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Kuwajima K. The Molten Globule, and Two-State vs. Non-Two-State Folding of Globular Proteins. Biomolecules 2020; 10:biom10030407. [PMID: 32155758 PMCID: PMC7175247 DOI: 10.3390/biom10030407] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2020] [Revised: 03/03/2020] [Accepted: 03/06/2020] [Indexed: 11/16/2022] Open
Abstract
From experimental studies of protein folding, it is now clear that there are two types of folding behavior, i.e., two-state folding and non-two-state folding, and understanding the relationships between these apparently different folding behaviors is essential for fully elucidating the molecular mechanisms of protein folding. This article describes how the presence of the two types of folding behavior has been confirmed experimentally, and discusses the relationships between the two-state and the non-two-state folding reactions, on the basis of available data on the correlations of the folding rate constant with various structure-based properties, which are determined primarily by the backbone topology of proteins. Finally, a two-stage hierarchical model is proposed as a general mechanism of protein folding. In this model, protein folding occurs in a hierarchical manner, reflecting the hierarchy of the native three-dimensional structure, as embodied in the case of non-two-state folding with an accumulation of the molten globule state as a folding intermediate. The two-state folding is thus merely a simplified version of the hierarchical folding caused either by an alteration in the rate-limiting step of folding or by destabilization of the intermediate.
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Affiliation(s)
- Kunihiro Kuwajima
- Department of Physics, School of Science, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; ; Tel.: +81-90-5435-6540
- School of Computational Sciences, Korea Institute for Advanced Study (KIAS), Seoul 02455, Korea
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Liu L, Ma M, Cui J. A novel model-based on FCM-LM algorithm for prediction of protein folding rate. J Bioinform Comput Biol 2017; 15:1750012. [PMID: 28513252 DOI: 10.1142/s0219720017500123] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The prediction of protein folding rates is of paramount importance in describing the protein folding mechanism, which has broad applications in fields such as enzyme engineering and protein engineering. Therefore, predicting protein folding rates using the first-order of protein sequence, secondary structure and amino acid properties has become a very active research topic in recent years. This paper presents a new fuzzy cognitive map (FCM) model based on deep learning neural networks which uses data obtained from biological experiments to predict the protein folding rate. FCM extracts the important data features from the protein sequence which then initializes the deep neural networks effectively. It was found that the Levenberg-Marquardt (LM) algorithm for deep neural networks can improve the prediction accuracy of the protein folding rates. The correlation coefficient between the predicted values and those real values obtained from experiments reached 0.94 and 0.9 in two independent numerical tests.
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Affiliation(s)
- Longlong Liu
- 1 Department of Mathematics, Ocean University of China, Qingdao 266000, P. R. China
| | - Mingjiao Ma
- 1 Department of Mathematics, Ocean University of China, Qingdao 266000, P. R. China
| | - Jing Cui
- 1 Department of Mathematics, Ocean University of China, Qingdao 266000, P. R. China
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Finkelstein AV, Badretdin AJ, Galzitskaya OV, Ivankov DN, Bogatyreva NS, Garbuzynskiy SO. There and back again: Two views on the protein folding puzzle. Phys Life Rev 2017; 21:56-71. [PMID: 28190683 DOI: 10.1016/j.plrev.2017.01.025] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2016] [Revised: 01/05/2017] [Accepted: 01/19/2017] [Indexed: 02/08/2023]
Abstract
The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured folding times of single-domain globular proteins range from microseconds to hours: the difference (10-11 orders of magnitude) is the same as that between the life span of a mosquito and the age of the universe. This review describes physical theories of rates of overcoming the free-energy barrier separating the natively folded (N) and unfolded (U) states of protein chains in both directions: "U-to-N" and "N-to-U". In the theory of protein folding rates a special role is played by the point of thermodynamic (and kinetic) equilibrium between the native and unfolded state of the chain; here, the theory obtains the simplest form. Paradoxically, a theoretical estimate of the folding time is easier to get from consideration of protein unfolding (the "N-to-U" transition) rather than folding, because it is easier to outline a good unfolding pathway of any structure than a good folding pathway that leads to the stable fold, which is yet unknown to the folding protein chain. And since the rates of direct and reverse reactions are equal at the equilibrium point (as follows from the physical "detailed balance" principle), the estimated folding time can be derived from the estimated unfolding time. Theoretical analysis of the "N-to-U" transition outlines the range of protein folding rates in a good agreement with experiment. Theoretical analysis of folding (the "U-to-N" transition), performed at the level of formation and assembly of protein secondary structures, outlines the upper limit of protein folding times (i.e., of the time of search for the most stable fold). Both theories come to essentially the same results; this is not a surprise, because they describe overcoming one and the same free-energy barrier, although the way to the top of this barrier from the side of the unfolded state is very different from the way from the side of the native state; and both theories agree with experiment. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control and explain the observed maximal size of the "foldable" protein domains.
