1
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Becht DC, Leavens MJ, Zeng B, Rothfuss MT, Briknarová K, Bowler BE. Residual Structure in the Denatured State of the Fast-Folding UBA(1) Domain from the Human DNA Excision Repair Protein HHR23A. Biochemistry 2022; 61:767-784. [PMID: 35430812 PMCID: PMC9150713 DOI: 10.1021/acs.biochem.2c00011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The structure of the first ubiquitin-associated domain from HHR23A, UBA(1), was determined by X-ray crystallography at a 1.60 Å resolution, and its stability, folding kinetics, and residual structure under denaturing conditions have been investigated. The concentration dependence of thermal denaturation and size-exclusion chromatography indicate that UBA(1) is monomeric. Guanidine hydrochloride (GdnHCl) denaturation experiments reveal that the unfolding free energy, ΔGu°'(H2O), of UBA(1) is 2.4 kcal mol-1. Stopped-flow folding kinetics indicates sub-millisecond folding with only proline isomerization phases detectable at 25 °C. The full folding kinetics are observable at 4 °C, yielding a folding rate constant, kf, in the absence of a denaturant of 13,000 s-1 and a Tanford β-value of 0.80, consistent with a compact transition state. Evaluation of the secondary structure via circular dichroism shows that the residual helical structure in the denatured state is replaced by polyproline II structure as the GdnHCl concentration increases. Analysis of NMR secondary chemical shifts for backbone 15NH, 13CO, and 13Cα atoms between 4 and 7 M GdnHCl shows three islands of residual helical secondary structure that align in sequence with the three native-state helices. Extrapolation of the NMR data to 0 M GdnHCl demonstrates that helical structure would populate to 17-33% in the denatured state under folding conditions. Comparison with NMR data for a peptide corresponding to helix 1 indicates that this helix is stabilized by transient tertiary interactions in the denatured state of UBA(1). The high helical content in the denatured state, which is enhanced by transient tertiary interactions, suggests a diffusion-collision folding mechanism.
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Affiliation(s)
- Dustin C Becht
- Department of Chemistry & Biochemistry, University of Montana, Missoula, Montana 59812, United States
- Center for Biomolecular Structure & Dynamics, University of Montana, Missoula, Montana 59812, United States
| | - Moses J Leavens
- Department of Chemistry & Biochemistry, University of Montana, Missoula, Montana 59812, United States
- Center for Biomolecular Structure & Dynamics, University of Montana, Missoula, Montana 59812, United States
| | - Baisen Zeng
- Department of Chemistry & Biochemistry, University of Montana, Missoula, Montana 59812, United States
- Center for Biomolecular Structure & Dynamics, University of Montana, Missoula, Montana 59812, United States
| | - Michael T Rothfuss
- Department of Chemistry & Biochemistry, University of Montana, Missoula, Montana 59812, United States
- Center for Biomolecular Structure & Dynamics, University of Montana, Missoula, Montana 59812, United States
| | - Klára Briknarová
- Department of Chemistry & Biochemistry, University of Montana, Missoula, Montana 59812, United States
- Center for Biomolecular Structure & Dynamics, University of Montana, Missoula, Montana 59812, United States
| | - Bruce E Bowler
- Department of Chemistry & Biochemistry, University of Montana, Missoula, Montana 59812, United States
- Center for Biomolecular Structure & Dynamics, University of Montana, Missoula, Montana 59812, United States
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2
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Pal S, Banerjee S, Prabhakaran EN. Helix-Coil Transition at a Glycine Following a Nascent α-Helix: A Synergetic Guidance Mechanism for Helix Growth. J Phys Chem A 2020; 124:7478-7490. [PMID: 32877193 DOI: 10.1021/acs.jpca.0c05489] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
A detailed understanding of forces guiding the rapid folding of a polypeptide from an apparently random coil state to an ordered α-helical structure following the rate-limiting preorganization of the initial three residue backbones into helical conformation is imperative to comprehending and regulating protein folding and for the rational design of biological mimetics. However, several details of this process are still unknown. First, although the helix-coil transition was proposed to originate at the residue level (J. Chem. Phys. 1959, 31, 526-535; J. Chem. Phys. 1961, 34, 1963-1974), all helix-folding studies have only established it between time-averaged bulk states of a long-lived helix and several transiently populated random coils, along the whole helix model sequence. Second, the predominant thermodynamic forces driving either this two-state transition or the faster helix growth following helix nucleation are still unclear. Third, the conformational space of the random coil state is not well-defined unlike its corresponding α-helix. Here we investigate the restrictions placed on the conformational space of a Gly residue backbone, as a result of it immediately succeeding a nascent α-helical turn. Analyses of the temperature-dependent 1D-, 2D-NMR, FT-IR, and CD spectra and GROMACS MD simulation trajectory of a Gly residue backbone following a model α-helical turn, which is artificially rigidified by a covalent hydrogen bond surrogate, reveal that: (i) the α-helical turn guides the ϕ torsion of the Gly exclusively into either a predominantly populated entropically favored α-helical (α-ϕ) state or a scarcely populated random coil (RC-ϕ) state; (ii) the α-ϕ state of Gly in turn favors the stability of the preceding α-helical turn, while the RC-ϕ state disrupts it, revealing an entropy-driven synergetic guidance for helix growth in the residue following helix nucleation. The applicability of a current synergetic guidance mechanism to explain rapid helix growth in folded and unfolded states of proteins and helical peptides is discussed.
