1
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Wessén J, Das S, Pal T, Chan HS. Analytical Formulation and Field-Theoretic Simulation of Sequence-Specific Phase Separation of Protein-Like Heteropolymers with Short- and Long-Spatial-Range Interactions. J Phys Chem B 2022; 126:9222-9245. [PMID: 36343363 DOI: 10.1021/acs.jpcb.2c06181] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
A theory for sequence-dependent liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) in the study of biomolecular condensates is formulated by extending the random phase approximation (RPA) and field-theoretic simulation (FTS) of heteropolymers with spatially long-range Coulomb interactions to include the fundamental effects of short-range, hydrophobic-like interactions between amino acid residues. To this end, short-range effects are modeled by Yukawa interactions between multiple nonelectrostatic charges derived from an eigenvalue decomposition of pairwise residue-residue contact energies. Chain excluded volume is afforded by incompressibility constraints. A mean-field approximation leads to an effective Flory-Huggins χ parameter, which, in conjunction with RPA, accounts for the contact-interaction effects of amino acid composition and the sequence-pattern effects of long-range electrostatics in IDP LLPS, whereas FTS based on the formulation provides full sequence dependence for both short- and long-range interactions. This general approach is illustrated here by applications to variants of a natural IDP in the context of several different amino-acid interaction schemes as well as a set of different model hydrophobic-polar sequences sharing the same composition. Effectiveness of the methodology is verified by coarse-grained explicit-chain molecular dynamics simulations.
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Affiliation(s)
- Jonas Wessén
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Suman Das
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Tanmoy Pal
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
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2
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Khor S. Folding with a protein's native shortcut network. Proteins 2019; 86:924-934. [PMID: 29790602 DOI: 10.1002/prot.25524] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2017] [Revised: 04/13/2018] [Accepted: 05/14/2018] [Indexed: 11/09/2022]
Abstract
A complex network approach to protein folding is proposed, wherein a protein's contact map is reconceptualized as a network of shortcut edges, and folding is steered by a structural characteristic of this network. Shortcut networks are generated by a known message passing algorithm operating on protein residue networks. It is found that the shortcut networks of native structures (SCN0s) are relevant graph objects with which to study protein folding at a formal level. The logarithm form of their contact order (SCN0_lnCO) correlates significantly with folding rate of two-state and nontwo-state proteins. The clustering coefficient of SCN0s (CSCN0 ) correlates significantly with folding rate, transition-state placement and stability of two-state folders. Reasonable folding pathways for several model proteins are produced when CSCN0 is used to combine protein segments incrementally to form the native structure. The folding bias captured by CSCN0 is detectable in non-native structures, as evidenced by Molecular Dynamics simulation generated configurations for the fast folding Villin-headpiece peptide. These results support the use of shortcut networks to investigate the role protein geometry plays in the folding of both small and large globular proteins, and have implications for the design of multibody interaction schemes in folding models. One facet of this geometry is the set of native shortcut triangles, whose attributes are found to be well-suited to identify dehydrated intraprotein areas in tight turns, or at the interface of different secondary structure elements.
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Affiliation(s)
- Susan Khor
- Department of Computer Science, Memorial University of Newfoundland, St. John's, Newfoundland and Labrador, Canada
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3
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Wu J, Cheng C, Liu G, Zhang P, Chen T. The folding pathways and thermodynamics of semiflexible polymers. J Chem Phys 2018; 148:184901. [PMID: 29764123 DOI: 10.1063/1.5018114] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Inspired by the protein folding and DNA packing, we have systematically studied the thermodynamic and kinetic behaviors of single semiflexible homopolymers by Langevin dynamics simulations. In line with experiments, a rich variety of folding products, such as rod-like bundles, hairpins, toroids, and a mixture of them, are observed in the complete diagram of states. Moreover, knotted structures with a significant population are found in a certain range of bending stiffness in thermal equilibrium. As the solvent quality becomes poorer, the population of the intermediate occurring in the folding process increases, which leads to a severe chevron rollover for the folding arm. However, the population of the intermediates in the unfolding process is very low, insufficient to induce unfolding arm rollover. The total types of folding pathways from the coil state to the toroidal state for a semiflexible polymer chain remain unchanged by varying the solvent quality or temperature, whereas the kinetic partitioning into different folding events can be tuned significantly. In the process of knotting, three types of mechanisms, namely, plugging, slipknotting, and sliding, are discovered. Along the folding evolution, a semiflexible homopolymer chain can knot at any stage of folding upon leaving the extended coil state, and the probability to find a knot increases with chain compactness. In addition, we find rich types of knotted topologies during the folding of a semiflexible homopolymer chain. This study should be helpful in gaining insight into the general principles of biopolymer folding.
