1
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Dalton BA, Kiefer H, Netz RR. The role of memory-dependent friction and solvent viscosity in isomerization kinetics in viscogenic media. Nat Commun 2024; 15:3761. [PMID: 38704367 PMCID: PMC11069540 DOI: 10.1038/s41467-024-48016-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2023] [Accepted: 04/18/2024] [Indexed: 05/06/2024] Open
Abstract
Molecular isomerization kinetics in liquid solvent depends on a complex interplay between the solvent friction acting on the molecule, internal dissipation effects (also known as internal friction), the viscosity of the solvent, and the dihedral free energy profile. Due to the absence of accurate techniques to directly evaluate isomerization friction, it has not been possible to explore these relationships in full. By combining extensive molecular dynamics simulations with friction memory-kernel extraction techniques we consider a variety of small, isomerising molecules under a range of different viscogenic conditions and directly evaluate the viscosity dependence of the friction acting on a rotating dihedral. We reveal that the influence of different viscogenic media on isomerization kinetics can be dramatically different, even when measured at the same viscosity. This is due to the dynamic solute-solvent coupling, mediated by time-dependent friction memory kernels. We also show that deviations from the linear dependence of isomerization rates on solvent viscosity, which are often simply attributed to internal friction effects, are due to the simultaneous violation of two fundamental relationships: the Stokes-Einstein relation and the overdamped Kramers prediction for the barrier-crossing rate, both of which require explicit knowledge of friction.
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Affiliation(s)
| | - Henrik Kiefer
- Freie Universität Berlin, Fachbereich Physik, Berlin, Germany
| | - Roland R Netz
- Freie Universität Berlin, Fachbereich Physik, Berlin, Germany.
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2
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Dorbath E, Gulzar A, Stock G. Log-periodic oscillations as real-time signatures of hierarchical dynamics in proteins. J Chem Phys 2024; 160:074103. [PMID: 38364004 DOI: 10.1063/5.0188220] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Accepted: 01/23/2024] [Indexed: 02/18/2024] Open
Abstract
The time-dependent relaxation of a dynamical system may exhibit a power-law behavior that is superimposed by log-periodic oscillations. D. Sornette [Phys. Rep. 297, 239 (1998)] showed that this behavior can be explained by a discrete scale invariance of the system, which is associated with discrete and equidistant timescales on a logarithmic scale. Examples include such diverse fields as financial crashes, random diffusion, and quantum topological materials. Recent time-resolved experiments and molecular dynamics simulations suggest that discrete scale invariance may also apply to hierarchical dynamics in proteins, where several fast local conformational changes are a prerequisite for a slow global transition to occur. Employing entropy-based timescale analysis and Markov state modeling to a simple one-dimensional hierarchical model and biomolecular simulation data, it is found that hierarchical systems quite generally give rise to logarithmically spaced discrete timescales. By introducing a one-dimensional reaction coordinate that collectively accounts for the hierarchically coupled degrees of freedom, the free energy landscape exhibits a characteristic staircase shape with two metastable end states, which causes the log-periodic time evolution of the system. The period of the log-oscillations reflects the effective roughness of the energy landscape and can, in simple cases, be interpreted in terms of the barriers of the staircase landscape.
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Affiliation(s)
- Emanuel Dorbath
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
| | - Adnan Gulzar
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
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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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Post M, Wolf S, Stock G. Investigation of Rare Protein Conformational Transitions via Dissipation-Corrected Targeted Molecular Dynamics. J Chem Theory Comput 2023; 19:8978-8986. [PMID: 38011829 DOI: 10.1021/acs.jctc.3c01017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2023]
Abstract
To sample rare events, dissipation-corrected targeted molecular dynamics (dcTMD) applies a constant velocity constraint along a one-dimensional reaction coordinate s, which drives an atomistic system from an initial state into a target state. Employing a cumulant approximation of Jarzynski's identity, the free energy ΔG(s) is calculated from the mean external work and dissipated work of the process. By calculating the friction coefficient Γ(s) from the dissipated work, in a second step, the equilibrium dynamics of the process can be studied by propagating a Langevin equation. While so far dcTMD has been mostly applied to study the unbinding of protein-ligand complexes, here its applicability to rare conformational transitions within a protein and the prediction of their kinetics are investigated. As this typically requires the introduction of multiple collective variables {xj} = x, a theoretical framework is outlined to calculate the associated free energy ΔG(x) and friction Γ(x) from dcTMD simulations along coordinate s. Adopting the α-β transition of alanine dipeptide as well as the open-closed transition of T4 lysozyme as representative examples, the virtues and shortcomings of dcTMD to predict protein conformational transitions and the related kinetics are studied.
