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Fersht AR. From covalent transition states in chemistry to noncovalent in biology: from β- to Φ-value analysis of protein folding. Q Rev Biophys 2024; 57:e4. [PMID: 38597675 DOI: 10.1017/s0033583523000045] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/11/2024]
Abstract
Solving the mechanism of a chemical reaction requires determining the structures of all the ground states on the pathway and the elusive transition states linking them. 2024 is the centenary of Brønsted's landmark paper that introduced the β-value and structure-activity studies as the only experimental means to infer the structures of transition states. It involves making systematic small changes in the covalent structure of the reactants and analysing changes in activation and equilibrium-free energies. Protein engineering was introduced for an analogous procedure, Φ-value analysis, to analyse the noncovalent interactions in proteins central to biological chemistry. The methodology was developed first by analysing noncovalent interactions in transition states in enzyme catalysis. The mature procedure was then applied to study transition states in the pathway of protein folding - 'part (b) of the protein folding problem'. This review describes the development of Φ-value analysis of transition states and compares and contrasts the interpretation of β- and Φ-values and their limitations. Φ-analysis afforded the first description of transition states in protein folding at the level of individual residues. It revealed the nucleation-condensation folding mechanism of protein domains with the transition state as an expanded, distorted native structure, containing little fully formed secondary structure but many weak tertiary interactions. A spectrum of transition states with various degrees of structural polarisation was then uncovered that spanned from nucleation-condensation to the framework mechanism of fully formed secondary structure. Φ-analysis revealed how movement of the expanded transition state on an energy landscape accommodates the transition from framework to nucleation-condensation mechanisms with a malleability of structure as a unifying feature of folding mechanisms. Such movement follows the rubric of analysis of classical covalent chemical mechanisms that began with Brønsted. Φ-values are used to benchmark computer simulation, and Φ and simulation combine to describe folding pathways at atomic resolution.
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Affiliation(s)
- Alan R Fersht
- MRC Laboratory of Molecular Biology, Cambridge, UK
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, UK
- Gonville and Caius College, University of Cambridge, Cambridge, UK
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2
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Li MG, Hu M, Fan LM, Bao JD, Li PC. Quantifying the energy landscape in weakly and strongly disordered frictional media. J Chem Phys 2024; 160:024903. [PMID: 38189619 DOI: 10.1063/5.0178092] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2023] [Accepted: 12/19/2023] [Indexed: 01/09/2024] Open
Abstract
We investigate the "roughness" of the energy landscape of a system that diffuses in a heterogeneous medium with a random position-dependent friction coefficient α(x). This random friction acting on the system stems from spatial inhomogeneity in the surrounding medium and is modeled using the generalized Caldira-Leggett model. For a weakly disordered medium exhibiting a Gaussian random diffusivity D(x) = kBT/α(x) characterized by its average value ⟨D(x)⟩ and a pair-correlation function ⟨D(x1)D(x2)⟩, we find that the renormalized intrinsic diffusion coefficient is lower than the average one due to the fluctuations in diffusivity. The induced weak internal friction leads to increased roughness in the energy landscape. When applying this idea to diffusive motion in liquid water, the dissociation energy for a hydrogen bond gradually approaches experimental findings as fluctuation parameters increase. Conversely, for a strongly disordered medium (i.e., ultrafast-folding proteins), the energy landscape ranges from a few to a few kcal/mol, depending on the strength of the disorder. By fitting protein folding dynamics to the escape process from a metastable potential, the decreased escape rate conceptualizes the role of strong internal friction. Studying the energy landscape in complex systems is helpful because it has implications for the dynamics of biological, soft, and active matter systems.
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Affiliation(s)
- Ming-Gen Li
- Department of Physics, Shantou University, Shantou, Guangdong 515063, China
| | - Meng Hu
- Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China
| | - Li-Ming Fan
- College of Physical Science and Technology, Shenyang Normal University, Shenyang 110034, China
| | - Jing-Dong Bao
- Department of Physics, Beijing Normal University, Beijing 100048, China
| | - Peng-Cheng Li
- Department of Physics, Shantou University, Shantou, Guangdong 515063, China
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3
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Vancraenenbroeck R, Hofmann H. Electrostatics and hydrophobicity in the dynamics of intrinsically disordered proteins. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:133. [PMID: 38127117 PMCID: PMC10739388 DOI: 10.1140/epje/s10189-023-00383-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Accepted: 11/20/2023] [Indexed: 12/23/2023]
Abstract
Internal friction is a major contribution to the dynamics of intrinsically disordered proteins (IDPs). Yet, the molecular origin of internal friction has so far been elusive. Here, we investigate whether attractive electrostatic interactions in IDPs modulate internal friction differently than the hydrophobic effect. To this end, we used nanosecond fluorescence correlation spectroscopy (nsFCS) and single-molecule Förster resonance energy transfer (FRET) to quantify the conformation and dynamics of the disordered DNA-binding domains Myc, Max and Mad at different salt concentrations. We find that internal friction effects are stronger when the chain is compacted by electrostatic attractions compared to the hydrophobic effect. Although the effect is moderate, the results show that the heteropolymeric nature of IDPs is reflected in their dynamics.
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Affiliation(s)
- Renee Vancraenenbroeck
- Department of Chemical and Structural Biology, Weizmann Institute of Science, Herzl St. 234, 76100, Rehovot, Israel
- Present Address: Department of Structural and Molecular Biology, University College London, Darwin Building, 107 Gower Street, London, WC1E 6BT, UK
| | - Hagen Hofmann
- Department of Chemical and Structural Biology, Weizmann Institute of Science, Herzl St. 234, 76100, Rehovot, Israel.
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4
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Pan Z, Mu J, Chen HF. Balanced Three-Point Water Model OPC3-B for Intrinsically Disordered and Ordered Proteins. J Chem Theory Comput 2023; 19:4837-4850. [PMID: 37452752 DOI: 10.1021/acs.jctc.3c00297] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/18/2023]
Abstract
Intrinsically disordered proteins (IDPs) play a critical role in many biological processes. Due to the inherent structural flexibility of IDPs, experimental methods present significant challenges for sampling their conformational information at the atomic level. Therefore, molecular dynamics (MD) simulations have emerged as the primary tools for modeling IDPs whose accuracy depend on force field and water model. To enhance the accuracy of physical modeling of IDPs, several force fields have been developed. However, current water models lack precision and underestimate the interaction between water molecules and proteins. Here, we used Monte-Carlo re-weighting method to re-parameterize a three-point water model based on OPC3 for IDPs (named OPC3-B). We benchmarked the performance of OPC3-B compared with nine different water models for 10 IDPs and three ordered proteins. The results indicate that the performance of OPC3-B is better than other water models for both IDPs and ordered proteins. At the same time, OPC3-B possess the power of transferability with other force field to simulate IDPs. This newly developed water model can be used to insight into the research of sequence-disordered-function paradigm for IDPs.
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Affiliation(s)
- Zhengsong Pan
- State Key Laboratory of Microbial Metabolism, Joint International Research Laboratory of Metabolic & Developmental Sciences, Department of Bioinformatics and Biostatistics, National Experimental Teaching Center for Life Sciences and Biotechnology, School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai 200240, China
- 4+4 Medical Doctor Program, Chinese Academy of Medical Science and Peking Union Medical College, Beijing 100730, China
| | - Junxi Mu
- State Key Laboratory of Microbial Metabolism, Joint International Research Laboratory of Metabolic & Developmental Sciences, Department of Bioinformatics and Biostatistics, National Experimental Teaching Center for Life Sciences and Biotechnology, School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Hai-Feng Chen
- State Key Laboratory of Microbial Metabolism, Joint International Research Laboratory of Metabolic & Developmental Sciences, Department of Bioinformatics and Biostatistics, National Experimental Teaching Center for Life Sciences and Biotechnology, School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Center for Bioinformation Technology, Shanghai 200235, China
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5
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Zhu JJ, Zhang NJ, Wei T, Chen HF. Enhancing Conformational Sampling for Intrinsically Disordered and Ordered Proteins by Variational Autoencoder. Int J Mol Sci 2023; 24:ijms24086896. [PMID: 37108059 PMCID: PMC10138423 DOI: 10.3390/ijms24086896] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2023] [Revised: 03/26/2023] [Accepted: 03/27/2023] [Indexed: 04/29/2023] Open
Abstract
Intrinsically disordered proteins (IDPs) account for more than 50% of the human proteome and are closely associated with tumors, cardiovascular diseases, and neurodegeneration, which have no fixed three-dimensional structure under physiological conditions. Due to the characteristic of conformational diversity, conventional experimental methods of structural biology, such as NMR, X-ray diffraction, and CryoEM, are unable to capture conformational ensembles. Molecular dynamics (MD) simulation can sample the dynamic conformations at the atomic level, which has become an effective method for studying the structure and function of IDPs. However, the high computational cost prevents MD simulations from being widely used for IDPs conformational sampling. In recent years, significant progress has been made in artificial intelligence, which makes it possible to solve the conformational reconstruction problem of IDP with fewer computational resources. Here, based on short MD simulations of different IDPs systems, we use variational autoencoders (VAEs) to achieve the generative reconstruction of IDPs structures and include a wider range of sampled conformations from longer simulations. Compared with the generative autoencoder (AEs), VAEs add an inference layer between the encoder and decoder in the latent space, which can cover the conformational landscape of IDPs more comprehensively and achieve the effect of enhanced sampling. Through experimental verification, the Cα RMSD between VAE-generated and MD simulation sampling conformations in the 5 IDPs test systems was significantly lower than that of AE. The Spearman correlation coefficient on the structure was higher than that of AE. VAE can also achieve excellent performance regarding structured proteins. In summary, VAEs can be used to effectively sample protein structures.
