1
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Yanaka S, Yagi-Utsumi M, Kato K, Kuwajima K. The B domain of protein A retains residual structures in 6 M guanidinium chloride as revealed by hydrogen/deuterium-exchange NMR spectroscopy. Protein Sci 2023; 32:e4569. [PMID: 36659853 PMCID: PMC9926473 DOI: 10.1002/pro.4569] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2022] [Revised: 01/10/2023] [Accepted: 01/13/2023] [Indexed: 01/21/2023]
Abstract
The characterization of residual structures persistent in unfolded proteins is an important issue in studies of protein folding, because the residual structures present, if any, may form a folding initiation site and guide the subsequent folding reactions. Here, we studied the residual structures of the isolated B domain (BDPA) of staphylococcal protein A in 6 M guanidinium chloride. BDPA is a small three-helix-bundle protein, and until recently its folding/unfolding reaction has been treated as a simple two-state process between the native and the fully unfolded states. We employed a dimethylsulfoxide (DMSO)-quenched hydrogen/deuterium (H/D)-exchange 2D NMR techniques with the use of spin desalting columns, which allowed us to investigate the H/D-exchange behavior of individually identified peptide amide (NH) protons. We obtained H/D-exchange protection factors of the 21 NH protons that form an α-helical hydrogen bond in the native structure, and the majority of these NH protons were significantly protected with a protection factor of 2.0-5.2 in 6 M guanidinium chloride, strongly suggesting that these weakly protected NH protons form much stronger hydrogen bonds under native folding conditions. The results can be used to deduce the structure of an early folding intermediate, when such an intermediate is shown by other methods. Among three native helical regions, the third helix in the C-terminal side was highly protected and stabilized by side-chain salt bridges, probably acting as the folding initiation site of BDPA. The present results are discussed in relation to previous experimental and computational findings on the folding mechanisms of BDPA.
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Affiliation(s)
- Saeko Yanaka
- Exploratory Research Center on Life and Living Systems (ExCELLS) and Institute for Molecular Science (IMS), National Institutes of Natural Sciences, Myodaiji, Okazaki, Aichi, Japan.,Department of Functional Molecular Science, School of Physical Sciences, SOKENDAI (the Graduate University for Advanced Studies), Myodaiji, Okazaki, Aichi, Japan.,Graduate School of Pharmaceutical Sciences, Nagoya City University, Mizuho-ku, Nagoya, Aichi, Japan
| | - Maho Yagi-Utsumi
- Exploratory Research Center on Life and Living Systems (ExCELLS) and Institute for Molecular Science (IMS), National Institutes of Natural Sciences, Myodaiji, Okazaki, Aichi, Japan.,Department of Functional Molecular Science, School of Physical Sciences, SOKENDAI (the Graduate University for Advanced Studies), Myodaiji, Okazaki, Aichi, Japan.,Graduate School of Pharmaceutical Sciences, Nagoya City University, Mizuho-ku, Nagoya, Aichi, Japan
| | - Koichi Kato
- Exploratory Research Center on Life and Living Systems (ExCELLS) and Institute for Molecular Science (IMS), National Institutes of Natural Sciences, Myodaiji, Okazaki, Aichi, Japan.,Department of Functional Molecular Science, School of Physical Sciences, SOKENDAI (the Graduate University for Advanced Studies), Myodaiji, Okazaki, Aichi, Japan.,Graduate School of Pharmaceutical Sciences, Nagoya City University, Mizuho-ku, Nagoya, Aichi, Japan
| | - Kunihiro Kuwajima
- Department of Physics, School of Science, University of Tokyo, Bunkyo-ku, Tokyo, Japan
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2
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Joshi SY, Deshmukh SA. A review of advancements in coarse-grained molecular dynamics simulations. MOLECULAR SIMULATION 2020. [DOI: 10.1080/08927022.2020.1828583] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Soumil Y. Joshi
- Department of Chemical Engineering, Virginia Tech, Blacksburg, VA, USA
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3
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Trotter D, Wallin S. Effects of Topology and Sequence in Protein Folding Linked via Conformational Fluctuations. Biophys J 2020; 118:1370-1380. [PMID: 32061276 DOI: 10.1016/j.bpj.2020.01.020] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2019] [Revised: 12/17/2019] [Accepted: 01/13/2020] [Indexed: 01/18/2023] Open
Abstract
Experiments have compared the folding of proteins with different amino acid sequences but the same basic structure, or fold. Results indicate that folding is robust to sequence variations for proteins with some nonlocal folds, such as all-β, whereas the folding of more local, all-α proteins typically exhibits a stronger sequence dependence. Here, we use a coarse-grained model to systematically study how variations in sequence perturb the folding energy landscapes of three model sequences with 3α, 4β + α, and β-barrel folds, respectively. These three proteins exhibit folding features in line with experiments, including expected rank order in the cooperativity of the folding transition and stability-dependent shifts in the location of the free-energy barrier to folding. Using a generalized-ensemble simulation approach, we determine the thermodynamics of around 2000 sequence variants representing all possible hydrophobic or polar single- and double-point mutations. From an analysis of the subset of stability-neutral mutations, we find that folding is perturbed in a topology-dependent manner, with the β-barrel protein being the most robust. Our analysis shows, in particular, that the magnitude of mutational perturbations of the transition state is controlled in part by the size or "width" of the underlying conformational ensemble. This result suggests that the mutational robustness of the folding of the β-barrel protein is underpinned by its conformationally restricted transition state ensemble, revealing a link between sequence and topological effects in protein folding.
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Affiliation(s)
- Daniel Trotter
- Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's, Newfoundland, Canada
| | - Stefan Wallin
- Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's, Newfoundland, Canada.
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4
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Shao Q, Zhu W. The effects of implicit modeling of nonpolar solvation on protein folding simulations. Phys Chem Chem Phys 2018; 20:18410-18419. [PMID: 29946610 DOI: 10.1039/c8cp03156h] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Implicit solvent models, in which the polar and nonpolar solvation free-energies of solute molecules are treated separately, have been widely adopted for molecular dynamics simulation of protein folding. While the development of the implicit models is mainly focused on the methodological improvement and key parameter optimization for polar solvation, nonpolar solvation has been either ignored or described by a simplistic surface area (SA) model. In this work, we performed the folding simulations of multiple β-hairpin and α-helical proteins with varied surface tension coefficients embedded in the SA model to clearly demonstrate the effects of nonpolar solvation treated by a popular SA model on protein folding. The results indicate that the change in the surface tension coefficient does not alter the ability of implicit solvent simulations to reproduce a protein native structure but indeed controls the components of the equilibrium conformational ensemble and modifies the energetic characterization of the folding transition pathway. The suitably set surface tension coefficient can yield explicit solvent simulations and/or experimentally suggested folding mechanism of protein. In addition, the implicit treatment of both polar and nonpolar components of solvation free-energy contributes to the overestimation of the secondary structure in implicit solvent simulations.