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Affiliation(s)
- Matthias Post
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, Freiburg 79104, Germany
| | - Steffen Wolf
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, Freiburg 79104, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, Freiburg 79104, Germany
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5
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Krieger F, Stecher K, Nyffenegger C, Schleeger M, Kiefhaber T. Local and Large-Scale Conformational Dynamics in Unfolded Proteins and IDPs. II. Effect of Temperature and Internal Friction. J Phys Chem B 2023; 127:8106-8115. [PMID: 37722680 PMCID: PMC10544017 DOI: 10.1021/acs.jpcb.3c04072] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2023] [Revised: 08/15/2023] [Indexed: 09/20/2023]
Abstract
Internal dynamics of proteins are essential for protein folding and function. Dynamics in unfolded proteins are of particular interest since they are the basis for many cellular processes like folding, misfolding, aggregation, and amyloid formation and also determine the properties of intrinsically disordered proteins (IDPs). It is still an open question of what governs motions in unfolded proteins and whether they encounter major energy barriers. Here we use triplet-triplet energy transfer (TTET) in unfolded homopolypeptide chains and IDPs to characterize the barriers for local and long-range loop formation. The results show that the formation of short loops encounters major energy barriers with activation energies (Ea) up to 18 kJ/mol (corrected for effects of temperature on water viscosity) with very little dependence on amino acid sequence. For poly(Gly-Ser) and polySer chains the barrier decreases with increasing loop size and reaches a limiting value of 4.6 ± 0.4 kJ/mol for long and flexible chains. This observation is in accordance with the concept of internal friction encountered by chain motions due to steric effects, which is high for local motions and decreases with increasing loop size. Comparison with the results from the viscosity dependence of loop formation shows a negative correlation between Ea and the sensitivity of the reaction to solvent viscosity (α) in accordance with the Grote-Hynes theory of memory friction. The Arrhenius pre-exponential factor (A) also decreases with increasing loop size, indicating increased entropic costs for loop formation. Long-range loop formation in the investigated sequences derived from IDPs shows increased Ea and A compared with poly(Gly-Ser) and polySer chains. This increase is exclusively due to steric effects that cause additional internal friction, whereas intramolecular hydrogen bonds, dispersion forces, and charge interactions do not affect the activation parameters.
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Affiliation(s)
- Florian Krieger
- Biozentrum
der Universität Basel, Klingelbergstrasse 70, CH-4056 Basel, Switzerland
| | - Karin Stecher
- Technische
Universität München, Chemistry
Department, Lichtenbergstrasse
4, D-85747 Garching, Germany
| | - Christian Nyffenegger
- Technische
Universität München, Chemistry
Department, Lichtenbergstrasse
4, D-85747 Garching, Germany
| | - Michael Schleeger
- Martin-Luther-Universität
Halle-Wittenberg, Institut für
Biochemie und Biotechnologie, Abteilung Proteinbiochemie, Kurt-Mothes-Str. 3, 06120 Halle (Saale), Germany
| | - Thomas Kiefhaber
- Martin-Luther-Universität
Halle-Wittenberg, Institut für
Biochemie und Biotechnologie, Abteilung Proteinbiochemie, Kurt-Mothes-Str. 3, 06120 Halle (Saale), Germany
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6
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Cai W, Jäger M, Bullerjahn JT, Hugel T, Wolf S, Balzer BN. Anisotropic Friction in a Ligand-Protein Complex. NANO LETTERS 2023; 23:4111-4119. [PMID: 36948207 DOI: 10.1021/acs.nanolett.2c04632] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
The effect of an externally applied directional force on molecular friction is so far poorly understood. Here, we study the force-driven dissociation of the ligand-protein complex biotin-streptavidin and identify anisotropic friction as a not yet described type of molecular friction. Using AFM-based stereographic single molecule force spectroscopy and targeted molecular dynamics simulations, we find that the rupture force and friction for biotin-streptavidin vary with the pulling angle. This observation holds true for friction extracted from Kramers' rate expression and by dissipation-corrected targeted molecular dynamics simulations based on Jarzynski's identity. We rule out ligand solvation and protein-internal friction as sources of the angle-dependent friction. Instead, we observe a heterogeneity in free energy barriers along an experimentally uncontrolled orientation parameter, which increases the rupture force variance and therefore the overall friction. We anticipate that anisotropic friction needs to be accounted for in a complete understanding of friction in biomolecular dynamics and anisotropic mechanical environments.
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Affiliation(s)
- Wanhao Cai
- Institute of Physical Chemistry, University of Freiburg, Albertstr. 21, 79104 Freiburg, Germany
| | - Miriam Jäger
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Jakob T Bullerjahn
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Max-von-Laue-Str. 3, 60438 Frankfurt am Main, Germany
| | - Thorsten Hugel
- Institute of Physical Chemistry, University of Freiburg, Albertstr. 21, 79104 Freiburg, Germany
- Cluster of Excellence livMatS @ FIT - Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, 79110 Freiburg, Germany
| | - Steffen Wolf
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Bizan N Balzer
- Institute of Physical Chemistry, University of Freiburg, Albertstr. 21, 79104 Freiburg, Germany
- Cluster of Excellence livMatS @ FIT - Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, 79110 Freiburg, Germany
- Freiburg Materials Research Center (FMF), University of Freiburg, Stefan-Meier-Str. 21, 79104 Freiburg, Germany
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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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Wosztyl A, Kuczera K, Szoszkiewicz R. Analytical Approaches for Deriving Friction Coefficients for Selected α-Helical Peptides Based Entirely on Molecular Dynamics Simulations. J Phys Chem B 2022; 126:8901-8912. [PMID: 36300354 PMCID: PMC9661531 DOI: 10.1021/acs.jpcb.2c03076] [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] [Indexed: 01/11/2023]
Abstract
In this paper we derive analytically from molecular dynamics (MD) simulations the friction coefficients related to conformational transitions within several model peptides with α-helical structures. We study a series of alanine peptides with various length from ALA5 to ALA21 as well as their two derivatives, the (AAQAA)3 peptide and a 13-residue KR1 peptide that is a derivative of the (AAQAA)2 peptide with the formula GN(AAQAA)2G. We use two kinds of approaches to derive their friction coefficients. In the local approach, friction associated with fluctuations of single hydrogen bonds are studied. In the second approach, friction coefficients associated with a folding transitions within the studied peptides are obtained. In both cases, the respective friction coefficients differentiated very well the subtle structural changes between studied peptides and compared favorably to experimentally available data.
