1
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Ji J, Carpentier B, Chakraborty A, Nangia S. An Affordable Topography-Based Protocol for Assigning a Residue's Character on a Hydropathy (PARCH) Scale. J Chem Theory Comput 2024; 20:1656-1672. [PMID: 37018141 PMCID: PMC10902853 DOI: 10.1021/acs.jctc.3c00106] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2023] [Indexed: 04/06/2023]
Abstract
The hydropathy of proteins or quantitative assessment of protein-water interactions has been a topic of interest for decades. Most hydropathy scales use a residue-based or atom-based approach to assign fixed numerical values to the 20 amino acids and categorize them as hydrophilic, hydroneutral, or hydrophobic. These scales overlook the protein's nanoscale topography, such as bumps, crevices, cavities, clefts, pockets, and channels, in calculating the hydropathy of the residues. Some recent studies have included protein topography in determining hydrophobic patches on protein surfaces, but these methods do not provide a hydropathy scale. To overcome the limitations in the existing methods, we have developed a Protocol for Assigning a Residue's Character on the Hydropathy (PARCH) scale that adopts a holistic approach to assigning the hydropathy of a residue. The parch scale evaluates the collective response of the water molecules in the protein's first hydration shell to increasing temperatures. We performed the parch analysis of a set of well-studied proteins that include the following─enzymes, immune proteins, and integral membrane proteins, as well as fungal and virus capsid proteins. Since the parch scale evaluates every residue based on its location, a residue may have very different parch values inside a crevice versus a surface bump. Thus, a residue can have a range of parch values (or hydropathies) dictated by the local geometry. The parch scale calculations are computationally inexpensive and can compare hydropathies of different proteins. The parch analysis can affordably and reliably aid in designing nanostructured surfaces, identifying hydrophilic and hydrophobic patches, and drug discovery.
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Affiliation(s)
- Jingjing Ji
- Department
of Biomedical and Chemical Engineering, Syracuse University, Syracuse, New York 13244, United States
| | - Britnie Carpentier
- Department
of Biomedical and Chemical Engineering, Syracuse University, Syracuse, New York 13244, United States
| | - Arindam Chakraborty
- Department
of Chemistry, Syracuse University, Syracuse, New York 13244, United States
| | - Shikha Nangia
- Department
of Biomedical and Chemical Engineering, Syracuse University, Syracuse, New York 13244, United States
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2
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Sinha A, Roy S. Intrinsically Disordered Regions Function as a Cervical Collar to Remotely Regulate the Nodding Dynamics of SARS-CoV-2 Prefusion Spike Heads. J Phys Chem B 2023; 127:8393-8405. [PMID: 37738458 DOI: 10.1021/acs.jpcb.3c05338] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/24/2023]
Abstract
The SARS-CoV-2 prefusion spike heads (receptor binding domains, RBDs) frequently nod down and up to interact with host cell receptors. As the spike protein is a trimeric unit of significant size, to understand its large-scale structural dynamics associated with the nodding mechanism and the mutational impact on the same, we develop a topological symmetry-information-loaded coarse-grained structure-based model of a spike trimer using recent cryo-EM structural data. Our study reveals the control of two distant intrinsically disordered regions (IDRs), namely, 630 and FPPR loops, over the nodding dynamics of spike heads. We find that the order-disorder transition of IDRs becomes more evident in the variants of concern (VOCs) that are associated with the characteristic mutation, D614G, in the proximity of these IDRs. In some VOCs, the two other mutations A570D and S982A also show an integral effect. The driver mutation D614G instigates a salt-bridge disruption, altering the order-disorder dynamics of both 630 and FPPR loops and their interaction with the C-terminal domains (CTD1/CTD2). This altered connectivity in these mutants allows the two IDRs to act collectively as a "cervical collar" for the RBD, supporting various spike head postures, consistent with cryo-EM results available for specific cases. The IDRs' control over the spike structure and dynamics presents an exciting opportunity where they can be targeted as remote operational switches to artificially maneuver the nod for effective therapeutic interventions.
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Affiliation(s)
- Anushree Sinha
- Department of Chemical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, West Bengal, India
| | - Susmita Roy
- Department of Chemical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, West Bengal, India
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3
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Dicks L, Wales DJ. Elucidating the solution structure of the K-means cost function using energy landscape theory. J Chem Phys 2022; 156:054109. [DOI: 10.1063/5.0078793] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- L. Dicks
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - D. J. Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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4
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Ballard AF, Panter JR, Wales DJ. The energy landscapes of bidisperse particle assemblies on a sphere. SOFT MATTER 2021; 17:9019-9027. [PMID: 34541597 DOI: 10.1039/d1sm01140e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The interplay between crystalline ordering, curvature, and size dispersity make the packing of bidisperse mixtures of particles on a sphere a varied and complex phenomenon. These structures have functional significance in a broad range of systems, such as cellular organisation in spherical epithelia, catalytic activity in binary colloidosomes, and chemical activity in heterofullerenes. In this contribution, we elucidate the potential energy landscapes for systems of repulsive, bidisperse particles confined to the surface of a sphere. It is commonly asserted that particle size dispersity destroys ordered arrangements, leading to glassy landscapes. Surprisingly, across a range of compositions, we find highly ordered global minima. Moreover, a minority of small particles is able to passivate defects, stabilising bidisperse global minima relative to monodisperse systems. However, our landscape analysis also reveals that bidispersity introduces numerous defective, low-lying states that are expected to cause broken ergodicity in corresponding experimental and computational systems. Probing the global minimum structures further, particle segregation is energetically preferred at intermediate compositions, contrasting with the approximate icosahedral global packing at either end of the composition range. Finally, changing the composition has a dramatic effect on the heat capacity: systems with low-symmetry global minima have melting temperatures an order of magnitude lower than monodisperse or high-symmetry systems. This observation may provide a further example of the principle of maximum symmetry: higher symmetry global minima exhibit a larger energy separation from the minima that define the high-entropy phase-like region of configuration space, raising the transition temperature.
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Affiliation(s)
- Alexander F Ballard
- Yusuf Hamied Department of Chemistry, Lensfield Road, Cambridge, CB2 1EW, UK.
| | - Jack R Panter
- Yusuf Hamied Department of Chemistry, Lensfield Road, Cambridge, CB2 1EW, UK.
| | - David J Wales
- Yusuf Hamied Department of Chemistry, Lensfield Road, Cambridge, CB2 1EW, UK.
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5
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Gianni S, Freiberger MI, Jemth P, Ferreiro DU, Wolynes PG, Fuxreiter M. Fuzziness and Frustration in the Energy Landscape of Protein Folding, Function, and Assembly. Acc Chem Res 2021; 54:1251-1259. [PMID: 33550810 PMCID: PMC8023570 DOI: 10.1021/acs.accounts.0c00813] [Citation(s) in RCA: 72] [Impact Index Per Article: 24.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Indexed: 12/20/2022]
Abstract
Are all protein interactions fully optimized? Do suboptimal interactions compromise specificity? What is the functional impact of frustration? Why does evolution not optimize some contacts? Proteins and their complexes are best described as ensembles of states populating an energy landscape. These ensembles vary in breadth from narrow ensembles clustered around a single average X-ray structure to broader ensembles encompassing a few different functional "taxonomic" states on to near continua of rapidly interconverting conformations, which are called "fuzzy" or even "intrinsically disordered". Here we aim to provide a comprehensive framework for confronting the structural and dynamical continuum of protein assemblies by combining the concepts of energetic frustration and interaction fuzziness. The diversity of the protein structural ensemble arises from the frustrated conflicts between the interactions that create the energy landscape. When frustration is minimal after folding, it results in a narrow ensemble, but residual frustrated interactions result in fuzzy ensembles, and this fuzziness allows a versatile repertoire of biological interactions. Here we discuss how fuzziness and frustration play off each other as proteins fold and assemble, viewing their significance from energetic, functional, and evolutionary perspectives.We demonstrate, in particular, that the common physical origin of both concepts is related to the ruggedness of the energy landscapes, intramolecular in the case of frustration and intermolecular in the case of fuzziness. Within this framework, we show that alternative sets of suboptimal contacts may encode specificity without achieving a single structural optimum. Thus, we demonstrate that structured complexes may not be optimized, and energetic frustration is realized via different sets of contacts leading to multiplicity of specific complexes. Furthermore, we propose that these suboptimal, frustrated, or fuzzy interactions are under evolutionary selection and expand the biological repertoire by providing a multiplicity of biological activities. In accord, we show that non-native interactions in folding or interaction landscapes can cooperate to generate diverse functional states, which are essential to facilitate adaptation to different cellular conditions. Thus, we propose that not fully optimized structures may actually be beneficial for biological activities of proteins via an alternative set of suboptimal interactions. The importance of such variability has not been recognized across different areas of biology.This account provides a modern view on folding, function, and assembly across the protein universe. The physical framework presented here is applicable to the structure and dynamics continuum of proteins and opens up new perspectives for drug design involving not fully structured, highly dynamic protein assemblies.
