1
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Chalyavi F, Schmitz AJ, Tucker MJ. Unperturbed Detection of the Dynamic Structure in the Hydrophobic Core of Trp-Cage via Two-Dimensional Infrared Spectroscopy. J Phys Chem Lett 2020; 11:832-837. [PMID: 31931573 PMCID: PMC7026909 DOI: 10.1021/acs.jpclett.9b03706] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
The tyrosine ring mode is an intrinsic non-perturbing site-specific infrared reporter for conformational dynamics within protein systems. This transition is influenced by direct and indirect interactions associated with the electron-donating ability and the hydrophobicity of the surrounding molecules. Utilizing an intrinsic tyrosine moiety, two-dimensional infrared spectra of Trp-cage, often called the "hydrogen atom" of protein folding, were measured in the folded and denatured states to uncover the dynamics of the hydrophobic core. The vibrational lifetimes and the correlation decays of the tyrosine ring mode showed significant changes upon both temperature and chemical denaturation of the Trp-cage miniprotein, indicating important structural features of the hydrophobic core and its dynamics. The observed Trp6-Tyr3 interactions are in good agreement with the prior studies of the folded state, but they reach beyond the static structure. These stacking interactions and orientations fluctuate on the picosecond time scale as measured through the spectral dephasing within a dehydrated environment.
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Affiliation(s)
- Farzaneh Chalyavi
- Department of Chemistry , University of Nevada, Reno , Reno , Nevada 89557 , United States
| | - Andrew J Schmitz
- Department of Chemistry , University of Nevada, Reno , Reno , Nevada 89557 , United States
| | - Matthew J Tucker
- Department of Chemistry , University of Nevada, Reno , Reno , Nevada 89557 , United States
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2
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Shao Q, Zhu W. Effective Conformational Sampling in Explicit Solvent with Gaussian Biased Accelerated Molecular Dynamics. J Chem Theory Comput 2017; 13:4240-4252. [DOI: 10.1021/acs.jctc.7b00242] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Qiang Shao
- Drug
Discovery and Design Center, CAS Key Laboratory of Receptor Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 555 Zuchongzhi
Road, Shanghai, 201203, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Weiliang Zhu
- Drug
Discovery and Design Center, CAS Key Laboratory of Receptor Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 555 Zuchongzhi
Road, Shanghai, 201203, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
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3
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Shen L, Xie L, Yang M. Thermodynamic properties of solvated peptides from selective integrated tempering sampling with a new weighting factor estimation algorithm. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1292009] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Lin Shen
- Department of Chemistry, The University of Hong Kong, Hong Kong, P. R. China
| | - Liangxu Xie
- Department of Chemistry, The University of Hong Kong, Hong Kong, P. R. China
| | - Mingjun Yang
- Department of Chemistry, The University of Hong Kong, Hong Kong, P. R. China
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4
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Semino R, Ramsahye NA, Ghoufi A, Maurin G. Microscopic Model of the Metal-Organic Framework/Polymer Interface: A First Step toward Understanding the Compatibility in Mixed Matrix Membranes. ACS APPLIED MATERIALS & INTERFACES 2016; 8:809-19. [PMID: 26653765 DOI: 10.1021/acsami.5b10150] [Citation(s) in RCA: 82] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
An innovative computational methodology integrating density functional theory calculations and force field-based molecular dynamics simulations was developed to provide a first microscopic model of the interactions at the metal-organic framework (MOF) surface/polymer interface. This was applied to the case of the composite formed by the polymer of intrinsic microporosity, PIM-1, and the zeolitic imidazolate framework, ZIF-8, as a model system. We found that the structure of the composite at the interface is the result of both the chemical affinity between PIM-1 and ZIF-8 and the rigidity of the polymer. Specifically, there is a preferential interaction between the -CN groups of PIM-1 and the NH terminal functions of the organic linker at the ZIF-8 surface. Additionally, the resulting conformation of the polymer gives rise to interfacial microvoids at the vicinity of the MOF surface. The porosity, rigidity, and density of the interfacial polymer were analyzed and compared to those for the bulk polymer. It was shown that the polymer still feels the impact of the MOF surface even at long distances above 15-20 Å. Further, both the polydispersity of the polymer and the flexibility of the MOF surface were revealed to only slightly affect the properties of the MOF/interface. This work, which delivers a microscopic picture of the MOF surface/polymer interactions at the interface, would lead, in turn, to the understanding of the compatibility in MOF-based mixed-matrix membranes.