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Affiliation(s)
- Sunit Pal
- Department of Chemistry, Indian Institute of Science, Bangalore, Karnataka-560012, India
| | - Shreya Banerjee
- Department of Chemistry, Indian Institute of Science, Bangalore, Karnataka-560012, India
| | - Erode N Prabhakaran
- Department of Chemistry, Indian Institute of Science, Bangalore, Karnataka-560012, India
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3
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Ciemny MP, Badaczewska-Dawid AE, Pikuzinska M, Kolinski A, Kmiecik S. Modeling of Disordered Protein Structures Using Monte Carlo Simulations and Knowledge-Based Statistical Force Fields. Int J Mol Sci 2019; 20:E606. [PMID: 30708941 PMCID: PMC6386871 DOI: 10.3390/ijms20030606] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2018] [Revised: 01/23/2019] [Accepted: 01/29/2019] [Indexed: 12/20/2022] Open
Abstract
The description of protein disordered states is important for understanding protein folding mechanisms and their functions. In this short review, we briefly describe a simulation approach to modeling protein interactions, which involve disordered peptide partners or intrinsically disordered protein regions, and unfolded states of globular proteins. It is based on the CABS coarse-grained protein model that uses a Monte Carlo (MC) sampling scheme and a knowledge-based statistical force field. We review several case studies showing that description of protein disordered states resulting from CABS simulations is consistent with experimental data. The case studies comprise investigations of protein⁻peptide binding and protein folding processes. The CABS model has been recently made available as the simulation engine of multiscale modeling tools enabling studies of protein⁻peptide docking and protein flexibility. Those tools offer customization of the modeling process, driving the conformational search using distance restraints, reconstruction of selected models to all-atom resolution, and simulation of large protein systems in a reasonable computational time. Therefore, CABS can be combined in integrative modeling pipelines incorporating experimental data and other modeling tools of various resolution.
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Affiliation(s)
- Maciej Pawel Ciemny
- Faculty of Chemistry, Biological and Chemical Research Center, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland.
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland.
| | | | - Monika Pikuzinska
- Faculty of Chemistry, Biological and Chemical Research Center, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland.
| | - Andrzej Kolinski
- Faculty of Chemistry, Biological and Chemical Research Center, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland.
| | - Sebastian Kmiecik
- Faculty of Chemistry, Biological and Chemical Research Center, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland.
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4
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Zhang S, Zhang Y, Stenzoski NE, Zou J, Peran I, McCallum SA, Raleigh DP, Royer CA. Pressure-Temperature Analysis of the Stability of the CTL9 Domain Reveals Hidden Intermediates. Biophys J 2019; 116:445-453. [PMID: 30685054 DOI: 10.1016/j.bpj.2019.01.002] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2018] [Revised: 12/13/2018] [Accepted: 01/02/2019] [Indexed: 11/30/2022] Open
Abstract
The observation of two-state unfolding for many small single-domain proteins by denaturants has led to speculation that protein sequences may have evolved to limit the population of partially folded states that could be detrimental to fitness. How such strong cooperativity arises from a multitude of individual interactions is not well understood. Here, we investigate the stability and folding cooperativity of the C-terminal domain of the ribosomal protein L9 in the pressure-temperature plane using site-specific NMR. In contrast to apparent cooperative unfolding detected with denaturant-induced and thermal-induced unfolding experiments and stopped-flow refolding studies at ambient pressure, NMR-detected pressure unfolding revealed significant deviation from two-state behavior, with a core region that was selectively destabilized by increasing temperature. Comparison of pressure-dependent NMR signals from both the folded and unfolded states revealed the population of at least one invisible excited state at atmospheric pressure. The core destabilizing cavity-creating I98A mutation apparently increased the cooperativity of the loss of folded-state peak intensity while also increasing the population of this invisible excited state present at atmospheric pressure. These observations highlight how local stability is subtly modulated by sequence to tune protein conformational landscapes and illustrate the ability of pressure- and temperature-dependent studies to reveal otherwise hidden states.
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Affiliation(s)
- Siwen Zhang
- Department of Chemistry and Chemical Biology, Rensselaer Polytechnic Institute, Troy, New York
| | - Yi Zhang
- Department of Chemistry and Chemical Biology, Rensselaer Polytechnic Institute, Troy, New York
| | - Natalie E Stenzoski
- Graduate Program in Biochemistry and Structural Biology, Stony Brook University, Stony Brook, New York
| | - Junjie Zou
- Department of Chemistry, Stony Brook University, Stony Brook, New York; Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York
| | - Ivan Peran
- Department of Chemistry, Stony Brook University, Stony Brook, New York
| | | | - Daniel P Raleigh
- Graduate Program in Biochemistry and Structural Biology, Stony Brook University, Stony Brook, New York; Department of Chemistry, Stony Brook University, Stony Brook, New York; Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York; Institue of Structural and Molecular Biology, University College London, London, United Kingdom.
| | - Catherine A Royer
- Department of Chemistry and Chemical Biology, Rensselaer Polytechnic Institute, Troy, New York; Department of Biological Sciences, Rensselaer Polytechnic Institute, Troy, New York.