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Affiliation(s)
- Stefano Gianni
- Istituto
Pasteur - Fondazione Cenci Bolognetti, Dipartimento di Scienze Biochimiche
“A. Rossi Fanelli” and Istituto di Biologia e Patologia
Molecolari del CNR, Sapienza Università
di Roma, 00185 Rome, Italy
| | - María Inés Freiberger
- Protein
Physiology Lab, Departamento de Química Biológica, Facultad
de Ciencias Exactas y Naturales, Universidad
de Buenos Aires-CONICET-IQUIBICEN, 1428 Buenos Aires, Argentina
| | - Per Jemth
- Department
of Medical Biochemistry and Microbiology, Uppsala University, Husargatan 3, SE-75123 Uppsala, Sweden
| | - Diego U. Ferreiro
- Protein
Physiology Lab, Departamento de Química Biológica, Facultad
de Ciencias Exactas y Naturales, Universidad
de Buenos Aires-CONICET-IQUIBICEN, 1428 Buenos Aires, Argentina
| | - Peter G. Wolynes
- Center
for Theoretical Biological Physics, Rice
University, 6500 Main Street, Houston, Texas 77251-1892, United States
| | - Monika Fuxreiter
- MTA-DE
Laboratory of Protein Dynamics, Department of Biochemistry and Molecular
Biology, University of Debrecen, Nagyerdei krt 98, H-4032 Debrecen, Hungary
- Department
of Biomedical Sciences, University of Padova, Via Ugo Bassi 58/B, 35131 Padova, Italy
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6
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Abstract
This Feature Article presents a view of the protein folding transition based on the hypothesis that Nature has built features within the sequences that enable a Shortcut to efficient folding. Nature's Shortcut is proposed to be the early establishment of a set of nonlocal weak contacts, constituting protein loops that significantly constrain regions of the collapsed disordered protein into a native-like low-resolution fluctuating topology of major sections of the backbone. Nature's establishment of this scaffold of nonlocal contacts is claimed to bypass what would otherwise be a nearly hopeless unaided search for the final three-dimensional structure in proteins longer than ∼100 amino acids. To support this main contention of the Feature Article, the loop hypothesis (LH) description of early folding events is experimentally tested with time-resolved Förster resonance energy transfer techniques for adenylate kinase, and the data are shown to be consistent with theoretical predictions from the sequential collapse model (SCM). The experimentally based LH and the theoretically founded SCM are argued to provide a unified picture of the role of nonlocal contacts as constituting Nature's Shortcut to protein folding. Importantly, the SCM is shown to reliably predict key nonlocal contacts utilizing only primary sequence information. This view on Nature's Shortcut is open to the protein community for further detailed assessment, including its practical consequences, by suitable application of advanced experimental and computational techniques.
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Affiliation(s)
| | - Elisha Haas
- The Goodman Faculty of Life Sciences , Bar-Ilan University , Ramat Gan 52900 , Israel
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7
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Uversky VN. Protein intrinsic disorder and structure-function continuum. PROGRESS IN MOLECULAR BIOLOGY AND TRANSLATIONAL SCIENCE 2019; 166:1-17. [DOI: 10.1016/bs.pmbts.2019.05.003] [Citation(s) in RCA: 56] [Impact Index Per Article: 11.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
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8
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Dodd PM, Damasceno PF, Glotzer SC. Universal folding pathways of polyhedron nets. Proc Natl Acad Sci U S A 2018; 115:E6690-E6696. [PMID: 29970420 PMCID: PMC6055160 DOI: 10.1073/pnas.1722681115] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Low-dimensional objects such as molecular strands, ladders, and sheets have intrinsic features that affect their propensity to fold into 3D objects. Understanding this relationship remains a challenge for de novo design of functional structures. Using molecular dynamics simulations, we investigate the refolding of the 24 possible 2D unfoldings ("nets") of the three simplest Platonic shapes and demonstrate that attributes of a net's topology-net compactness and leaves on the cutting graph-correlate with thermodynamic folding propensity. To explain these correlations we exhaustively enumerate the pathways followed by nets during folding and identify a crossover temperature [Formula: see text] below which nets fold via nonnative contacts (bonds must break before the net can fold completely) and above which nets fold via native contacts (newly formed bonds are also present in the folded structure). Folding above [Formula: see text] shows a universal balance between reduction of entropy via the elimination of internal degrees of freedom when bonds are formed and gain in potential energy via local, cooperative edge binding. Exploiting this universality, we devised a numerical method to efficiently compute all high-temperature folding pathways for any net, allowing us to predict, among the combined 86,760 nets for the remaining Platonic solids, those with highest folding propensity. Our results provide a general heuristic for the design of 2D objects to stochastically fold into target 3D geometries and suggest a mechanism by which geometry and folding propensity are related above [Formula: see text], where native bonds dominate folding.
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Affiliation(s)
- Paul M Dodd
- Chemical Engineering Department, University of Michigan, Ann Arbor, MI 48109
| | - Pablo F Damasceno
- Applied Physics Program, University of Michigan, Ann Arbor, MI 48109
| | - Sharon C Glotzer
- Chemical Engineering Department, University of Michigan, Ann Arbor, MI 48109;
- Applied Physics Program, University of Michigan, Ann Arbor, MI 48109
- Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109
- Biointerfaces Institute, University of Michigan, Ann Arbor, MI 48109
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9
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p53 Proteoforms and Intrinsic Disorder: An Illustration of the Protein Structure-Function Continuum Concept. Int J Mol Sci 2016; 17:ijms17111874. [PMID: 27834926 PMCID: PMC5133874 DOI: 10.3390/ijms17111874] [Citation(s) in RCA: 114] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2016] [Revised: 10/27/2016] [Accepted: 11/03/2016] [Indexed: 01/10/2023] Open
Abstract
Although it is one of the most studied proteins, p53 continues to be an enigma. This protein has numerous biological functions, possesses intrinsically disordered regions crucial for its functionality, can form both homo-tetramers and isoform-based hetero-tetramers, and is able to interact with many binding partners. It contains numerous posttranslational modifications, has several isoforms generated by alternative splicing, alternative promoter usage or alternative initiation of translation, and is commonly mutated in different cancers. Therefore, p53 serves as an important illustration of the protein structure–function continuum concept, where the generation of multiple proteoforms by various mechanisms defines the ability of this protein to have a multitude of structurally and functionally different states. Considering p53 in the light of a proteoform-based structure–function continuum represents a non-canonical and conceptually new contemplation of structure, regulation, and functionality of this important protein.