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Affiliation(s)
- Rocio Semino
- Institut Charles Gerhardt Montpellier UMR 5253 CNRS, Université de Montpellier , Place E. Bataillon, 34095 Montpellier Cedex 05, France
| | - Naseem A Ramsahye
- Institut Charles Gerhardt Montpellier UMR 5253 CNRS, Université de Montpellier , Place E. Bataillon, 34095 Montpellier Cedex 05, France
- Institut Charles Gerhardt Montpellier, UMR 5253 CNRS, UM, ENSCM , 8 rue de l'Ecole Normale, 34296 Montpellier Cedex 05, France
| | - Aziz Ghoufi
- Institut de Physique de Rennes, IPR, UMR 6251 CNRS , 263 Avenue du Général Leclerc, 35042 Rennes, France
| | - Guillaume Maurin
- Institut Charles Gerhardt Montpellier UMR 5253 CNRS, Université de Montpellier , Place E. Bataillon, 34095 Montpellier Cedex 05, France
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5
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Abaskharon RM, Culik RM, Woolley GA, Gai F. Tuning the Attempt Frequency of Protein Folding Dynamics via Transition-State Rigidification: Application to Trp-Cage. J Phys Chem Lett 2015; 6:521-6. [PMID: 26120378 PMCID: PMC4479204 DOI: 10.1021/jz502654q] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2014] [Accepted: 01/22/2015] [Indexed: 05/23/2023]
Abstract
The attempt frequency or prefactor (k0) of the transition-state rate equation of protein folding kinetics has been estimated to be on the order of 10(6) s(-1), which is many orders of magnitude smaller than that of chemical reactions. Herein we use the mini-protein Trp-cage to show that it is possible to significantly increase the value of k0 for a protein folding reaction by rigidifying the transition state. This is achieved by reducing the conformational flexibility of a key structural element (i.e., an α-helix) formed in the transition state via photoisomerization of an azobenzene cross-linker. We find that this strategy not only decreases the folding time of the Trp-cage peptide by more than an order of magnitude (to ∼100 ns at 25°C) but also exposes parallel folding pathways, allowing us to provide, to the best of our knowledge, the first quantitative assessment of the curvature of the transition-state free-energy surface of a protein.
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Affiliation(s)
- Rachel M. Abaskharon
- Department of Chemistry and Department
of Biochemistry & Biophysics, University of Pennsylvania,
231 South 34th Street, Philadelphia, Pennsylvania 19104, United
States
| | - Robert M. Culik
- Department of Chemistry and Department
of Biochemistry & Biophysics, University of Pennsylvania,
231 South 34th Street, Philadelphia, Pennsylvania 19104, United
States
| | - G. Andrew Woolley
- Department of Chemistry, University of
Toronto, 80 Saint George Street, Toronto, Ontario M5S 3H6,
Canada
| | - Feng Gai
- Department of Chemistry and Department
of Biochemistry & Biophysics, University of Pennsylvania,
231 South 34th Street, Philadelphia, Pennsylvania 19104, United
States
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6
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Hirai H. Practical hyperdynamics method for systems with large changes in potential energy. J Chem Phys 2014; 141:234109. [PMID: 25527921 DOI: 10.1063/1.4903787] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A practical hyperdynamics method is proposed to accelerate systems with highly endothermic and exothermic reactions such as hydrocarbon pyrolysis and oxidation reactions. In this method, referred to as the "adaptive hyperdynamics (AHD) method," the bias potential parameters are adaptively updated according to the change in potential energy. The approach is intensively examined for JP-10 (exo-tetrahydrodicyclopentadiene) pyrolysis simulations using the ReaxFF reactive force field. Valid boost parameter ranges are clarified as a result. It is shown that AHD can be used to model pyrolysis at temperatures as low as 1000 K while achieving a boost factor of around 10(5).
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Affiliation(s)
- Hirotoshi Hirai
- Toyota Central R&D Labs., Inc., 41-1 Yokomichi, Nagakute, Aichi 480-1192, Japan
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7
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Roe D, Bergonzo C, Cheatham TE. Evaluation of enhanced sampling provided by accelerated molecular dynamics with Hamiltonian replica exchange methods. J Phys Chem B 2014; 118:3543-52. [PMID: 24625009 PMCID: PMC3983400 DOI: 10.1021/jp4125099] [Citation(s) in RCA: 77] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2013] [Revised: 03/10/2014] [Indexed: 11/28/2022]
Abstract
Many problems studied via molecular dynamics require accurate estimates of various thermodynamic properties, such as the free energies of different states of a system, which in turn requires well-converged sampling of the ensemble of possible structures. Enhanced sampling techniques are often applied to provide faster convergence than is possible with traditional molecular dynamics simulations. Hamiltonian replica exchange molecular dynamics (H-REMD) is a particularly attractive method, as it allows the incorporation of a variety of enhanced sampling techniques through modifications to the various Hamiltonians. In this work, we study the enhanced sampling of the RNA tetranucleotide r(GACC) provided by H-REMD combined with accelerated molecular dynamics (aMD), where a boosting potential is applied to torsions, and compare this to the enhanced sampling provided by H-REMD in which torsion potential barrier heights are scaled down to lower force constants. We show that H-REMD and multidimensional REMD (M-REMD) combined with aMD does indeed enhance sampling for r(GACC), and that the addition of the temperature dimension in the M-REMD simulations is necessary to efficiently sample rare conformations. Interestingly, we find that the rate of convergence can be improved in a single H-REMD dimension by simply increasing the number of replicas from 8 to 24 without increasing the maximum level of bias. The results also indicate that factors beyond replica spacing, such as round trip times and time spent at each replica, must be considered in order to achieve optimal sampling efficiency.