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Affiliation(s)
- Aleksandra Wosztyl
- Faculty
of Chemistry, Biological and Chemical Research Centre, University of Warsaw, Żwirki i Wigury 101, 02-089Warsaw, Poland
| | - Krzysztof Kuczera
- Department
of Chemistry, The University of Kansas, Lawrence, Kansas66045, United States,Department
of Molecular Biosciences, The University
of Kansas, Lawrence, Kansas66045, United States,
| | - Robert Szoszkiewicz
- Faculty
of Chemistry, Biological and Chemical Research Centre, University of Warsaw, Żwirki i Wigury 101, 02-089Warsaw, Poland,
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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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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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11
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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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12
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Tian Z, Wang Y, He J. Nanofiber formation of self‐crosslinking dialdehyde carboxymethyl cellulose/collagen composites. POLYM ENG SCI 2021. [DOI: 10.1002/pen.25739] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Zhenhua Tian
- College of Bioresources Chemical and Materials Engineering Shaanxi University of Science and Technology Xi'an China
- National Demonstration Center for Experimental Light Chemistry Engineering Education Shaanxi University of Science and Technology Xi'an China
| | - Ying Wang
- College of Bioresources Chemical and Materials Engineering Shaanxi University of Science and Technology Xi'an China
| | - Jingxuan He
- College of Bioresources Chemical and Materials Engineering Shaanxi University of Science and Technology Xi'an China
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13
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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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14
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Vincenzi D. Effect of internal friction on the coil-stretch transition in turbulent flows. SOFT MATTER 2021; 17:2421-2428. [PMID: 33491720 DOI: 10.1039/d0sm01981j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
A polymer in a turbulent flow undergoes the coil-stretch transition when the Weissenberg number, i.e. the product of the Lyapunov exponent of the flow and the relaxation time of the polymer, surpasses a critical value. The effect of internal friction on the transition is studied by means of Brownian dynamics simulations of the elastic dumbbell model in a homogeneous and isotropic, incompressible, turbulent flow and analytical calculations for a stochastic velocity gradient. The results are explained by adapting the large deviations theory of Balkovsky et al. [Phys. Rev. Lett., 2000, 84, 4765] to an elastic dumbbell with internal viscosity. In turbulent flows, a distinctive feature of the probability distribution of polymer extensions is its power-law behaviour for extensions greater than the equilibrium length and smaller than the contour length. It is shown that although internal friction does not modify the critical Weissenberg number for the coil-stretch transition, it makes the slope of the probability distribution of the extension steeper, thus rendering the transition sharper. Internal friction therefore provides a possible explanation for the steepness of the distribution of polymer extensions observed in experiments at large Weissenberg numbers.
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15
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Lickert B, Stock G. Modeling non-Markovian data using Markov state and Langevin models. J Chem Phys 2020; 153:244112. [DOI: 10.1063/5.0031979] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Benjamin Lickert
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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16
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Wang C, Yang H, Wang X, Qi C, Qu M, Sheng N, Wan R, Tu Y, Shi G. Unexpected large impact of small charges on surface frictions with similar wetting properties. Commun Chem 2020; 3:27. [PMID: 36703380 PMCID: PMC9814279 DOI: 10.1038/s42004-020-0271-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2019] [Accepted: 02/04/2020] [Indexed: 01/29/2023] Open
Abstract
Generally, the interface friction on solid surfaces is regarded as consistent with wetting behaviors, characterized by the contact angles. Here using molecular dynamics simulations, we find that even a small charge difference (≤0.36 e) causes a change in the friction coefficient of over an order of magnitude on two-dimensional material and lipid surfaces, despite similar contact angles. This large difference is confirmed by experimentally measuring interfacial friction of graphite and MoS2 contacting on water, using atomic force microscopy. The large variation in the friction coefficient is attributed to the different fluctuations of localized potential energy under inhomogeneous charge distribution. Our results help to understand the dynamics of two-dimensional materials and biomolecules, generally formed by atoms with small charge, including nanomaterials, such as nitrogen-doped graphene, hydrogen-terminated graphene, or MoS2, and molecular transport through cell membranes.