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Affiliation(s)
- Qiang Shao
- Drug Discovery and Design Center, CAS Key Laboratory of Receptor Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 555 Zuchongzhi Road, Shanghai, 201203, China.
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5
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Shao Q, Zhu W. How Well Can Implicit Solvent Simulations Explore Folding Pathways? A Quantitative Analysis of α-Helix Bundle Proteins. J Chem Theory Comput 2017; 13:6177-6190. [DOI: 10.1021/acs.jctc.7b00726] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Qiang Shao
- Drug
Discovery and Design Center, CAS Key Laboratory of Receptor Research,
Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 555 Zuchongzhi Road, Shanghai 201203, China
- University of
Chinese Academy of Sciences, Beijing 100049, China
| | - Weiliang Zhu
- Drug
Discovery and Design Center, CAS Key Laboratory of Receptor Research,
Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 555 Zuchongzhi Road, Shanghai 201203, China
- University of
Chinese Academy of Sciences, Beijing 100049, China
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6
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7
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Accounting for a mirror-image conformation as a subtle effect in protein folding. Proc Natl Acad Sci U S A 2014; 111:8458-63. [PMID: 24912167 DOI: 10.1073/pnas.1407837111] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
By using local (free-energy profiles along the amino acid sequence and (13)C(α) chemical shifts) and global (principal component) analyses to examine the molecular dynamics of protein-folding trajectories, generated with the coarse-grained united-residue force field, for the B domain of staphylococcal protein A, we are able to (i) provide the main reason for formation of the mirror-image conformation of this protein, namely, a slow formation of the second loop and part of the third helix (Asp29-Asn35), caused by the presence of multiple local conformational states in this portion of the protein; (ii) show that formation of the mirror-image topology is a subtle effect resulting from local interactions; (iii) provide a mechanism for how protein A overcomes the barrier between the metastable mirror-image state and the native state; and (iv) offer a plausible reason to explain why protein A does not remain in the metastable mirror-image state even though the mirror-image and native conformations are at least energetically compatible.
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8
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Shao Q. Probing Sequence Dependence of Folding Pathway of α-Helix Bundle Proteins through Free Energy Landscape Analysis. J Phys Chem B 2014; 118:5891-900. [DOI: 10.1021/jp5043393] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Qiang Shao
- Drug Discovery and Design
Center, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 555 Zuchongzhi Road, Shanghai 201203, China
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9
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Hills RD. Balancing bond, nonbond, and gō-like terms in coarse grain simulations of conformational dynamics. Methods Mol Biol 2014; 1084:123-140. [PMID: 24061919 DOI: 10.1007/978-1-62703-658-0_7] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Characterization of the protein conformational landscape remains a challenging problem, whether it concerns elucidating folding mechanisms, predicting native structures or modeling functional transitions. Coarse-grained molecular dynamics simulation methods enable exhaustive sampling of the energetic landscape at resolutions of biological interest. The general utility of structure-based models is reviewed along with their differing levels of approximation. Simple Gō models incorporate attractive native interactions and repulsive nonnative contacts, resulting in an ideal smooth landscape. Non-Gō coarse-grained models reduce the parameter set as needed but do not include bias to any desired native structure. While non-Gō models have achieved limited success in protein coarse-graining, they can be combined with native structured-based potentials to create a balanced and powerful force field. Recent applications of such Gō-like models have yielded insight into complex folding mechanisms and conformational transitions in large macromolecules. The accuracy and usefulness of reduced representations are also revealed to be a function of the mathematical treatment of the intrinsic bonded topology.
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Affiliation(s)
- Ronald D Hills
- Department of Pharmaceutical Sciences, University of New England, Portland, ME, USA
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10
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Kapoor A, Travesset A. Folding 19 proteins to their native state and stability of large proteins from a coarse-grained model. Proteins 2013; 82:505-16. [PMID: 24115081 DOI: 10.1002/prot.24416] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2013] [Revised: 08/23/2013] [Accepted: 09/04/2013] [Indexed: 11/10/2022]
Abstract
We develop an intermediate resolution model, where the backbone is modeled with atomic resolution but the side chain with a single bead, by extending our previous model (Proteins (2013) DOI: 10.1002/prot.24269) to properly include proline, preproline residues and backbone rigidity. Starting from random configurations, the model properly folds 19 proteins (including a mutant 2A3D sequence) into native states containing β sheet, α helix, and mixed α/β. As a further test, the stability of H-RAS (a 169 residue protein, critical in many signaling pathways) is investigated: The protein is stable, with excellent agreement with experimental B-factors. Despite that proteins containing only α helices fold to their native state at lower backbone rigidity, and other limitations, which we discuss thoroughly, the model provides a reliable description of the dynamics as compared with all atom simulations, but does not constrain secondary structures as it is typically the case in more coarse-grained models. Further implications are described.
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Affiliation(s)
- Abhijeet Kapoor
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa, 50011
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11
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Wagenmann A, Geyer T. Coarse-Grained Simulations of Protein Backbone Dynamics. 1. Local Sterics Define the Dihedral Angles. J Chem Theory Comput 2012; 8:4732-45. [PMID: 26605627 DOI: 10.1021/ct3005529] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Here, we present a coarse-grained model targeted for implicit solvent simulations of unfolded or intrinsically disordered proteins. The hierarchical model with its nonspherical building blocks allows one to reproduce the local dynamics of the backbone with simple harmonic bonds and steric collisions between a small number of atoms at the correct off-center positions on the building blocks. Here in part 1, we also describe the implementation of the global shape of the protein chain and the extended local interactions that add a first secondary structure bias, which will subsequently be augmented by additional hydrophobic interactions, hydrogen bonds, and dipole dipole couplings along the backbone. Due to its hierarchical setup, the model has a near-atomistic resolution on the local scale and the overall numerical efficiency of a coarse-grained model such that even long protein chains can be simulated efficiently.