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Affiliation(s)
- Daniel
R. Roe
- Department of Medicinal Chemistry,
College of Pharmacy, University of Utah, 2000 South 30 East Room 105, Salt Lake City, Utah 84112, United States
| | - Christina Bergonzo
- Department of Medicinal Chemistry,
College of Pharmacy, University of Utah, 2000 South 30 East Room 105, Salt Lake City, Utah 84112, United States
| | - Thomas E. Cheatham
- Department of Medicinal Chemistry,
College of Pharmacy, University of Utah, 2000 South 30 East Room 105, Salt Lake City, Utah 84112, United States
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8
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Li J, Mach P, Koehl P. Measuring the shapes of macromolecules - and why it matters. Comput Struct Biotechnol J 2013; 8:e201309001. [PMID: 24688748 PMCID: PMC3962087 DOI: 10.5936/csbj.201309001] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2013] [Revised: 11/22/2013] [Accepted: 11/22/2013] [Indexed: 11/22/2022] Open
Abstract
The molecular basis of life rests on the activity of biological macromolecules, mostly nucleic acids and proteins. A perhaps surprising finding that crystallized over the last handful of decades is that geometric reasoning plays a major role in our attempt to understand these activities. In this paper, we address this connection between geometry and biology, focusing on methods for measuring and characterizing the shapes of macromolecules. We briefly review existing numerical and analytical approaches that solve these problems. We cover in more details our own work in this field, focusing on the alpha shape theory as it provides a unifying mathematical framework that enable the analytical calculations of the surface area and volume of a macromolecule represented as a union of balls, the detection of pockets and cavities in the molecule, and the quantification of contacts between the atomic balls. We have shown that each of these quantities can be related to physical properties of the molecule under study and ultimately provides insight on its activity. We conclude with a brief description of new challenges for the alpha shape theory in modern structural biology.
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Affiliation(s)
- Jie Li
- Genome Center, University of California, Davis, 451 Health Sciences Drive, Davis, CA 95616, United States
| | - Paul Mach
- Graduate Group of Applied Mathematics, University of California, Davis, 1, Shields Ave, Davis, CA, 95616, United States
| | - Patrice Koehl
- Department of Computer Science and Genome Center, University of California, Davis, 1, Shields Ave, Davis, CA, 95616, United States
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9
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Markiewicz BN, Jo H, Culik RM, DeGrado WF, Gai F. Assessment of local friction in protein folding dynamics using a helix cross-linker. J Phys Chem B 2013; 117:14688-96. [PMID: 24205975 DOI: 10.1021/jp409334h] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Internal friction arising from local steric hindrance and/or the excluded volume effect plays an important role in controlling not only the dynamics of protein folding but also conformational transitions occurring within the native state potential well. However, experimental assessment of such local friction is difficult because it does not manifest itself as an independent experimental observable. Herein, we demonstrate, using the miniprotein trp-cage as a testbed, that it is possible to selectively increase the local mass density in a protein and hence the magnitude of local friction, thus making its effect directly measurable via folding kinetic studies. Specifically, we show that when a helix cross-linker, m-xylene, is placed near the most congested region of the trp-cage it leads to a significant decrease in both the folding rate (by a factor of 3.8) and unfolding rate (by a factor of 2.5 at 35 °C) but has little effect on protein stability. Thus, these results, in conjunction with those obtained with another cross-linked trp-cage and two uncross-linked variants, demonstrate the feasibility of using a nonperturbing cross-linker to help quantify the effect of internal friction. In addition, we estimate that a m-xylene cross-linker could lead to an increase in the roughness of the folding energy landscape by as much as 0.4-1.0k(B)T.