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Affiliation(s)
- Jun-Jie Zhu
- State Key Laboratory of Microbial Metabolism, Joint International Research Laboratory of Metabolic & Developmental Sciences, Department of Bioinformatics and Biostatistics, National Experimental Teaching Center for Life Sciences and Biotechnology, School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ning-Jie Zhang
- State Key Laboratory of Microbial Metabolism, Joint International Research Laboratory of Metabolic & Developmental Sciences, Department of Bioinformatics and Biostatistics, National Experimental Teaching Center for Life Sciences and Biotechnology, School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ting Wei
- State Key Laboratory of Microbial Metabolism, Joint International Research Laboratory of Metabolic & Developmental Sciences, Department of Bioinformatics and Biostatistics, National Experimental Teaching Center for Life Sciences and Biotechnology, School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Hai-Feng Chen
- State Key Laboratory of Microbial Metabolism, Joint International Research Laboratory of Metabolic & Developmental Sciences, Department of Bioinformatics and Biostatistics, National Experimental Teaching Center for Life Sciences and Biotechnology, School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Center for Bioinformation Technology, Shanghai 200240, China
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6
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da Silva FB, Martins de Oliveira V, de Oliveira Junior AB, Contessoto VDG, Leite VBP. Probing the Energy Landscape of Spectrin R15 and R16 and the Effects of Non-native Interactions. J Phys Chem B 2023; 127:1291-1300. [PMID: 36723393 DOI: 10.1021/acs.jpcb.2c06178] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
Understanding the details of a protein folding mechanism can be a challenging and complex task. One system with an interesting folding behavior is the α-spectrin domain, where the R15 folds three-orders of magnitude faster than its homologues R16 and R17, despite having similar structures. The molecular origins that explain these folding rate differences remain unclear, but our previous work revealed that a combined effect produced by non-native interactions could be a reasonable cause for these differences. In this study, we explore further the folding process by identifying the molecular paths, metastable states, and the collective motions that lead these unfolded proteins to their native state conformation. Our results uncovered the differences between the folding pathways for the wild-type R15 and R16 and an R16 mutant. The metastable ensembles that speed down the folding were identified using an energy landscape visualization method (ELViM). These ensembles correspond to similar experimentally reported configurations. Our observations indicate that the non-native interactions are also associated with secondary structure misdocking. This computational methodology can be used as a fast, straightforward protocol for shedding light on systems with unclear folding or conformational traps.
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Affiliation(s)
- Fernando Bruno da Silva
- Department of Physics, São Paulo State University (UNESP), Institute of Biosciences, Humanities and Exact Sciences, São José do Rio Preto, São Paulo15054-000, Brazil
| | - Vinícius Martins de Oliveira
- Department of Pharmaceutical Sciences, University of Maryland School of Pharmacy, Baltimore, Maryland21201, United States
| | | | | | - Vitor B P Leite
- Department of Physics, São Paulo State University (UNESP), Institute of Biosciences, Humanities and Exact Sciences, São José do Rio Preto, São Paulo15054-000, Brazil
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7
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Das D, Mukhopadhyay S. Molecular Origin of Internal Friction in Intrinsically Disordered Proteins. Acc Chem Res 2022; 55:3470-3480. [PMID: 36346711 DOI: 10.1021/acs.accounts.2c00528] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Protein folding and dynamics are controlled by an interplay of thermal and viscosity effects. The effect of viscous drag through the solvent molecules is described by the classic Kramers theory in the high friction limit, which considers the dampening of the reactant molecules in the solution and quantifies the dependence of the reaction rate on the frictional drag. In addition to the external energy dissipation originating from the surrounding solvent molecules, there is an additional mode of internal energy dissipative force operative within the polypeptide chain reflecting the internal resistance of the chain to its conformational alterations. This dry, solvent-independent intrinsic frictional drag is termed internal friction. In the case of natively folded proteins, the physical origin of internal friction is primarily attributed to the intrachain interactions or other nonnative interactions in their compact states. However, the molecular origin of internal friction in intrinsically disordered proteins (IDPs) remains elusive.In this Account, we address this fundamental issue: what are the principal drivers of viscosity-independent (dry) friction in highly solvated, expanded, conformationally flexible, rapidly fluctuating IDPs that do not possess persistent intrachain interactions? IDPs exhibit diffusive conformational dynamics that is predominantly dominated by the segmental motion of the backbone arising due to the dihedral rotations in the Ramachandran Φ-Ψ space. The physical origin of friction in a complex biopolymeric system such as IDPs can be described by classic polymer models, namely, Rouse/Zimm models with internal friction. These one-dimensional models do not invoke torsional fluctuation components. Kuhn's classic description includes the connection between internal friction and microscopic dihedral hopping. Based on our time-resolved fluorescence anisotropy results, we describe that the sequence-dependent, collective, short-range backbone dihedral rotations govern localized internal friction in an archetypal IDP, namely, α-synuclein. The highly sensitive, residue-specific fluorescence depolarization kinetics offers a potent methodology to characterize and quantify the directional decorrelation engendered due to the short-range dihedral relaxation of the polypeptide backbone in the dihedral space. We utilized this characteristic relaxation time scale as our dynamic readout to quantify the site-specific frictional component. Our linear viscosity-dependent model of torsional relaxation time scale furnished a finite nonzero time constant at the zero solvent viscosity representing the solvent-independent internal friction. These results unveil the effect of the degree of dihedral restraining parameter on the internal friction component by showing that a restrained proline residue imparts higher torsional stiffness in the chain segments and, therefore, exhibits higher internal friction. This Account sheds light on the molecular underpinning of the sequence-specific internal friction in IDPs and will be of interest to unmask the role of internal friction in a diverse range of biomolecular processes involving binding-induced folding, allosteric interaction, protein misfolding and aggregation, and biomolecular condensation via phase separation.
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Affiliation(s)
- Debapriya Das
- Centre for Protein Science, Design and Engineering, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, SAS Nagar, Mohali, Punjab 140306, India.,Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, SAS Nagar, Mohali, Punjab 140306, India
| | - Samrat Mukhopadhyay
- Centre for Protein Science, Design and Engineering, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, SAS Nagar, Mohali, Punjab 140306, India.,Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, SAS Nagar, Mohali, Punjab 140306, India.,Department of Biological Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, SAS Nagar, Mohali, Punjab 140306, India
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8
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León-González JA, Flatet P, Juárez-Ramírez MS, Farías-Rico JA. Folding and Evolution of a Repeat Protein on the Ribosome. Front Mol Biosci 2022; 9:851038. [PMID: 35707224 PMCID: PMC9189291 DOI: 10.3389/fmolb.2022.851038] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2022] [Accepted: 04/27/2022] [Indexed: 12/04/2022] Open
Abstract
Life on earth is the result of the work of proteins, the cellular nanomachines that fold into elaborated 3D structures to perform their functions. The ribosome synthesizes all the proteins of the biosphere, and many of them begin to fold during translation in a process known as cotranslational folding. In this work we discuss current advances of this field and provide computational and experimental data that highlight the role of ribosome in the evolution of protein structures. First, we used the sequence of the Ankyrin domain from the Drosophila Notch receptor to launch a deep sequence-based search. With this strategy, we found a conserved 33-residue motif shared by different protein folds. Then, to see how the vectorial addition of the motif would generate a full structure we measured the folding on the ribosome of the Ankyrin repeat protein. Not only the on-ribosome folding data is in full agreement with classical in vitro biophysical measurements but also it provides experimental evidence on how folded proteins could have evolved by duplication and fusion of smaller fragments in the RNA world. Overall, we discuss how the ribosomal exit tunnel could be conceptualized as an active site that is under evolutionary pressure to influence protein folding.
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Affiliation(s)
- José Alberto León-González
- Synthetic Biology Program, Center for Genome Sciences, National Autonomous University of Mexico, Cuernavaca, Mexico
| | - Perline Flatet
- Department of Biochemistry and Biophysics, Stockholm University, Stockholm, Sweden
| | - María Soledad Juárez-Ramírez
- Synthetic Biology Program, Center for Genome Sciences, National Autonomous University of Mexico, Cuernavaca, Mexico
| | - José Arcadio Farías-Rico
- Synthetic Biology Program, Center for Genome Sciences, National Autonomous University of Mexico, Cuernavaca, Mexico
- *Correspondence: José Arcadio Farías-Rico,
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9
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Das D, Arora L, Mukhopadhyay S. Short-Range Backbone Dihedral Rotations Modulate Internal Friction in Intrinsically Disordered Proteins. J Am Chem Soc 2022; 144:1739-1747. [DOI: 10.1021/jacs.1c11236] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Affiliation(s)
- Debapriya Das
- Centre for Protein Science, Design and Engineering, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, Mohali, SAS Nagar, Punjab 140306, India
- Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, Mohali, SAS Nagar, Punjab 140306, India
| | - Lisha Arora
- Centre for Protein Science, Design and Engineering, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, Mohali, SAS Nagar, Punjab 140306, India
- Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, Mohali, SAS Nagar, Punjab 140306, India
| | - Samrat Mukhopadhyay
- Centre for Protein Science, Design and Engineering, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, Mohali, SAS Nagar, Punjab 140306, India
- Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, Mohali, SAS Nagar, Punjab 140306, India
- Department of Biological Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, Mohali, SAS Nagar, Punjab 140306, India
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10
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Mu J, Pan Z, Chen HF. Balanced Solvent Model for Intrinsically Disordered and Ordered Proteins. J Chem Inf Model 2021; 61:5141-5151. [PMID: 34546059 DOI: 10.1021/acs.jcim.1c00407] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Intrinsically disordered proteins (IDPs) have no fixed three-dimensional (3D) structures under physiological conditions, with the content being about 51% in human proteomics. IDPs are associated with many human diseases, such as cancer, diabetes, and neurodegenerative diseases. Because IDPs do not crystallize and have diverse conformers, traditional experimental methods such as crystallization and NMR can hardly capture their conformation ensemble and just provide average structural characters of IDPs. Therefore, molecular dynamics (MD) simulations become a valuable complement to the experimental data. However, the accuracy of molecular dynamics simulation for IDPs depends on the combination of force fields and solvent models. Recently, we released an environment-specific force field (ESFF1) for IDPs, which can well reproduce the local structural properties (such as J-coupling and secondary chemical shifts). However, there is still a large deviation for the radius of gyration (Rg). Therefore, a solvent model combined with ESFF1 is necessary to capture the local and global characters for IDPs and ordered proteins. Here, we investigated the underestimation or overestimation of the solvent interaction for four solvent models (TIP3P, TIP4P-Ew, TIP4P-D, OPC) under ESFF1 and found the important ε parameter of the solvent model to play a key role in scaling Rg. A near-linear relationship between the simulation Rg and the ε parameter was used to develop the new solvent model, named TIP4P-B. The results indicate that the simulated Rg with TIP4P-B is in better agreement with the experimental observations than the other four solvent models. Simultaneously, TIP4P-B can also maintain the advantages of the ESFF1 force field for the local structural properties. Additionally, TIP4P-B can successfully sample the conformation of ordered proteins. These findings confirm that TIP4P-B is a balanced solvent model and can improve sampling Rg performance for folded proteins and IDPs.