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5
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Bigman LS, Levy Y. Stability Effects of Protein Mutations: The Role of Long-Range Contacts. J Phys Chem B 2018; 122:11450-11459. [DOI: 10.1021/acs.jpcb.8b07379] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Lavi S. Bigman
- Department of Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Yaakov Levy
- Department of Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel
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6
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Danielson TA, Bowler BE. Helical Propensity Affects the Conformational Properties of the Denatured State of Cytochrome c'. Biophys J 2018; 114:311-322. [PMID: 29401429 DOI: 10.1016/j.bpj.2017.11.3744] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2017] [Revised: 10/18/2017] [Accepted: 11/21/2017] [Indexed: 10/18/2022] Open
Abstract
Changing the helical propensity of a polypeptide sequence might be expected to affect the conformational properties of the denatured state of a protein. To test this hypothesis, alanines at positions 83 and 87 near the center of helix 3 of cytochrome c' from Rhodopseudomonas palustris were mutated to serine to decrease the stability of this helix. A set of 13 single histidine variants in the A83S/A87S background were prepared to permit assessment of the conformational properties of the denatured state using histidine-loop formation in 3 M guanidine hydrochloride. The data are compared with previous histidine-heme loop formation data for wild-type cytochrome c'. As expected, destabilization of helix 3 decreases the global stabilities of the histidine variants in the A83S/A87S background relative to the wild-type background. Loop stability versus loop size data yields a scaling exponent of 2.1 ± 0.2, similar to the value of 2.3 ± 0.2 obtained for wild-type cytochrome c'. However, the stabilities of all histidine-heme loops, which contain the helix 3 sequence segment, are increased in the A83S/A87S background compared to the wild-type background. Rate constants for histidine-heme loop breakage are similar for the wild-type and A83S/A87S variants. However, for histidine-heme loops that contain the helix 3 sequence segment, the rate constants for loop formation increase in the A83S/A87S background compared to the wild-type background. Thus, residual helical structure appears to stiffen the polypeptide chain slowing loop formation in the denatured state. The implications of these results for protein folding mechanisms are discussed.
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Affiliation(s)
- Travis A Danielson
- Department of Chemistry and Biochemistry and Center for Biomolecular Structure and Dynamics, University of Montana, Missoula, Montana
| | - Bruce E Bowler
- Department of Chemistry and Biochemistry and Center for Biomolecular Structure and Dynamics, University of Montana, Missoula, Montana.
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7
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Danielson TA, Stine JM, Dar TA, Briknarova K, Bowler BE. Effect of an Imposed Contact on Secondary Structure in the Denatured State of Yeast Iso-1-cytochrome c. Biochemistry 2017; 56:6662-6676. [PMID: 29148740 DOI: 10.1021/acs.biochem.7b01002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
There is considerable evidence that long-range interactions stabilize residual protein structure under denaturing conditions. However, evaluation of the effect of a specific contact on structure in the denatured state has been difficult. Iso-1-cytochrome c variants with a Lys54 → His mutation form a particularly stable His-heme loop in the denatured state, suggestive of loop-induced residual structure. We have used multidimensional nuclear magnetic resonance methods to assign 1H and 15N backbone amide and 13C backbone and side chain chemical shifts in the denatured state of iso-1-cytochrome c carrying the Lys54 → His mutation in 3 and 6 M guanidine hydrochloride and at both pH 6.4, where the His54-heme loop is formed, and pH 3.6, where the His54-heme loop is broken. Using the secondary structure propensity score, with the 6 M guanidine hydrochloride chemical shift data as a random coil reference state for data collected in 3 M guanidine hydrochloride, we found residual helical structure in the denatured state for the 60s helix and the C-terminal helix, but not in the N-terminal helix in the presence or absence of the His54-heme loop. Non-native helical structure is observed in two regions that form Ω-loops in the native state. There is more residual helical structure in the C-terminal helix at pH 6.4 when the loop is formed. Loop formation also appears to stabilize helical structure near His54, consistent with induction of helical structure observed when His-heme bonds form in heme-peptide model systems. The results are discussed in the context of the folding mechanism of cytochrome c.
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Affiliation(s)
- Travis A Danielson
- Department of Chemistry and Biochemistry, University of Montana , Missoula, Montana 59812, United States
| | - Jessica M Stine
- Department of Chemistry and Biochemistry, University of Montana , Missoula, Montana 59812, United States
| | - Tanveer A Dar
- Department of Chemistry and Biochemistry, University of Montana , Missoula, Montana 59812, United States
| | - Klara Briknarova
- Department of Chemistry and Biochemistry, University of Montana , Missoula, Montana 59812, United States.,Center for Biomolecular Structure and Dynamics, University of Montana , Missoula, Montana 59812, United States
| | - Bruce E Bowler
- Department of Chemistry and Biochemistry, University of Montana , Missoula, Montana 59812, United States.,Center for Biomolecular Structure and Dynamics, University of Montana , Missoula, Montana 59812, United States
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8
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Zhang Y, Kitazawa S, Peran I, Stenzoski N, McCallum SA, Raleigh DP, Royer CA. High Pressure ZZ-Exchange NMR Reveals Key Features of Protein Folding Transition States. J Am Chem Soc 2016; 138:15260-15266. [PMID: 27781428 DOI: 10.1021/jacs.6b09887] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Understanding protein folding mechanisms and their sequence dependence requires the determination of residue-specific apparent kinetic rate constants for the folding and unfolding reactions. Conventional two-dimensional NMR, such as HSQC experiments, can provide residue-specific information for proteins. However, folding is generally too fast for such experiments. ZZ-exchange NMR spectroscopy allows determination of folding and unfolding rates on much faster time scales, yet even this regime is not fast enough for many protein folding reactions. The application of high hydrostatic pressure slows folding by orders of magnitude due to positive activation volumes for the folding reaction. We combined high pressure perturbation with ZZ-exchange spectroscopy on two autonomously folding protein domains derived from the ribosomal protein, L9. We obtained residue-specific apparent rates at 2500 bar for the N-terminal domain of L9 (NTL9), and rates at atmospheric pressure for a mutant of the C-terminal domain (CTL9) from pressure dependent ZZ-exchange measurements. Our results revealed that NTL9 folding is almost perfectly two-state, while small deviations from two-state behavior were observed for CTL9. Both domains exhibited large positive activation volumes for folding. The volumetric properties of these domains reveal that their transition states contain most of the internal solvent excluded voids that are found in the hydrophobic cores of the respective native states. These results demonstrate that by coupling it with high pressure, ZZ-exchange can be extended to investigate a large number of protein conformational transitions.
