. [PMID: 33307683 PMCID: PMC7872324 DOI: 10.1021/acs.jctc.0c01064] [Citation(s) in RCA: 87] [Impact Index Per Article: 29.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2020] [Indexed: 01/02/2023]
Abstract
Disordered proteins and nucleic acids can condense into droplets that resemble the membraneless organelles observed in living cells. MD simulations offer a unique tool to characterize the molecular interactions governing the formation of these biomolecular condensates, their physicochemical properties, and the factors controlling their composition and size. However, biopolymer condensation depends sensitively on the balance between different energetic and entropic contributions. Here, we develop a general strategy to fine-tune the potential energy function for molecular dynamics simulations of biopolymer phase separation. We rebalance protein-protein interactions against solvation and entropic contributions to match the excess free energy of transferring proteins between dilute solution and condensate. We illustrate this formalism by simulating liquid droplet formation of the FUS low-complexity domain (LCD) with a rebalanced MARTINI model. By scaling the strength of the nonbonded interactions in the coarse-grained MARTINI potential energy function, we map out a phase diagram in the plane of protein concentration and interaction strength. Above a critical scaling factor of αc ≈ 0.6, FUS-LCD condensation is observed, where α = 1 and 0 correspond to full and repulsive interactions in the MARTINI model. For a scaling factor α = 0.65, we recover experimental densities of the dilute and dense phases, and thus the excess protein transfer free energy into the droplet and the saturation concentration where FUS-LCD condenses. In the region of phase separation, we simulate FUS-LCD droplets of four different sizes in stable equilibrium with the dilute phase and slabs of condensed FUS-LCD for tens of microseconds, and over one millisecond in aggregate. We determine surface tensions in the range of 0.01-0.4 mN/m from the fluctuations of the droplet shape and from the capillary-wave-like broadening of the interface between the two phases. From the dynamics of the protein end-to-end distance, we estimate shear viscosities from 0.001 to 0.02 Pa s for the FUS-LCD droplets with scaling factors α in the range of 0.625-0.75, where we observe liquid droplets. Significant hydration of the interior of the droplets keeps the proteins mobile and the droplets fluid.
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Affiliation(s)
- Zakarya Benayad
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
- Département
de Chimie, École Normale Supérieure, PSL University, 75005 Paris, France
| | - Sören von Bülow
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
| | - Lukas S. Stelzl
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
| | - Gerhard Hummer
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
- Institute
for Biophysics, Goethe University Frankfurt, 60438 Frankfurt
am Main, Germany
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