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Affiliation(s)
- Junxi Mu
- State Key Laboratory of Microbial metabolism, Joint International Research Laboratory of Metabolic & Developmental Sciences, Department of Bioinformatics and Biostatistics, National Experimental Teaching Center for Life Sciences and Biotechnology, School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Zhengsong Pan
- State Key Laboratory of Microbial metabolism, Joint International Research Laboratory of Metabolic & Developmental Sciences, Department of Bioinformatics and Biostatistics, National Experimental Teaching Center for Life Sciences and Biotechnology, School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai 200240, China.,MD Program, Chinese Academy of Medical Sciences & Peking Union Medical College, Beijing 100730, China
| | - Hai-Feng Chen
- State Key Laboratory of Microbial metabolism, Joint International Research Laboratory of Metabolic & Developmental Sciences, Department of Bioinformatics and Biostatistics, National Experimental Teaching Center for Life Sciences and Biotechnology, School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai 200240, China.,Shanghai Center for Bioinformation Technology, Shanghai 200235, China
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11
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Jas GS, Childs EW, Middaugh CR, Kuczera K. Probing the Internal Dynamics and Shape of Simple Peptides in Urea, Guanidinium Hydrochloride, and Proline Solutions with Time-Resolved Fluorescence Anisotropy and Atomistic Cosolvent Simulations. J Phys Chem B 2021; 125:10972-10984. [PMID: 34559968 DOI: 10.1021/acs.jpcb.1c06838] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Picosecond time-resolved fluorescence anisotropy was used to measure the effect of denaturants and osmolytes on the reorientation dynamics of the simplest dipeptide. The solvent denaturants guanidinium hydrochloride (gdm), urea, and the osmolyte proline were used at several concentrations. Analysis of the concentration dependence of denaturants at a fixed temperature showed faster and slower reorientation time in two different denaturants at a nearly identical solvent viscosity (η). The reorientation time τ significantly deviates from Kramers' theory (τ ∝ η1) in the high friction limit for guanidinium and urea with r ≈ 0.4 and r ≈ 0.6 at pH 7.2, respectively. In proline, τ is nearly proportional to η. Atomistic molecular dynamics simulations of the dipeptide in identical cosolvents showed excellent agreement with the measured rotational orientation time. The dipeptide dihedral (ϕ, ψ) isomerization times in water and 6 M urea are almost identical and significantly slower in guanidinium. If a faster and slower reorientation time can be associated with the compact and expanded shapes, the fractional viscosity dependence for guanidinium and urea may result from the fact that internal dynamics of peptides in these cosolvents involve higher and lower internal friction within the dynamic elements.
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Affiliation(s)
- Gouri S Jas
- Department of Pharmaceutical Chemistry, The University of Kansas, Lawrence, Kansas 66047, United States
| | - Ed W Childs
- Department of Surgery, Morehouse School of Medicine, Atlanta, Georgia 30310, United States
| | - C Russell Middaugh
- Department of Pharmaceutical Chemistry, The University of Kansas, Lawrence, Kansas 66047, United States
| | - Krzysztof Kuczera
- Department of Chemistry and Department of Molecular Biosciences, The University of Kansas, Lawrence, Kansas 66045, United States
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12
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Abstract
Flexibility in complexes between intrinsically disordered proteins and folded ligands is widespread in nature. However, timescales and spatial amplitudes of such dynamics remained unexplored for most systems. Our results show that the disordered cytoplasmic tail of the cell adhesion protein E-cadherin diffuses across the entire surface of its folded binding partner β-catenin at fast submillisecond timescales. The nanometer amplitude of these motions could allow kinases to access their recognition motifs without requiring a dissociation of the complex. We expect that the rugged energy landscape found in the E-cadherin/β-catenin complex is a defining feature of dynamic and partially disordered protein complexes. Intrinsically disordered proteins often form dynamic complexes with their ligands. Yet, the speed and amplitude of these motions are hidden in classical binding kinetics. Here, we directly measure the dynamics in an exceptionally mobile, high-affinity complex. We show that the disordered tail of the cell adhesion protein E-cadherin dynamically samples a large surface area of the protooncogene β-catenin. Single-molecule experiments and molecular simulations resolve these motions with high resolution in space and time. Contacts break and form within hundreds of microseconds without a dissociation of the complex. The energy landscape of this complex is rugged with many small barriers (3 to 4 kBT) and reconciles specificity, high affinity, and extreme disorder. A few persistent contacts provide specificity, whereas unspecific interactions boost affinity.
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13
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Kailasham R, Chakrabarti R, Prakash JR. How important are fluctuations in the treatment of internal friction in polymers? SOFT MATTER 2021; 17:7133-7157. [PMID: 34259278 DOI: 10.1039/d1sm00613d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The Rouse model with internal friction (RIF), a widely used theoretical framework to interpret the effects of internal friction on conformational transitions in biomolecules, is shown to be an approximate treatment that is based on preaveraging internal friction. By comparison with Brownian dynamics simulations of an exact coarse-grained model that incorporates fluctuations in internal friction, the accuracy of the preaveraged model predictions is examined both at and away from equilibrium. While the two models predict intrachain autocorrelations that approach each other for long enough chain segments, they differ in their predictions for shorter segments. Furthermore, the two models differ qualitatively in their predictions for the chain extension and viscosity in shear flow, which is taken to represent a prototypical out-of-equilibrium condition.
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Affiliation(s)
- R Kailasham
- IITB-Monash Research Academy, Indian Institute of Technology Bombay, Mumbai, Maharashtra - 400076, India and Department of Chemistry, Indian Institute of Technology Bombay, Mumbai, Maharashtra - 400076, India. and Department of Chemical Engineering, Monash University, Melbourne, VIC 3800, Australia.
| | - Rajarshi Chakrabarti
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai, Maharashtra - 400076, India.
| | - J Ravi Prakash
- Department of Chemical Engineering, Monash University, Melbourne, VIC 3800, Australia.
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14
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Abstract
The thermal motion of charged proteins causes randomly fluctuating electric fields inside cells. According to the fluctuation-dissipation theorem, there is an additional friction force associated with such fluctuations. However, the impact of these fluctuations on the diffusion and dynamics of proteins in the cytoplasm is unclear. Here, we provide an order-of-magnitude estimate of this effect by treating electric field fluctuations within a generalized Langevin equation model with a time-dependent friction memory kernel. We find that electric friction is generally negligible compared to solvent friction. However, a significant slowdown of protein diffusion and dynamics is expected for biomolecules with high net charges such as intrinsically disordered proteins and RNA. The results show that direct contacts between biomolecules in a cell are not necessarily required to alter their dynamics.
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Affiliation(s)
- Dmitrii E Makarov
- Department of Chemistry and Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, United States
| | - Hagen Hofmann
- Department of Chemical and Structural Biology, Weizmann Institute of Science, 76100 Rehovot, Israel
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15
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Xia C, Kang W, Wang J, Wang W. Temperature Dependence of Internal Friction of Peptides. J Phys Chem B 2021; 125:2821-2832. [PMID: 33689339 DOI: 10.1021/acs.jpcb.0c09056] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Internal friction is a valuable concept to describe the kinetics of proteins. As is well known, internal friction can be modulated by solvent features (such as viscosity). How can internal friction be affected by environmental temperature? The answer to this question is not evident. In the present work, we approach this problem with simulations on two model peptides. The thermodynamics and relaxation kinetics are characterized through long molecular dynamics simulations, with the viscosity modulated by varying the mass of solvent molecules. Based on the extrapolation to zero viscosity together with scaling of the relaxation time scales, we discover that internal friction is almost invariant at various temperatures. Controlled simulations further support the idea that internal friction is independent of environmental temperature. Comparisons between the two model peptides help us to understand the diverse phenomena in experiments.
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Affiliation(s)
- Chenliang Xia
- School of Physics, Nanjing University, Nanjing 210093, P.R.China.,National Laboratory of Solid State Microstructure, Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, P.R.China
| | - Wenbin Kang
- School of Public Health and Management, Hubei University of Medicine, Shiyan 442000, P.R. China
| | - Jun Wang
- School of Physics, Nanjing University, Nanjing 210093, P.R.China.,National Laboratory of Solid State Microstructure, Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, P.R.China
| | - Wei Wang
- School of Physics, Nanjing University, Nanjing 210093, P.R.China.,National Laboratory of Solid State Microstructure, Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, P.R.China
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16
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Mehlich A, Fang J, Pelz B, Li H, Stigler J. Slow Transition Path Times Reveal a Complex Folding Barrier in a Designed Protein. Front Chem 2020; 8:587824. [PMID: 33365300 PMCID: PMC7750197 DOI: 10.3389/fchem.2020.587824] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2020] [Accepted: 10/26/2020] [Indexed: 11/30/2022] Open
Abstract
De-novo designed proteins have received wide interest as potential platforms for nano-engineering and biomedicine. While much work is being done in the design of thermodynamically stable proteins, the folding process of artificially designed proteins is not well-studied. Here we used single-molecule force spectroscopy by optical tweezers to study the folding of ROSS, a de-novo designed 2x2 Rossmann fold. We measured a barrier crossing time in the millisecond range, much slower than what has been reported for other systems. While long transition times can be explained by barrier roughness or slow diffusion, we show that isotropic roughness cannot explain the measured transition path time distribution. Instead, this study shows that the slow barrier crossing of ROSS is caused by the population of three short-lived high-energy intermediates. In addition, we identify incomplete and off-pathway folding events with different barrier crossing dynamics. Our results hint at the presence of a complex transition barrier that may be a common feature of many artificially designed proteins.