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Affiliation(s)
- Alexei V Finkelstein
- Institute of Protein Research, Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russian Federation.
| | - Azat J Badretdin
- National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD 20894, USA
| | - Oxana V Galzitskaya
- Institute of Protein Research, Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russian Federation
| | - Dmitry N Ivankov
- Institute of Protein Research, Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russian Federation; Bioinformatics and Genomics Programme, Centre for Genomic Regulation (CRG), The Barcelona Institute of Science and Technology, 08003 Barcelona, Spain; Universitat Pompeu Fabra (UPF), 08003 Barcelona, Spain
| | - Natalya S Bogatyreva
- Institute of Protein Research, Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russian Federation; Bioinformatics and Genomics Programme, Centre for Genomic Regulation (CRG), The Barcelona Institute of Science and Technology, 08003 Barcelona, Spain; Universitat Pompeu Fabra (UPF), 08003 Barcelona, Spain
| | - Sergiy O Garbuzynskiy
- Institute of Protein Research, Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russian Federation
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Banach M, Prudhomme N, Carpentier M, Duprat E, Papandreou N, Kalinowska B, Chomilier J, Roterman I. Contribution to the prediction of the fold code: application to immunoglobulin and flavodoxin cases. PLoS One 2015; 10:e0125098. [PMID: 25915049 PMCID: PMC4411048 DOI: 10.1371/journal.pone.0125098] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2014] [Accepted: 03/20/2015] [Indexed: 12/19/2022] Open
Abstract
Background Folding nucleus of globular proteins formation starts by the mutual interaction of a group of hydrophobic amino acids whose close contacts allow subsequent formation and stability of the 3D structure. These early steps can be predicted by simulation of the folding process through a Monte Carlo (MC) coarse grain model in a discrete space. We previously defined MIRs (Most Interacting Residues), as the set of residues presenting a large number of non-covalent neighbour interactions during such simulation. MIRs are good candidates to define the minimal number of residues giving rise to a given fold instead of another one, although their proportion is rather high, typically [15-20]% of the sequences. Having in mind experiments with two sequences of very high levels of sequence identity (up to 90%) but different folds, we combined the MIR method, which takes sequence as single input, with the “fuzzy oil drop” (FOD) model that requires a 3D structure, in order to estimate the residues coding for the fold. FOD assumes that a globular protein follows an idealised 3D Gaussian distribution of hydrophobicity density, with the maximum in the centre and minima at the surface of the “drop”. If the actual local density of hydrophobicity around a given amino acid is as high as the ideal one, then this amino acid is assigned to the core of the globular protein, and it is assumed to follow the FOD model. Therefore one obtains a distribution of the amino acids of a protein according to their agreement or rejection with the FOD model. Results We compared and combined MIR and FOD methods to define the minimal nucleus, or keystone, of two populated folds: immunoglobulin-like (Ig) and flavodoxins (Flav). The combination of these two approaches defines some positions both predicted as a MIR and assigned as accordant with the FOD model. It is shown here that for these two folds, the intersection of the predicted sets of residues significantly differs from random selection. It reduces the number of selected residues by each individual method and allows a reasonable agreement with experimentally determined key residues coding for the particular fold. In addition, the intersection of the two methods significantly increases the specificity of the prediction, providing a robust set of residues that constitute the folding nucleus.
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Affiliation(s)
- Mateusz Banach
- Department of Bioinformatics and Telemedicine, Medical College, Jagiellonian University, Krakow, Poland
| | - Nicolas Prudhomme
- Protein Structure Prediction group, IMPMC, UPMC & CNRS, Paris, France
| | - Mathilde Carpentier
- Protein Structure Prediction group, IMPMC, UPMC & CNRS, Paris, France
- RPBS, 35 rue Hélène Brion, 75013, Paris, France
| | - Elodie Duprat
- Protein Structure Prediction group, IMPMC, UPMC & CNRS, Paris, France
- RPBS, 35 rue Hélène Brion, 75013, Paris, France
| | - Nikolaos Papandreou
- Genetics Department, Agricultural University of Athens, Iera Odos 75, Athens, Greece
| | - Barbara Kalinowska
- Department of Bioinformatics and Telemedicine, Medical College, Jagiellonian University, Krakow, Poland
| | - Jacques Chomilier
- Protein Structure Prediction group, IMPMC, UPMC & CNRS, Paris, France
- RPBS, 35 rue Hélène Brion, 75013, Paris, France
- * E-mail: (JC); (IR)
| | - Irena Roterman
- Department of Bioinformatics and Telemedicine, Medical College, Jagiellonian University, Krakow, Poland
- * E-mail: (JC); (IR)
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Savol AJ, Chennubhotla CS. Quantifying the Sources of Kinetic Frustration in Folding Simulations of Small Proteins. J Chem Theory Comput 2014; 10:2964-2974. [PMID: 25136267 PMCID: PMC4132847 DOI: 10.1021/ct500361w] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2014] [Indexed: 11/28/2022]
Abstract
![]()
Experiments
and atomistic simulations of polypeptides have revealed
structural intermediates that promote or inhibit conformational transitions
to the native state during folding. We invoke a concept of “kinetic
frustration” to quantify the prevalence and impact of these
behaviors on folding rates within a large set of atomistic simulation
data for 10 fast-folding proteins, where each protein’s conformational
space is represented as a Markov state model of conformational transitions.