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Affiliation(s)
- Chunlei Wang
- grid.450275.10000 0000 9989 3072Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai, 201800 China ,grid.458506.a0000 0004 0497 0637Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai, 201210 China
| | - Haijun Yang
- grid.450275.10000 0000 9989 3072Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai, 201800 China ,grid.458506.a0000 0004 0497 0637Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai, 201210 China
| | - Xian Wang
- grid.268415.cCollege of Physics Science and Technology, Yangzhou University, Jiangsu, 225009 China
| | - Chonghai Qi
- grid.450275.10000 0000 9989 3072Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai, 201800 China ,grid.27255.370000 0004 1761 1174School of Physics, Shandong University, Jinan, 250100 China
| | - Mengyang Qu
- grid.450275.10000 0000 9989 3072Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai, 201800 China
| | - Nan Sheng
- grid.450275.10000 0000 9989 3072Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai, 201800 China ,grid.458506.a0000 0004 0497 0637Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai, 201210 China
| | - Rongzheng Wan
- grid.450275.10000 0000 9989 3072Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai, 201800 China ,grid.458506.a0000 0004 0497 0637Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai, 201210 China
| | - Yusong Tu
- grid.268415.cCollege of Physics Science and Technology, Yangzhou University, Jiangsu, 225009 China
| | - Guosheng Shi
- grid.39436.3b0000 0001 2323 5732Shanghai Applied Radiation Institute and State Key Lab. Advanced Special Steel, Shanghai University, Shanghai, 200444 China
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17
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Yang Q, Guo C, Deng F, Ding C, Yang J, Wu H, Ni Y, Huang L, Chen L, Zhang M. Fabrication of highly concentrated collagens using cooled urea/HAc as novel binary solvent. J Mol Liq 2019. [DOI: 10.1016/j.molliq.2019.111304] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
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18
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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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19
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Sikdar S, Ghosh M, Adak A, Chakrabarti J. Structural and dynamic responses of calcium ion binding loop residues in metallo-proteins. Biophys Chem 2019; 252:106207. [PMID: 31252378 DOI: 10.1016/j.bpc.2019.106207] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2019] [Revised: 06/11/2019] [Accepted: 06/11/2019] [Indexed: 10/26/2022]
Abstract
Conformational changes in bio-molecular systems are fundamental to several biological processes. It is important to study changes in responses of underlying microscopic variables, like dihedral angles as conformational change takes place. We perform all-atom simulations and modelling via Langevin equation to illustrate the changes in structural and dynamic responses of dihedral angles of calcium ion binding residues of different proteins in metal ion free (apo) and bound (holo) states. The equilibrium distributions of dihedral angles in apo- and holo-states represent structural response. Our studies show the presence of dihedrals with multiple peaks (isomeric states) separated by barrier heights is more frequent in apo- than in holo-state. The relaxation time-scale of dihedral fluctuations is found to increase linearly with decreasing barrier height due to more frequent barrier re-crossing events. The slow kinetic response of the dihedrals also contributes to slowing down of macro-scale fluctuations, which may be useful to understand kinetics of various bio-molecular processes.
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Affiliation(s)
- Samapan Sikdar
- Department of Chemical, Biological & Macro-Molecular Sciences, S. N. Bose National Centre for Basic Sciences, Sector III, Block JD, Salt Lake, Kolkata 700106, India.
| | - Mahua Ghosh
- Department of Chemical, Biological & Macro-Molecular Sciences, S. N. Bose National Centre for Basic Sciences, Sector III, Block JD, Salt Lake, Kolkata 700106, India
| | - Arunava Adak
- Department of Chemical, Biological & Macro-Molecular Sciences, S. N. Bose National Centre for Basic Sciences, Sector III, Block JD, Salt Lake, Kolkata 700106, India
| | - J Chakrabarti
- Department of Chemical, Biological & Macro-Molecular Sciences, S. N. Bose National Centre for Basic Sciences, Sector III, Block JD, Salt Lake, Kolkata 700106, India; The Thematic Unit of Excellence on Computational Materials Science, S. N. Bose National Centre for Basic Sciences, Sector III, Block JD, Salt Lake, Kolkata 700106, India.
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20
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Post M, Wolf S, Stock G. Principal component analysis of nonequilibrium molecular dynamics simulations. J Chem Phys 2019; 150:204110. [PMID: 31153204 DOI: 10.1063/1.5089636] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Principal component analysis (PCA) represents a standard approach to identify collective variables {xi} = x, which can be used to construct the free energy landscape ΔG(x) of a molecular system. While PCA is routinely applied to equilibrium molecular dynamics (MD) simulations, it is less obvious as to how to extend the approach to nonequilibrium simulation techniques. This includes, e.g., the definition of the statistical averages employed in PCA as well as the relation between the equilibrium free energy landscape ΔG(x) and the energy landscapes ΔG(x) obtained from nonequilibrium MD. As an example for a nonequilibrium method, "targeted MD" is considered which employs a moving distance constraint to enforce rare transitions along some biasing coordinate s. The introduced bias can be described by a weighting function P(s), which provides a direct relation between equilibrium and nonequilibrium data, and thus establishes a well-defined way to perform PCA on nonequilibrium data. While the resulting distribution P(x) and energy ΔG∝lnP will not reflect the equilibrium state of the system, the nonequilibrium energy landscape ΔG(x) may directly reveal the molecular reaction mechanism. Applied to targeted MD simulations of the unfolding of decaalanine, for example, a PCA performed on backbone dihedral angles is shown to discriminate several unfolding pathways. Although the formulation is in principle exact, its practical use depends critically on the choice of the biasing coordinate s, which should account for a naturally occurring motion between two well-defined end-states of the system.