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Affiliation(s)
- Alexander Mehlich
- Physics Department E22, Technische Universität München, Garching, Germany
| | - Jie Fang
- Department of Chemistry, University of British Columbia, Vancouver, BC, Canada
| | - Benjamin Pelz
- Physics Department E22, Technische Universität München, Garching, Germany
| | - Hongbin Li
- Department of Chemistry, University of British Columbia, Vancouver, BC, Canada
| | - Johannes Stigler
- Gene Center Munich, Ludwig-Maximilians-Universität München, Munich, Germany
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17
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Subramanian S, Golla H, Divakar K, Kannan A, de Sancho D, Naganathan AN. Slow Folding of a Helical Protein: Large Barriers, Strong Internal Friction, or a Shallow, Bumpy Landscape? J Phys Chem B 2020; 124:8973-8983. [PMID: 32955882 PMCID: PMC7659034 DOI: 10.1021/acs.jpcb.0c05976] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
The rate at which a protein molecule
folds is determined by opposing
energetic and entropic contributions to the free energy that shape
the folding landscape. Delineating the extent to which they impact
the diffusional barrier-crossing events, including the magnitude of
internal friction and barrier height, has largely been a challenging
task. In this work, we extract the underlying thermodynamic and dynamic
contributions to the folding rate of an unusually slow-folding helical
DNA-binding domain, PurR, which shares the characteristics of ultrafast
downhill-folding proteins but nonetheless appears to exhibit an apparent
two-state equilibrium. We combine equilibrium spectroscopy, temperature-viscosity-dependent
kinetics, statistical mechanical modeling, and coarse-grained simulations
to show that the conformational behavior of PurR is highly heterogeneous
characterized by a large spread in melting temperatures, marginal
thermodynamic barriers, and populated partially structured states.
PurR appears to be at the threshold of disorder arising from frustrated
electrostatics and weak packing that in turn slows down folding due
to a shallow, bumpy landscape and not due to large thermodynamic barriers
or strong internal friction. Our work highlights how a strong temperature
dependence on the pre-exponential could signal a shallow landscape
and not necessarily a slow-folding diffusion coefficient, thus determining
the folding timescales of even millisecond folding proteins and hints
at possible structural origins for the shallow landscape.
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Affiliation(s)
- Sandhyaa Subramanian
- Department of Biotechnology, Bhupat & Jyoti Mehta School of Biosciences, Indian Institute of Technology Madras, Chennai 600036, India
| | - Hemashree Golla
- Department of Biotechnology, Bhupat & Jyoti Mehta School of Biosciences, Indian Institute of Technology Madras, Chennai 600036, India
| | - Kalivarathan Divakar
- Department of Biotechnology, National Institute of Technology Warangal, Warangal 506004, India
| | - Adithi Kannan
- Department of Biotechnology, Bhupat & Jyoti Mehta School of Biosciences, Indian Institute of Technology Madras, Chennai 600036, India
| | - David de Sancho
- Polimero eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, Donostia-San Sebastián 20080, Spain.,Donostia International Physics Center (DIPC), PK 1072, Donostia-San Sebastián 20080, Spain
| | - Athi N Naganathan
- Department of Biotechnology, Bhupat & Jyoti Mehta School of Biosciences, Indian Institute of Technology Madras, Chennai 600036, India
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18
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Narayan A, Gopi S, Lukose B, Naganathan AN. Electrostatic Frustration Shapes Folding Mechanistic Differences in Paralogous Bacterial Stress Response Proteins. J Mol Biol 2020; 432:4830-4839. [DOI: 10.1016/j.jmb.2020.06.026] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Revised: 06/30/2020] [Accepted: 06/30/2020] [Indexed: 01/06/2023]
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19
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Cotranslational folding cooperativity of contiguous domains of α-spectrin. Proc Natl Acad Sci U S A 2020; 117:14119-14126. [PMID: 32513720 DOI: 10.1073/pnas.1909683117] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Proteins synthesized in the cell can begin to fold during translation before the entire polypeptide has been produced, which may be particularly relevant to the folding of multidomain proteins. Here, we study the cotranslational folding of adjacent domains from the cytoskeletal protein α-spectrin using force profile analysis (FPA). Specifically, we investigate how the cotranslational folding behavior of the R15 and R16 domains are affected by their neighboring R14 and R16, and R15 and R17 domains, respectively. Our results show that the domains impact each other's folding in distinct ways that may be important for the efficient assembly of α-spectrin, and may reduce its dependence on chaperones. Furthermore, we directly relate the experimentally observed yield of full-length protein in the FPA assay to the force exerted by the folding protein in piconewtons. By combining pulse-chase experiments to measure the rate at which the arrested protein is converted into full-length protein with a Bell model of force-induced rupture, we estimate that the R16 domain exerts a maximal force on the nascent chain of ∼15 pN during cotranslational folding.
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20
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Cohen NR, Kayatekin C, Zitzewitz JA, Bilsel O, Matthews CR. Friction-Limited Folding of Disulfide-Reduced Monomeric SOD1. Biophys J 2020; 118:1992-2000. [PMID: 32191862 DOI: 10.1016/j.bpj.2020.02.028] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2019] [Revised: 02/04/2020] [Accepted: 02/28/2020] [Indexed: 11/16/2022] Open
Abstract
The folding reaction of a stable monomeric variant of Cu/Zn superoxide dismutase (mSOD1), an enzyme responsible for the conversion of superoxide free radicals into hydrogen peroxide and oxygen, is known to be among the slowest folding processes that adhere to two-state behavior. The long lifetime, ∼10 s, of the unfolded state presents ample opportunities for the polypeptide chain to transiently sample nonnative structures before the formation of the productive folding transition state. We recently observed the formation of a nonnative structure in a peptide model of the C-terminus of SOD1, a sequence that might serve as a potential source of internal chain friction-limited folding. To test for friction-limited folding, we performed a comprehensive thermodynamic and kinetic analysis of the folding mechanism of mSOD1 in the presence of the viscogens glycerol and glucose. Using a, to our knowledge, novel analysis of the folding reactions, we found the disulfide-reduced form of the protein that exposes the C-terminal sequence, but not its disulfide-oxidized counterpart that protects it, experiences internal chain friction during folding. The sensitivity of the internal friction to the disulfide bond status suggests that one or both of the cross-linked regions play a critical role in driving the friction-limited folding. We speculate that the molecular mechanisms giving rise to the internal friction of disulfide-reduced mSOD1 might play a role in the amyotrophic lateral sclerosis-linked aggregation of SOD1.
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Affiliation(s)
- Noah R Cohen
- Department of Biochemistry and Molecular Pharmacology, University of Massachusetts Medical School, Worcester, Massachusetts
| | - Can Kayatekin
- Department of Biochemistry and Molecular Pharmacology, University of Massachusetts Medical School, Worcester, Massachusetts; Rare and Neurological Therapeutic Area, Sanofi, Framingham, Massachusetts
| | - Jill A Zitzewitz
- Department of Biochemistry and Molecular Pharmacology, University of Massachusetts Medical School, Worcester, Massachusetts
| | - Osman Bilsel
- Department of Biochemistry and Molecular Pharmacology, University of Massachusetts Medical School, Worcester, Massachusetts
| | - C R Matthews
- Department of Biochemistry and Molecular Pharmacology, University of Massachusetts Medical School, Worcester, Massachusetts.
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21
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Abstract
We show by molecular dynamics simulations that the friction constant of a freely diffusing methane molecule in explicit water increases with the methane mass by a factor of up to 1.8 in the infinite mass limit compared to the massless limit. This effect is rationalized by the mass dependence of the friction memory kernel which is extracted from the simulation data by mapping on the generalized Langevin equation. On the basis of the mass-dependent memory kernels, we obtain perfect agreement between simulation results and analytic predictions for both mean-square displacements and force autocorrelation functions. The memory kernels, which account for methane interactions with the solvent, decay significantly slower with increasing methane mass. The mass-dependent friction is correlated with the mean escape time of water molecules from the first hydration shell, which increases monotonically with the methane mass by a factor of 3 over the mass range considered. Our proposed scaling expression allows the direct prediction of diffusion constants for stable methane isotopes, which will help to better understand bacterial methane isotope fractionation. Our scaling analysis suggests that mass-dependent friction will be relevant also for larger solutes in sufficiently viscous solvents.
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Affiliation(s)
- Jan O Daldrop
- Department of Physics , Freie Universität Berlin , 14195 Berlin , Germany
| | - Roland R Netz
- Department of Physics , Freie Universität Berlin , 14195 Berlin , Germany
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22
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Liu C, Luo L, Wu Y, Yang X, Dong J, Luo F, Zou Y, Shen Y, Lin Q. Inactivation of Soybean Bowman-Birk Inhibitor by Stevioside: Interaction Studies and Application to Soymilk. JOURNAL OF AGRICULTURAL AND FOOD CHEMISTRY 2019; 67:2255-2264. [PMID: 30729785 DOI: 10.1021/acs.jafc.8b05609] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
In this work, the interaction of the soybean Bowman-Birk inhibitor (BBI) with stevioside (STE) was studied by stopped-flow-fluorescence and molecular docking. STE's inactivation of protease-inhibitor activities in soymilk and the influence of STE addition on the sensory character of soymilk were also evaluated. The results indicate that STE binds BBI with a binding constant ( Ka) of 3.38 × 105 L mol-1 to form a 1:1 complex. The docking study reveals that two hydrogen bonds are formed between the side-chain of Lys16 (reactive site 1) of BBI and the glucose-ring hydroxyl groups of STE, which may block BBI from contacting trypsin and thus deactivate the trypsin-inhibitor activity (TIA) of BBI. Moreover, the residual TIA in soymilk could also be inactivated by STE. A mixture of 159 mg/L STE and 60 g/L sucrose could be used for sweetening soymilk without affecting the sensory characteristics when compared to a reference product sweetened with 9% sucrose.