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Affiliation(s)
- Yi Zhang
- Department of Chemistry & Chemical Biology, Rensselaer Polytechnic Institute , Troy, New York 12180, United States
| | - Soichiro Kitazawa
- Department of Biological Sciences, Rensselaer Polytechnic Institute , Troy, New York 12180, United States
| | - Ivan Peran
- Department of Chemistry, Stony Brook University , Stony Brook, New York 11794, United States
| | - Natalie Stenzoski
- Graduate Program in Biochemistry and Structural Biology, Stony Brook University , Stony Brook, New York 11794, United States
| | - Scott A McCallum
- NMR Core Facility, Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute , Troy, New York 12180, United States
| | - Daniel P Raleigh
- Department of Chemistry, Stony Brook University , Stony Brook, New York 11794, United States
| | - Catherine A Royer
- Department of Chemistry & Chemical Biology, Rensselaer Polytechnic Institute , Troy, New York 12180, United States.,Department of Biological Sciences, Rensselaer Polytechnic Institute , Troy, New York 12180, United States
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9
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Malhotra P, Udgaonkar JB. How cooperative are protein folding and unfolding transitions? Protein Sci 2016; 25:1924-1941. [PMID: 27522064 PMCID: PMC5079258 DOI: 10.1002/pro.3015] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2016] [Revised: 08/09/2016] [Accepted: 08/09/2016] [Indexed: 11/12/2022]
Abstract
A thermodynamically and kinetically simple picture of protein folding envisages only two states, native (N) and unfolded (U), separated by a single activation free energy barrier, and interconverting by cooperative two-state transitions. The folding/unfolding transitions of many proteins occur, however, in multiple discrete steps associated with the formation of intermediates, which is indicative of reduced cooperativity. Furthermore, much advancement in experimental and computational approaches has demonstrated entirely non-cooperative (gradual) transitions via a continuum of states and a multitude of small energetic barriers between the N and U states of some proteins. These findings have been instrumental towards providing a structural rationale for cooperative versus noncooperative transitions, based on the coupling between interaction networks in proteins. The cooperativity inherent in a folding/unfolding reaction appears to be context dependent, and can be tuned via experimental conditions which change the stabilities of N and U. The evolution of cooperativity in protein folding transitions is linked closely to the evolution of function as well as the aggregation propensity of the protein. A large activation energy barrier in a fully cooperative transition can provide the kinetic control required to prevent the accumulation of partially unfolded forms, which may promote aggregation. Nevertheless, increasing evidence for barrier-less "downhill" folding, as well as for continuous "uphill" unfolding transitions, indicate that gradual non-cooperative processes may be ubiquitous features on the free energy landscape of protein folding.
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Affiliation(s)
- Pooja Malhotra
- National Centre for Biological Sciences, Tata Institute of Fundamental Research, Bengaluru, 560065, India
| | - Jayant B Udgaonkar
- National Centre for Biological Sciences, Tata Institute of Fundamental Research, Bengaluru, 560065, India.
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10
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Kmiecik S, Gront D, Kolinski M, Wieteska L, Dawid AE, Kolinski A. Coarse-Grained Protein Models and Their Applications. Chem Rev 2016; 116:7898-936. [DOI: 10.1021/acs.chemrev.6b00163] [Citation(s) in RCA: 555] [Impact Index Per Article: 69.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Sebastian Kmiecik
- Faculty
of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Dominik Gront
- Faculty
of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Michal Kolinski
- Bioinformatics
Laboratory, Mossakowski Medical Research Center of the Polish Academy of Sciences, Pawinskiego 5, 02-106 Warsaw, Poland
| | - Lukasz Wieteska
- Faculty
of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
- Department
of Medical Biochemistry, Medical University of Lodz, Mazowiecka 6/8, 92-215 Lodz, Poland
| | | | - Andrzej Kolinski
- Faculty
of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
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11
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Holehouse AS, Garai K, Lyle N, Vitalis A, Pappu RV. Quantitative assessments of the distinct contributions of polypeptide backbone amides versus side chain groups to chain expansion via chemical denaturation. J Am Chem Soc 2015; 137:2984-95. [PMID: 25664638 PMCID: PMC4418562 DOI: 10.1021/ja512062h] [Citation(s) in RCA: 90] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
In aqueous solutions with high concentrations of chemical denaturants such as urea and guanidinium chloride (GdmCl) proteins expand to populate heterogeneous conformational ensembles. These denaturing environments are thought to be good solvents for generic protein sequences because properties of conformational distributions align with those of canonical random coils. Previous studies showed that water is a poor solvent for polypeptide backbones, and therefore, backbones form collapsed globular structures in aqueous solvents. Here, we ask if polypeptide backbones can intrinsically undergo the requisite chain expansion in aqueous solutions with high concentrations of urea and GdmCl. We answer this question using a combination of molecular dynamics simulations and fluorescence correlation spectroscopy. We find that the degree of backbone expansion is minimal in aqueous solutions with high concentrations of denaturants. Instead, polypeptide backbones sample conformations that are denaturant-specific mixtures of coils and globules, with a persistent preference for globules. Therefore, typical denaturing environments cannot be classified as good solvents for polypeptide backbones. How then do generic protein sequences expand in denaturing environments? To answer this question, we investigated the effects of side chains using simulations of two archetypal sequences with amino acid compositions that are mixtures of charged, hydrophobic, and polar groups. We find that side chains lower the effective concentration of backbone amides in water leading to an intrinsic expansion of polypeptide backbones in the absence of denaturants. Additional dilution of the effective concentration of backbone amides is achieved through preferential interactions with denaturants. These effects lead to conformational statistics in denaturing environments that are congruent with those of canonical random coils. Our results highlight the role of side chain-mediated interactions as determinants of the conformational properties of unfolded states in water and in influencing chain expansion upon denaturation.