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Affiliation(s)
- Jing Wu
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Chenqian Cheng
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Gaoyuan Liu
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Ping Zhang
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Tao Chen
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
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4
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Song B, Charest N, Alexander Morriss-Andrews H, Molinero V, Shea JE. Systematic derivation of implicit solvent models for the study of polymer collapse. J Comput Chem 2017; 38:1353-1361. [DOI: 10.1002/jcc.24754] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2016] [Revised: 01/08/2017] [Accepted: 01/10/2017] [Indexed: 11/09/2022]
Affiliation(s)
- Bin Song
- Department of Chemistry; The University of Utah; Salt Lake City Utah 84112-0850
| | - Nathaniel Charest
- Department of Chemistry and Biochemistry; University of California; Santa Barbara California 93106
| | - Herbert Alexander Morriss-Andrews
- Department of Chemistry and Biochemistry; University of California; Santa Barbara California 93106
- Department of Physics; University of California; Santa Barbara California 93106
| | - Valeria Molinero
- Department of Chemistry; The University of Utah; Salt Lake City Utah 84112-0850
| | - Joan-Emma Shea
- Department of Chemistry and Biochemistry; University of California; Santa Barbara California 93106
- Department of Physics; University of California; Santa Barbara California 93106
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5
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Krobath H, Chen T, Chan HS. Volumetric Physics of Polypeptide Coil–Helix Transitions. Biochemistry 2016; 55:6269-6281. [DOI: 10.1021/acs.biochem.6b00802] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Heinrich Krobath
- Departments of Biochemistry
and Molecular Genetics, Faculty of Medicine, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Tao Chen
- Departments of Biochemistry
and Molecular Genetics, Faculty of Medicine, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Hue Sun Chan
- Departments of Biochemistry
and Molecular Genetics, Faculty of Medicine, University of Toronto, Toronto, Ontario M5S 1A8, Canada
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6
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He E, Ren W, Wang J, Li W, Wang W. Effects of heme binding on myoglobin folding: Coarse grained molecular simulations. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2016. [DOI: 10.1142/s0219633615500595] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Many proteins contain cofactors, such as heme, ATP and metal ions. Binding of cofactors is not only essential for their biological functions, but also can reshape the intrinsic energy landscape of protein molecules and modulate the folding and stability. However, the molecular mechanism of cofactor coupled protein folding is not well understood. In this work, we study the cofactor coupled folding of myoglobin, which is a typical cofactor (heme) containing protein, by performing molecular dynamics simulations with a structure-based protein model developed based on the energy landscape theory. We showed that the heme binding increases the stability of the myoglobin. More importantly, the heme binding tends to increase the protein folding cooperativity, and switch the folding process from a “three-state” mechanism to a “two-state” mechanism. We also showed that the folding pathways of the myoglobin can be modulated by the heme binding. By performing comparative simulations, we revealed that the above effects of heme binding are resulted from the heme induced folding of F-helix, which is otherwise unstructured at apo state, and the heme mediated contacting interactions around the heme binding site. The simulation results are consistent with available experimental data, and provide insights into the molecular mechanism of the effects of cofactor binding on the protein folding and stability.
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Affiliation(s)
- Erbin He
- National Laboratory of Solid State Microstructure and Department of Physics, Nanjing University Nanjing, 210093, P. R. China
| | - Weitong Ren
- National Laboratory of Solid State Microstructure and Department of Physics, Nanjing University Nanjing, 210093, P. R. China
| | - Jun Wang
- National Laboratory of Solid State Microstructure and Department of Physics, Nanjing University Nanjing, 210093, P. R. China
| | - Wenfei Li
- National Laboratory of Solid State Microstructure and Department of Physics, Nanjing University Nanjing, 210093, P. R. China
| | - Wei Wang
- National Laboratory of Solid State Microstructure and Department of Physics, Nanjing University Nanjing, 210093, P. R. China
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7
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Miura Y. NMR chemical shift analysis of the conformational transition between the monomer and tetramer of melittin in an aqueous solution. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2015; 45:347-54. [PMID: 26658745 DOI: 10.1007/s00249-015-1102-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2015] [Accepted: 11/16/2015] [Indexed: 12/25/2022]
Abstract
It is known that melittin in an aqueous solution undergoes a conformational transition between the monomer and tetramer by variation in temperature. The transition correlates closely with isomers of the proline residue; monomeric melittin including a trans proline peptide bond (trans-monomer) is involved directly in the transition, whereas monomeric melittin having a cis proline peptide bond (cis-monomer) is virtually not. The transition has been explored by using nuclear magnetic resonance spectroscopy in order to clarify the stability of the tetrameric conformation and the cooperativity of the transition. In the light of temperature dependence of chemical shifts of resonances from the isomeric monomers, we qualitatively estimate the temperature-, salt-, and concentration-dependence of the relative equilibrium populations of the trans-monomer and tetramer, and show that the tetramer has a maximum conformational stability at 30-45 °C and that the transition cooperativity is very low.