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Affiliation(s)
- Chun Liu
- National Engineering Laboratory for Rice and Byproduct Deep Processing, Hunan Key Laboratory of Processed Food For Special Medical Purpose, School of Food Science and Engineering , Center South University of Forestry and Technology , Changsha 410004 , China
| | - Lijuan Luo
- National Engineering Laboratory for Rice and Byproduct Deep Processing, Hunan Key Laboratory of Processed Food For Special Medical Purpose, School of Food Science and Engineering , Center South University of Forestry and Technology , Changsha 410004 , China
| | - Ying Wu
- National Engineering Laboratory for Rice and Byproduct Deep Processing, Hunan Key Laboratory of Processed Food For Special Medical Purpose, School of Food Science and Engineering , Center South University of Forestry and Technology , Changsha 410004 , China
| | - Xiaoquan Yang
- Research and Development Center of Food Proteins, School of Food Science and Engineering , South China University of Technology , Guangzhou 510640 , China
| | - Jie Dong
- National Engineering Laboratory for Rice and Byproduct Deep Processing, Hunan Key Laboratory of Processed Food For Special Medical Purpose, School of Food Science and Engineering , Center South University of Forestry and Technology , Changsha 410004 , China
- Xiangya School of Pharmaceutical Sciences , Central South University , Changsha 410013 , China
| | - Feijun Luo
- National Engineering Laboratory for Rice and Byproduct Deep Processing, Hunan Key Laboratory of Processed Food For Special Medical Purpose, School of Food Science and Engineering , Center South University of Forestry and Technology , Changsha 410004 , China
| | - Yuan Zou
- School of Food Science , South China Agricultural University , Guangzhou 510642 , China
| | - Yingbin Shen
- Department of Food Science and Engineering, School of Science and Engineering , Jinan University , Guangzhou 510632 , China
| | - Qinlu Lin
- National Engineering Laboratory for Rice and Byproduct Deep Processing, Hunan Key Laboratory of Processed Food For Special Medical Purpose, School of Food Science and Engineering , Center South University of Forestry and Technology , Changsha 410004 , China
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23
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Lowe AR, Perez-Riba A, Itzhaki LS, Main ERG. PyFolding: Open-Source Graphing, Simulation, and Analysis of the Biophysical Properties of Proteins. Biophys J 2019; 114:516-521. [PMID: 29414697 DOI: 10.1016/j.bpj.2017.11.3779] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2017] [Revised: 11/21/2017] [Accepted: 11/27/2017] [Indexed: 11/25/2022] Open
Abstract
For many years, curve-fitting software has been heavily utilized to fit simple models to various types of biophysical data. Although such software packages are easy to use for simple functions, they are often expensive and present substantial impediments to applying more complex models or for the analysis of large data sets. One field that is reliant on such data analysis is the thermodynamics and kinetics of protein folding. Over the past decade, increasingly sophisticated analytical models have been generated, but without simple tools to enable routine analysis. Consequently, users have needed to generate their own tools or otherwise find willing collaborators. Here we present PyFolding, a free, open-source, and extensible Python framework for graphing, analysis, and simulation of the biophysical properties of proteins. To demonstrate the utility of PyFolding, we have used it to analyze and model experimental protein folding and thermodynamic data. Examples include: 1) multiphase kinetic folding fitted to linked equations, 2) global fitting of multiple data sets, and 3) analysis of repeat protein thermodynamics with Ising model variants. Moreover, we demonstrate how PyFolding is easily extensible to novel functionality beyond applications in protein folding via the addition of new models. Example scripts to perform these and other operations are supplied with the software, and we encourage users to contribute notebooks and models to create a community resource. Finally, we show that PyFolding can be used in conjunction with Jupyter notebooks as an easy way to share methods and analysis for publication and among research teams.
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Affiliation(s)
- Alan R Lowe
- London Centre for Nanotechnology, University College London, London, United Kingdom; Department of Structural and Molecular Biology, University College London, London, United Kingdom; Department of Biological Sciences, Birkbeck College, University of London, London, United Kingdom.
| | - Albert Perez-Riba
- Department of Pharmacology, University of Cambridge, Cambridge, United Kingdom
| | - Laura S Itzhaki
- Department of Pharmacology, University of Cambridge, Cambridge, United Kingdom
| | - Ewan R G Main
- School of Biological and Chemical Sciences, Queen Mary University of London, London, United Kingdom.
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24
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Abstract
Dystrophin is the largest protein isoform (427 kDa) expressed from the gene defective in Duchenne muscular dystrophy, a lethal muscle-wasting and genetically inherited disease. Dystrophin, localized within a cytoplasmic lattice termed costameres, connects the intracellular cytoskeleton of a myofiber through the cell membrane (sarcolemma) to the surrounding extracellular matrix. In spite of its mechanical regulation roles in stabilizing the sarcolemma during muscle contraction, the underlying molecular mechanism is still elusive. Here, we systematically investigated the mechanical stability and kinetics of the force-bearing central domain of human dystrophin that contains 24 spectrin repeats using magnetic tweezers. We show that the stochastic unfolding and refolding of central domain of dystrophin is able to keep the forces below 25 pN over a significant length change up to ∼800 nm in physiological level of pulling speeds. These results suggest that dystrophin may serve as a molecular shock absorber that defines the physiological level of force in the dystrophin-mediated force-transmission pathway during muscle contraction/stretch, thereby stabilizing the sarcolemma.
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Affiliation(s)
- Shimin Le
- Department of Physics, National University of Singapore, Singapore, 117551
| | - Miao Yu
- Mechanobiology Institute, National University of Singapore, Singapore, 117411
| | - Ladislav Hovan
- Mechanobiology Institute, National University of Singapore, Singapore, 117411
| | - Zhihai Zhao
- Department of Physics, National University of Singapore, Singapore, 117551
| | - James Ervasti
- College of Biological Sciences, University of Minnesota, MN, USA, 55455
| | - Jie Yan
- Department of Physics, National University of Singapore, Singapore, 117551
- Mechanobiology Institute, National University of Singapore, Singapore, 117411
- Centre for BioImaging Sciences, National University of Singapore, Singapore, 117546
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25
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Wu J, Huang Y, Yin H, Chen T. The role of solvent quality and chain stiffness on the end-to-end contact kinetics of semiflexible polymers. J Chem Phys 2018; 149:234903. [PMID: 30579311 DOI: 10.1063/1.5054829] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Abstract
Motivated by loop closure during protein folding and DNA packing, we systemically studied the effects of the solvent quality and chain stiffness on the thermodynamics and kinetics of the end-to-end contact formation for semiflexible polymer chains with reactive ends by Langevin dynamics simulations. In thermodynamics, a rich variety of products of the end-to-end contact have been discovered, such as loop, hairpin, toroid, and rodlike bundle, the populations of which are dependent on the solvent quality and chain stiffness. In kinetics, the overall pathways to form the end-to-end contact have been identified. The change of solvent quality and chain stiffness can tune the roughness of energy landscape and modulate the kinetic partitioning of the end-to-end contact formation pathways, leading to differing kinetic behaviors. In good or poor solvents, the first end-to-end contact rate k c decreases with increasing the strength of bending stiffness k θ monotonically. In very poor solvents, however, the dependence of the logarithm of the first end-to-end contact rate ln k c on k θ exhibits erratic behavior, which stems from more rugged energy landscape due to the polymer chain getting trapped into the intermediate state composed of the rodlike bundles with two ends in separation. For semiflexible chains, with increasing chain length N, the rate k c increases initially and then decreases: in good solvents, the rate k c exhibits a power-law relationship to chain length N with an exponent of ∼-1.50 in the region of long chains, which is in good agreement with the value derived from the experiment in the asymptotic limit of large N; and in poor solvents, the rate k c exhibits a significantly stronger chain length dependence than those observed in good solvents in the region of long chains due to frustration to form the end-to-end contact along a specific path, especially the scaling exponent between the rate k c and chain length N is ∼-3.62 for the case of polymer chains with k θ = 4 at the solvent quality ε ij = 1, in accord with the value obtained from the experiments.
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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
| | - Yiran Huang
- 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
| | - Hongmei Yin
- 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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26
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Soranno A, Zosel F, Hofmann H. Internal friction in an intrinsically disordered protein-Comparing Rouse-like models with experiments. J Chem Phys 2018; 148:123326. [PMID: 29604877 DOI: 10.1063/1.5009286] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
Internal friction is frequently found in protein dynamics. Its molecular origin however is difficult to conceptualize. Even unfolded and intrinsically disordered polypeptide chains exhibit signs of internal friction despite their enormous solvent accessibility. Here, we compare four polymer theories of internal friction with experimental results on the intrinsically disordered protein ACTR (activator of thyroid hormone receptor). Using nanosecond fluorescence correlation spectroscopy combined with single-molecule Förster resonance energy transfer (smFRET), we determine the time scales of the diffusive chain dynamics of ACTR at different solvent viscosities and varying degrees of compaction. Despite pronounced differences between the theories, we find that all models can capture the experimental viscosity-dependence of the chain relaxation time. In contrast, the observed slowdown upon chain collapse of ACTR is not captured by any of the theories and a mechanistic link between chain dimension and internal friction is still missing, implying that the current theories are incomplete. In addition, a discrepancy between early results on homopolymer solutions and recent single-molecule experiments on unfolded and disordered proteins suggests that internal friction is likely to be a composite phenomenon caused by a variety of processes.
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Affiliation(s)
- Andrea Soranno
- Department of Biochemistry and Molecular Biophysics, Washington University in St. Louis, St. Louis, Missouri 63110, USA
| | - Franziska Zosel
- Department of Biochemistry, University of Zurich, Zurich 8057, Switzerland
| | - Hagen Hofmann
- Department of Structural Biology, Weizmann Institute of Science, Rehovot 7610001, Israel
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27
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Sturzenegger F, Zosel F, Holmstrom ED, Buholzer KJ, Makarov DE, Nettels D, Schuler B. Transition path times of coupled folding and binding reveal the formation of an encounter complex. Nat Commun 2018; 9:4708. [PMID: 30413694 PMCID: PMC6226497 DOI: 10.1038/s41467-018-07043-x] [Citation(s) in RCA: 63] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2018] [Accepted: 10/15/2018] [Indexed: 11/09/2022] Open
Abstract
The association of biomolecules is the elementary event of communication in biology. Most mechanistic information of how the interactions between binding partners form or break is, however, hidden in the transition paths, the very short parts of the molecular trajectories from the encounter of the two molecules to the formation of a stable complex. Here we use single-molecule spectroscopy to measure the transition path times for the association of two intrinsically disordered proteins that form a folded dimer upon binding. The results reveal the formation of a metastable encounter complex that is electrostatically favored and transits to the final bound state within tens of microseconds. Such measurements thus open a new window into the microscopic events governing biomolecular interactions.
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Affiliation(s)
| | - Franziska Zosel
- Department of Biochemistry, University of Zurich, 8057, Zurich, Switzerland.,Novo Nordisk A/S, Novo Nordisk Park 1, 2760, Måløv, Denmark
| | - Erik D Holmstrom
- Department of Biochemistry, University of Zurich, 8057, Zurich, Switzerland
| | - Karin J Buholzer
- Department of Biochemistry, University of Zurich, 8057, Zurich, Switzerland
| | - Dmitrii E Makarov
- Department of Chemistry and Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, 78712, USA
| | - Daniel Nettels
- Department of Biochemistry, University of Zurich, 8057, Zurich, Switzerland
| | - Benjamin Schuler
- Department of Biochemistry, University of Zurich, 8057, Zurich, Switzerland. .,Department of Physics, University of Zurich, 8057, Zurich, Switzerland.