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10
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Ota C, Ikeguchi M, Tanaka A, Hamada D. Residual structures in the unfolded state of starch-binding domain of glucoamylase revealed by near-UV circular dichroism and protein engineering techniques. BIOCHIMICA ET BIOPHYSICA ACTA-PROTEINS AND PROTEOMICS 2016; 1864:1464-72. [PMID: 27164491 DOI: 10.1016/j.bbapap.2016.05.002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2016] [Revised: 05/03/2016] [Accepted: 05/05/2016] [Indexed: 11/29/2022]
Abstract
Protein folding is a thermodynamic process driven by energy gaps between the native and unfolded states. Although a wealth of information is available on the structure of folded species, there is a paucity of data on unfolded species. Here, we analyzed the structural properties of the unfolded state of the starch-binding domain of glucoamylase from Aspergillus niger (SBD) formed in the presence of guanidinium hydrochloride (GuHCl). Although far-UV CD and intrinsic tryptophan fluorescence spectra as well as small angle X-ray scattering suggested that SBD assumes highly unfolded structures in the presence of GuHCl, near-UV circular dichroism of wild-type SBD suggested the presence of residual structures in the unfolded state. Analyses of the unfolded states of tryptophan mutants (W543L, W563A, W590A and W615L) using Similarity Parameter, a modified version of root mean square deviation as a measure of similarity between two spectra, suggested that W543 and W563 have preferences to form native-like residual structures in the GuHCl-unfolded state. In contrast, W615 was entirely unstructured, while W590 tended to form non-native ordered structures in the unfolded state. These data and the amino acid sequence of SBD suggest that local structural propensities in the unfolded state can be determined by the probability of the presence of hydrophobic or charged residues nearby tryptophan residues.
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Affiliation(s)
- Chiaki Ota
- Department of Life Science, Faculty of Bioresources, Mie University, 1577 Kurimamachiya, Tsu, Mie 514-8507, Japan
| | - Masamichi Ikeguchi
- Department of Bioinformatics, Soka University, 1-236 Tangi-cho, Hachioji, Tokyo 192-8577, Japan
| | - Akiyoshi Tanaka
- Department of Life Science, Faculty of Bioresources, Mie University, 1577 Kurimamachiya, Tsu, Mie 514-8507, Japan
| | - Daizo Hamada
- Department of Life Science, Faculty of Bioresources, Mie University, 1577 Kurimamachiya, Tsu, Mie 514-8507, Japan; Graduate School of Engineering and Center for Applied Structural Science (CASS), Kobe University, 7-1-48 Minatojima Minami Machi, Chuo-ku, Kobe 650-0047, Japan.
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11
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Chandrasekaran SN, Das J, Dokholyan NV, Carter CW. A modified PATH algorithm rapidly generates transition states comparable to those found by other well established algorithms. STRUCTURAL DYNAMICS (MELVILLE, N.Y.) 2016; 3:012101. [PMID: 26958584 PMCID: PMC4769271 DOI: 10.1063/1.4941599] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/01/2015] [Accepted: 01/22/2016] [Indexed: 06/05/2023]
Abstract
PATH rapidly computes a path and a transition state between crystal structures by minimizing the Onsager-Machlup action. It requires input parameters whose range of values can generate different transition-state structures that cannot be uniquely compared with those generated by other methods. We outline modifications to estimate these input parameters to circumvent these difficulties and validate the PATH transition states by showing consistency between transition-states derived by different algorithms for unrelated protein systems. Although functional protein conformational change trajectories are to a degree stochastic, they nonetheless pass through a well-defined transition state whose detailed structural properties can rapidly be identified using PATH.
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Affiliation(s)
- Srinivas Niranj Chandrasekaran
- Department of Biochemistry and Biophysics, The University of North Carolina at Chapel Hill , Chapel Hill, North Carolina 27599-7260, USA
| | - Jhuma Das
- Department of Biochemistry and Biophysics, The University of North Carolina at Chapel Hill , Chapel Hill, North Carolina 27599-7260, USA
| | - Nikolay V Dokholyan
- Department of Biochemistry and Biophysics, The University of North Carolina at Chapel Hill , Chapel Hill, North Carolina 27599-7260, USA
| | - Charles W Carter
- Department of Biochemistry and Biophysics, The University of North Carolina at Chapel Hill , Chapel Hill, North Carolina 27599-7260, USA
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12
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Li W, Kinch LN, Karplus PA, Grishin NV. ChSeq: A database of chameleon sequences. Protein Sci 2015; 24:1075-86. [PMID: 25970262 DOI: 10.1002/pro.2689] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2015] [Revised: 04/15/2015] [Accepted: 04/24/2015] [Indexed: 11/11/2022]
Abstract
Chameleon sequences (ChSeqs) refer to sequence strings of identical amino acids that can adopt different conformations in protein structures. Researchers have detected and studied ChSeqs to understand the interplay between local and global interactions in protein structure formation. The different secondary structures adopted by one ChSeq challenge sequence-based secondary structure predictors. With increasing numbers of available Protein Data Bank structures, we here identify a large set of ChSeqs ranging from 6 to 10 residues in length. The homologous ChSeqs discovered highlight the structural plasticity involved in biological function. When compared with previous studies, the set of unrelated ChSeqs found represents an about 20-fold increase in the number of detected sequences, as well as an increase in the longest ChSeq length from 8 to 10 residues. We applied secondary structure predictors on our ChSeqs and found that methods based on a sequence profile outperformed methods based on a single sequence. For the unrelated ChSeqs, the evolutionary information provided by the sequence profile typically allows successful prediction of the prevailing secondary structure adopted in each protein family. Our dataset will facilitate future studies of ChSeqs, as well as interpretations of the interplay between local and nonlocal interactions. A user-friendly web interface for this ChSeq database is available at prodata.swmed.edu/chseq.
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Affiliation(s)
- Wenlin Li
- Department of Biophysics, University of Texas Southwestern Medical Center, Dallas, Texas, 75390-9050.,Department of Biochemistry, University of Texas Southwestern Medical Center, Dallas, Texas, 75390-9050
| | - Lisa N Kinch
- Howard Hughes Medical Institute, University of Texas Southwestern Medical Center, Dallas, Texas, 75390-9050
| | - P Andrew Karplus
- Department of Biochemistry and Biophysics, Oregon State University, Corvallis, Oregon, 97331
| | - Nick V Grishin
- Department of Biophysics, University of Texas Southwestern Medical Center, Dallas, Texas, 75390-9050.,Department of Biochemistry, University of Texas Southwestern Medical Center, Dallas, Texas, 75390-9050.,Howard Hughes Medical Institute, University of Texas Southwestern Medical Center, Dallas, Texas, 75390-9050
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13
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Chekmarev SF. Protein folding as a complex reaction: a two-component potential for the driving force of folding and its variation with folding scenario. PLoS One 2015; 10:e0121640. [PMID: 25848943 PMCID: PMC4388825 DOI: 10.1371/journal.pone.0121640] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2014] [Accepted: 02/11/2015] [Indexed: 11/19/2022] Open
Abstract
The Helmholtz decomposition of the vector field of probability fluxes in a two-dimensional space of collective variables makes it possible to introduce a potential for the driving force of protein folding [Chekmarev, J. Chem. Phys. 139 (2013) 145103]. The potential has two components: one component (Φ) is responsible for the source and sink of the folding flow, which represent, respectively, the unfolded and native state of the protein, and the other (Ψ) accounts for the flow vorticity inherently generated at the periphery of the flow field and provides the canalization of the flow between the source and sink. Both components obey Poisson’s equations with the corresponding source/sink terms. In the present paper, we consider how the shape of the potential changes depending on the scenario of protein folding. To mimic protein folding dynamics projected onto a two-dimensional space of collective variables, the two-dimensional Müller and Brown potential is employed. Three characteristic scenarios are considered: a single pathway from the unfolded to the native state without intermediates, two parallel pathways without intermediates, and a single pathway with an off-pathway intermediate. To determine the probability fluxes, the hydrodynamic description of the folding reaction is used, in which the first-passage folding is viewed as a steady flow of the representative points of the protein from the unfolded to the native state. We show that despite the possible complexity of the folding process, the Φ-component is simple and universal in shape. The Ψ-component is more complex and reveals characteristic features of the process of folding. The present approach is potentially applicable to other complex reactions, for which the transition from the reactant to the product can be described in a space of two (collective) variables.