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Affiliation(s)
- Yoshinori Miura
- Center for Advanced Instrumental Analysis, Kyushu University, Kasuga, 816-8580, Japan.
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8
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Huang JT, Wang T, Huang SR, Li X. Prediction of protein folding rates from simplified secondary structure alphabet. J Theor Biol 2015; 383:1-6. [PMID: 26247139 DOI: 10.1016/j.jtbi.2015.07.024] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2014] [Revised: 06/20/2015] [Accepted: 07/23/2015] [Indexed: 10/23/2022]
Abstract
Protein folding is a very complicated and highly cooperative dynamic process. However, the folding kinetics is likely to depend more on a few key structural features. Here we find that secondary structures can determine folding rates of only large, multi-state folding proteins and fails to predict those for small, two-state proteins. The importance of secondary structures for protein folding is ordered as: extended β strand > α helix > bend > turn > undefined secondary structure>310 helix > isolated β strand > π helix. Only the first three secondary structures, extended β strand, α helix and bend, can achieve a good correlation with folding rates. This suggests that the rate-limiting step of protein folding would depend upon the formation of regular secondary structures and the buckling of chain. The reduced secondary structure alphabet provides a simplified description for the machine learning applications in protein design.
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Affiliation(s)
- Jitao T Huang
- Department of Chemistry and National Laboratory of Elemento-Organic Chemistry, Nankai University, Tianjin 300071, China.
| | - Titi Wang
- Department of Chemistry and National Laboratory of Elemento-Organic Chemistry, Nankai University, Tianjin 300071, China
| | - Shanran R Huang
- Department of Chemistry and National Laboratory of Elemento-Organic Chemistry, Nankai University, Tianjin 300071, China
| | - Xin Li
- Department of Chemistry and National Laboratory of Elemento-Organic Chemistry, Nankai University, Tianjin 300071, China
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9
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Exploring the balance between folding and functional dynamics in proteins and RNA. Int J Mol Sci 2015; 16:6868-89. [PMID: 25822873 PMCID: PMC4424993 DOI: 10.3390/ijms16046868] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2014] [Revised: 03/11/2015] [Accepted: 03/11/2015] [Indexed: 11/17/2022] Open
Abstract
As our understanding of biological dynamics continues to be refined, it is becoming clear that biomolecules can undergo transitions between ordered and disordered states as they execute functional processes. From a computational perspective, studying disorder events poses a challenge, as they typically occur on long timescales, and the associated molecules are often large (i.e., hundreds of residues). These size and time requirements make it advantageous to use computationally inexpensive models to characterize large-scale dynamics, where more highly detailed models can provide information about individual sub-steps associated with function. To reduce computational demand, one often uses a coarse-grained representation of the molecule or a simplified description of the energetics. In order to use simpler models to identify transient disorder in RNA and proteins, it is imperative that these models can accurately capture structural fluctuations about folded configurations, as well as the overall stability of each molecule. Here, we explore a class of simplified model for which all non-hydrogen atoms are explicitly represented. We find that this model can provide a consistent description of protein folding and native-basin dynamics for several representative biomolecules. We additionally show that the native-basin fluctuations of tRNA and the ribosome are robust to variations in the model. Finally, the extended variable loop in tRNAIle is predicted to be very dynamic, which may facilitate biologically-relevant rearrangements. Together, this study provides a foundation that will aid in the application of simplified models to study disorder during function in ribonucleoprotein (RNP) assemblies.
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10
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Chen T, Song J, Chan HS. Theoretical perspectives on nonnative interactions and intrinsic disorder in protein folding and binding. Curr Opin Struct Biol 2014; 30:32-42. [PMID: 25544254 DOI: 10.1016/j.sbi.2014.12.002] [Citation(s) in RCA: 63] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2014] [Revised: 12/02/2014] [Accepted: 12/02/2014] [Indexed: 11/29/2022]
Abstract
The diverse biological functions of intrinsically disordered proteins (IDPs) have markedly raised our appreciation of protein conformational versatility, whereas the existence of energetically favorable yet functional detrimental nonnative interactions underscores the physical limitations of evolutionary optimization. Here we survey recent advances in using biophysical modeling to gain insight into experimentally observed nonnative behaviors and IDP properties. Simulations of IDP interactions to date focus mostly on coupled folding-binding, which follows essentially the same organizing principle as the local-nonlocal coupling mechanism in cooperative folding of monomeric globular proteins. By contrast, more innovative theories of electrostatic and aromatic interactions are needed for the conceptually novel but less-explored 'fuzzy' complexes in which the functionally bound IDPs remain largely disordered.