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Affiliation(s)
- Matthias Post
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Steffen Wolf
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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21
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Kappler J, Noé F, Netz RR. Cyclization and Relaxation Dynamics of Finite-Length Collapsed Self-Avoiding Polymers. PHYSICAL REVIEW LETTERS 2019; 122:067801. [PMID: 30822085 DOI: 10.1103/physrevlett.122.067801] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2018] [Revised: 11/23/2018] [Indexed: 06/09/2023]
Abstract
We study the cyclization and relaxation dynamics of ideal as well as interacting polymers as a function of chain length N. For the cyclization time τ_{cyc} of ideal chains we recover the known scaling τ_{cyc}∼N^{2} for different backbone models, for a self-avoiding slightly collapsed chain we obtain from Langevin simulations and scaling theory a modified scaling τ_{cyc}∼N^{5/3}. The cyclization and relaxation dynamics of a finite-length collapsed chain scale differently; this unexpected dynamic multiscale behavior is rationalized by the crossover between swollen and collapsed chain behavior.
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Affiliation(s)
- Julian Kappler
- Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, 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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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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23
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Wolf S, Stock G. Targeted Molecular Dynamics Calculations of Free Energy Profiles Using a Nonequilibrium Friction Correction. J Chem Theory Comput 2018; 14:6175-6182. [DOI: 10.1021/acs.jctc.8b00835] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Affiliation(s)
- Steffen Wolf
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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24
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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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25
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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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26
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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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27
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Das A, Makarov DE. Dynamics of Disordered Proteins under Confinement: Memory Effects and Internal Friction. J Phys Chem B 2018; 122:9049-9060. [PMID: 30092636 DOI: 10.1021/acs.jpcb.8b06112] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
Many proteins are disordered under physiological conditions. How efficiently they can search for their cellular targets and how fast they can fold upon target binding is determined by their intrinsic dynamics, which have thus attracted much recent attention. Experiments and molecular simulations show that the inherent reconfiguration timescale for unfolded proteins has a solvent friction component and an internal friction component, and the microscopic origin of the latter, along with its proper mathematical description, has been a topic of considerable debate. Internal friction varies across different proteins of comparable length and increases with decreasing denaturant concentration, showing that it depends on how compact the protein is. Here we report on a systematic atomistic simulation study of how confinement, which induces a more compact unfolded state, affects dynamics and friction in disordered peptides. We find that the average reconfiguration timescales increase exponentially as the peptide's spatial dimensions are reduced; at the same time, confinement broadens the spectrum of relaxation timescales exhibited by the peptide. There are two important implications of this broadening: First, it limits applicability of the common Rouse and Zimm models with internal friction, as those models attempt to capture internal friction effects by introducing a single internal friction timescale. Second, the long-tailed distribution of relaxation times leads to anomalous diffusion effects in the dynamics of intramolecular distances. Analysis and interpretation of experimental signals from various measurements that probe intramolecular protein dynamics (such as single-molecule fluorescence correlation spectroscopy and single-molecule force spectroscopy) rely on the assumption of diffusive dynamics along the distances being probed; hence, our results suggest the need for more general models allowing for anomalous diffusion effects.
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Affiliation(s)
- Atanu Das
- Department of Chemistry , University of Texas at Austin , Austin , Texas 78712 , United States
| | - Dmitrii E Makarov
- Department of Chemistry , University of Texas at Austin , Austin , Texas 78712 , United States.,Institute for Computational Engineering and Sciences , University of Texas at Austin , Austin , Texas 78712 , United States
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28
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Schuler B. Perspective: Chain dynamics of unfolded and intrinsically disordered proteins from nanosecond fluorescence correlation spectroscopy combined with single-molecule FRET. J Chem Phys 2018; 149:010901. [PMID: 29981536 DOI: 10.1063/1.5037683] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
The dynamics of unfolded proteins are important both for the process of protein folding and for the behavior of intrinsically disordered proteins. However, methods for investigating the global chain dynamics of these structurally diverse systems have been limited. A versatile experimental approach is single-molecule spectroscopy in combination with Förster resonance energy transfer and nanosecond fluorescence correlation spectroscopy. The concepts of polymer physics offer a powerful framework both for interpreting the results and for understanding and classifying the properties of unfolded and intrinsically disordered proteins. This information on long-range chain dynamics can be complemented with spectroscopic techniques that probe different length scales and time scales, and integration of these results greatly benefits from recent advances in molecular simulations. This increasing convergence between the experiment, theory, and simulation is thus starting to enable an increasingly detailed view of the dynamics of disordered proteins.