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Affiliation(s)
- Beatrice N Markiewicz
- Department of Chemistry and §Department of Biochemistry & Biophysics, University of Pennsylvania , Philadelphia, Pennsylvania 19104, United States
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10
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Culik RM, Annavarapu S, Nanda V, Gai F. Using D-Amino Acids to Delineate the Mechanism of Protein Folding: Application to Trp-cage. Chem Phys 2013; 422:10.1016/j.chemphys.2013.01.021. [PMID: 24307748 PMCID: PMC3844134 DOI: 10.1016/j.chemphys.2013.01.021] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
Using the miniprotein Trp-cage as a model, we show that D-amino acids can be used to facilitate the delineation of protein folding mechanism. Specifically, we study the folding-unfolding kinetics of three Trp-cage mutants where the native glycine residue near the C-terminus of the α-helix is replaced by a D-amino acid. A previous study showed that these mutations increase the Trp-cage stability, due to a terminal capping effect. Our results show that the stabilizing effect of D-asparagine and D-glutamine originates almost exclusively from a decrease in the unfolding rate, while the D-alanine mutation results in a similar decrease in the unfolding rate, but it also increases the folding rate. Together, these results support a folding mechanism wherein the α-helix formation in the transition state is nucleated at the N-terminus, whereas those long-range native interactions stabilizing this helix are developed at the downhill side of the folding free energy barrier.
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Affiliation(s)
- Robert M. Culik
- Department of Biochemistry and Biophysics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104
| | - Srinivas Annavarapu
- Department of Biochemistry, University of Medicine and Dentistry of New Jersey, Piscataway, NJ 08854
| | - Vikas Nanda
- Department of Biochemistry, University of Medicine and Dentistry of New Jersey, Piscataway, NJ 08854
| | - Feng Gai
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104
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11
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Shao Q, Yang L, Gao YQ. Structure change of β-hairpin induced by turn optimization: An enhanced sampling molecular dynamics simulation study. J Chem Phys 2011; 135:235104. [DOI: 10.1063/1.3668288] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Culik RM, Serrano AL, Bunagan MR, Gai F. Achieving secondary structural resolution in kinetic measurements of protein folding: a case study of the folding mechanism of Trp-cage. Angew Chem Int Ed Engl 2011; 50:10884-7. [PMID: 21956888 DOI: 10.1002/anie.201104085] [Citation(s) in RCA: 59] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2011] [Indexed: 01/27/2023]
Affiliation(s)
- Robert M Culik
- Department of Biochemistry and Molecular Biophysics, University of Pennsylvania, Philadelphia, PA 19104, USA
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13
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Culik RM, Serrano AL, Bunagan MR, Gai F. Achieving Secondary Structural Resolution in Kinetic Measurements of Protein Folding: A Case Study of the Folding Mechanism of Trp-cage. Angew Chem Int Ed Engl 2011. [DOI: 10.1002/ange.201104085] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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14
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Pierce LCT, Markwick PRL, McCammon JA, Doltsinis NL. Accelerating chemical reactions: exploring reactive free-energy surfaces using accelerated ab initio molecular dynamics. J Chem Phys 2011; 134:174107. [PMID: 21548673 DOI: 10.1063/1.3581093] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A biased potential molecular dynamics simulation approach, accelerated molecular dynamics (AMD), has been implemented in the framework of ab initio molecular dynamics for the study of chemical reactions. Using two examples, the double proton transfer reaction in formic acid dimer and the hypothetical adiabatic ring opening and subsequent rearrangement reactions in methylenecyclopropane, it is demonstrated that ab initio AMD can be readily employed to efficiently explore the reactive potential energy surface, allowing the prediction of chemical reactions and the identification of metastable states. An adaptive variant of the AMD method is developed, which additionally affords an accurate representation of both the free-energy surface and the mechanism associated with the chemical reaction of interest and can also provide an estimate of the reaction rate.
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Affiliation(s)
- Levi C T Pierce
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92003-0365, USA
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15
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Velez-Vega C, Borrero EE, Escobedo FA. Kinetics and mechanism of the unfolding native-to-loop transition of Trp-cage in explicit solvent via optimized forward flux sampling simulations. J Chem Phys 2011; 133:105103. [PMID: 20849192 DOI: 10.1063/1.3474803] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The native-to-loop (N-L) unfolding transition of Trp-cage protein was studied via optimized forward flux sampling (FFS) methods with trajectories evolved using molecular dynamics. The rate constant calculated from our simulations is in good agreement with the experimental value for the native-to-unfolded transition of this protein; furthermore, the trajectories sampled a phase region consistent with that reported in previous studies for the N-L transition using transition path sampling and transition interface sampling. A new variant of FFS is proposed and implemented that allows a better control of a constant flux of partial paths. A reaction coordinate model was obtained, at no extra cost, from the transition path ensemble generated by FFS, through iterative use of the FFS-least-square estimation method [E. E. Borrero and F. A. Escobedo, J. Chem. Phys. 127, 164101 (2007)] and an adaptive staging optimization algorithm [E. E. Borrero and F. A. Escobedo, J. Chem. Phys. 129, 024115 (2008)]. Finally, we further elucidate the unfolding mechanism by correlating the unfolding progress with changes in the root mean square deviation from the α carbons of the native state, the root mean square deviation from an ideal α-helix, and other structural properties of the protein.