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Affiliation(s)
- Sergei F. Chekmarev
- Institute of Thermophysics, 630090 Novosibirsk, Russia and Department of Physics, Novosibirsk State University, 630090 Novosibirsk, Russia
- * E-mail:
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14
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Kalgin IV, Chekmarev SF. Folding of a β-sheet miniprotein: probability fluxes, streamlines, and the potential for the driving force. J Phys Chem B 2015; 119:1380-7. [PMID: 25544646 DOI: 10.1021/jp5112795] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this work we continue the study of the first-passage folding of an antiparallel β-sheet miniprotein (beta3s) that was initiated in the previous work [Kalgin et al. J. Phys. Chem. B, 2014, 118, 4287]. We consider a larger ensemble of folding trajectories, which allows us to gain a closer insight into the folding dynamics. In particular, we calculate the potential for the driving force of folding in a reduced space of collective variables. The potential has two components. One component (Φ) is responsible for the source and sink of the folding flow, which are formed, respectively, in the regions of the unfolded and native states of the protein, and the other (Ψ) accounts for the flow vorticity inherently generated at the sides of the reaction channel and provides the canalization of the folding flow between the source and sink. We show that both components obey Poisson's equations with the corresponding source/sink terms. The resulting components have a very simple form: the Φ-surface consists of two well-defined peaks of different signs, which correspond, respectively, to the source and sink of the folding flow, and the Ψ-surface consists of two ridges of different signs that connect the source and sink of the flow.
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Affiliation(s)
- Igor V Kalgin
- Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, Russia
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15
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Wolynes PG. Evolution, energy landscapes and the paradoxes of protein folding. Biochimie 2014; 119:218-30. [PMID: 25530262 DOI: 10.1016/j.biochi.2014.12.007] [Citation(s) in RCA: 110] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2014] [Accepted: 12/11/2014] [Indexed: 01/25/2023]
Abstract
Protein folding has been viewed as a difficult problem of molecular self-organization. The search problem involved in folding however has been simplified through the evolution of folding energy landscapes that are funneled. The funnel hypothesis can be quantified using energy landscape theory based on the minimal frustration principle. Strong quantitative predictions that follow from energy landscape theory have been widely confirmed both through laboratory folding experiments and from detailed simulations. Energy landscape ideas also have allowed successful protein structure prediction algorithms to be developed. The selection constraint of having funneled folding landscapes has left its imprint on the sequences of existing protein structural families. Quantitative analysis of co-evolution patterns allows us to infer the statistical characteristics of the folding landscape. These turn out to be consistent with what has been obtained from laboratory physicochemical folding experiments signaling a beautiful confluence of genomics and chemical physics.
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Affiliation(s)
- Peter G Wolynes
- Department of Chemistry and Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA.
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16
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Baiz CR, Lin YS, Peng CS, Beauchamp KA, Voelz VA, Pande VS, Tokmakoff A. A molecular interpretation of 2D IR protein folding experiments with Markov state models. Biophys J 2014; 106:1359-70. [PMID: 24655511 DOI: 10.1016/j.bpj.2014.02.008] [Citation(s) in RCA: 46] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2013] [Revised: 01/28/2014] [Accepted: 02/03/2014] [Indexed: 11/24/2022] Open
Abstract
The folding mechanism of the N-terminal domain of ribosomal protein L9 (NTL91-39) is studied using temperature-jump (T-jump) amide I' two-dimensional infrared (2D IR) spectroscopy in combination with spectral simulations based on a Markov state model (MSM) built from millisecond-long molecular dynamics trajectories. The results provide evidence for a compact well-structured folded state and a heterogeneous fast-exchanging denatured state ensemble exhibiting residual secondary structure. The folding rate of 26.4 μs(-1) (at 80°C), extracted from the T-jump response of NTL91-39, compares favorably with the 18 μs(-1) obtained from the MSM. Structural decomposition of the MSM and analysis along the folding coordinate indicates that helix-formation nucleates the global folding. Simulated difference spectra, corresponding to the global folding transition of the MSM, are in qualitative agreement with measured T-jump 2D IR spectra. The experiments demonstrate the use of T-jump 2D IR spectroscopy as a valuable tool for studying protein folding, with direct connections to simulations. The results suggest that in addition to predicting the correct native structure and folding time constant, molecular dynamics simulations carried out with modern force fields provide an accurate description of folding mechanisms in small proteins.
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Affiliation(s)
- Carlos R Baiz
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts
| | - Yu-Shan Lin
- Department of Chemistry, Stanford University, Stanford, California
| | - Chunte Sam Peng
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts
| | | | - Vincent A Voelz
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania
| | - Vijay S Pande
- Department of Chemistry, Stanford University, Stanford, California; Biophysics Program, Stanford University, Stanford, California; Department of Structural Biology, Stanford University, Stanford, California
| | - Andrei Tokmakoff
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts.
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17
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Visualization of protein folding funnels in lattice models. PLoS One 2014; 9:e100861. [PMID: 25010343 PMCID: PMC4091862 DOI: 10.1371/journal.pone.0100861] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Accepted: 05/31/2014] [Indexed: 11/19/2022] Open
Abstract
Protein folding occurs in a very high dimensional phase space with an exponentially large number of states, and according to the energy landscape theory it exhibits a topology resembling a funnel. In this statistical approach, the folding mechanism is unveiled by describing the local minima in an effective one-dimensional representation. Other approaches based on potential energy landscapes address the hierarchical structure of local energy minima through disconnectivity graphs. In this paper, we introduce a metric to describe the distance between any two conformations, which also allows us to go beyond the one-dimensional representation and visualize the folding funnel in 2D and 3D. In this way it is possible to assess the folding process in detail, e.g., by identifying the connectivity between conformations and establishing the paths to reach the native state, in addition to regions where trapping may occur. Unlike the disconnectivity maps method, which is based on the kinetic connections between states, our methodology is based on structural similarities inferred from the new metric. The method was developed in a 27-mer protein lattice model, folded into a 3×3×3 cube. Five sequences were studied and distinct funnels were generated in an analysis restricted to conformations from the transition-state to the native configuration. Consistent with the expected results from the energy landscape theory, folding routes can be visualized to probe different regions of the phase space, as well as determine the difficulty in folding of the distinct sequences. Changes in the landscape due to mutations were visualized, with the comparison between wild and mutated local minima in a single map, which serves to identify different trapping regions. The extension of this approach to more realistic models and its use in combination with other approaches are discussed.
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18
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Chekmarev SF. Protein folding: complex potential for the driving force in a two-dimensional space of collective variables. J Chem Phys 2014; 139:145103. [PMID: 24116649 DOI: 10.1063/1.4824133] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using the Helmholtz decomposition of the vector field of folding fluxes in a two-dimensional space of collective variables, a potential of the driving force for protein folding is introduced. The potential has two components. One component is responsible for the source and sink of the folding flows, which represent respectively, the unfolded states and the native state of the protein, and the other, which accounts for the flow vorticity inherently generated at the periphery of the flow field, is responsible for the canalization of the flow between the source and sink. The theoretical consideration is illustrated by calculations for a model β-hairpin protein.
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Affiliation(s)
- Sergei F Chekmarev
- Institute of Thermophysics, 630090 Novosibirsk, Russia and Department of Physics, Novosibirsk State University, 630090 Novosibirsk, Russia
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19
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Abstract
Kinetic folding of the large two-domain maltose binding protein (MBP; 370 residues) was studied at high structural resolution by an advanced hydrogen-exchange pulse-labeling mass-spectrometry method (HX MS). Dilution into folding conditions initiates a fast molecular collapse into a polyglobular conformation (<20 ms), determined by various methods including small angle X-ray scattering. The compaction produces a structurally heterogeneous state with widespread low-level HX protection and spectroscopic signals that match the equilibrium melting posttransition-state baseline. In a much slower step (7-s time constant), all of the MBP molecules, although initially heterogeneously structured, form the same distinct helix plus sheet folding intermediate with the same time constant. The intermediate is composed of segments that are distant in the MBP sequence but adjacent in the native protein where they close the longest residue-to-residue contact. Segments that are most HX protected in the early molecular collapse do not contribute to the initial intermediate, whereas the segments that do participate are among the less protected. The 7-s intermediate persists through the rest of the folding process. It contains the sites of three previously reported destabilizing mutations that greatly slow folding. These results indicate that the intermediate is an obligatory step on the MBP folding pathway. MBP then folds to the native state on a longer time scale (~100 s), suggestively in more than one step, the first of which forms structure adjacent to the 7-s intermediate. These results add a large protein to the list of proteins known to fold through distinct native-like intermediates in distinct pathways.