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Affiliation(s)
- Andreas Wagenmann
- Zentrum für Bioinformatik, Universität des Saarlandes, D-66041 Saarbrücken, Germany
| | - Tihamér Geyer
- Zentrum für Bioinformatik, Universität des Saarlandes, D-66041 Saarbrücken, Germany
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12
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Noel JK, Schug A, Verma A, Wenzel W, Garcia AE, Onuchic JN. Mirror images as naturally competing conformations in protein folding. J Phys Chem B 2012; 116:6880-8. [PMID: 22497217 DOI: 10.1021/jp212623d] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Evolution has selected a protein's sequence to be consistent with the native state geometry, as this configuration must be both thermodynamically stable and kinetically accessible to prevent misfolding and loss of function. In simple protein geometries, such as coiled-coil helical bundles, symmetry produces a competing, globally different, near mirror image with identical secondary structure and similar native contact interactions. Experimental techniques such as circular dichroism, which rely on probing secondary structure content, cannot readily distinguish these folds. Here, we want to clarify whether the native fold and mirror image are energetically competitive by investigating the free energy landscape of three-helix bundles. To prevent a bias from a specific computational approach, the present study employs the structure prediction forcefield PFF01/02, explicit solvent replica exchange molecular dynamics (REMD) with the Amber94 forcefield, and structure-based simulations based on energy landscape theory. We observe that the native fold and its mirror image have a similar enthalpic stability and are thermodynamically competitive. There is evidence that the mirror fold has faster folding kinetics and could function as a kinetic trap. All together, our simulations suggest that mirror images might not just be a computational annoyance but are competing folds that might switch depending on environmental conditions or functional considerations.
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Affiliation(s)
- Jeffrey K Noel
- Center for Theoretical Biological Physics and Department of Physics, Rice University, Houston, Texas 77005, USA
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13
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Kmiecik S, Gront D, Kouza M, Kolinski A. From coarse-grained to atomic-level characterization of protein dynamics: transition state for the folding of B domain of protein A. J Phys Chem B 2012; 116:7026-32. [PMID: 22486297 DOI: 10.1021/jp301720w] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Atomic-level molecular dynamics simulations are widely used for the characterization of the structural dynamics of proteins; however, they are limited to shorter time scales than the duration of most of the relevant biological processes. Properly designed coarse-grained models that trade atomic resolution for efficient sampling allow access to much longer time-scales. In-depth understanding of the structural dynamics, however, must involve atomic details. In this study, we tested a method for the rapid reconstruction of all-atom models from α carbon atom positions in the application to convert a coarse-grained folding trajectory of a well described model system: the B domain of protein A. The results show that the method and the spatial resolution of the resulting coarse-grained models enable computationally inexpensive reconstruction of realistic all-atom models. Additionally, by means of structural clustering, we determined the most persistent ensembles of the key folding step, the transition state. Importantly, the analysis of the overall structural topologies suggests a dominant folding pathway. This, together with the all-atom characterization of the obtained ensembles, in the form of contact maps, matches the experimental results well.
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Affiliation(s)
- Sebastian Kmiecik
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland.
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14
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Abstract
The evolution of many systems is dominated by rare activated events that occur on timescale
ranging from nanoseconds to the hour or more. For such systems, simulations must leave aside the
full thermal description to focus specifically on mechanisms that generate a configurational change.
We present here the activation relaxation technique (ART), an open-ended saddle point search
algorithm, and a series of recent improvements to ART nouveau and kinetic ART, an ART-based
on-the-fly off-lattice self-learning kinetic Monte Carlo method.
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15
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Shao Q, Qin Gao Y. The relative helix and hydrogen bond stability in the B domain of protein A as revealed by integrated tempering sampling molecular dynamics simulation. J Chem Phys 2011; 135:135102. [DOI: 10.1063/1.3630127] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
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16
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Grahnen JA, Kubelka J, Liberles DA. Fast Side Chain Replacement in Proteins Using a Coarse-Grained Approach for Evaluating the Effects of Mutation During Evolution. J Mol Evol 2011; 73:23-33. [DOI: 10.1007/s00239-011-9454-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2010] [Accepted: 07/14/2011] [Indexed: 11/28/2022]
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17
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Kmiecik S, Kolinski A. Simulation of chaperonin effect on protein folding: a shift from nucleation-condensation to framework mechanism. J Am Chem Soc 2011; 133:10283-9. [PMID: 21618995 PMCID: PMC3132998 DOI: 10.1021/ja203275f] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
The iterative annealing mechanism (IAM) of chaperonin-assisted protein folding is explored in a framework of a well-established coarse-grained protein modeling tool, which enables the study of protein dynamics in a time-scale well beyond classical all-atom molecular mechanics. The chaperonin mechanism of action is simulated for two paradigm systems of protein folding, B domain of protein A (BdpA) and B1 domain of protein G (GB1), and compared to chaperonin-free simulations presented here for BdpA and recently published for GB1. The prediction of the BdpA transition state ensemble (TSE) is in perfect agreement with experimental findings. It is shown that periodic distortion of the polypeptide chains by hydrophobic chaperonin interactions can promote rapid folding and leads to a decrease in folding temperature. It is also demonstrated how chaperonin action prevents kinetically trapped conformations and modulates the observed folding mechanisms from nucleation-condensation to a more framework-like.
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Affiliation(s)
- Sebastian Kmiecik
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland.
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18
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Arkin H, Bilsel M. How conformational transition depends on hydrophobicity of elastin-like polypeptides. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2010; 31:327-332. [PMID: 20229015 DOI: 10.1140/epje/i2010-10573-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2009] [Revised: 01/19/2010] [Accepted: 01/27/2010] [Indexed: 05/28/2023]
Abstract
The three-dimensional structures of elastin-like polypeptides Val1-Pro2-Gly3-Xaa4-Gly5 were investigated by using the multicanonical Monte Carlo (MC) simulation procedure. By substituting different amino acids in the fourth position of the sequence, the thermodynamical variables are calculated in vacuo and in solvent to determine the hydrophobicity dependence of the conformational transition temperatures of the peptides. Resultant hydrophobicity scale is in good agreement with many hydrophobicity scales.
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Affiliation(s)
- H Arkin
- Department of Physics Engineering, Ankara University, Dögol Caddesi 06100 Tandoğan, Ankara, Turkey.
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19
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Zamparo M, Pelizzola A. Nearly symmetrical proteins: folding pathways and transition states. J Chem Phys 2009; 131:035101. [PMID: 19624233 DOI: 10.1063/1.3170984] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The folding pathways of the B domain of protein A have been the subject of many experimental and computational studies. Based on a statistical mechanical model, it has been suggested that the native state symmetry leads to multiple pathways, highly dependent on temperature and denaturant concentration. Experiments, however, have not confirmed this scenario. By considering four nearly symmetrical proteins, one of them being the above molecule, here we show that, if contact energies are properly taken into account, a different picture emerges from kinetic simulations of the above-mentioned model. This is characterized by a dominant folding pathway, which is consistent with the most recent experimental results. Given the simplicity of the model, we also report on a direct sampling of the transition state.