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Affiliation(s)
- Camilo Velez-Vega
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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16
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Markwick PRL, McCammon JA. Studying functional dynamics in bio-molecules using accelerated molecular dynamics. Phys Chem Chem Phys 2011; 13:20053-65. [DOI: 10.1039/c1cp22100k] [Citation(s) in RCA: 139] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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17
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Zhou Y, Duan Y, Yang Y, Faraggi E, Lei H. Trends in template/fragment-free protein structure prediction. Theor Chem Acc 2011; 128:3-16. [PMID: 21423322 PMCID: PMC3030773 DOI: 10.1007/s00214-010-0799-2] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2010] [Accepted: 08/15/2010] [Indexed: 12/13/2022]
Abstract
Predicting the structure of a protein from its amino acid sequence is a long-standing unsolved problem in computational biology. Its solution would be of both fundamental and practical importance as the gap between the number of known sequences and the number of experimentally solved structures widens rapidly. Currently, the most successful approaches are based on fragment/template reassembly. Lacking progress in template-free structure prediction calls for novel ideas and approaches. This article reviews trends in the development of physical and specific knowledge-based energy functions as well as sampling techniques for fragment-free structure prediction. Recent physical- and knowledge-based studies demonstrated that it is possible to sample and predict highly accurate protein structures without borrowing native fragments from known protein structures. These emerging approaches with fully flexible sampling have the potential to move the field forward.
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Affiliation(s)
- Yaoqi Zhou
- School of Informatics, Indiana Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, Indiana University Purdue University, 719 Indiana Ave #319, Walker Plaza Building, Indianapolis, IN 46202 USA
| | - Yong Duan
- UC Davis Genome Center and Department of Applied Science, University of California, One Shields Avenue, Davis, CA USA
- College of Physics, Huazhong University of Science and Technology, 1037 Luoyu Road, 430074 Wuhan, China
| | - Yuedong Yang
- School of Informatics, Indiana Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, Indiana University Purdue University, 719 Indiana Ave #319, Walker Plaza Building, Indianapolis, IN 46202 USA
| | - Eshel Faraggi
- School of Informatics, Indiana Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, Indiana University Purdue University, 719 Indiana Ave #319, Walker Plaza Building, Indianapolis, IN 46202 USA
| | - Hongxing Lei
- UC Davis Genome Center and Department of Applied Science, University of California, One Shields Avenue, Davis, CA USA
- Beijing Institute of Genomics, Chinese Academy of Sciences, 100029 Beijing, China
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18
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Tjong H, Zhou HX. The folding transition-state ensemble of a four-helix bundle protein: helix propensity as a determinant and macromolecular crowding as a probe. Biophys J 2010; 98:2273-80. [PMID: 20483336 DOI: 10.1016/j.bpj.2010.01.052] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2009] [Revised: 12/21/2009] [Accepted: 01/05/2010] [Indexed: 10/19/2022] Open
Abstract
The four-helix bundle protein Rd-apocyt b(562), a redesigned stable variant of apocytochrome b(562), exhibits two-state folding kinetics. Its transition-state ensemble has been characterized by Phi-value analysis. To elucidate the molecular basis of the transition-state ensemble, we have carried out high-temperature molecular dynamics simulations of the unfolding process. In six parallel simulations, unfolding started with the melting of helix I and the C-terminal half of helix IV, and followed by helix III, the N-terminal half of helix IV and helix II. This ordered melting of the helices is consistent with the conclusion from native-state hydrogen exchange, and can be rationalized by differences in intrinsic helix propensity. Guided by experimental Phi-values, a putative transition-state ensemble was extracted from the simulations. The residue helical probabilities of this transition-state ensemble show good correlation with the Phi-values. To further validate the putative transition-state ensemble, the effect of macromolecular crowding on the relative stability between the unfolded ensemble and the transition-state ensemble was calculated. The resulting effect of crowding on the folding kinetics agrees well with experimental observations. This study shows that molecular dynamics simulations combined with calculation of crowding effects provide an avenue for characterize the transition-state ensemble in atomic details.