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28
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Bruno da Silva F, Contessoto VG, de Oliveira VM, Clarke J, Leite VBP. Non-Native Cooperative Interactions Modulate Protein Folding Rates. J Phys Chem B 2018; 122:10817-10824. [DOI: 10.1021/acs.jpcb.8b08990] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Fernando Bruno da Silva
- Department of Physics, Institute of Biosciences, Humanities and Exact Sciences, São Paulo State University (UNESP), São José do Rio Preto - São Paulo 15054-000, Brazil
| | - Vinícius G. Contessoto
- Brazilian Bioethanol Science and Technology Laboratory - CTBE, Campinas - São Paulo 13083-100, Brazil
| | - Vinícius M. de Oliveira
- Department of Physics, Institute of Biosciences, Humanities and Exact Sciences, São Paulo State University (UNESP), São José do Rio Preto - São Paulo 15054-000, Brazil
| | - Jane Clarke
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Vitor B. P. Leite
- Department of Physics, Institute of Biosciences, Humanities and Exact Sciences, São Paulo State University (UNESP), São José do Rio Preto - São Paulo 15054-000, Brazil
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29
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Yrazu FM, Pinamonti G, Clementi C. The Effect of Electrostatic Interactions on the Folding Kinetics of a 3-α-Helical Bundle Protein Family. J Phys Chem B 2018; 122:11800-11806. [PMID: 30277393 DOI: 10.1021/acs.jpcb.8b08676] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
The trio of protein segment repeats called spectrins diverges by more than 2 orders of magnitude in their folding and unfolding rates, despite having very similar stabilities and almost coincidental topologies. Experimental studies revealed that the mutation of five particular residues dramatically alters the kinetic rates in the slow folders, making them similar to the rates of the fast folder. This is considered to be an exceptional behavior which seems in principle to challenge the current understanding of the protein folding process. In this work, we analyze this scenario, using a simplified computational model, combined with state-of-the-art kinetic analysis techniques. Our model faithfully separates the kinetics of the fast and slow folders and captures the effect of the five mutations. We show that the inclusion of electrostatics in the model is necessary to explain the experimental findings.
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Affiliation(s)
- Fernando Miguel Yrazu
- Department of Chemical and Biomolecular Engineering , Rice University , Houston , Texas 77005 , United States
| | - Giovanni Pinamonti
- Department of Informatics and Mathematics , Freie Universität Berlin , 14195 Berlin , Germany
| | - Cecilia Clementi
- Department of Chemical and Biomolecular Engineering , Rice University , Houston , Texas 77005 , United States.,Department of Informatics and Mathematics , Freie Universität Berlin , 14195 Berlin , Germany.,Center for Theoretical Biological Physics and Department of Chemistry , Rice University , Houston , Texas 77005 , United States
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30
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Zheng W, Hofmann H, Schuler B, Best RB. Origin of Internal Friction in Disordered Proteins Depends on Solvent Quality. J Phys Chem B 2018; 122:11478-11487. [PMID: 30277791 DOI: 10.1021/acs.jpcb.8b07425] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
Protein dynamics often exhibit internal friction; i.e., contributions to friction that cannot solely be attributed to the viscosity of the solvent. Remarkably, even unfolded and intrinsically disordered proteins (IDPs) exhibit this behavior, despite typically being solvent-exposed. Several competing molecular mechanisms have been suggested to underlie this phenomenon, in particular dihedral relaxation and intrachain interactions. It has also recently been shown that single-molecule data reflecting internal friction in the disordered protein ACTR cannot be explained using polymer models unless this friction is dependent on protein collapse. However, the connection between the collapse of the chain and the underlying mechanism of internal friction has been unclear. To address this issue, we combine molecular simulation and single-molecule experimental data to investigate how chain compaction affects protein dynamics in the context of ACTR. Chain reconfiguration times and internal friction estimated from all-atom simulations are in semiquantitative agreement with experimental data. We dissect the underlying molecular mechanism with all-atom and coarse-grained simulations and clearly identify both intrachain interactions and dihedral angle transitions as contributions to internal friction. However, their relative contribution is strongly dependent on the compactness of the IDP; while dihedral relaxation dominates internal friction in expanded configurations, intrachain interactions dominate for more compact chains. Our results thus imply a continuous transition between mechanisms and provide a link between internal friction in IDPs and that in more compact and folded states of proteins.
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Affiliation(s)
- Wenwei Zheng
- College of Integrative Sciences and Arts , Arizona State University , Mesa , Arizona 85212 , United States.,Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases , National Institutes of Health , Bethesda , Maryland 20892-0520 , United States
| | - Hagen Hofmann
- Department of Structural Biology , Weizmann Institute of Science , 76100 Rehovot , Israel
| | | | - Robert B Best
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases , National Institutes of Health , Bethesda , Maryland 20892-0520 , United States
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31
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Hridya VM, Mukherjee A. Probing the Viscosity Dependence of Rate: Internal Friction or the Lack of Friction? J Phys Chem B 2018; 122:9081-9086. [DOI: 10.1021/acs.jpcb.8b05585] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- V. M. Hridya
- Department of Chemistry, Indian Institute of Science Education and Research, Pune 411008, India
| | - Arnab Mukherjee
- Department of Chemistry, Indian Institute of Science Education and Research, Pune 411008, India
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32
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Dupuis NF, Holmstrom ED, Nesbitt DJ. Tests of Kramers’ Theory at the Single-Molecule Level: Evidence for Folding of an Isolated RNA Tertiary Interaction at the Viscous Speed Limit. J Phys Chem B 2018; 122:8796-8804. [DOI: 10.1021/acs.jpcb.8b04014] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Nicholas F. Dupuis
- JILA, University of Colorado and National Institute of Standards and Technology, Department of Chemistry and Biochemistry, and Department of Physics, University of Colorado, Boulder, Boulder, Colorado 80309, United States
| | - Erik D. Holmstrom
- JILA, University of Colorado and National Institute of Standards and Technology, Department of Chemistry and Biochemistry, and Department of Physics, University of Colorado, Boulder, Boulder, Colorado 80309, United States
| | - David J. Nesbitt
- JILA, University of Colorado and National Institute of Standards and Technology, Department of Chemistry and Biochemistry, and Department of Physics, University of Colorado, Boulder, Boulder, Colorado 80309, United States
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33
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Nonnative Energetic Frustrations in Protein Folding at Residual Level: A Simulation Study of Homologous Immunoglobulin-like β-Sandwich Proteins. Int J Mol Sci 2018; 19:ijms19051515. [PMID: 29783701 PMCID: PMC5983731 DOI: 10.3390/ijms19051515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2018] [Revised: 05/08/2018] [Accepted: 05/09/2018] [Indexed: 11/16/2022] Open
Abstract
Nonnative interactions cause energetic frustrations in protein folding and were found to dominate key events in folding intermediates. However, systematically characterizing energetic frustrations that are caused by nonnative intra-residue interactions at residual resolution is still lacking. Recently, we studied the folding of a set of homologous all-α proteins and found that nonnative-contact-based energetic frustrations are highly correlated to topology of the protein native-contact network. Here, we studied the folding of nine homologous immunoglobulin-like (Ig-like) β-sandwich proteins, and examined nonnative-contact-based energetic frustrations Gō-like model. Our calculations showed that nonnative-interaction-based energetic frustrations in β-sandwich proteins are much more complicated than those in all-α proteins, and they exhibit highly heterogeneous effects on the folding of secondary structures. Further, the nonnative interactions introduced distinct correlations in the folding of different folding-patches of β-sandwich proteins. Taken together, a strong interplay might exist between nonnative-interaction energetic frustrations and the protein native-contact networks, which ensures that β-sandwich domains adopt a common folding mechanism.
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34
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Sriramoju MK, Chen Y, Lee YTC, Hsu STD. Topologically knotted deubiquitinases exhibit unprecedented mechanostability to withstand the proteolysis by an AAA+ protease. Sci Rep 2018; 8:7076. [PMID: 29728659 PMCID: PMC5935755 DOI: 10.1038/s41598-018-25470-0] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2018] [Accepted: 04/23/2018] [Indexed: 01/03/2023] Open
Abstract
More than one thousand knotted protein structures have been identified so far, but the functional roles of these knots remain elusive. It has been postulated that backbone entanglement may provide additional mechanostability. Here, we employed a bacterial proteasome, ClpXP, to mechanically unfold 52-knotted human ubiquitin C-terminal hydrolase (UCH) paralogs from their C-termini, followed by processive translocation into the proteolytic chamber for degradation. Our results revealed unprecedentedly slow kinetics of ClpXP-mediated proteolysis for the proteasome-associated UCHL5: ten thousand times slower than that of a green fluorescence protein (GFP), which has a comparable size to the UCH domain but much higher chemical and thermal stabilities. The ClpXP-dependent mechanostability positively correlates with the intrinsic unfolding rates of the substrates, spanning over several orders of magnitude for the UCHs. The broad range of mechanostability within the same protein family may be associated with the functional requirements for their differential malleabilities.
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Affiliation(s)
| | - Yen Chen
- Institute of Biological Chemistry, Academia Sinica, Taipei, 11529, Taiwan
| | - Yun-Tzai Cloud Lee
- Institute of Biological Chemistry, Academia Sinica, Taipei, 11529, Taiwan.,Institute of Biochemical Sciences, National Taiwan University, Taipei, 106, Taiwan
| | - Shang-Te Danny Hsu
- Institute of Biological Chemistry, Academia Sinica, Taipei, 11529, Taiwan. .,Institute of Biochemical Sciences, National Taiwan University, Taipei, 106, Taiwan.