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Affiliation(s)
- Marco Zamparo
- Dipartimento di Fisica, CNISM Unità di Torino and INFN, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
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20
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Bereau T, Deserno M. Generic coarse-grained model for protein folding and aggregation. J Chem Phys 2009; 130:235106. [PMID: 19548767 DOI: 10.1063/1.3152842] [Citation(s) in RCA: 156] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A generic coarse-grained (CG) protein model is presented. The intermediate level of resolution (four beads per amino acid, implicit solvent) allows for accurate sampling of local conformations. It relies on simple interactions that emphasize structure, such as hydrogen bonds and hydrophobicity. Realistic alpha/beta content is achieved by including an effective nearest-neighbor dipolar interaction. Parameters are tuned to reproduce both local conformations and tertiary structures. The thermodynamics and kinetics of a three-helix bundle are studied. We check that the CG model is able to fold proteins with tertiary structures and amino acid sequences different from the one used for parameter tuning. By studying both helical and extended conformations we make sure the force field is not biased toward any particular secondary structure. The accuracy involved in folding not only the test protein but also other ones show strong evidence for amino acid cooperativity embedded in the model. Without any further adjustments or bias a realistic oligopeptide aggregation scenario is observed.
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Affiliation(s)
- Tristan Bereau
- Department of Physics, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, Pennsylvania 15213, USA.
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21
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Shen H, Liwo A, Scheraga HA. An improved functional form for the temperature scaling factors of the components of the mesoscopic UNRES force field for simulations of protein structure and dynamics. J Phys Chem B 2009; 113:8738-44. [PMID: 19480420 PMCID: PMC2766665 DOI: 10.1021/jp901788q] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Coarse-grained or mesoscopic models of proteins and the corresponding force fields are of great importance because they enable us to reduce the folding simulation time by several orders of magnitude compared to the all-atom approach and, consequently, reach the millisecond time scale of simulations. In the coarse-grained UNRES model for simulations of protein structure and dynamics, developed by our group, each amino acid residue is represented by a united side chain and a united peptide group located in the middle between the two neighboring alpha-carbon atoms, which assist only in the definition of the geometry. The prototype of the UNRES force field has been defined as a potential of mean force or restricted free-energy function corresponding to averaging out the degrees of freedom not present in the coarse-grained representation, which has further been approximated by a truncated Kubo cumulant series to enable us to derive analytical expressions for the corresponding terms. This force field should depend on temperature, and in its simplest form, a term corresponding to the cumulant of order n should be multiplied by f(n) = 1/T(n-1). The temperature dependence has been introduced in recent work ( J. Phys. Chem. B , 2007 , 111 , 260 - 285 ), and in order to prevent too steep a variation with temperature, the factors at the nth order cumulant terms were assumed to have a form f(n) = ln[exp(1) + exp(-1)]/ln{exp[(T/T(0))(n-1)] + exp[-(T/T(0))(n-1)]}, where T(0) = 300 K is the reference temperature. In this work, we have introduced a modified scaling factor f(n) = ln[exp(c) + exp(-c)]/ln{exp[c(T/T(0))(n-1)] + exp[-c(T/T(0))(n-1)]}, where c is an adjustable parameter, and determined c by fitting the analytical approximation of the temperature dependence of the virtual bond torsional term corresponding to rotation about the C(alpha)...C(alpha) virtual bond in terminally blocked dialanine to the respective potential of mean force calculated from the MP2/6-31G(d, p) ab initio energy surfaces of terminally blocked alanine (Ac-Ala-NHMe) and, independently, by optimizing it to obtain a sharp heat capacity curve and the lowest ensemble-averaged root-mean-square deviation over the C(alpha) atoms of 1GAB used as a training protein. Both approaches gave consistent results, and c = 1.4 has been selected as the optimal value of this parameter. The force field with the new temperature scaling factors has been optimized using 1GAB as the training protein. The new force field has been tested on a series of medium size alpha-helical proteins and found to perform better than that with the original temperature scaling factors.
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Affiliation(s)
- Hujun Shen
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca NY, USA 14853
| | - Adam Liwo
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca NY, USA 14853
| | - Harold A. Scheraga
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca NY, USA 14853
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22
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Meli M, Colombo G. Molecular simulations of peptides: a useful tool for the development of new drugs and for the study of molecular recognition. Methods Mol Biol 2009; 570:77-153. [PMID: 19649590 DOI: 10.1007/978-1-60327-394-7_4] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
The study of the molecular recognition and self-organization properties of peptides has emerged in recent years as a very active and diverse field of research, ranging from biomedicine to biotechnology and even to material sciences. In the case of biomedicine, peptides can be used as ligands of biological receptors to gain insights into the structural, dynamical, and chemical determinants underlying the formation of complexes and identify new effectors of biological processes of interest. In the case of biotechnology and material science, short sequences have been used to understand the sequence determinants of the formation of ordered supra-molecular structures of nanoscale dimensions. In this work, we will describe our research activities in these two areas of modern chemical biology. In the first part, we will describe the development of a new, specific, potent, and selective anticancer peptide and its use to obtain the information needed to identify a non-peptidic small molecular lead to be used as an inhibitor of cancer growth. In the second part, we will describe the introduction of a new method for the description of the self-organization process at the basis of the growth of ordered supra-molecular structures held together by weak, non-covalent, yet specific interactions.
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Affiliation(s)
- Massimiliano Meli
- Istituto di Chimica del Riconoscimento Molecolare (ICRM)-C.N.R, Milano, Italy
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23
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St-Pierre JF, Mousseau N, Derreumaux P. The complex folding pathways of protein A suggest a multiple-funnelled energy landscape. J Chem Phys 2008; 128:045101. [PMID: 18248008 DOI: 10.1063/1.2812562] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
Folding proteins into their native states requires the formation of both secondary and tertiary structures. Many questions remain, however, as to whether these form into a precise order, and various pictures have been proposed that place the emphasis on the first or the second level of structure in describing folding. One of the favorite test models for studying this question is the B domain of protein A, which has been characterized by numerous experiments and simulations. Using the activation-relaxation technique coupled with a generic energy model (optimized potential for efficient peptide structure prediction), we generate more than 50 folding trajectories for this 60-residue protein. While the folding pathways to the native state are fully consistent with the funnel-like description of the free energy landscape, we find a wide range of mechanisms in which secondary and tertiary structures form in various orders. Our nonbiased simulations also reveal the presence of a significant number of non-native beta and alpha conformations both on and off pathway, including the visit, for a non-negligible fraction of trajectories, of fully ordered structures resembling the native state of nonhomologous proteins.