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Affiliation(s)
- Harianto Tjong
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida, USA
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19
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Sindhikara DJ, Emerson DJ, Roitberg AE. Exchange Often and Properly in Replica Exchange Molecular Dynamics. J Chem Theory Comput 2010; 6:2804-8. [PMID: 26616081 DOI: 10.1021/ct100281c] [Citation(s) in RCA: 81] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
Previous work by us showed that in replica exchange molecular dynamics, exchanges should be attempted extremely often, providing gains in efficiency and no undesired effects. Since that time some questions have been raised about the extendability of these claims to the general case. In this work, we answer this question in two ways. First, we perform a study measuring the effect of exchange attempt frequency in explicit solvent simulations including thousands of atoms. This shows, consistent with the previous assertion, that high exchange attempt frequency allows an optimal rate of exploration of configurational space. Second, we present an explanation of many theoretical and technical pitfalls when implementing replica exchange that cause "improper" exchanges resulting in erroneous data, exacerbated by high exchange attempt frequency.
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Affiliation(s)
- Daniel J Sindhikara
- Department of Physics, School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan, Quantum Theory Project and Department of Chemistry, University of Florida, Gainesville, Florida 32611
| | - Daniel J Emerson
- Department of Physics, School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan, Quantum Theory Project and Department of Chemistry, University of Florida, Gainesville, Florida 32611
| | - Adrian E Roitberg
- Department of Physics, School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan, Quantum Theory Project and Department of Chemistry, University of Florida, Gainesville, Florida 32611
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20
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Bruce NJ, Bryce RA. Ab Initio Protein Folding Using a Cooperative Swarm of Molecular Dynamics Trajectories. J Chem Theory Comput 2010; 6:1925-30. [PMID: 26615921 DOI: 10.1021/ct100060t] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The use of atomistic simulation techniques to directly resolve the protein tertiary structure from the primary amino acid sequence is hindered by the rough topology of the protein free energy surface and the resulting simulation time scales required. We explore here the use of a molecular dynamics technique based on swarm intelligence to identify the native states of two peptides and a Trp-cage miniprotein. In all cases, the presence of cooperative swarm interactions significantly enhanced the efficiency of molecular dynamics simulations in predicting the native conformation.
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Affiliation(s)
- Neil J Bruce
- School of Pharmacy and Pharmaceutical Sciences, University of Manchester, Oxford Road, Manchester, M13 9PT, United Kingdom
| | - Richard A Bryce
- School of Pharmacy and Pharmaceutical Sciences, University of Manchester, Oxford Road, Manchester, M13 9PT, United Kingdom
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Zhang C, Ma J. Enhanced sampling and applications in protein folding in explicit solvent. J Chem Phys 2010; 132:244101. [PMID: 20590175 PMCID: PMC2905458 DOI: 10.1063/1.3435332] [Citation(s) in RCA: 74] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2010] [Accepted: 05/05/2010] [Indexed: 12/11/2022] Open
Abstract
We report a single-copy tempering method for simulating large complex systems. In a generalized ensemble, the method uses runtime estimate of the thermal average energy computed from a novel integral identity to guide a continuous temperature-space random walk. We first validated the method in a two-dimensional Ising model and a Lennard-Jones liquid system. It was then applied to folding of three small proteins, trpzip2, trp-cage, and villin headpiece in explicit solvent. Within 0.5-1 microsecond, all three systems were reversibly folded into atomic accuracy: the alpha carbon root mean square deviations of the best folded conformations from the native states were 0.2, 0.4, and 0.4 A, for trpzip2, trp-cage, and villin headpiece, respectively.
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Affiliation(s)
- Cheng Zhang
- Department of Bioengineering and Applied Physics Program, Rice University Houston, Texas 77005, USA
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Fernandez-Lima FA, Wei H, Gao YQ, Russell DH. On the Structure Elucidation Using Ion Mobility Spectrometry and Molecular Dynamics. J Phys Chem A 2009; 113:8221-34. [DOI: 10.1021/jp811150q] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Affiliation(s)
| | - H. Wei
- Department of Chemistry, Texas A&M University, College Station, Texas, 77843
| | - Y. Q. Gao
- Department of Chemistry, Texas A&M University, College Station, Texas, 77843
| | - D. H. Russell
- Department of Chemistry, Texas A&M University, College Station, Texas, 77843
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Yang L, Shao Q, Gao YQ. Comparison between integrated and parallel tempering methods in enhanced sampling simulations. J Chem Phys 2009; 130:124111. [DOI: 10.1063/1.3097129] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
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Yang L, Shao Q, Gao YQ. Thermodynamics and folding pathways of trpzip2: an accelerated molecular dynamics simulation study. J Phys Chem B 2009; 113:803-8. [PMID: 19113829 DOI: 10.1021/jp803160f] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
In this paper, we apply an enhanced sampling method introduced earlier to study the folding mechanism of a beta-hairpin, trpzip2, using an all-atom potential for the protein and an implicit model for the solvent. The enhanced sampling method allows us to obtain multiple protein folding and unfolding trajectories in relatively short simulations. The sufficient sampling of folding and unfolding events of trpzip2 makes possible a more detailed investigation of its folding landscape and thermodynamics, leading to the identification of folding pathways. The analysis of the thermodynamics involved in the folding of trpzip2 showed that this polypeptide folds by two stages: a downhill hydrophobic collapse followed by formation of native hydrogen bonds. During the hydrogen bond formation, a transition state can be identified with only one native hydrogen bond being formed, which is more consistent with a 'zip-out' mechanism. To address the dynamics in a more reliable way, explicit solvent was used for the estimation of the diffusion constant, which was used in the Kramer's theory, together with the free energy profile calculated using the enhanced sampling and the implicit solvent, to calculate the folding rate. The calculated folding time agrees well with the experimental value of 2.5 micros.