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35
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Abstract
The dihedral dynamics of butane in water is known to be rather insensitive to the water viscosity; possible explanations for this involve inertial effects or Kramers' turnover, the finite memory time of friction, and the presence of so-called internal friction. To disentangle these factors, we introduce a method to directly extract the friction memory function from unconstrained simulations in the presence of an arbitrary free-energy landscape. By analysis of the dihedral friction in butane for varying water viscosity, we demonstrate the existence of an internal friction contribution that does not scale linearly with water viscosity. At normal water viscosity, the internal friction turns out to be eight times larger than the solvent friction and thus completely dominates the effective friction. By comparison with simulations of a constrained butane molecule that has the dihedral as the only degree of freedom, we show that internal friction comes from the six additional degrees of freedom in unconstrained butane that are orthogonal to the dihedral angle reaction coordinate. While the insensitivity of butane's dihedral dynamics to water viscosity is solely due to the presence of internal friction, inertial effects nevertheless crucially influence the resultant transition rates. In contrast, non-Markovian effects due to the finite memory time are present but do not significantly influence the dihedral barrier-crossing rate of butane. These results not only settle the character of dihedral dynamics in small solvated molecular systems such as butane, they also have important implications for the folding of polymers and proteins.
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36
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Comparative mechanical unfolding studies of spectrin domains R15, R16 and R17. J Struct Biol 2017; 201:162-170. [PMID: 29221897 DOI: 10.1016/j.jsb.2017.12.003] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2017] [Revised: 11/08/2017] [Accepted: 12/04/2017] [Indexed: 11/20/2022]
Abstract
Spectrins belong to repetitive three-helix bundle proteins that have vital functions in multicellular organisms and are of potential value in nanotechnology. To reveal the unique physical features of repeat proteins we have studied the structural and mechanical properties of three repeats of chicken brain α-spectrin (R15, R16 and R17) at the atomic level under stretching at constant velocities (0.01, 0.05 and 0.1 Å·ps-1) and constant forces (700 and 900 pN) using molecular dynamics (MD) simulations at T = 300 K. 114 independent MD simulations were performed and their analysis has been done. Despite structural similarity of these domains we have found that R15 is less mechanically stable than R16, which is less stable than R17. This result is in agreement with the thermal unfolding rates. Moreover, we have observed the relationship between mechanical stability, flexibility of the domains and the number of aromatic residues involved in aromatic clusters.
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37
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Abstract
Protein sequences are evolved to encode generally one folded structure, out of a nearly infinite array of possible folds. Underlying this code is a funneled free energy landscape that guides folding to the native conformation. Protein misfolding and aggregation are also a manifestation of free-energy landscapes. The detailed mechanisms of these processes are poorly understood, but often involve rare, transient species and a variety of different pathways. The inherent complexity of misfolding has hampered efforts to measure aggregation pathways and the underlying energy landscape, especially using traditional methods where ensemble averaging obscures important rare and transient events. We recently studied the misfolding and aggregation of prion protein by examining 2 monomers tethered in close proximity as a dimer, showing how the steps leading to the formation of a stable aggregated state can be resolved in the single-molecule limit and the underlying energy landscape thereby reconstructed. This approach allows a more quantitative comparison of native folding versus misfolding, including fundamental differences in the dynamics for misfolding. By identifying key steps and interactions leading to misfolding, it should help to identify potential drug targets. Here we describe the importance of characterizing free-energy landscapes for aggregation and the challenges involved in doing so, and we discuss how single-molecule studies can help test proposed structural models for PrP aggregates.
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Affiliation(s)
- Derek R Dee
- a Department of Physics , University of Alberta , Edmonton , AB , Canada
| | - Michael T Woodside
- a Department of Physics , University of Alberta , Edmonton , AB , Canada;,b National Institute for Nanotechnology, National Research Council , Edmonton , AB , Canada
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38
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Aina A, Wallin S. Multisequence algorithm for coarse-grained biomolecular simulations: Exploring the sequence-structure relationship of proteins. J Chem Phys 2017; 147:095102. [DOI: 10.1063/1.4986933] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Affiliation(s)
- A. Aina
- Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John’s, Newfoundland and Labrador A1B 3X7, Canada
| | - S. Wallin
- Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John’s, Newfoundland and Labrador A1B 3X7, Canada
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39
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Malhotra P, Jethva PN, Udgaonkar JB. Chemical Denaturants Smoothen Ruggedness on the Free Energy Landscape of Protein Folding. Biochemistry 2017; 56:4053-4063. [DOI: 10.1021/acs.biochem.7b00367] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Affiliation(s)
- Pooja Malhotra
- National Centre for Biological Sciences, Tata Institute
of Fundamental Research, Bengaluru 560065, India
| | - Prashant N. Jethva
- National Centre for Biological Sciences, Tata Institute
of Fundamental Research, Bengaluru 560065, India
| | - Jayant B. Udgaonkar
- National Centre for Biological Sciences, Tata Institute
of Fundamental Research, Bengaluru 560065, India
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40
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Lu Y, Wu J, Dong Y, Chen S, Sun S, Ma YB, Ouyang Q, Finley D, Kirschner MW, Mao Y. Conformational Landscape of the p28-Bound Human Proteasome Regulatory Particle. Mol Cell 2017; 67:322-333.e6. [PMID: 28689658 PMCID: PMC5580496 DOI: 10.1016/j.molcel.2017.06.007] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2016] [Revised: 04/14/2017] [Accepted: 06/07/2017] [Indexed: 10/19/2022]
Abstract
The proteasome holoenzyme is activated by its regulatory particle (RP) consisting of two subcomplexes, the lid and the base. A key event in base assembly is the formation of a heterohexameric ring of AAA-ATPases, which is guided by at least four RP assembly chaperones in mammals: PAAF1, p28/gankyrin, p27/PSMD9, and S5b. Using cryogenic electron microscopy, we analyzed the non-AAA structure of the p28-bound human RP at 4.5 Å resolution and determined seven distinct conformations of the Rpn1-p28-AAA subcomplex within the p28-bound RP at subnanometer resolutions. Remarkably, the p28-bound AAA ring does not form a channel in the free RP and spontaneously samples multiple "open" and "closed" topologies at the Rpt2-Rpt6 and Rpt3-Rpt4 interfaces. Our analysis suggests that p28 assists the proteolytic core particle to select a specific conformation of the ATPase ring for RP engagement and is released in a shoehorn-like fashion in the last step of the chaperone-mediated proteasome assembly.
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Affiliation(s)
- Ying Lu
- Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA
| | - Jiayi Wu
- State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, Institute of Condensed Matter Physics, School of Physics, Center for Quantitative Biology, Peking University, Beijing 100871, China
| | - Yuanchen Dong
- Intel Parallel Computing Center for Structural Biology, Dana-Farber Cancer Institute, Boston, MA 02215, USA; Department of Cancer Immunology and Virology, Dana-Farber Cancer Institute, Department of Microbiology and Immunobiology, Harvard Medical School, Boston, MA 02115, USA
| | - Shuobing Chen
- State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, Institute of Condensed Matter Physics, School of Physics, Center for Quantitative Biology, Peking University, Beijing 100871, China
| | - Shuangwu Sun
- Department of Cell Biology, Harvard Medical School, Boston, MA 02115, USA
| | - Yong-Bei Ma
- State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, Institute of Condensed Matter Physics, School of Physics, Center for Quantitative Biology, Peking University, Beijing 100871, China
| | - Qi Ouyang
- State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, Institute of Condensed Matter Physics, School of Physics, Center for Quantitative Biology, Peking University, Beijing 100871, China; Peking-Tsinghua Joint Center for Life Science, Peking University, Beijing 100871, China
| | - Daniel Finley
- Department of Cell Biology, Harvard Medical School, Boston, MA 02115, USA
| | - Marc W Kirschner
- Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA.
| | - Youdong Mao
- State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, Institute of Condensed Matter Physics, School of Physics, Center for Quantitative Biology, Peking University, Beijing 100871, China; Intel Parallel Computing Center for Structural Biology, Dana-Farber Cancer Institute, Boston, MA 02215, USA; Department of Cancer Immunology and Virology, Dana-Farber Cancer Institute, Department of Microbiology and Immunobiology, Harvard Medical School, Boston, MA 02115, USA.
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41
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Chung HS. Transition Path Times Measured by Single-Molecule Spectroscopy. J Mol Biol 2017; 430:409-423. [PMID: 28551335 DOI: 10.1016/j.jmb.2017.05.018] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2017] [Accepted: 05/18/2017] [Indexed: 11/28/2022]
Abstract
The transition path is a tiny fraction of a molecular trajectory during which the free-energy barrier is crossed. It is a single-molecule property and contains all mechanistic information of folding processes of biomolecules such as proteins and nucleic acids. However, the transition path has been difficult to probe because it is short and rarely visited when transitions actually occur. Recent technical advances in single-molecule spectroscopy have made it possible to directly probe transition paths, which has opened up new theoretical and experimental approaches to investigating folding mechanisms. This article reviews recent single-molecule fluorescence and force spectroscopic measurements of transition path times and their connection to both theory and simulations.
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Affiliation(s)
- Hoi Sung Chung
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, 5 Memorial Dr., Bethesda, MD 20892-0520, USA.
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42
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Integrated view of internal friction in unfolded proteins from single-molecule FRET, contact quenching, theory, and simulations. Proc Natl Acad Sci U S A 2017. [PMID: 28223518 DOI: 10.1073/pnas.1616672114.] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Internal friction is an important contribution to protein dynamics at all stages along the folding reaction. Even in unfolded and intrinsically disordered proteins, internal friction has a large influence, as demonstrated with several experimental techniques and in simulations. However, these methods probe different facets of internal friction and have been applied to disparate molecular systems, raising questions regarding the compatibility of the results. To obtain an integrated view, we apply here the combination of two complementary experimental techniques, simulations, and theory to the same system: unfolded protein L. We use single-molecule Förster resonance energy transfer (FRET) to measure the global reconfiguration dynamics of the chain, and photoinduced electron transfer (PET), a contact-based method, to quantify the rate of loop formation between two residues. This combination enables us to probe unfolded-state dynamics on different length scales, corresponding to different parts of the intramolecular distance distribution. Both FRET and PET measurements show that internal friction dominates unfolded-state dynamics at low denaturant concentration, and the results are in remarkable agreement with recent large-scale molecular dynamics simulations using a new water model. The simulations indicate that intrachain interactions and dihedral angle rotation correlate with the presence of internal friction, and theoretical models of polymer dynamics provide a framework for interrelating the contribution of internal friction observed in the two types of experiments and in the simulations. The combined results thus provide a coherent and quantitative picture of internal friction in unfolded proteins that could not be attained from the individual techniques.