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Affiliation(s)
- Jean-Francois St-Pierre
- Département de Physique, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec H3C 3J7, Canada
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24
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Wei Y, Nadler W, Hansmann UHE. Backbone and side-chain ordering in a small protein. J Chem Phys 2008; 128:025105. [PMID: 18205480 DOI: 10.1063/1.2819679] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the relation between backbone and side-chain ordering in a small protein. For this purpose, we have performed multicanonical simulations of the villin headpiece subdomain HP-36, an often used toy model in protein studies. Concepts of circular statistics are introduced to analyze side-chain fluctuations. In contrast to earlier studies on homopolypeptides [Wei et al., J. Phys. Chem. B 111, 4244 (2007)], we do not find collective effects leading to a separate transition. Rather, side-chain ordering is spread over a wide temperature range. Our results indicate a thermal hierarchy of ordering events, with side-chain ordering appearing at temperatures below the helix-coil transition but above the folding transition. We conjecture that this thermal hierarchy reflects an underlying temporal order, and that side-chain ordering facilitates the search for the correct backbone topology.
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Affiliation(s)
- Yanjie Wei
- Department of Physics, Michigan Technological University, Houghton, Michigan 49931, USA
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25
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Universality and diversity of folding mechanics for three-helix bundle proteins. Proc Natl Acad Sci U S A 2008; 105:895-900. [PMID: 18195374 DOI: 10.1073/pnas.0707284105] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
In this study we evaluate, at full atomic detail, the folding processes of two small helical proteins, the B domain of protein A and the Villin headpiece. Folding kinetics are studied by performing a large number of ab initio Monte Carlo folding simulations using a single transferable all-atom potential. Using these trajectories, we examine the relaxation behavior, secondary structure formation, and transition-state ensembles (TSEs) of the two proteins and compare our results with experimental data and previous computational studies. To obtain a detailed structural information on the folding dynamics viewed as an ensemble process, we perform a clustering analysis procedure based on graph theory. Moreover, rigorous p(fold) analysis is used to obtain representative samples of the TSEs and a good quantitative agreement between experimental and simulated Phi values is obtained for protein A. Phi values for Villin also are obtained and left as predictions to be tested by future experiments. Our analysis shows that the two-helix hairpin is a common partially stable structural motif that gets formed before entering the TSE in the studied proteins. These results together with our earlier study of Engrailed Homeodomain and recent experimental studies provide a comprehensive, atomic-level picture of folding mechanics of three-helix bundle proteins.
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26
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Trebst S, Hansmann UHE. Optimized folding simulations of protein A. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2007; 24:311-316. [PMID: 18071628 DOI: 10.1140/epje/i2007-10241-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2007] [Accepted: 11/09/2007] [Indexed: 05/25/2023]
Abstract
We describe optimized parallel tempering simulations of the 46-residue B-fragment of protein A. Native-like configurations with a root-mean-square deviation of approximately 3 A to the experimentally determined structure (Protein Data Bank identifier 1BDD) are found. However, at biologically relevant temperatures such conformations appear with only approximately 10 % frequency in our simulations. Possible shortcomings in our energy function are discussed.
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Affiliation(s)
- S Trebst
- Microsoft Research, Station Q, University of California, Santa Barbara, CA 93106, USA
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27
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Carr JM, Wales DJ. Global optimization and folding pathways of selected alpha-helical proteins. J Chem Phys 2007; 123:234901. [PMID: 16392943 DOI: 10.1063/1.2135783] [Citation(s) in RCA: 86] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The results of basin-hopping global optimization simulations are presented for four small, alpha-helical proteins described by a coarse-grained potential. A step-taking scheme that incorporates the local conformational preferences extracted from a large number of high-resolution protein structures is compared with an unbiased scheme. In addition, the discrete path sampling method is used to investigate the folding of one of the proteins, namely, the villin headpiece subdomain. Folding times from kinetic Monte Carlo simulations and iterative calculations based on a Markovian first-step analysis for the resulting stationary-point database are in good mutual agreement, but differ significantly from the experimental values, probably because the native state is not the global free energy minimum for the potential employed.
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Affiliation(s)
- Joanne M Carr
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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28
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Abstract
We present a minimal model for proteins, which is able to capture the structural conversion between the alpha-helix and beta-hairpin. In most regimes of the parameter space, the model produces a stable structure at a low temperature; in a few limited regimes of the parameter space, the model displays an beta-hairpin transition as the physical conditions vary. These variations include a perturbation on hydrogen bonding propensity at the middle of the modeled chain, or the change of the hydrophobicity of a designated pair along the chain. Using Monte Carlo simulations, we demonstrate the structural conversion by means of state diagrams, heat capacity maps, and free energy maps.
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Affiliation(s)
- Hideo Imamura
- Department of Physics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
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29
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Dyer RB. Ultrafast and downhill protein folding. Curr Opin Struct Biol 2007; 17:38-47. [PMID: 17223539 DOI: 10.1016/j.sbi.2007.01.001] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2006] [Revised: 12/05/2006] [Accepted: 01/03/2007] [Indexed: 11/24/2022]
Abstract
Ultrafast folding proteins have served an important role in benchmarking molecular dynamics simulations and testing protein folding theories. These proteins are simple enough and fold fast enough that realistic simulations are possible, which facilitates the direct comparison of absolute folding rates and folding mechanisms with those observed experimentally. Such comparisons have achieved remarkable success, but have also revealed the shortcomings that remain in experiment, theory and simulation alike. Some ultrafast folding proteins may fold without encountering an activation barrier (downhill folding), allowing the exploration of the molecular timescale of folding and the roughness of the energy landscape. The biological significance of ultrafast folding remains uncertain, but its practical significance is crucial to progress in understanding how proteins fold.
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Affiliation(s)
- R Brian Dyer
- Chemistry Division, MS J567, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
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30
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Abstract
Backbone hydrogen bonds contribute very importantly to the stability of proteins and therefore they must be appropriately represented in protein folding simulations. Simple models are frequently used in theoretical approaches to this process, but their simplifications are often confronted with the need to be true to the physics of the interactions. Here we study the effects of different levels of coarse graining in the modeling of backbone hydrogen bonds. We study three different models taken from the bibliography in a twofold fashion. First, we calculate the hydrogen bonds in 2gb1, an (alpha + beta)-protein, and see how different backbone representations and potentials can mimic the effects of real hydrogen bonds both in helices and sheets. Second, we use an evolutionary method for protein fragment assembly to locate the global energy minimum for a set of small beta-proteins with these models. This way, we assess the effects of coarse graining in hydrogen bonding models and show what can be expected from them when used in simulation experiments.