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Affiliation(s)
- Alex S. Holehouse
- Department of Biomedical Engineering and Center for Biological Systems Engineering, Washington University in St. Louis, One Brookings Drive, Campus Box 1097, St. Louis, MO 63130, USA
| | - Kanchan Garai
- Department of Biomedical Engineering and Center for Biological Systems Engineering, Washington University in St. Louis, One Brookings Drive, Campus Box 1097, St. Louis, MO 63130, USA
- TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad, 500075, India
| | - Nicholas Lyle
- Department of Biomedical Engineering and Center for Biological Systems Engineering, Washington University in St. Louis, One Brookings Drive, Campus Box 1097, St. Louis, MO 63130, USA
| | - Andreas Vitalis
- Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-5807, Zurich, Switzerland
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12
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Kathuria SV, Chan A, Graceffa R, Nobrega RP, Matthews CR, Irving TC, Perot B, Bilsel O. Advances in turbulent mixing techniques to study microsecond protein folding reactions. Biopolymers 2013; 99:888-96. [PMID: 23868289 PMCID: PMC3843316 DOI: 10.1002/bip.22355] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2013] [Accepted: 07/03/2013] [Indexed: 02/01/2023]
Abstract
Recent experimental and computational advances in the protein folding arena have shown that the readout of the one-dimensional sequence information into three-dimensional structure begins within the first few microseconds of folding. The initiation of refolding reactions has been achieved by several means, including temperature jumps, flash photolysis, pressure jumps, and rapid mixing methods. One of the most commonly used means of initiating refolding of chemically denatured proteins is by turbulent flow mixing with refolding dilution buffer, where greater than 99% mixing efficiency has been achieved within 10's of microseconds. Successful interfacing of turbulent flow mixers with complementary detection methods, including time-resolved Fluorescence Spectroscopy (trFL), Förster Resonance Energy Transfer, Circular Dichroism, Small-Angle X-ray Scattering, Hydrogen Exchange followed by Mass Spectrometry and Nuclear Magnetic Resonance Spectroscopy, Infrared Spectroscopy (IR), and Fourier Transform IR Spectroscopy, has made this technique very attractive for monitoring various aspects of structure formation during folding. Although continuous-flow (CF) mixing devices interfaced with trFL detection have a dead time of only 30 µs, burst phases have been detected in this time scale during folding of peptides and of large proteins (e.g., CheY and TIM barrels). Furthermore, a major limitation of the CF mixing technique has been the requirement of large quantities of sample. In this brief communication, we will discuss the recent flurry of activity in micromachining and microfluidics, guided by computational simulations, which are likely to lead to dramatic improvements in time resolution and sample consumption for CF mixers over the next few years.
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Affiliation(s)
- Sagar V. Kathuria
- Department of Biochemistry and Molecular Pharmacology, University of Massachusetts Medical School, 364 Plantation St., Worcester, MA 01605
| | - Alexander Chan
- Department of Mechanical and Industrial Engineering, Engineering Laboratory, University of Massachusetts, Box 32210-219, Amherst, MA, 01003-2210
| | - Rita Graceffa
- BioCAT, Department of Biological and Chemical Science, Illinois Institute of Technology, 3101 S. Dearborn St., Chicago, IL 60616
| | - R. Paul Nobrega
- Department of Biochemistry and Molecular Pharmacology, University of Massachusetts Medical School, 364 Plantation St., Worcester, MA 01605
| | - C. Robert Matthews
- Department of Biochemistry and Molecular Pharmacology, University of Massachusetts Medical School, 364 Plantation St., Worcester, MA 01605
| | - Thomas C. Irving
- BioCAT, Department of Biological and Chemical Science, Illinois Institute of Technology, 3101 S. Dearborn St., Chicago, IL 60616
| | - Blair Perot
- Department of Mechanical and Industrial Engineering, Engineering Laboratory, University of Massachusetts, Box 32210-219, Amherst, MA, 01003-2210
| | - Osman Bilsel
- Department of Biochemistry and Molecular Pharmacology, University of Massachusetts Medical School, 364 Plantation St., Worcester, MA 01605
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13
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Bowler BE. Residual structure in unfolded proteins. Curr Opin Struct Biol 2011; 22:4-13. [PMID: 21978577 DOI: 10.1016/j.sbi.2011.09.002] [Citation(s) in RCA: 66] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2011] [Accepted: 09/07/2011] [Indexed: 11/27/2022]
Abstract
The denatured state ensemble (DSE) of unfolded proteins, once considered to be well-modeled by an energetically featureless random coil, is now well-known to contain flickering elements of residual structure. The position and nature of DSE residual structure may provide clues toward deciphering the protein folding code. This review focuses on recent advances in our understanding of the nature of DSE collapse under folding conditions, the quantification of the stability of residual structure in the DSE, the determination of the location and types of residues involved in thermodynamically significant residual structure and advances in detection of long-range interactions in the DSE.