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20
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Somani S, Wales DJ. Energy landscapes and global thermodynamics for alanine peptides. J Chem Phys 2013; 139:121909. [DOI: 10.1063/1.4813627] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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21
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Discrete kinetic models from funneled energy landscape simulations. PLoS One 2012; 7:e50635. [PMID: 23251375 PMCID: PMC3520928 DOI: 10.1371/journal.pone.0050635] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2012] [Accepted: 10/23/2012] [Indexed: 01/01/2023] Open
Abstract
A general method for facilitating the interpretation of computer simulations of protein folding with minimally frustrated energy landscapes is detailed and applied to a designed ankyrin repeat protein (4ANK). In the method, groups of residues are assigned to foldons and these foldons are used to map the conformational space of the protein onto a set of discrete macrobasins. The free energies of the individual macrobasins are then calculated, informing practical kinetic analysis. Two simple assumptions about the universality of the rate for downhill transitions between macrobasins and the natural local connectivity between macrobasins lead to a scheme for predicting overall folding and unfolding rates, generating chevron plots under varying thermodynamic conditions, and inferring dominant kinetic folding pathways. To illustrate the approach, free energies of macrobasins were calculated from biased simulations of a non-additive structure-based model using two structurally motivated foldon definitions at the full and half ankyrin repeat resolutions. The calculated chevrons have features consistent with those measured in stopped flow chemical denaturation experiments. The dominant inferred folding pathway has an “inside-out”, nucleation-propagation like character.
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22
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Whitford PC, Sanbonmatsu KY, Onuchic JN. Biomolecular dynamics: order-disorder transitions and energy landscapes. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:076601. [PMID: 22790780 PMCID: PMC3695400 DOI: 10.1088/0034-4885/75/7/076601] [Citation(s) in RCA: 87] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
While the energy landscape theory of protein folding is now a widely accepted view for understanding how relatively weak molecular interactions lead to rapid and cooperative protein folding, such a framework must be extended to describe the large-scale functional motions observed in molecular machines. In this review, we discuss (1) the development of the energy landscape theory of biomolecular folding, (2) recent advances toward establishing a consistent understanding of folding and function and (3) emerging themes in the functional motions of enzymes, biomolecular motors and other biomolecular machines. Recent theoretical, computational and experimental lines of investigation have provided a very dynamic picture of biomolecular motion. In contrast to earlier ideas, where molecular machines were thought to function similarly to macroscopic machines, with rigid components that move along a few degrees of freedom in a deterministic fashion, biomolecular complexes are only marginally stable. Since the stabilizing contribution of each atomic interaction is on the order of the thermal fluctuations in solution, the rigid body description of molecular function must be revisited. An emerging theme is that functional motions encompass order-disorder transitions and structural flexibility provides significant contributions to the free energy. In this review, we describe the biological importance of order-disorder transitions and discuss the statistical-mechanical foundation of theoretical approaches that can characterize such transitions.
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Affiliation(s)
- Paul C Whitford
- Center for Theoretical Biological Physics, Department of Physics, Rice University, 6100 Main, Houston, TX 77005-1827, USA
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23
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Movahed HB, van Zon R, Schofield J. Free energy landscape of protein-like chains with discontinuous potentials. J Chem Phys 2012; 136:245103. [PMID: 22755604 DOI: 10.1063/1.4729850] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this article the configurational space of two simple protein models consisting of polymers composed of a periodic sequence of four different kinds of monomers is studied as a function of temperature. In the protein models, hydrogen bond interactions, electrostatic repulsion, and covalent bond vibrations are modeled by discontinuous step, shoulder, and square-well potentials, respectively. The protein-like chains exhibit a secondary alpha helix structure in their folded states at low temperatures, and allow a natural definition of a configuration by considering which beads are bonded. Free energies and entropies of configurations are computed using the parallel tempering method in combination with hybrid Monte Carlo sampling of the canonical ensemble of the discontinuous potential system. The probability of observing the most common configuration is used to analyze the nature of the free energy landscape, and it is found that the model with the least number of possible bonds exhibits a funnel-like free energy landscape at low enough temperature for chains with fewer than 30 beads. For longer proteins, the free landscape consists of several minima, where the configuration with the lowest free energy changes significantly by lowering the temperature and the probability of observing the most common configuration never approaches one due to the degeneracy of the lowest accessible potential energy.
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Affiliation(s)
- Hanif Bayat Movahed
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada.
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24
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Jas GS, Hegefeld W, Májek P, Kuczera K, Elber R. Experiments and comprehensive simulations of the formation of a helical turn. J Phys Chem B 2012; 116:6598-610. [PMID: 22335541 PMCID: PMC3361543 DOI: 10.1021/jp211645s] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
We investigate the kinetics and thermodynamics of a helical turn formation in the peptide Ac-WAAAH-NH(2). NMR measurements indicate that this peptide has significant tendency to form a structure of a helical turn, while temperature dependent CD establishes the helix fraction at different temperatures. Molecular dynamics and milestoning simulations agree with experimental observables and suggest an atomically detailed picture for the turn formation. Using a network representation, two alternative mechanisms of folding are identified: (i) a direct co-operative mechanism from the unfolded to the folded state without intermediate formation of hydrogen bonds and (ii) an indirect mechanism with structural intermediates with two residues in a helical conformation. This picture is consistent with kinetic measurements that reveal two experimental time scales of sub-nanosecond and several nanoseconds.
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Affiliation(s)
- Gouri S. Jas
- Department of Chemistry, Biochemistry, and Institute of Biomedical Studies, Baylor University, Waco, TX 76706
| | - Wendy Hegefeld
- Department of Chemistry, Biochemistry, and Institute of Biomedical Studies, Baylor University, Waco, TX 76706
| | - Peter Májek
- Institute of Computational Engineering and Sciences (ICES), University of Texas at Austin, Austin, TX 78712
| | - Krzysztof Kuczera
- Departments of Chemistry and Molecular Biosciences, The University of Kansas, Lawrence, KS 66045
| | - Ron Elber
- Institute of Computational Engineering and Sciences (ICES), University of Texas at Austin, Austin, TX 78712
- Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, TX 78712
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25
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Ceres N, Lavery R. Coarse-grain Protein Models. INNOVATIONS IN BIOMOLECULAR MODELING AND SIMULATIONS 2012. [DOI: 10.1039/9781849735049-00219] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
Coarse-graining is a powerful approach for modeling biomolecules that, over the last few decades, has been extensively applied to proteins. Coarse-grain models offer access to large systems and to slow processes without becoming computationally unmanageable. In addition, they are very versatile, enabling both the protein representation and the energy function to be adapted to the biological problem in hand. This review concentrates on modeling soluble proteins and their assemblies. It presents an overview of the coarse-grain representations, of the associated interaction potentials, and of the optimization procedures used to define them. It then shows how coarse-grain models have been used to understand processes involving proteins, from their initial folding to their functional properties, their binary interactions, and the assembly of large complexes.