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Affiliation(s)
- David De Sancho
- Departamento de Química Física I, Universidad Complutense, Madrid, Spain
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31
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Jagielska A, Scheraga HA. Influence of temperature, friction, and random forces on folding of the B-domain of staphylococcal protein A: All-atom molecular dynamics in implicit solvent. J Comput Chem 2007; 28:1068-82. [PMID: 17279497 DOI: 10.1002/jcc.20631] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
The influences of temperature, friction, and random forces on the folding of protein A have been analyzed. A series of all-atom molecular dynamics folding simulations with the Amber ff99 potential and Generalized Born solvation, starting from the fully extended chain, were carried out for temperatures from 300 to 500 K, using (a) the Berendsen thermostat (with no explicit friction or random forces) and (b) Langevin dynamics (with friction and stochastic forces explicitly present in the system). The simulation temperature influences the relative time scale of the major events on the folding pathways of protein A. At lower temperatures, helix 2 folds significantly later than helices 1 and 3. However, with increasing temperature, the folding time of helix 2 approaches the folding times of helices 1 and 3. At lower temperatures, the complete formation of secondary and tertiary structure is significantly separated in time whereas, at higher temperatures, they occur simultaneously. These results suggest that some earlier experimental and theoretical observations of folding events, e.g., the order of helix formation, could depend on the temperature used in those studies. Therefore, the differences in temperature used could be one of the reasons for the discrepancies among published experimental and computational studies of the folding of protein A. Friction and random forces do not change the folding pathway that was observed in the simulations with the Berendsen thermostat, but their explicit presence in the system extends the folding time of protein A.
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Affiliation(s)
- Anna Jagielska
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, USA
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32
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Jayachandran G, Vishal V, García AE, Pande VS. Local structure formation in simulations of two small proteins. J Struct Biol 2006; 157:491-9. [PMID: 17098444 PMCID: PMC1931413 DOI: 10.1016/j.jsb.2006.10.001] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2006] [Revised: 09/28/2006] [Accepted: 10/04/2006] [Indexed: 11/30/2022]
Abstract
Massively parallel all-atom, explicit solvent molecular dynamics simulations were used to explore the formation and existence of local structure in two small alpha-helical proteins, the villin headpiece and the helical fragment B of protein A. We report on the existence of transient helices and combinations of helices in the unfolded ensemble, and on the order of formation of helices, which appears to largely agree with previous experimental results. Transient local structure is observed even in the absence of overall native structure. We also calculate sets of residue-residue pairs that are statistically predictive of the formation of given local structures in our simulations.
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Affiliation(s)
- Guha Jayachandran
- Computer Science Department, Stanford University, Stanford, CA 94305, USA
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33
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Imamura H, Chen JZY. Dependence of folding dynamics and structural stability on the location of a hydrophobic pair in beta-hairpins. Proteins 2006; 63:555-70. [PMID: 16485280 DOI: 10.1002/prot.20846] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
We study the dependence of folding time, nucleation site, and stability of a model beta-hairpin on the location of a cross-strand hydrophobic pair, using a coarse-grained off-lattice model with the aid of Monte Carlo simulations. Our simulations have produced 6500 independent folding trajectories dynamically, forming the basis for extensive statistical analysis. Four folding pathways, zipping-out, middle-out, zipping-in, and reptation, have been closely monitored and discussed in all seven sequences studied. A hydrophobic pair placed near the beta-turn or in the middle section effectively speed up folding; a hydrophobic pair placed close to the terminal ends or next to the beta-turn encourages stability of the entire chain.
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Affiliation(s)
- Hideo Imamura
- Department of Physics, University of Waterloo, Waterloo, Ontario, Canada
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34
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De Mori GMS, Colombo G, Micheletti C. Study of the Villin headpiece folding dynamics by combining coarse-grained Monte Carlo evolution and all-atom molecular dynamics. Proteins 2006; 58:459-71. [PMID: 15521059 DOI: 10.1002/prot.20313] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
The folding mechanism of the Villin headpiece (HP36) is studied by means of a novel approach which entails an initial coarse-grained Monte Carlo (MC) scheme followed by all-atom molecular dynamics (MD) simulations in explicit solvent. The MC evolution occurs in a simplified free-energy landscape and allows an efficient selection of marginally-compact structures which are taken as viable initial conformations for the MD. The coarse-grained MC structural representation is connected to the one with atomic resolution through a "fine-graining" reconstruction algorithm. This two-stage strategy is used to select and follow the dynamics of seven different unrelated conformations of HP36. In a notable case the MD trajectory rapidly evolves towards the folded state, yielding a typical root-mean-square deviation (RMSD) of the core region of only 2.4 A from the closest NMR model (the typical RMSD over the whole structure being 4.0 A). The analysis of the various MC-MD trajectories provides valuable insight into the details of the folding and mis-folding mechanisms and particularly about the delicate influence of local and nonlocal interactions in steering the folding process.
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35
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Itoh K, Sasai M. Flexibly varying folding mechanism of a nearly symmetrical protein: B domain of protein A. Proc Natl Acad Sci U S A 2006; 103:7298-303. [PMID: 16648265 PMCID: PMC1564280 DOI: 10.1073/pnas.0510324103] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The folding pathway of the B domain of protein A is the pathway most intensively studied by computer simulations. Recent systematic measurement of Phi values by Sato et al., however, has shown that none of the published computational predictions is consistent with the detailed features of the experimentally observed folding mechanism. In this article we use a statistical mechanical model of folding to show that sensitive dependence of multiple transition state ensembles on temperature and the denaturant concentration is the key to resolving the inconsistency among simulations and the experiment. Such sensitivity in multiple transition state ensembles is a natural consequence of symmetry-breaking in a nearly symmetrical protein.
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Affiliation(s)
- Kazuhito Itoh
- Department of Complex Systems Science, Graduate School of Information Science, Graduate School of Engineering, Nagoya University, Nagoya 464-8601, Japan.
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36
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Tozzini V, Rocchia W, McCammon JA. Mapping all-atom models onto one-bead Coarse Grained Models: general properties and applications to a minimal polypeptide model. J Chem Theory Comput 2006; 2:667-673. [PMID: 19461947 PMCID: PMC2600716 DOI: 10.1021/ct050294k] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
In the one and two beads Coarse Grained (CG) models for proteins, the two conformational dihedrals ϕ and ψ that describe the backbone geometry are no longer present as explicit internal coordinates, thus the information contained in the Ramachandran plot cannot be used directly. We derive an analytical mapping between these dihedrals and the internal variable describing the backbone conformation in the one(two) beads CG models, namely the pseudo-bond angle and pseudo-dihedral between subsequent Cαs. This is used to derive a new density plot that contains the same information as the Ramachandran plot and can be used with the one(two) beads CG models. The use of this mapping is then illustrated with a new one bead polypeptide model that accounts for transitions between α-helices and β-sheets.