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Affiliation(s)
- Bruce E Bowler
- Department of Chemistry and Biochemistry and Center for Biomolecular Structure and Dynamics, The University of Montana, Missoula, MT 59812, USA.
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14
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Gong H, Porter LL, Rose GD. Counting peptide-water hydrogen bonds in unfolded proteins. Protein Sci 2011; 20:417-27. [PMID: 21280132 DOI: 10.1002/pro.574] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
It is often assumed that the peptide backbone forms a substantial number of additional hydrogen bonds when a protein unfolds. We challenge that assumption in this article. Early surveys of hydrogen bonding in proteins of known structure typically found that most, but not all, backbone polar groups are satisfied, either by intramolecular partners or by water. When the protein is folded, these groups form approximately two hydrogen bonds per peptide unit, one donor or acceptor for each carbonyl oxygen or amide hydrogen, respectively. But when unfolded, the backbone chain is often believed to form three hydrogen bonds per peptide unit, one partner for each oxygen lone pair or amide hydrogen. This assumption is based on the properties of small model compounds, like N-methylacetamide, or simply accepted as self-evident fact. If valid, a chain of N residues would have approximately 2N backbone hydrogen bonds when folded but 3N backbone hydrogen bonds when unfolded, a sufficient difference to overshadow any uncertainties involved in calculating these per-residue averages. Here, we use exhaustive conformational sampling to monitor the number of H-bonds in a statistically adequate population of blocked polyalanyl-six-mers as the solvent quality ranges from good to poor. Solvent quality is represented by a scalar parameter used to Boltzmann-weight the population energy. Recent experimental studies show that a repeating (Gly-Ser) polypeptide undergoes a denaturant-induced expansion accompanied by breaking intramolecular peptide H-bonds. Results from our simulations augment this experimental finding by showing that the number of H-bonds is approximately conserved during such expansion⇋compaction transitions.
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Affiliation(s)
- Haipeng Gong
- MOE Key Laboratory of Bioinformatics, School of Life Science, Tsinghua University, Beijing 100084, China.
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15
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Kathuria SV, Guo L, Graceffa R, Barrea R, Nobrega RP, Matthews CR, Irving TC, Bilsel O. Minireview: structural insights into early folding events using continuous-flow time-resolved small-angle X-ray scattering. Biopolymers 2011; 95:550-8. [PMID: 21442608 DOI: 10.1002/bip.21628] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2011] [Revised: 03/15/2011] [Accepted: 03/16/2011] [Indexed: 11/08/2022]
Abstract
Small-angle X-ray scattering (SAXS) is a powerful method for obtaining quantitative structural information on the size and shape of proteins, and it is increasingly used in kinetic studies of folding and association reactions. In this minireview, we discuss recent developments in using SAXS to obtain structural information on the unfolded ensemble and early folding intermediates of proteins using continuous-flow mixing devices. Interfacing of these micromachined devices to SAXS beamlines has allowed access to the microsecond time regime. The experimental constraints in implementation of turbulence and laminar flow-based mixers with SAXS detection and a comparison of the two approaches are presented. Current improvements and future prospects of microsecond time-resolved SAXS and the synergy with ab initio structure prediction and molecular dynamics simulations are discussed.
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Affiliation(s)
- Sagar V Kathuria
- Department of Biochemistry and Molecular Pharmacology, University of Massachusetts Medical School, Worcester, MA 01605, USA
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16
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Goldstein RA. The evolution and evolutionary consequences of marginal thermostability in proteins. Proteins 2011; 79:1396-407. [DOI: 10.1002/prot.22964] [Citation(s) in RCA: 107] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2010] [Revised: 11/17/2010] [Accepted: 11/25/2010] [Indexed: 11/11/2022]
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17
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Bowman GR, Voelz VA, Pande VS. Taming the complexity of protein folding. Curr Opin Struct Biol 2011; 21:4-11. [PMID: 21081274 PMCID: PMC3042729 DOI: 10.1016/j.sbi.2010.10.006] [Citation(s) in RCA: 137] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2010] [Revised: 10/21/2010] [Accepted: 10/24/2010] [Indexed: 12/01/2022]
Abstract
Protein folding is an important problem in structural biology with significant medical implications, particularly for misfolding disorders like Alzheimer's disease. Solving the folding problem will ultimately require a combination of theory and experiment, with theoretical models providing a comprehensive view of folding and experiments grounding these models in reality. Here we review progress towards this goal over the past decade, with an emphasis on recent theoretical advances that are empowering chemically detailed models of folding and the new results these technologies are providing. In particular, we discuss new insights made possible by Markov state models (MSMs), including the role of non-native contacts and the hub-like character of protein folded states.
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Affiliation(s)
- Gregory R Bowman
- Department of Chemistry, Stanford University, Stanford, CA 94305, USA
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18
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Sosnick TR, Barrick D. The folding of single domain proteins--have we reached a consensus? Curr Opin Struct Biol 2010; 21:12-24. [PMID: 21144739 DOI: 10.1016/j.sbi.2010.11.002] [Citation(s) in RCA: 123] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2010] [Revised: 11/03/2010] [Accepted: 11/04/2010] [Indexed: 10/18/2022]
Abstract
Rather than stressing the most recent advances in the field, this review highlights the fundamental topics where disagreement remains and where adequate experimental data are lacking. These topics include properties of the denatured state and the role of residual structure, the nature of the fundamental steps and barriers, the extent of pathway heterogeneity and non-native interactions, recent comparisons between theory and experiment, and finally, dynamical properties of the folding reaction.