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Affiliation(s)
- Tao Chen
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada; Department of Molecular Genetics, University of Toronto, Toronto, Ontario M5S 1A8, Canada; Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
| | - Jianhui Song
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada; Department of Molecular Genetics, University of Toronto, Toronto, Ontario M5S 1A8, Canada; Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada; Department of Molecular Genetics, University of Toronto, Toronto, Ontario M5S 1A8, Canada; Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada.
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11
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Schafer NP, Kim BL, Zheng W, Wolynes PG. Learning To Fold Proteins Using Energy Landscape Theory. Isr J Chem 2014; 54:1311-1337. [PMID: 25308991 PMCID: PMC4189132 DOI: 10.1002/ijch.201300145] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
This review is a tutorial for scientists interested in the problem of protein structure prediction, particularly those interested in using coarse-grained molecular dynamics models that are optimized using lessons learned from the energy landscape theory of protein folding. We also present a review of the results of the AMH/AMC/AMW/AWSEM family of coarse-grained molecular dynamics protein folding models to illustrate the points covered in the first part of the article. Accurate coarse-grained structure prediction models can be used to investigate a wide range of conceptual and mechanistic issues outside of protein structure prediction; specifically, the paper concludes by reviewing how AWSEM has in recent years been able to elucidate questions related to the unusual kinetic behavior of artificially designed proteins, multidomain protein misfolding, and the initial stages of protein aggregation.
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Affiliation(s)
- N P Schafer
- Department of Physics, Rice University, Houston, TX 77005, USA ; Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
| | - B L Kim
- Department of Chemistry, Rice University, Houston, TX 77005, USA ; Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
| | - W Zheng
- Department of Chemistry, Rice University, Houston, TX 77005, USA ; Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
| | - P G Wolynes
- Department of Physics, Rice University, Houston, TX 77005, USA ; Department of Chemistry, Rice University, Houston, TX 77005, USA ; Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
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12
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Dias CL, Chan HS. Pressure-Dependent Properties of Elementary Hydrophobic Interactions: Ramifications for Activation Properties of Protein Folding. J Phys Chem B 2014; 118:7488-7509. [DOI: 10.1021/jp501935f] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Affiliation(s)
- Cristiano L. Dias
- Department
of Physics, New Jersey Institute of Technology, University Heights, Tiernan Hall, Room 463, Newark, New Jersey 07102, United States
- Departments
of Biochemistry, Molecular Genetics, and Physics, University of Toronto, 1 King’s College Circle, Toronto, Ontario Canada M5S 1A8
| | - Hue Sun Chan
- Departments
of Biochemistry, Molecular Genetics, and Physics, University of Toronto, 1 King’s College Circle, Toronto, Ontario Canada M5S 1A8
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13
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Huang JT, Huang W, Huang SR, Li X. How the folding rates of two- and multistate proteins depend on the amino acid properties. Proteins 2014; 82:2375-82. [DOI: 10.1002/prot.24599] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2014] [Revised: 04/27/2014] [Accepted: 05/05/2014] [Indexed: 01/05/2023]
Affiliation(s)
- Jitao T. Huang
- Department of Chemistry and State Key Laboratory of EOC; College of Chemistry, Nankai University; Tianjin 300071 China
| | - Wei Huang
- Department of Chemistry and State Key Laboratory of EOC; College of Chemistry, Nankai University; Tianjin 300071 China
| | - Shanran R. Huang
- Department of Chemistry and State Key Laboratory of EOC; College of Chemistry, Nankai University; Tianjin 300071 China
| | - Xin Li
- Department of Chemistry and State Key Laboratory of EOC; College of Chemistry, Nankai University; Tianjin 300071 China
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14
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Chen T, Chan HS. Effects of desolvation barriers and sidechains on local–nonlocal coupling and chevron behaviors in coarse-grained models of protein folding. Phys Chem Chem Phys 2014; 16:6460-79. [DOI: 10.1039/c3cp54866j] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Coarse-grained protein chain models with desolvation barriers or sidechains lead to stronger local–nonlocal coupling and more linear chevron plots.
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Affiliation(s)
- Tao Chen
- Departments of Biochemistry
- of Molecular Genetics
- of Physics
- University of Toronto
- Toronto, Canada
| | - Hue Sun Chan
- Departments of Biochemistry
- of Molecular Genetics
- of Physics
- University of Toronto
- Toronto, Canada
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