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Affiliation(s)
- Lijiang Yang
- Department of Chemistry, Texas A&M University, College Station, Texas 77843, USA
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26
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Mardis KL, Sutton HM, Zuo X, Lindsey JS, Tiede DM. Solution-state conformational ensemble of a hexameric porphyrin array characterized using molecular dynamics and X-ray scattering. J Phys Chem A 2009; 113:2516-23. [PMID: 19243123 PMCID: PMC4965877 DOI: 10.1021/jp808318x] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Solution-phase X-ray scattering measurements in combination with coordinate-based modeling have been used to characterize the conformational ensemble of a hexameric, diphenylethyne-linked porphyrin array in solution. Configurationally broadened X-ray scattering patterns measured at room temperature for dilute toluene solutions of the porphyrin array were compared to scattering patterns calculated from structural ensembles in constant pressure and temperature molecular dynamics simulations. Thermal fluctuations sampled at picosecond intervals within nanosecond time scale dynamic simulations show large-amplitude motions that include porphyrin ring "tipping" around the porphyrin linkage axes and extended hexameric porphyrin array "breathing" motions involving torsional distortions collectively distributed along porphyrin and diphenylethyne groups. Each type of group motion produced characteristic, angle-dependent dampening of scattering features that are needed to reproduce dampening features in the experimental X-ray scattering. However, mismatches in the magnitudes of experimental and simulated dampening of high-angle X-ray scattering patterns show that large-amplitude hexamer array breathing-type motions are significantly under-represented in the simulated ensembles. This comparison between experiment and simulation provides a means not only to interpret scattering data in terms of an explicit atomic model but more generally demonstrates the use of solution X-ray scattering as an experimental benchmark for the development of simulation methods that more accurately predict configurational dynamics of supramolecular assemblies.
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Affiliation(s)
- Kristy L Mardis
- Department of Chemistry and Physics, Chicago State University, Chicago, Illinois 60628, USA.
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Shen T, Hamelberg D. A statistical analysis of the precision of reweighting-based simulations. J Chem Phys 2008; 129:034103. [PMID: 18647012 DOI: 10.1063/1.2944250] [Citation(s) in RCA: 98] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Various advanced simulation techniques, which are used to sample the statistical ensemble of systems with complex Hamiltonians, such as those displayed in condensed matters and biomolecular systems, rely heavily on successfully reweighting the sampled configurations. The sampled points of a system from an elevated thermal environment or on a modified Hamiltonian are reused with different statistical weights to evaluate its properties at the initial desired temperature or of the original Hamiltonian. Often, the decrease of accuracy induced by this procedure is ignored and the final results can be far from what is expected. We have addressed the reasons behind such a phenomenon and have provided a quantitative method to estimate the number of sampled points required in the crucial step of reweighting of these advanced simulation methods. We also provided examples from temperature histogram reweighting and accelerated molecular dynamics reweighting to illustrate this idea, which can be generalized to the dynamic reweighting as well. The study shows that this analysis may provide a priori guidance for the strategy of setting up the parameters of advanced simulations before a lengthy one is carried out. The method can therefore provide insights for optimizing the parameters for high accuracy simulations with finite amount of computational resources.
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Affiliation(s)
- Tongye Shen
- Theoretical Biology & Biophysics Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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Abstract
A simple method is introduced to achieve efficient random walking in the energy space in molecular dynamics simulations which thus enhances the sampling over a large energy range. The approach is closely related to multicanonical and replica exchange simulation methods in that it allows configurations of the system to be sampled in a wide energy range by making use of Boltzmann distribution functions at multiple temperatures. A biased potential is quickly generated using this method and is then used in accelerated molecular dynamics simulations.