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Affiliation(s)
- Benjamin Schuler
- Department of Biochemistry and Department of Physics, University of Zurich, Winterthurerstrasse 190, Zurich, Switzerland
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29
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30
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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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31
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Affiliation(s)
- Yukun Bian
- College of Physical Science and Technology, Sichuan University, Chengdu, China
| | - Peng Li
- College of Physical Science and Technology, Sichuan University, Chengdu, China
| | - Nanrong Zhao
- College of Chemistry, Sichuan University, Chengdu, China
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32
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Kwon S, Cho HW, Kim J, Sung BJ. Fractional Viscosity Dependence of Reaction Kinetics in Glass-Forming Liquids. PHYSICAL REVIEW LETTERS 2017; 119:087801. [PMID: 28952769 DOI: 10.1103/physrevlett.119.087801] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2017] [Indexed: 06/07/2023]
Abstract
The diffusion of molecules in complex systems such as glasses and cell cytoplasm is slow, heterogeneous, and sometimes nonergodic. The effects of such intriguing diffusion on the kinetics of chemical and biological reactions remain elusive. In this Letter, we report that the kinetics of the polymer loop formation reaction in a Kob-Andersen (KA) glass forming liquid is influenced significantly by the dynamic heterogeneity. The diffusion coefficient D of a KA liquid deviates from the Stokes-Einstein relation at low temperatures and D shows a fractional dependence on the solvent viscosity η_{s}, i.e., D∼η_{s}^{-ξ_{D}} with ξ_{D}=0.85. The dynamic heterogeneity of a KA liquid affects the rate constant k_{rxn} of the loop formation and leads to the identical fractional dependence of k_{rxn} on η_{s} with k_{rxn}∼η_{s}^{-ξ} and ξ=ξ_{D}, contrary to reactions in dynamically homogeneous solutions where k_{rxn}∼η_{s}^{-1}.
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Affiliation(s)
- Seulki Kwon
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 121-742, Republic of Korea
| | - Hyun Woo Cho
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 121-742, Republic of Korea
| | - Jeongmin Kim
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 121-742, Republic of Korea
| | - Bong June Sung
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 121-742, Republic of Korea
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33
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Abstract
Allostery represents a fundamental mechanism of biological regulation that is mediated via long-range communication between distant protein sites. Although little is known about the underlying dynamical process, recent time-resolved infrared spectroscopy experiments on a photoswitchable PDZ domain (PDZ2S) have indicated that the allosteric transition occurs on multiple timescales. Here, using extensive nonequilibrium molecular dynamics simulations, a time-dependent picture of the allosteric communication in PDZ2S is developed. The simulations reveal that allostery amounts to the propagation of structural and dynamical changes that are genuinely nonlinear and can occur in a nonlocal fashion. A dynamic network model is constructed that illustrates the hierarchy and exceeding structural heterogeneity of the process. In compelling agreement with experiment, three physically distinct phases of the time evolution are identified, describing elastic response ([Formula: see text] ns), inelastic reorganization ([Formula: see text] ns), and structural relaxation ([Formula: see text]s). Issues such as the similarity to downhill folding as well as the interpretation of allosteric pathways are discussed.
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34
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Theoretical and computational validation of the Kuhn barrier friction mechanism in unfolded proteins. Sci Rep 2017; 7:269. [PMID: 28325911 PMCID: PMC5428071 DOI: 10.1038/s41598-017-00287-5] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2016] [Accepted: 02/20/2017] [Indexed: 11/08/2022] Open
Abstract
A long time ago, Kuhn predicted that long polymers should approach a limit where their global motion is controlled by solvent friction alone, with ruggedness of their energy landscapes having no consequences for their dynamics. In contrast, internal friction effects are important for polymers of modest length. Internal friction in proteins, in particular, affects how fast they fold or find their binding targets and, as such, has attracted much recent attention. Here we explore the molecular origins of internal friction in unfolded proteins using atomistic simulations, coarse-grained models and analytic theory. We show that the characteristic internal friction timescale is directly proportional to the timescale of hindered dihedral rotations within the polypeptide chain, with a proportionality coefficient b that is independent of the chain length. Such chain length independence of b provides experimentally testable evidence that internal friction arises from concerted, crankshaft-like dihedral rearrangements. In accord with phenomenological models of internal friction, we find the global reconfiguration timescale of a polypeptide to be the sum of solvent friction and internal friction timescales. At the same time, the time evolution of inter-monomer distances within polypeptides deviates both from the predictions of those models and from a simple, one-dimensional diffusion model.