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Affiliation(s)
- Tobin R Sosnick
- Department of Biochemistry and Molecular Biology, Institute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637, USA.
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19
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Oliveira RJ, Whitford PC, Chahine J, Wang J, Onuchic JN, Leite VBP. The origin of nonmonotonic complex behavior and the effects of nonnative interactions on the diffusive properties of protein folding. Biophys J 2010; 99:600-8. [PMID: 20643080 DOI: 10.1016/j.bpj.2010.04.041] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2009] [Revised: 04/06/2010] [Accepted: 04/14/2010] [Indexed: 11/17/2022] Open
Abstract
We present a method for calculating the configurational-dependent diffusion coefficient of a globular protein as a function of the global folding process. Using a coarse-grained structure-based model, we determined the diffusion coefficient, in reaction coordinate space, as a function of the fraction of native contacts formed Q for the cold shock protein (TmCSP). We find nonmonotonic behavior for the diffusion coefficient, with high values for the folded and unfolded ensembles and a lower range of values in the transition state ensemble. We also characterized the folding landscape associated with an energetically frustrated variant of the model. We find that a low-level of frustration can actually stabilize the native ensemble and increase the associated diffusion coefficient. These findings can be understood from a mechanistic standpoint, in that the transition state ensemble has a more homogeneous structural content when frustration is present. Additionally, these findings are consistent with earlier calculations based on lattice models of protein folding and more recent single-molecule fluorescence measurements.
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Affiliation(s)
- Ronaldo J Oliveira
- Departamento de Física, Instituto de Biociências, Letras e Ciências Exatas, Universidade Estadual Paulista, São José do Rio Preto, Brazil
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20
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Shan B, McClendon S, Rospigliosi C, Eliezer D, Raleigh DP. The cold denatured state of the C-terminal domain of protein L9 is compact and contains both native and non-native structure. J Am Chem Soc 2010; 132:4669-77. [PMID: 20225821 DOI: 10.1021/ja908104s] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Cold denaturation is a general property of globular proteins, and the process provides insight into the origins of the cooperativity of protein folding and the nature of partially folded states. Unfortunately, studies of protein cold denaturation have been hindered by the fact that the cold denatured state is normally difficult to access experimentally. Special conditions such as addition of high concentrations of denaturant, encapsulation into reverse micelles, the formation of emulsified solutions, high pressure, or extremes of pH have been applied, but these can perturb the unfolded state of proteins. The cold denatured state of the C-terminal domain of the ribosomal protein L9 can be populated under native-like conditions by taking advantage of a destabilizing point mutation which leads to cold denaturation at temperatures above 0 degrees C. This state is in slow exchange with the native state on the NMR time scale. Virtually complete backbone (15)N, (13)C, and (1)H as well as side-chain (13)C(beta) and (1)H(beta) chemical shift assignments were obtained for the cold denatured state at pH 5.7, 12 degrees C. Chemical shift analysis, backbone N-H residual dipolar couplings, amide proton NOEs, and R(2) relaxation rates all indicate that the cold denatured state of CTL9 (the C-terminal domain of the ribosomal protein L9) not only contains significant native-like secondary structure but also non-native structure. The regions corresponding to the two native alpha-helices show a strong tendency to populate helical Phi and Psi angles. The segment which connects alpha-helix 2 and beta-strand 2 (residues 107-124) in the native state exhibits a significant preference to form non-native helical structure in the cold denatured state. The structure observed in the cold denatured state of the I98A mutant is similar to that observed in the pH 3.8 unfolded state of wild type CTL9 at 25 degrees C, suggesting that it is a robust feature of the denatured state ensemble of this protein. The implications for protein folding and for studies of cold denatured states are discussed.
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Affiliation(s)
- Bing Shan
- Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794-3400, USA
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21
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Cooperative formation of native-like tertiary contacts in the ensemble of unfolded states of a four-helix protein. Proc Natl Acad Sci U S A 2010; 107:13306-11. [PMID: 20624986 DOI: 10.1073/pnas.1003004107] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
In studies of the ensembles of unfolded structures of a four-helix bundle protein, we have detected the presence of potential precursors of native tertiary structures. These observations were based on the perturbation of NMR chemical shifts of the protein backbone atoms by single site mutations. Some mutations change the chemical shifts of residues remote from the site of mutation indicating the presence of an interaction between the mutated and the remote residues, suggesting that the formation of helix segments and helix-helix interactions is cooperative. We can begin to track down the folding mechanism of this protein using only experimental data by combining the information available for the rate limiting structure formation during the folding process with measurements of the site specific hydrogen bond formation in the burst phase, and with the existence prior to the folding reaction of tertiary structures in the ensemble of otherwise unfolded structures observed in the present study.
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22
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Abstract
Understanding molecular kinetics, and particularly protein folding, is a classic grand challenge in molecular biophysics. Network models, such as Markov state models (MSMs), are one potential solution to this problem. MSMs have recently yielded quantitative agreement with experimentally derived structures and folding rates for specific systems, leaving them positioned to potentially provide a deeper understanding of molecular kinetics that can lead to experimentally testable hypotheses. Here we use existing MSMs for the villin headpiece and NTL9, which were constructed from atomistic simulations, to accomplish this goal. In addition, we provide simpler, humanly comprehensible networks that capture the essence of molecular kinetics and reproduce qualitative phenomena like the apparent two-state folding often seen in experiments. Together, these models show that protein dynamics are dominated by stochastic jumps between numerous metastable states and that proteins have heterogeneous unfolded states (many unfolded basins that interconvert more rapidly with the native state than with one another) yet often still appear two-state. Most importantly, we find that protein native states are hubs that can be reached quickly from any other state. However, metastability and a web of nonnative states slow the average folding rate. Experimental tests for these findings and their implications for other fields, like protein design, are also discussed.