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Affiliation(s)
- N. Ceres
- Bases Moléculaires et Structurales des Systèmes Infectieux Université Lyon1/CNRS UMR 5086, IBCP, 7 Passage du Vercors, 69367, Lyon France
| | - R. Lavery
- Bases Moléculaires et Structurales des Systèmes Infectieux Université Lyon1/CNRS UMR 5086, IBCP, 7 Passage du Vercors, 69367, Lyon France
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26
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Shandiz AT, Baxa MC, Sosnick TR. A "Link-Psi" strategy using crosslinking indicates that the folding transition state of ubiquitin is not very malleable. Protein Sci 2012; 21:819-27. [PMID: 22528473 DOI: 10.1002/pro.2065] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2012] [Revised: 03/19/2012] [Accepted: 03/19/2012] [Indexed: 11/09/2022]
Abstract
Using a combined crosslinking-ψ analysis strategy, we examine whether the structural content of the transition state of ubiquitin can be altered. A synthetic dichloroacetone crosslink is first introduced across two β strands. Whether the structural content in the transition state ensemble has shifted towards the region containing the crosslink is probed by remeasuring the ψ value at another region (ψ identifies the degree to which an inserted bi-Histidine metal ion binding site is formed in the transition state). For sites around the periphery of the obligate transition state nucleus, we find that the resulting changes in ψ values are near or at our detection limit, thereby indicating that the structural content of the transition state has not measurably changed upon crosslinking. This work demonstrates the utility of the simultaneous application of crosslinking and ψ-analysis for examining potential transition state heterogeneity in globular proteins.
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Affiliation(s)
- Ali T Shandiz
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, Illinois 60637, USA
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27
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Greene LH, Grant TM. Protein folding by ‘levels of separation’: A hypothesis. FEBS Lett 2012; 586:962-6. [DOI: 10.1016/j.febslet.2012.02.040] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2011] [Revised: 01/31/2012] [Accepted: 02/23/2012] [Indexed: 11/16/2022]
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28
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29
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Prigozhin MB, Gruebele M. The fast and the slow: folding and trapping of λ6-85. J Am Chem Soc 2011; 133:19338-41. [PMID: 22066714 DOI: 10.1021/ja209073z] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Molecular dynamics simulations combining many microsecond trajectories have recently predicted that a very fast folding protein like lambda repressor fragment λ(6-85) D14A could have a slow millisecond kinetic phase. We investigated this possibility by detecting temperature-jump relaxation to 5 ms. While λ(6-85) D14A has no significant slow phase, two even more stable mutants do. A slow phase of λ(6-85) D14A does appear in mild denaturant. The experimental data and computational modeling together suggest the following hypothesis: λ(6-85) takes only microseconds to reach its native state from an extensively unfolded state, while the latter takes milliseconds to reach compact β-rich traps. λ(6-85) is not only thermodynamically but also kinetically protected from reaching such "intramolecular amyloids" while folding.
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Affiliation(s)
- Maxim B Prigozhin
- Department of Chemistry and Center for Biophysics and Computational Biology, University of Illinois, Urbana, Illinois 61801, USA
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30
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Dixit A, Verkhivker GM. The energy landscape analysis of cancer mutations in protein kinases. PLoS One 2011; 6:e26071. [PMID: 21998754 PMCID: PMC3188581 DOI: 10.1371/journal.pone.0026071] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2011] [Accepted: 09/19/2011] [Indexed: 11/18/2022] Open
Abstract
The growing interest in quantifying the molecular basis of protein kinase activation and allosteric regulation by cancer mutations has fueled computational studies of allosteric signaling in protein kinases. In the present study, we combined computer simulations and the energy landscape analysis of protein kinases to characterize the interplay between oncogenic mutations and locally frustrated sites as important catalysts of allostetric kinase activation. While structurally rigid kinase core constitutes a minimally frustrated hub of the catalytic domain, locally frustrated residue clusters, whose interaction networks are not energetically optimized, are prone to dynamic modulation and could enable allosteric conformational transitions. The results of this study have shown that the energy landscape effect of oncogenic mutations may be allosteric eliciting global changes in the spatial distribution of highly frustrated residues. We have found that mutation-induced allosteric signaling may involve a dynamic coupling between structurally rigid (minimally frustrated) and plastic (locally frustrated) clusters of residues. The presented study has demonstrated that activation cancer mutations may affect the thermodynamic equilibrium between kinase states by allosterically altering the distribution of locally frustrated sites and increasing the local frustration in the inactive form, while eliminating locally frustrated sites and restoring structural rigidity of the active form. The energy landsape analysis of protein kinases and the proposed role of locally frustrated sites in activation mechanisms may have useful implications for bioinformatics-based screening and detection of functional sites critical for allosteric regulation in complex biomolecular systems.
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Affiliation(s)
- Anshuman Dixit
- Department of Pharmaceutical Chemistry, School of Pharmacy, The University of Kansas, Lawrence, Kansas, United States of America
| | - Gennady M. Verkhivker
- School of Computational Sciences and Crean School of Health and Life Sciences, Schmid College of Science and Technology, Chapman University, Orange, California, United States of America
- Department of Pharmacology, University of California, San Diego, La Jolla, California, United States of America
- * E-mail:
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31
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Yang Z, Shi B, Lu H, Xiu P, Zhou R. Dewetting Transitions in the Self-Assembly of Two Amyloidogenic β-Sheets and the Importance of Matching Surfaces. J Phys Chem B 2011; 115:11137-44. [DOI: 10.1021/jp2046454] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Zaixing Yang
- Bio-X Lab, Department of Physics, and Soft Matter Research Center, Zhejiang University, Hangzhou 310027, China
| | - Biyun Shi
- Bio-X Lab, Department of Physics, and Soft Matter Research Center, Zhejiang University, Hangzhou 310027, China
| | - Hangjun Lu
- Department of Physics, Zhejiang Normal University, 321004, Jinhua, China
| | - Peng Xiu
- Bio-X Lab, Department of Physics, and Soft Matter Research Center, Zhejiang University, Hangzhou 310027, China
| | - Ruhong Zhou
- Computational Biology Center, IBM Thomas J. Watson Research Center, 1101 Kitchawan Road, Yorktown Heights, New York 10598, United States
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32
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Affiliation(s)
- Jose M. Sanchez-Ruiz
- Facultad de Ciencias, Departamento de Quimica Fisica, Universidad de Granada, 18071 Granada, Spain;
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33
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Chang JY. Diverse pathways of oxidative folding of disulfide proteins: underlying causes and folding models. Biochemistry 2011; 50:3414-31. [PMID: 21410235 DOI: 10.1021/bi200131j] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The pathway of oxidative folding of disulfide proteins exhibits a high degree of diversity, which is manifested mainly by distinct structural heterogeneity and diverse rearrangement pathways of folding intermediates. During the past two decades, the scope of this diversity has widened through studies of more than 30 disulfide-rich proteins by various laboratories. A more comprehensive landscape of the mechanism of protein oxidative folding has emerged. This review will cover three themes. (1) Elaboration of the scope of diversity of disulfide folding pathways, including the two opposite extreme models, represented by bovine pancreatic trypsin inhibitor (BPTI) and hirudin. (2) Demonstration of experimental evidence accounting for the underlying mechanism of the folding diversity. (3) Discussion of the convergence between the extreme models of oxidative folding and models of conventional conformational folding (framework model, hydrophobic collapse model).
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Affiliation(s)
- Jui-Yoa Chang
- Research Center for Protein Chemistry, Institute of Molecular Medicine, Department of Biochemistry and Molecular Biology, Medical School, The University of Texas, Houston, 77030, USA.
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34
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Roh JH, Guo L, Kilburn JD, Briber RM, Irving T, Woodson SA. Multistage collapse of a bacterial ribozyme observed by time-resolved small-angle X-ray scattering. J Am Chem Soc 2010; 132:10148-54. [PMID: 20597502 PMCID: PMC2918669 DOI: 10.1021/ja103867p] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Ribozymes must fold into compact, native structures to function properly in the cell. The first step in forming the RNA tertiary structure is the neutralization of the phosphate charge by cations, followed by collapse of the unfolded molecules into more compact structures. The specificity of the collapse transition determines the structures of the folding intermediates and the folding time to the native state. However, the forces that enable specific collapse in RNA are not understood. Using time-resolved SAXS, we report that upon addition of 5 mM Mg(2+) to the Azoarcus group I ribozyme up to 80% of chains form compact structures in less than 1 ms. In 1 mM Mg(2+), the collapse transition produces extended structures that slowly approach the folded state, while > or = 1.5 mM Mg(2+) leads to an ensemble of random coils that fold with multistage kinetics. Increased flexibility of molecules in the intermediate ensemble correlates with a Mg(2+)-dependent increase in the fast folding population and a previously unobserved crossover in the collapse kinetics. Partial denaturation of the unfolded RNA with urea also increases the fraction of chains following the fast-folding pathway. These results demonstrate that the preferred collapse mechanism depends on the extent of Mg(2+)-dependent charge neutralization and that non-native interactions within the unfolded ensemble contribute to the heterogeneity of the ribozyme folding pathways at the very earliest stages of tertiary structure formation.