Our graph theoretic approach addresses what conformational features
correlate with folding inhibition and therefore permits comparison
among features within a single protein network and also more generally
between proteins. Nonnative contacts and nonnative secondary structure
formation can thus be quantitatively implicated in inhibiting folding
for several of the tested peptides.
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Affiliation(s)
- Andrej J Savol
- Dept. of Computational and Systems Biology, School of Medicine, University of Pittsburgh , Pittsburgh, Pennsylvania 15260, United States ; Joint Carnegie Mellon University-University of Pittsburgh PhD Program in Computational Biology, Pittsburgh, Pennsylvania 15260, United States
| | - Chakra S Chennubhotla
- Dept. of Computational and Systems Biology, School of Medicine, University of Pittsburgh , Pittsburgh, Pennsylvania 15260, United States
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Galzitskaya OV, Pereyaslavets LB, Glyakina AV. Folding of Right- and Left-Handed Three-Helix Proteins. Isr J Chem 2014. [DOI: 10.1002/ijch.201300146] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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Kaya H, Uzunoğlu Z, Chan HS. Spatial ranges of driving forces are a key determinant of protein folding cooperativity and rate diversity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:044701. [PMID: 24229309 DOI: 10.1103/physreve.88.044701] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2013] [Revised: 08/21/2013] [Indexed: 06/02/2023]
Abstract
The physical basis of two-state-like folding transitions and the tremendous diversity in folding rates is elucidated by directly simulating the folding kinetics of 52 representative proteins. Relative to the results from a common modeling approach, the diversity of the simulated folding rates can be increased from ~10(2.1) to the experimental ~10(6.0) by a modest decrease in the spatial range of the attractive potential. The required theoretical range is consistent with desolvation physics and is notably much more permissive than that needed for two-state-like homopolymer collapse.
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Affiliation(s)
- Hüseyin Kaya
- Department of Biophysics, Faculty of Medicine, University of Gaziantep, 27310 Gaziantep, Turkey
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Glyakina AV, Pereyaslavets LB, Galzitskaya OV. Right- and left-handed three-helix proteins. I. Experimental and simulation analysis of differences in folding and structure. Proteins 2013; 81:1527-41. [DOI: 10.1002/prot.24301] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2012] [Revised: 03/27/2013] [Accepted: 03/28/2013] [Indexed: 11/08/2022]
Affiliation(s)
- Anna V. Glyakina
- Institute of Protein Research; Russian Academy of Sciences; Pushchino, Moscow Region 142290 Russia
- Institute of Mathematical Problems of Biology; Russian Academy of Sciences; Pushchino, Moscow Region 142290 Russia
| | - Leonid B. Pereyaslavets
- Institute of Protein Research; Russian Academy of Sciences; Pushchino, Moscow Region 142290 Russia
| | - Oxana V. Galzitskaya
- Institute of Protein Research; Russian Academy of Sciences; Pushchino, Moscow Region 142290 Russia
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Zhdanov VP, Höök F. Nucleation in mesoscopic systems under transient conditions: peptide-induced pore formation in vesicles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:042718. [PMID: 23679460 DOI: 10.1103/physreve.87.042718] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2013] [Indexed: 06/02/2023]
Abstract
Attachment of lytic peptides to the lipid membrane of virions or bacteria is often accompanied by their aggregation and pore formation, resulting eventually in membrane rupture and pathogen neutralization. The membrane rupture may occur gradually via formation of many pores or abruptly after the formation of the first pore. In academic studies, this process is observed during interaction of peptides with lipid vesicles. We present an analytical model and the corresponding Monte Carlo simulations focused on the pore formation in such situations. Specifically, we calculate the time of the first nucleation-limited pore-formation event and show the distribution of this time in the regime when the fluctuations of the number of peptides attached to a vesicle are appreciable. The results obtained are used to clarify the mechanism of the pore formation and membrane destabilization observed recently during interaction of highly active α-helical peptide with sub-100-nm lipid vesicles that mimic enveloped viruses with nanoscale membrane curvature. The model proposed and the analysis presented are generic and may be applicable to other meso- and nanosystems.
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Affiliation(s)
- Vladimir P Zhdanov
- Department of Applied Physics, Chalmers University of Technology, S-41296 Göteborg, Sweden.
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