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35
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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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36
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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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Schaudinnus N, Lickert B, Biswas M, Stock G. Global Langevin model of multidimensional biomolecular dynamics. J Chem Phys 2016; 145:184114. [DOI: 10.1063/1.4967341] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
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38
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Palczynski K, Herrmann P, Heimel G, Dzubiella J. Characterization of step-edge barrier crossing of para-sexiphenyl on the ZnO (101[combining macron]0) surface. Phys Chem Chem Phys 2016; 18:25329-25341. [PMID: 27711631 DOI: 10.1039/c6cp05251g] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Mass transport processes of conjugated organic molecules (COMs) on inorganic surfaces are essential elements in thin film deposition for hybrid optoelectronic devices. Defects and in particular surface step-edges dictate the molecular nucleation and growth morphology, which itself determine many physical properties of the resulting hybrid interface. Here, we explore the detailed molecular kinetics and transport rates of a single physisorbed para-sexiphenyl (p-6P) molecule crossing a step-edge (a "hetero-Ehrlich-Schwoebel barrier") on the inorganic ZnO (101[combining macron]0) surface by a combination of all-atom molecular dynamics simulations and passage time theory. We determine temperature- and charge-dependent (free) energy landscapes, position-dependent diffusion coefficients, and ultimately the mean first passage time over the step-edges. We find two completely different step-edge crossing mechanisms, the occurrence and rates of which simultaneously depend on both electrostatic and thermal molecule-surface coupling. In weakly coupled systems, the molecule crosses the step relatively quickly (in nanoseconds) by log-roll mechanisms while for strongly coupled systems, it crosses relatively slowly (in microseconds) in a strictly perpendicular fashion. In the latter process, "internal friction" from intramolecular bending and torsional degrees of freedom contribute a significant corrugation to the overall crossing barrier. Furthermore, we show that crossing pathways can also change qualitatively with step-edge height. The great complexity in hetero-barrier crossing of COMs (in contrast to simple atoms) revealed in this study has implications on the interpretation and possible control of nucleation and growth mechanisms at surface defects in hybrid systems.
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Affiliation(s)
- Karol Palczynski
- Institut für Weiche Materie und Funktionale Materialien, Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner Platz 1, 14109 Berlin, Germany. and Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany
| | - Philipp Herrmann
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany
| | - Georg Heimel
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany
| | - Joachim Dzubiella
- Institut für Weiche Materie und Funktionale Materialien, Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner Platz 1, 14109 Berlin, Germany. and Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany
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39
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Aznauryan M, Delgado L, Soranno A, Nettels D, Huang JR, Labhardt AM, Grzesiek S, Schuler B. Comprehensive structural and dynamical view of an unfolded protein from the combination of single-molecule FRET, NMR, and SAXS. Proc Natl Acad Sci U S A 2016; 113:E5389-98. [PMID: 27566405 PMCID: PMC5027429 DOI: 10.1073/pnas.1607193113] [Citation(s) in RCA: 110] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
The properties of unfolded proteins are essential both for the mechanisms of protein folding and for the function of the large group of intrinsically disordered proteins. However, the detailed structural and dynamical characterization of these highly dynamic and conformationally heterogeneous ensembles has remained challenging. Here we combine and compare three of the leading techniques for the investigation of unfolded proteins, NMR spectroscopy (NMR), small-angle X-ray scattering (SAXS), and single-molecule Förster resonance energy transfer (FRET), with the goal of quantitatively testing their consistency and complementarity and for obtaining a comprehensive view of the unfolded-state ensemble. Using unfolded ubiquitin as a test case, we find that its average dimensions derived from FRET and from structural ensembles calculated using the program X-PLOR-NIH based on NMR and SAXS restraints agree remarkably well; even the shapes of the underlying intramolecular distance distributions are in good agreement, attesting to the reliability of the approaches. The NMR-based results provide a highly sensitive way of quantifying residual structure in the unfolded state. FRET-based nanosecond fluorescence correlation spectroscopy allows long-range distances and chain dynamics to be probed in a time range inaccessible by NMR. The combined techniques thus provide a way of optimally using the complementarity of the available methods for a quantitative structural and dynamical description of unfolded proteins both at the global and the local level.
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Affiliation(s)
- Mikayel Aznauryan
- Department of Biochemistry, University of Zurich, 8057 Zurich, Switzerland
| | | | - Andrea Soranno
- Department of Biochemistry, University of Zurich, 8057 Zurich, Switzerland
| | - Daniel Nettels
- Department of Biochemistry, University of Zurich, 8057 Zurich, Switzerland
| | - Jie-Rong Huang
- Institute of Biochemistry and Molecular Biology, National Yang Ming University, Taipei City 112, Taiwan
| | | | | | - Benjamin Schuler
- Department of Biochemistry, University of Zurich, 8057 Zurich, Switzerland; Department of Physics, University of Zurich, 8057 Zurich, Switzerland
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40
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Abstract
Tethering is used to deliver specific biological and industrial functions. For example, single-stranded DNA (ssDNA) is tethered to polymerases and long sequences of double-stranded DNA (dsDNA) during replication, and to solids in DNA microarrays. However, tethering ssDNA to a large object limits not only the available ssDNA conformations, but also the range of time-scales over which the mechanical responses of ssDNA are important. In this work we examine the effect of tethering by measurement of the mechanical response of ssDNA that is tethered at each end to two separate atomic force microscope cantilevers in aqueous solution. Thermal motion of the cantilevers drives the ends of the ssDNA chain at frequencies near 2 kHz. The presence of a tethered molecule makes a large difference to the asymmetric cross-correlation of two cantilevers, which enables resolution of the mechanical properties in our experiments. By analysis of the correlated motion of the cantilevers we extract the friction and stiffness of the ssDNA. We find that the measured friction is much larger than the friction that is usually associated with the unencumbered motion of ssDNA. We also find that the measured relaxation time, ∼30 μs, is much greater than prior measurements of the free-molecule relaxation time. We attribute the difference to the loss of conformational possibilities as a result of constraining the ends of the ssDNA.