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Affiliation(s)
- Yi Qin Gao
- Department of Chemistry, Texas A&M University, College Station, Texas 77843, USA.
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Gao YQ. Self-adaptive enhanced sampling in the energy and trajectory spaces: Accelerated thermodynamics and kinetic calculations. J Chem Phys 2008; 128:134111. [DOI: 10.1063/1.2901037] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
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Gao YQ, Yang L, Fan Y, Shao Q. Thermodynamics and kinetics simulations of multi-time-scale processes for complex systems. INT REV PHYS CHEM 2008. [DOI: 10.1080/01442350801920334] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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31
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de Oliveira CAF, Hamelberg D, McCammon JA. Estimating kinetic rates from accelerated molecular dynamics simulations: alanine dipeptide in explicit solvent as a case study. J Chem Phys 2008; 127:175105. [PMID: 17994855 DOI: 10.1063/1.2794763] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Molecular dynamics (MD) simulation is the standard computational technique used to obtain information on the time evolution of the conformations of proteins and many other molecular systems. However, for most biological systems of interest, the time scale for slow conformational transitions is still inaccessible to standard MD simulations. Several sampling methods have been proposed to address this issue, including the accelerated molecular dynamics method. In this work, we study the extent of sampling of the phi/psi space of alanine dipeptide in explicit water using accelerated molecular dynamics and present a framework to recover the correct kinetic rate constant for the helix to beta-strand transition. We show that the accelerated MD can drastically enhance the sampling of the phi/psi conformational phase space when compared to normal MD. In addition, the free energy density plots of the phi/psi space show that all minima regions are accurately sampled and the canonical distribution is recovered. Moreover, the kinetic rate constant for the helix to beta-strand transition is accurately estimated from these simulations by relating the diffusion coefficient to the local energetic roughness of the energy landscape. Surprisingly, even for such a low barrier transition, it is difficult to obtain enough transitions to accurately estimate the rate constant when one uses normal MD.
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Affiliation(s)
- César Augusto F de Oliveira
- Howard Hughes Medical Institute, Center for Theoretical Biological Physics, Department of Chemistry and Biochemistry, and Department of Pharmacology, University of California at San Diego, La Jolla, California 92093, USA.
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Hamelberg D, de Oliveira CAF, McCammon JA. Sampling of slow diffusive conformational transitions with accelerated molecular dynamics. J Chem Phys 2007; 127:155102. [PMID: 17949218 DOI: 10.1063/1.2789432] [Citation(s) in RCA: 197] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
Slow diffusive conformational transitions play key functional roles in biomolecular systems. Our ability to sample these motions with molecular dynamics simulation in explicit solvent is limited by the slow diffusion of the solvent molecules around the biomolecules. Previously, we proposed an accelerated molecular dynamics method that has been shown to efficiently sample the torsional degrees of freedom of biomolecules beyond the millisecond timescale. However, in our previous approach, large-amplitude displacements of biomolecules are still slowed by the diffusion of the solvent. Here we present a unified approach of efficiently sampling both the torsional degrees of freedom and the diffusive motions concurrently. We show that this approach samples the configuration space more efficiently than normal molecular dynamics and that ensemble averages converge faster to the correct values.
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Affiliation(s)
- Donald Hamelberg
- Howard Hughes Medical Institute, Center for Theoretical Biological Physics, Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California 92093-0365, USA.
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Mu Y, Gao YQ. Effects of hydrophobic and dipole-dipole interactions on the conformational transitions of a model polypeptide. J Chem Phys 2007; 127:105102. [PMID: 17867781 DOI: 10.1063/1.2768062] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We studied the effects of hydrophobicity and dipole-dipole interactions between the nearest-neighbor amide planes on the secondary structures of a model polypeptide by calculating the free energy differences between different peptide structures. The free energy calculations were performed with low computational costs using the accelerated Monte Carlo simulation (umbrella sampling) method, with a bias-potential method used earlier in our accelerated molecular dynamics simulations. It was found that the hydrophobic interaction enhances the stability of alpha helices at both low and high temperatures but stabilizes beta structures only at high temperatures at which alpha helices are not stable. The nearest-neighbor dipole-dipole interaction stabilizes beta structures under all conditions, especially in the low temperature region where alpha helices are the stable structures. Our results indicate clearly that the dipole-dipole interaction between the nearest neighboring amide planes plays an important role in determining the peptide structures. Current research provides a more unified and quantitative picture for understanding the effects of different forms of interactions on polypeptide structures. In addition, the present model can be extended to describe DNA/RNA, polymer, copolymer, and other chain systems.
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Affiliation(s)
- Yan Mu
- Department of Chemistry, Texas A&M University, College Station, Texas 77843, USA
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