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Affiliation(s)
- Valentina Tozzini
- NEST - Scuola Normale Superiore, Piazza dei Cavalieri, 7 I-56126 Pisa, Italy
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37
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Chen NY, Su ZY, Mou CY. Effective potentials for folding proteins. PHYSICAL REVIEW LETTERS 2006; 96:078103. [PMID: 16606145 DOI: 10.1103/physrevlett.96.078103] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2004] [Indexed: 05/08/2023]
Abstract
A coarse-grained off-lattice model that is not biased in any way to the native state is proposed to fold proteins. To predict the native structure in a reasonable time, the model has included the essential effects of water in an effective potential. Two new ingredients, the dipole-dipole interaction and the local hydrophobic interaction, are introduced and are shown to be as crucial as the hydrogen bonding. The model allows successful folding of the wild-type sequence of protein G and may have provided important hints to the study of protein folding.
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Affiliation(s)
- Nan-Yow Chen
- Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan
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38
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Khalili M, Liwo A, Scheraga HA. Kinetic Studies of Folding of the B-domain of Staphylococcal Protein A with Molecular Dynamics and a United-residue (UNRES) Model of Polypeptide Chains. J Mol Biol 2006; 355:536-47. [PMID: 16324712 DOI: 10.1016/j.jmb.2005.10.056] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2005] [Revised: 10/10/2005] [Accepted: 10/21/2005] [Indexed: 11/23/2022]
Abstract
Langevin dynamics is used with our physics-based united-residue (UNRES) force field to study the folding pathways of the B-domain of staphylococcal protein A (1BDD (alpha; 46 residues)). With 400 trajectories of protein A started from the extended state (to gather meaningful statistics), and simulated for more than 35 ns each, 380 of them folded to the native structure. The simulations were carried out at the optimal folding temperature of protein A with this force field. To the best of our knowledge, this is the first simulation study of protein-folding kinetics with a physics-based force field in which reliable statistics can be gathered. In all the simulations, the C-terminal alpha-helix forms first. The ensemble of the native basin has an average RMSD value of 4 A from the native structure. There is a stable intermediate along the folding pathway, in which the N-terminal alpha-helix is unfolded; this intermediate appears on the way to the native structure in less than one-fourth of the folding pathways, while the remaining ones proceed directly to the native state. Non-native structures persist until the end of the simulations, but the native-like structures dominate. To express the kinetics of protein A folding quantitatively, two observables were used: (i) the average alpha-helix content (averaged over all trajectories within a given time window); and (ii) the fraction of conformations (averaged over all trajectories within a given time window) with Calpha RMSD values from the native structure less than 5 A (fraction of completely folded structures). The alpha-helix content grows quickly with time, and its variation fits well to a single-exponential term, suggesting fast two-state kinetics. On the other hand, the fraction of folded structures changes more slowly with time and fits to a sum of two exponentials, in agreement with the appearance of the intermediate, found when analyzing the folding pathways. This observation demonstrates that different qualitative and quantitative conclusions about folding kinetics can be drawn depending on which observable is monitored.
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Affiliation(s)
- Mey Khalili
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853-1301, USA
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39
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Hubner IA, Deeds EJ, Shakhnovich EI. High-resolution protein folding with a transferable potential. Proc Natl Acad Sci U S A 2005; 102:18914-9. [PMID: 16365306 PMCID: PMC1323145 DOI: 10.1073/pnas.0502181102] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
A generalized computational method for folding proteins with a fully transferable potential and geometrically realistic all-atom model is presented and tested on seven helix bundle proteins. The protocol, which includes graph-theoretical analysis of the ensemble of resulting folded conformations, was systematically applied and consistently produced structure predictions of approximately 3 A without any knowledge of the native state. To measure and understand the significance of the results, extensive control simulations were conducted. Graph theoretic analysis provides a means for systematically identifying the native fold and provides physical insight, conceptually linking the results to modern theoretical views of protein folding. In addition to presenting a method for prediction of structure and folding mechanism, our model suggests that an accurate all-atom amino acid representation coupled with a physically reasonable atomic interaction potential and hydrogen bonding are essential features for a realistic protein model.
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Affiliation(s)
- Isaac A Hubner
- Departments of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA
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40
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Cheng S, Yang Y, Wang W, Liu H. Transition State Ensemble for the Folding of B Domain of Protein A: A Comparison of Distributed Molecular Dynamics Simulations with Experiments. J Phys Chem B 2005; 109:23645-54. [PMID: 16375343 DOI: 10.1021/jp0517798] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Folding pathways of the B domain of staphylococcal protein A have been sampled with a distributed computing approach. Starting from an extended structure, the method employs an index measuring topological similarity to the native structure to selectively sample trajectory branches leading to the native fold. Unperturbed and continuous folding trajectories are drawn on a physics-based atomic potential energy surface with an implicit solvent. The sampled folding trajectories demonstrate a similar sequence of events: the earlier stage involves a partial formation of helix 2 and to a less extent of helix 1 at their N terminals, followed by the hydrophobic collapse between residues F14, I17, and L18 on helix 1 and residues R28, F31, and I32 on helix 2, which results in the rigidification of the helix turn from R28 to I32. Helix 2 is then able to extend, allowing for the formation to turn 2. The above description explains one experimental result why a G30A mutant of the protein was observed to be the fastest folder among proteins of its size. And the ensemble of structures right before the final collapse is in good agreement with the transition state ensemble mapped by another recent experiment with Fersht Phi values. We emphasize that because the approach here does not provide quantifications of the free energy landscape, our model of the transition state ensemble emerges from comparisons of simulations and previous experimental results rather from the simulation results alone. On the other hand, as our approach does not rely on a low-dimensional free energy surface, it can complement methods based on the construction of free energy surfaces.
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Affiliation(s)
- Shanmei Cheng
- Key Laboratory of Structural Biology, School of Life Sciences, University of Science and Technology of China (USTC), and Hefei National Laboratory for Physical Sciences at Microscale, Hefei, Anhui, 230026, China
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41
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Kwak W, Hansmann UHE. Efficient sampling of protein structures by model hopping. PHYSICAL REVIEW LETTERS 2005; 95:138102. [PMID: 16197184 PMCID: PMC1356668 DOI: 10.1103/physrevlett.95.138102] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2005] [Indexed: 05/04/2023]
Abstract
We introduce a novel simulation method, model hopping, that enhances sampling of low-energy configurations in complex systems. The approach is illustrated for a protein-folding problem. Thermodynamic quantities of proteins with up to 46 residues are evaluated from all-atom simulations with this method.
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Affiliation(s)
- Wooseop Kwak
- Department of Physics, Michigan Technological University, Houghton, Michigan 49931-1295, USA.