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23
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Nick Pace C, Huyghues-Despointes BMP, Fu H, Takano K, Scholtz JM, Grimsley GR. Urea denatured state ensembles contain extensive secondary structure that is increased in hydrophobic proteins. Protein Sci 2010; 19:929-43. [PMID: 20198681 PMCID: PMC2868236 DOI: 10.1002/pro.370] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2009] [Accepted: 02/08/2010] [Indexed: 11/07/2022]
Abstract
The goal of this article is to gain a better understanding of the denatured state ensemble (DSE) of proteins through an experimental and computational study of their denaturation by urea. Proteins unfold to different extents in urea and the most hydrophobic proteins have the most compact DSE and contain almost as much secondary structure as folded proteins. Proteins that unfold to the greatest extent near pH 7 still contain substantial amounts of secondary structure. At low pH, the DSE expands due to charge-charge interactions and when the net charge per residue is high, most of the secondary structure is disrupted. The proteins in the DSE appear to contain substantial amounts of polyproline II conformation at high urea concentrations. In all cases considered, including staph nuclease, the extent of unfolding by urea can be accounted for using the data and approach developed in the laboratory of Wayne Bolen (Auton et al., Proc Natl Acad Sci 2007; 104:15317-15323).
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Affiliation(s)
- C Nick Pace
- Department of Biochemistry and Biophysics, Texas A&M University, College Station, Texas 77843, USA.
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24
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López-Alonso JP, Bruix M, Font J, Ribó M, Vilanova M, Jiménez MA, Santoro J, González C, Laurents DV. NMR Spectroscopy Reveals that RNase A is Chiefly Denatured in 40% Acetic Acid: Implications for Oligomer Formation by 3D Domain Swapping. J Am Chem Soc 2010; 132:1621-30. [DOI: 10.1021/ja9081638] [Citation(s) in RCA: 57] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Jorge Pedro López-Alonso
- Instituto de Química Física “Rocasolano”, C.S.I.C., Serrano 119, E-28006 Madrid, Spain, and Laboratori d’Enginyeria de Proteïnes, Department de Biologia, Facultat de Ciències, Universitat de Girona, Campus de Montilivi s/n, E-17071 Girona, Spain
| | - Marta Bruix
- Instituto de Química Física “Rocasolano”, C.S.I.C., Serrano 119, E-28006 Madrid, Spain, and Laboratori d’Enginyeria de Proteïnes, Department de Biologia, Facultat de Ciències, Universitat de Girona, Campus de Montilivi s/n, E-17071 Girona, Spain
| | - Josep Font
- Instituto de Química Física “Rocasolano”, C.S.I.C., Serrano 119, E-28006 Madrid, Spain, and Laboratori d’Enginyeria de Proteïnes, Department de Biologia, Facultat de Ciències, Universitat de Girona, Campus de Montilivi s/n, E-17071 Girona, Spain
| | - Marc Ribó
- Instituto de Química Física “Rocasolano”, C.S.I.C., Serrano 119, E-28006 Madrid, Spain, and Laboratori d’Enginyeria de Proteïnes, Department de Biologia, Facultat de Ciències, Universitat de Girona, Campus de Montilivi s/n, E-17071 Girona, Spain
| | - Maria Vilanova
- Instituto de Química Física “Rocasolano”, C.S.I.C., Serrano 119, E-28006 Madrid, Spain, and Laboratori d’Enginyeria de Proteïnes, Department de Biologia, Facultat de Ciències, Universitat de Girona, Campus de Montilivi s/n, E-17071 Girona, Spain
| | - María Angeles Jiménez
- Instituto de Química Física “Rocasolano”, C.S.I.C., Serrano 119, E-28006 Madrid, Spain, and Laboratori d’Enginyeria de Proteïnes, Department de Biologia, Facultat de Ciències, Universitat de Girona, Campus de Montilivi s/n, E-17071 Girona, Spain
| | - Jorge Santoro
- Instituto de Química Física “Rocasolano”, C.S.I.C., Serrano 119, E-28006 Madrid, Spain, and Laboratori d’Enginyeria de Proteïnes, Department de Biologia, Facultat de Ciències, Universitat de Girona, Campus de Montilivi s/n, E-17071 Girona, Spain
| | - Carlos González
- Instituto de Química Física “Rocasolano”, C.S.I.C., Serrano 119, E-28006 Madrid, Spain, and Laboratori d’Enginyeria de Proteïnes, Department de Biologia, Facultat de Ciències, Universitat de Girona, Campus de Montilivi s/n, E-17071 Girona, Spain
| | - Douglas V. Laurents
- Instituto de Química Física “Rocasolano”, C.S.I.C., Serrano 119, E-28006 Madrid, Spain, and Laboratori d’Enginyeria de Proteïnes, Department de Biologia, Facultat de Ciències, Universitat de Girona, Campus de Montilivi s/n, E-17071 Girona, Spain
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25
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Azia A, Levy Y. Nonnative Electrostatic Interactions Can Modulate Protein Folding: Molecular Dynamics with a Grain of Salt. J Mol Biol 2009; 393:527-42. [DOI: 10.1016/j.jmb.2009.08.010] [Citation(s) in RCA: 115] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2009] [Revised: 08/01/2009] [Accepted: 08/06/2009] [Indexed: 11/28/2022]
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