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Affiliation(s)
- Joon Ho Roh
- Department of Materials Science and Engineering, University of Maryland, College Park, MD 20742, USA
- T. C. Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD 21218, USA
- NIST Center for Neutron Scattering Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Liang Guo
- BioCAT, CSRRI and Department of BCPS, Illinois Institute of Technology, Chicago, IL 60616, USA
| | - J. Duncan Kilburn
- T. C. Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD 21218, USA
| | - Robert M. Briber
- Department of Materials Science and Engineering, University of Maryland, College Park, MD 20742, USA
| | - Thomas Irving
- BioCAT, CSRRI and Department of BCPS, Illinois Institute of Technology, Chicago, IL 60616, USA
| | - Sarah A. Woodson
- T. C. Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD 21218, USA
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35
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Chang JY. Structural heterogeneity of 6 M GdmCl-denatured proteins: implications for the mechanism of protein folding. Biochemistry 2009; 48:9340-6. [PMID: 19728745 DOI: 10.1021/bi901417f] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
An in vitro experiment with protein folding is typically initiated with 6 M GdmCl-denatured proteins, which are generally considered fully unfolded. However, studies conducted by various laboratories have shown that many 6 M GdmCl-denatured proteins are structurally heterogeneous and still retain nativelike residual structures. The extent of conformational heterogeneity of the 6 M GdmCl-denatured protein has significant implications for the folding landscape as well as the interpretation of the observed early stage folding mechanism. Using the method of disulfide scrambling, we are able to gain rough insight into the diverse structural properties of 6 M GdmCl-denatured proteins. It demonstrates that most 6 M GdmCl-denatured proteins are approximately fully denatured, but partially unfolded. Most of them comprise diverse conformational isomers. We review here the cumulative evidence obtained from various laboratories and also provide experimental data obtained in our laboratory.
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Affiliation(s)
- Jui-Yoa Chang
- Department of Biochemistry and Molecular Biology, Research Center for Protein Chemistry, Brown Foundation Institute of Molecular Medicine, University of Texas, Houston, Texas 77030, USA.
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36
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Gin BC, Garrahan JP, Geissler PL. The Limited Role of Nonnative Contacts in the Folding Pathways of a Lattice Protein. J Mol Biol 2009; 392:1303-14. [DOI: 10.1016/j.jmb.2009.06.058] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2009] [Revised: 06/19/2009] [Accepted: 06/23/2009] [Indexed: 11/15/2022]
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37
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Sakurai K, Konuma T, Yagi M, Goto Y. Structural dynamics and folding of β-lactoglobulin probed by heteronuclear NMR. Biochim Biophys Acta Gen Subj 2009; 1790:527-37. [DOI: 10.1016/j.bbagen.2009.04.003] [Citation(s) in RCA: 81] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2009] [Revised: 04/02/2009] [Accepted: 04/06/2009] [Indexed: 10/20/2022]
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38
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39
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Lenz P, Cho SS, Wolynes PG. Analysis of single molecule folding studies with replica correlation functions. Chem Phys Lett 2009; 471:310-314. [PMID: 20161316 PMCID: PMC2676848 DOI: 10.1016/j.cplett.2009.02.054] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
Single molecule experiments that can track individual trajectories of biomolecular processes provide a challenge for understanding how these stochastic trajectories relate to the global energy landscape. Using trajectories from a native structure based simulation, we use order parameters that accurately distinguish between protein folding mechanisms that involve a simple, single set of pathways versus a complex one with multiple sets of competing pathways. We show how the folding dynamics can be analyzed with replica correlation functions in a way compatible with single molecule experiments.
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Affiliation(s)
- Peter Lenz
- Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany
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40
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Abstract
Hydrophobicity manifests itself differently on large and small length scales. This review focuses on large-length-scale hydrophobicity, particularly on dewetting at single hydrophobic surfaces and drying in regions bounded on two or more sides by hydrophobic surfaces. We review applicable theories, simulations, and experiments pertaining to large-scale hydrophobicity in physical and biomolecular systems and clarify some of the critical issues pertaining to this subject. Given space constraints, we cannot review all the significant and interesting work in this active field.
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Affiliation(s)
- Bruce J Berne
- Department of Chemistry, Columbia University, New York, New York 10027, USA.
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41
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DNA energy landscapes via calorimetric detection of microstate ensembles of metastable macrostates and triplet repeat diseases. Proc Natl Acad Sci U S A 2008; 105:18326-30. [PMID: 19015511 DOI: 10.1073/pnas.0810376105] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Biopolymers exhibit rough energy landscapes, thereby allowing biological processes to access a broad range of kinetic and thermodynamic states. In contrast to proteins, the energy landscapes of nucleic acids have been the subject of relatively few experimental investigations. In this study, we use calorimetric and spectroscopic observables to detect, resolve, and selectively enrich energetically discrete ensembles of microstates within metastable DNA structures. Our results are consistent with metastable, "native" DNA states being composed of an ensemble of discrete and kinetically stable microstates of differential stabilities, rather than exclusively being a single, discrete thermodynamic species. This conceptual construct is important for understanding the linkage between biopolymer conformational/configurational space and biological function, such as in protein folding, allosteric control of enzyme activity, RNA and DNA folding and function, DNA structure and biological regulation, etc. For the specific DNA sequences and structures studied here, the demonstration of discrete, kinetically stable microstates potentially has biological consequences for understanding the development and onset of DNA expansion and triplet repeat diseases.
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42
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Kumar R, Bhuyan AK. Viscosity scaling for the glassy phase of protein folding. J Phys Chem B 2008; 112:12549-54. [PMID: 18781712 DOI: 10.1021/jp804021d] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Although commendable progress has been made in the understanding of the physics of protein folding, a key unresolved issue is whether Kramers' diffusion model of chemical reactions is generally applicable to activated barrier crossing events during folding. To examine the solvent viscosity effect on the folding transition of native-like trapped intermediates, laser flash photolysis has been used to measure the microsecond folding kinetics of a natively folded state of CO-liganded ferrocytochrome c (M-state) in the 1-250 cP range of glycerol viscosity at pH 7.0, 20 degrees C. The single rate coefficient for the folding of the M-state to the native state of the protein (i.e., the M --> N folding process) decreases initially when the solvent viscosity is low (<10 cP), but saturates at higher viscosity, indicating that Kramers model is not general enough for scaling the viscosity dependence of post-transition folding involving glassy dynamics. Analysis based on the Grote-Hynes idea of time dependent friction in conjunction with defect diffusion dynamics can account for the observed non-Kramers scaling.
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Affiliation(s)
- Rajesh Kumar
- Schools of Chemistry and Life Sciences, University of Hyderabad, Hyderabad, India
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43
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Kamerzell TJ, Russell Middaugh C. The Complex Inter-Relationships Between Protein Flexibility and Stability. J Pharm Sci 2008; 97:3494-517. [DOI: 10.1002/jps.21269] [Citation(s) in RCA: 90] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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44
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Ishii T, Murayama Y, Katano A, Maki K, Kuwajima K, Sano M. Probing force-induced unfolding intermediates of a single staphylococcal nuclease molecule and the effect of ligand binding. Biochem Biophys Res Commun 2008; 375:586-91. [PMID: 18755146 DOI: 10.1016/j.bbrc.2008.08.073] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2008] [Accepted: 08/12/2008] [Indexed: 10/21/2022]
Abstract
Single-molecule manipulation techniques have given experimental access to unfolding intermediates of proteins that are inaccessible in conventional experiments. A detailed characterization of the intermediates is a challenging problem that provides new possibilities for directly probing the energy landscape of proteins. We investigated single-molecule mechanical unfolding of a small globular protein, staphylococcal nuclease (SNase), using atomic force microscopy. The unfolding trajectories of the protein displayed sub-molecular and stochastic behavior with typical lengths corresponding to the size of the unfolded substructures. Our results support the view that the single protein unfolds along multiple pathways as suggested in recent theoretical studies. Moreover, we found the drastic change, caused by the ligand and inhibitor bindings, in the mechanical unfolding dynamics.