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43
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Wang P, Zheng Y, Fernandes MC, Sun Y, Xu K, Sun S, Kang SH, Tournat V, Bertoldi K. Harnessing Geometric Frustration to Form Band Gaps in Acoustic Channel Lattices. PHYSICAL REVIEW LETTERS 2017; 118:084302. [PMID: 28282189 DOI: 10.1103/physrevlett.118.084302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2016] [Indexed: 06/06/2023]
Abstract
We demonstrate both numerically and experimentally that geometric frustration in two-dimensional periodic acoustic networks consisting of arrays of narrow air channels can be harnessed to form band gaps (ranges of frequency in which the waves cannot propagate in any direction through the system). While resonant standing wave modes and interferences are ubiquitous in all the analyzed network geometries, we show that they give rise to band gaps only in the geometrically frustrated ones (i.e., those comprising of triangles and pentagons). Our results not only reveal a new mechanism based on geometric frustration to suppress the propagation of pressure waves in specific frequency ranges but also open avenues for the design of a new generation of smart systems that control and manipulate sound and vibrations.
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Affiliation(s)
- Pai Wang
- Harvard John A. Paulson School of Engineering and Applied Science, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Yue Zheng
- Jacobs School of Engineering, University of California, San Diego, California 92093, USA
| | - Matheus C Fernandes
- Harvard John A. Paulson School of Engineering and Applied Science, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Yushen Sun
- Tsinghua University, Beijing 100084, China
| | - Kai Xu
- Peking University Shenzhen Graduate School, Shenzhen 518055, China
| | - Sijie Sun
- Harvard John A. Paulson School of Engineering and Applied Science, Harvard University, Cambridge, Massachusetts 02138, USA
- Tsinghua University, Beijing 100084, China
| | - Sung Hoon Kang
- Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Vincent Tournat
- Harvard John A. Paulson School of Engineering and Applied Science, Harvard University, Cambridge, Massachusetts 02138, USA
- LAUM, CNRS, Université du Maine, Avenue O. Messiaen, 72085 Le Mans, France
| | - Katia Bertoldi
- Harvard John A. Paulson School of Engineering and Applied Science, Harvard University, Cambridge, Massachusetts 02138, USA
- Kavli Institute, Harvard University, Cambridge, Massachusetts 02138, USA
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44
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Integrated view of internal friction in unfolded proteins from single-molecule FRET, contact quenching, theory, and simulations. Proc Natl Acad Sci U S A 2017; 114:E1833-E1839. [PMID: 28223518 DOI: 10.1073/pnas.1616672114] [Citation(s) in RCA: 75] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Internal friction is an important contribution to protein dynamics at all stages along the folding reaction. Even in unfolded and intrinsically disordered proteins, internal friction has a large influence, as demonstrated with several experimental techniques and in simulations. However, these methods probe different facets of internal friction and have been applied to disparate molecular systems, raising questions regarding the compatibility of the results. To obtain an integrated view, we apply here the combination of two complementary experimental techniques, simulations, and theory to the same system: unfolded protein L. We use single-molecule Förster resonance energy transfer (FRET) to measure the global reconfiguration dynamics of the chain, and photoinduced electron transfer (PET), a contact-based method, to quantify the rate of loop formation between two residues. This combination enables us to probe unfolded-state dynamics on different length scales, corresponding to different parts of the intramolecular distance distribution. Both FRET and PET measurements show that internal friction dominates unfolded-state dynamics at low denaturant concentration, and the results are in remarkable agreement with recent large-scale molecular dynamics simulations using a new water model. The simulations indicate that intrachain interactions and dihedral angle rotation correlate with the presence of internal friction, and theoretical models of polymer dynamics provide a framework for interrelating the contribution of internal friction observed in the two types of experiments and in the simulations. The combined results thus provide a coherent and quantitative picture of internal friction in unfolded proteins that could not be attained from the individual techniques.
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45
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Cotranslational folding of spectrin domains via partially structured states. Nat Struct Mol Biol 2017; 24:221-225. [DOI: 10.1038/nsmb.3355] [Citation(s) in RCA: 83] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2016] [Accepted: 12/07/2016] [Indexed: 11/09/2022]
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46
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Malhotra P, Udgaonkar JB. How cooperative are protein folding and unfolding transitions? Protein Sci 2016; 25:1924-1941. [PMID: 27522064 PMCID: PMC5079258 DOI: 10.1002/pro.3015] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2016] [Revised: 08/09/2016] [Accepted: 08/09/2016] [Indexed: 11/12/2022]
Abstract
A thermodynamically and kinetically simple picture of protein folding envisages only two states, native (N) and unfolded (U), separated by a single activation free energy barrier, and interconverting by cooperative two-state transitions. The folding/unfolding transitions of many proteins occur, however, in multiple discrete steps associated with the formation of intermediates, which is indicative of reduced cooperativity. Furthermore, much advancement in experimental and computational approaches has demonstrated entirely non-cooperative (gradual) transitions via a continuum of states and a multitude of small energetic barriers between the N and U states of some proteins. These findings have been instrumental towards providing a structural rationale for cooperative versus noncooperative transitions, based on the coupling between interaction networks in proteins. The cooperativity inherent in a folding/unfolding reaction appears to be context dependent, and can be tuned via experimental conditions which change the stabilities of N and U. The evolution of cooperativity in protein folding transitions is linked closely to the evolution of function as well as the aggregation propensity of the protein. A large activation energy barrier in a fully cooperative transition can provide the kinetic control required to prevent the accumulation of partially unfolded forms, which may promote aggregation. Nevertheless, increasing evidence for barrier-less "downhill" folding, as well as for continuous "uphill" unfolding transitions, indicate that gradual non-cooperative processes may be ubiquitous features on the free energy landscape of protein folding.
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Affiliation(s)
- Pooja Malhotra
- National Centre for Biological Sciences, Tata Institute of Fundamental Research, Bengaluru, 560065, India
| | - Jayant B Udgaonkar
- National Centre for Biological Sciences, Tata Institute of Fundamental Research, Bengaluru, 560065, India.
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47
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Sacquin-Mora S. Fold and flexibility: what can proteins' mechanical properties tell us about their folding nucleus? J R Soc Interface 2016; 12:rsif.2015.0876. [PMID: 26577596 DOI: 10.1098/rsif.2015.0876] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
The determination of a protein's folding nucleus, i.e. a set of native contacts playing an important role during its folding process, remains an elusive yet essential problem in biochemistry. In this work, we investigate the mechanical properties of 70 protein structures belonging to 14 protein families presenting various folds using coarse-grain Brownian dynamics simulations. The resulting rigidity profiles combined with multiple sequence alignments show that a limited set of rigid residues, which we call the consensus nucleus, occupy conserved positions along the protein sequence. These residues' side chains form a tight interaction network within the protein's core, thus making our consensus nuclei potential folding nuclei. A review of experimental and theoretical literature shows that most (above 80%) of these residues were indeed identified as folding nucleus member in earlier studies.
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Affiliation(s)
- Sophie Sacquin-Mora
- Laboratoire de Biochimie Théorique, CNRS UPR9080, Institut de Biologie Physico-Chimique, 13 rue Pierre et Marie Curie, 75005 Paris, France
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Thermodynamics of emergent magnetic charge screening in artificial spin ice. Nat Commun 2016; 7:12635. [PMID: 27581972 PMCID: PMC5040513 DOI: 10.1038/ncomms12635] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2016] [Accepted: 07/19/2016] [Indexed: 11/09/2022] Open
Abstract
Electric charge screening is a fundamental principle governing the behaviour in a variety of systems in nature. Through reconfiguration of the local environment, the Coulomb attraction between electric charges is decreased, leading, for example, to the creation of polaron states in solids or hydration shells around proteins in water. Here, we directly visualize the real-time creation and decay of screened magnetic charge configurations in a two-dimensional artificial spin ice system, the dipolar dice lattice. By comparing the temperature dependent occurrence of screened and unscreened emergent magnetic charge defects, we determine that screened magnetic charges are indeed a result of local energy reduction and appear as a transient minimum energy state before the system relaxes towards the predicted ground state. These results highlight the important role of emergent magnetic charges in artificial spin ice, giving rise to screened charge excitations and the emergence of exotic low-temperature configurations. Inspired by the physics of bulk frustrated materials, arrays of coupled nanomagnets have been widely explored for the study of collective ordering and emergent behaviour. Here, the authors demonstrate interaction-driven charge screening in a thermally active artificial spin ice lattice.
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Sashi P, Ramakrishna D, Bhuyan AK. Dispersion Forces and the Molecular Origin of Internal Friction in Protein. Biochemistry 2016; 55:4595-602. [DOI: 10.1021/acs.biochem.6b00500] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Pulikallu Sashi
- School of Chemistry, University of Hyderabad, Hyderabad 500 046, India
| | | | - Abani K. Bhuyan
- School of Chemistry, University of Hyderabad, Hyderabad 500 046, India
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Slow Internal Dynamics and Charge Expansion in the Disordered Protein CGRP: A Comparison with Amylin. Biophys J 2016; 109:1038-48. [PMID: 26331261 DOI: 10.1016/j.bpj.2015.07.023] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2015] [Revised: 06/29/2015] [Accepted: 07/01/2015] [Indexed: 01/22/2023] Open
Abstract
We provide the first direct experimental comparison, to our knowledge, between the internal dynamics of calcitonin-gene-related peptide (CGRP) and amylin (islet amyloid polypeptide, IAPP), two intrinsically disordered proteins of the calcitonin peptide family. Our end-to-end contact formation measurements reveal that in aqueous solution (i.e., in the absence of structure-inducing organic solvents) CGRP preferentially populates conformations with short end-to-end distances. However, the end-to-end distance of CGRP is larger than that of IAPP. We find that electrostatic interactions can account for such a difference. At variance with previous reports on the secondary structure of CGRP, we find that the end-to-end distance of the peptide increases with decreasing pH and salt concentration, due to Coulomb repulsion by charged residues. Interestingly, our data show that the reconfiguration dynamics of CGRP is significantly slower than that of human IAPP in water but not in denaturant, providing experimental evidence for roughness in the energy landscape, or internal friction, in these peptides. The data reported here provide both structural and dynamical information that can be used to validate results from molecular simulations of calcitonin family peptides in aqueous solution.
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