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42
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Chen P. Self-assembly of ionic-complementary peptides: a physicochemical viewpoint. Colloids Surf A Physicochem Eng Asp 2005. [DOI: 10.1016/j.colsurfa.2004.12.048] [Citation(s) in RCA: 103] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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43
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Knott M, Chan HS. Exploring the effects of hydrogen bonding and hydrophobic interactions on the foldability and cooperativity of helical proteins using a simplified atomic model. Chem Phys 2004. [DOI: 10.1016/j.chemphys.2004.06.014] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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44
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Abstract
How fast can a protein possibly fold? This question has stimulated experimentalists to seek fast folding proteins and to engineer them to fold even faster. Proteins folding at or near the speed limit are prime candidates for all-atom molecular dynamics simulations. They may also have no free energy barrier, allowing the direct observation of intermediate structures on the pathways from the unfolded to the folded state. Both experimental and theoretical approaches predict a speed limit of approximately N/100micros for a generic N-residue single-domain protein, with alpha proteins folding faster than beta or alphabeta. The predicted limits suggest that most known ultrafast folding proteins can be engineered to fold more than ten times faster.
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Affiliation(s)
- Jan Kubelka
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Building 5, Room 104, Bethesda, MD 20892-0520, USA
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45
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Wolynes PG. Latest folding game results: protein A barely frustrates computationalists. Proc Natl Acad Sci U S A 2004; 101:6837-8. [PMID: 15123824 PMCID: PMC406427 DOI: 10.1073/pnas.0402034101] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Affiliation(s)
- Peter G Wolynes
- Department of Chemistry and Biochemistry, Department of Physics, and Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, CA 92093-0371, USA.
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Sato S, Religa TL, Daggett V, Fersht AR. Testing protein-folding simulations by experiment: B domain of protein A. Proc Natl Acad Sci U S A 2004; 101:6952-6. [PMID: 15069202 PMCID: PMC406447 DOI: 10.1073/pnas.0401396101] [Citation(s) in RCA: 116] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We have assessed the published predictions of the pathway of folding of the B domain of protein A, the pathway most studied by computer simulation. We analyzed the transition state for folding of the three-helix bundle protein, by using experimental Phi values on some 70 suitable mutants. Surprisingly, the third helix, which has the most stable alpha-helical structure as a peptide fragment, is poorly formed in the transition state, especially at its C terminus. The protein folds around a nearly fully formed central helix, which is stabilized by extensive hydrophobic side chain interactions. The turn connecting the poorly structured first helix to the central helix is unstructured, but the turn connecting the central helix to the third is in the process of being formed as the N-terminal region of the third helix begins to coalesce. The transition state is inconsistent with a classical framework mechanism and is closer to nucleation-condensation. None of the published atomistic simulations are fully consistent with the experimental picture although many capture important features. There is a continuing need for combining simulation with experiment to describe folding pathways, and of continued testing to improve predictive methods.
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Affiliation(s)
- Satoshi Sato
- Medical Research Council Centre for Protein Engineering, Hills Road, Cambridge CB2 2QH, United Kingdom
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48
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Vila JA, Ripoll DR, Scheraga HA. Atomically detailed folding simulation of the B domain of staphylococcal protein A from random structures. Proc Natl Acad Sci U S A 2003; 100:14812-6. [PMID: 14638943 PMCID: PMC299808 DOI: 10.1073/pnas.2436463100] [Citation(s) in RCA: 78] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The conformational space of the 10-55 fragment of the B-domain of staphylococcal protein A has been investigated by using the electrostatically driven Monte Carlo (EDMC) method. The ECEPP/3 (empirical conformational energy program for peptides) force-field plus two different continuum solvation models, namely SRFOPT (Solvent Radii Fixed with atomic solvation parameters OPTimized) and OONS (Ooi, Oobatake, Némethy, and Scheraga solvation model), were used to describe the conformational energy of the chain. After an exhaustive search, starting from two different random conformations, three of four runs led to native-like conformations. Boltzmann-averaged root-mean-square deviations (RMSD) for all of the backbone heavy atoms with respect to the native structure of 3.35 A and 4.54 A were obtained with SRFOPT and OONS, respectively. These results show that the protein-folding problem can be solved at the atomic detail level by an ab initio procedure, starting from random conformations, with no knowledge except the amino acid sequence. To our knowledge, the results reported here correspond to the largest protein ever folded from a random conformation by an initial-value formulation with a full atomic potential, without resort to knowledge-based information.
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Affiliation(s)
- Jorge A Vila
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853-1301, USA
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Favrin G, Irbäck A, Wallin S. Sequence-based study of two related proteins with different folding behaviors. Proteins 2003; 54:8-12. [PMID: 14705019 DOI: 10.1002/prot.10575] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
Z(SPA-1) is an engineered protein that binds to its parent, the three-helix-bundle Z domain of staphylococcal protein A. Uncomplexed Z(SPA-1) shows a reduced helix content and a melting behavior that is less cooperative, compared with the wild-type Z domain. Here we show that the difference in folding behavior between these two sequences can be partly understood in terms of an off-lattice model with 5-6 atoms per amino acid and a minimalistic potential, in which folding is driven by backbone hydrogen bonding and effective hydrophobic attraction.
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Affiliation(s)
- Giorgio Favrin
- Complex Systems Division, Department of Theoretical Physics, Lund University, Lund, Sweden
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50
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García AE, Onuchic JN. Folding a protein in a computer: an atomic description of the folding/unfolding of protein A. Proc Natl Acad Sci U S A 2003; 100:13898-903. [PMID: 14623983 PMCID: PMC283518 DOI: 10.1073/pnas.2335541100] [Citation(s) in RCA: 298] [Impact Index Per Article: 14.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We study the folding mechanism of a three-helix bundle protein at atomic resolution, including effects of explicit water. Using replica exchange molecular dynamics we perform enough sampling over a wide range of temperatures to obtain the free energy, entropy, and enthalpy surfaces as a function of structural reaction coordinates. Simulations were started from different configurations covering the folded and unfolded states. Because many transitions between all minima at the free energy surface are observed, a quantitative determination of the free energy barriers and the ensemble of configurations associated with them is now possible. The kinetic bottlenecks for folding can be determined from the thermal ensembles of structures on the free energy barriers, provided the kinetically determined transition-state ensembles are similar to those determined from free energy barriers. A mechanism incorporating the interplay among backbone ordering, sidechain packing, and desolvation arises from these calculations. Large Phi values arise not only from native contacts, which mostly form at the transition state, but also from contacts already present in the unfolded state that are partially destroyed at the transition.
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Affiliation(s)
- Angel E García
- Los Alamos National Laboratory, Theoretical Biology and Biophysics Group, Theoretical Division, T10 MS K710, Los Alamos, NM 87545, USA.
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