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Affiliation(s)
- Takaaki Ishii
- Department of Physics, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
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45
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Patel BA, Debenedetti PG, Stillinger FH, Rossky PJ. The effect of sequence on the conformational stability of a model heteropolymer in explicit water. J Chem Phys 2008; 128:175102. [PMID: 18465941 DOI: 10.1063/1.2909974] [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 properties of a two-dimensional lattice heteropolymer model for a protein in which water is explicitly represented. The model protein distinguishes between hydrophobic and polar monomers through the effect of the hydrophobic monomers on the entropy and enthalpy of the hydrogen bonding of solvation shell water molecules. As experimentally observed, model heteropolymer sequences fold into stable native states characterized by a hydrophobic core to avoid unfavorable interactions with the solvent. These native states undergo cold, pressure, and thermal denaturation into distinct configurations for each type of unfolding transition. However, the heteropolymer sequence is an important element, since not all sequences will fold into stable native states at positive pressures. Simulation of a large collection of sequences indicates that these fall into two general groups, those exhibiting highly stable native structures and those that do not. Statistical analysis of important patterns in sequences shows a strong tendency for observing long blocks of hydrophobic or polar monomers in the most stable sequences. Statistical analysis also shows that alternation of hydrophobic and polar monomers appears infrequently among the most stable sequences. These observations are not absolute design rules and, in practice, these are not sufficient to rationally design very stable heteropolymers. We also study the effect of mutations on improving the stability of the model proteins, and demonstrate that it is possible to obtain a very stable heteropolymer from directed evolution of an initially unstable heteropolymer.
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Affiliation(s)
- Bryan A Patel
- Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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46
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Yagi M, Kameda A, Sakurai K, Nishimura C, Goto Y. Disulfide-Linked Bovine β-Lactoglobulin Dimers Fold Slowly, Navigating a Glassy Folding Landscape. Biochemistry 2008; 47:5996-6006. [DOI: 10.1021/bi8001715] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Masanori Yagi
- Institute for Protein Research, Osaka University, and CREST, Japan Science and Technology Agency, Yamadaoka 3-2, Suita, Osaka 565-0871, Japan, and Department of Molecular Biology, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, California 92037
| | - Atsushi Kameda
- Institute for Protein Research, Osaka University, and CREST, Japan Science and Technology Agency, Yamadaoka 3-2, Suita, Osaka 565-0871, Japan, and Department of Molecular Biology, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, California 92037
| | - Kazumasa Sakurai
- Institute for Protein Research, Osaka University, and CREST, Japan Science and Technology Agency, Yamadaoka 3-2, Suita, Osaka 565-0871, Japan, and Department of Molecular Biology, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, California 92037
| | - Chiaki Nishimura
- Institute for Protein Research, Osaka University, and CREST, Japan Science and Technology Agency, Yamadaoka 3-2, Suita, Osaka 565-0871, Japan, and Department of Molecular Biology, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, California 92037
| | - Yuji Goto
- Institute for Protein Research, Osaka University, and CREST, Japan Science and Technology Agency, Yamadaoka 3-2, Suita, Osaka 565-0871, Japan, and Department of Molecular Biology, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, California 92037
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47
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Shibayama N. Slow Motion Analysis of Protein Folding Intermediates within Wet Silica Gels. Biochemistry 2008; 47:5784-94. [DOI: 10.1021/bi8003582] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Naoya Shibayama
- Department of Physiology, Division of Biophysics, Jichi Medical University, 3311-1 Yakushiji, Shimotsuke, Tochigi 329-0498, Japan
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48
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Sardiu ME, Cheung MS, Yu YK. Cysteine-cysteine contact preference leads to target-focusing in protein folding. Biophys J 2007; 93:938-51. [PMID: 17617551 PMCID: PMC1913149 DOI: 10.1529/biophysj.106.097824] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We perform a statistical analysis of amino-acid contacts to investigate possible preferences of amino-acid interactions. We include in the analysis only tertiary contacts, because they are less constrained--compared to secondary contacts--by proteins' backbone rigidity. Using proteins from the protein data bank, our analysis reveals an unusually high frequency of cysteine pairings relative to that expected from random. To elucidate the possible effects of cysteine interactions in folding, we perform molecular simulations on three cysteine-rich proteins. In particular, we investigate the difference in folding dynamics between a Gō-like model (where attraction only occurs between amino acids forming a native contact) and a variant model (where attraction between any two cysteines is introduced to mimic the formation/dissociation of native/nonnative disulfide bonds). We find that when attraction among cysteines is nonspecific and comparable to a solvent-averaged interaction, they produce a target-focusing effect that expedites folding of cysteine-rich proteins as a result of a reduction of conformational search space. In addition, the target-focusing effect also helps reduce glassiness by lowering activation energy barriers and kinetic frustration in the system. The concept of target-focusing also provides a qualitative understanding of a correlation between the rates of protein folding and parameters such as contact order and total contact distance.
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Affiliation(s)
- Mihaela E Sardiu
- Stowers Institute for Medical Research, Kansas City, Missouri, USA.
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49
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Biswas P, Zou J, Saven JG. Statistical theory for protein ensembles with designed energy landscapes. J Chem Phys 2007; 123:154908. [PMID: 16252973 DOI: 10.1063/1.2062047] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Combinatorial protein libraries provide a promising route to investigate the determinants and features of protein folding and to identify novel folding amino acid sequences. A library of sequences based on a pool of different monomer types are screened for folding molecules, consistent with a particular foldability criterion. The number of sequences grows exponentially with the length of the polymer, making both experimental and computational tabulations of sequences infeasible. Herein a statistical theory is extended to specify the properties of sequences having particular values of global energetic quantities that specify their energy landscape. The theory yields the site-specific monomer probabilities. A foldability criterion is derived that characterizes the properties of sequences by quantifying the energetic separation of the target state from low-energy states in the unfolded ensemble and the fluctuations of the energies in the unfolded state ensemble. For a simple lattice model of proteins, excellent agreement is observed between the theory and the results of exact enumeration. The theory may be used to provide a quantitative framework for the design and interpretation of combinatorial experiments.
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Affiliation(s)
- Parbati Biswas
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
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50
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Kim J, Straub JE, Keyes T. Structure optimization and folding mechanisms of off-lattice protein models using statistical temperature molecular dynamics simulation: Statistical temperature annealing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:011913. [PMID: 17677500 DOI: 10.1103/physreve.76.011913] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2007] [Revised: 03/28/2007] [Indexed: 05/16/2023]
Abstract
The recently proposed statistical temperature molecular dynamics (STMD) algorithm [Kim, Phys. Rev. Lett. 97, 050601 (2006)] is used as the core of an optimization algorithm, statistical temperature annealing (STA), for finding low-lying energy minima of complex potential energy landscapes. Since STMD realizes a random walk in energy, the idea is simply to initiate repeated minimizations from configurations in the low-energy segments of STMD trajectories. STA is tested in structural optimization of various off-lattice AB and extended AB protein models in two and three dimensions with different chain lengths. New putative ground states were found for the two- and three-dimensional AB 55-mer, and for the three-dimensional extended AB 21-mer and 55-mer. The distinct folding features of the models are analyzed in terms of the statistical temperature and other representations of the structure of the potential energy landscape. It is shown that the characteristic behavior of the statistical temperature undergoes a qualitative change with the inclusion of a torsional potential in the extended AB model, as the more rigid backbone makes the potential energy landscape more funnel-like.
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Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
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