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Affiliation(s)
- Milad Radiom
- Department of Chemical Engineering, Virginia Tech, Blacksburg, VA 24060, USA. Department of Inorganic and Analytic Chemistry, University of Geneva, 1205 Geneva, Switzerland
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41
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Ding B, Hilaire MR, Gai F. Infrared and Fluorescence Assessment of Protein Dynamics: From Folding to Function. J Phys Chem B 2016; 120:5103-13. [PMID: 27183318 DOI: 10.1021/acs.jpcb.6b03199] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
While folding or performing functions, a protein can sample a rich set of conformational space. However, experimentally capturing all of the important motions with sufficient detail to allow a mechanistic description of their dynamics is nontrivial since such conformational events often occur over a wide range of time and length scales. Therefore, many methods have been employed to assess protein conformational dynamics, and depending on the nature of the conformational transition in question, some may be more advantageous than others. Herein, we describe our recent efforts, and also those of others, wherever appropriate, to use infrared- and fluorescence-based techniques to interrogate protein folding and functional dynamics. Specifically, we focus on discussing how to use extrinsic spectroscopic probes to enhance the structural resolution of these techniques and how to exploit various cross-linking strategies to acquire dynamic and mechanistic information that was previously difficult to attain.
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Affiliation(s)
- Bei Ding
- Department of Chemistry and ‡The Ultrafast Optical Processes Laboratory, University of Pennsylvania , Philadelphia, Pennsylvania 19104, United States
| | - Mary Rose Hilaire
- Department of Chemistry and ‡The Ultrafast Optical Processes Laboratory, University of Pennsylvania , Philadelphia, Pennsylvania 19104, United States
| | - Feng Gai
- Department of Chemistry and ‡The Ultrafast Optical Processes Laboratory, University of Pennsylvania , Philadelphia, Pennsylvania 19104, United States
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42
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Schuler B, Soranno A, Hofmann H, Nettels D. Single-Molecule FRET Spectroscopy and the Polymer Physics of Unfolded and Intrinsically Disordered Proteins. Annu Rev Biophys 2016; 45:207-31. [PMID: 27145874 DOI: 10.1146/annurev-biophys-062215-010915] [Citation(s) in RCA: 221] [Impact Index Per Article: 27.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
The properties of unfolded proteins have long been of interest because of their importance to the protein folding process. Recently, the surprising prevalence of unstructured regions or entirely disordered proteins under physiological conditions has led to the realization that such intrinsically disordered proteins can be functional even in the absence of a folded structure. However, owing to their broad conformational distributions, many of the properties of unstructured proteins are difficult to describe with the established concepts of structural biology. We have thus seen a reemergence of polymer physics as a versatile framework for understanding their structure and dynamics. An important driving force for these developments has been single-molecule spectroscopy, as it allows structural heterogeneity, intramolecular distance distributions, and dynamics to be quantified over a wide range of timescales and solution conditions. Polymer concepts provide an important basis for relating the physical properties of unstructured proteins to folding and function.
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Affiliation(s)
- Benjamin Schuler
- Department of Biochemistry, University of Zurich, 8057 Zurich, Switzerland;
| | - Andrea Soranno
- Department of Biochemistry, University of Zurich, 8057 Zurich, Switzerland;
| | - Hagen Hofmann
- Department of Biochemistry, University of Zurich, 8057 Zurich, Switzerland;
| | - Daniel Nettels
- Department of Biochemistry, University of Zurich, 8057 Zurich, Switzerland;
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Zheng W, de Sancho D, Best RB. Modulation of Folding Internal Friction by Local and Global Barrier Heights. J Phys Chem Lett 2016; 7:1028-1034. [PMID: 26947615 PMCID: PMC5578457 DOI: 10.1021/acs.jpclett.6b00329] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Recent experiments have revealed an unexpected deviation from a first power dependence of protein relaxation times on solvent viscosity, an effect that has been attributed to "internal friction". One clear source of internal friction in protein dynamics is the isomerization of dihedral angles. A key outstanding question is whether the global folding barrier height influences the measured internal friction, based on the observation that the folding rates of fast-folding proteins, with smaller folding free energy barriers, tend to exhibit larger internal friction. Here, by studying two alanine-based peptides, we find that systematic variation of global folding barrier heights has little effect on the internal friction for folding rates. On the other hand, increasing local torsion angle barriers leads to increased internal friction, which is consistent with solvent memory effects being the origin of the viscosity dependence. Thus, it appears that local torsion transitions determine the viscosity dependence of the diffusion coefficient on the global coordinate and, in turn, internal friction effects on the folding rate.
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Affiliation(s)
- Wenwei Zheng
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892-0520, United States
| | - David de Sancho
- CIC nanoGUNE, 20018 Donostia-San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, María Díaz de Haro 3, 48013 Bilbao, Spain
| | - 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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44
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Rinne KF, Schulz JCF, Netz RR. Impact of secondary structure and hydration water on the dielectric spectrum of poly-alanine and possible relation to the debate on slaved versus slaving water. J Chem Phys 2016; 142:215104. [PMID: 26049528 DOI: 10.1063/1.4921777] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using extensive molecular dynamics simulations of a single eight-residue alanine polypeptide in explicit water, we investigate the influence of α-helix formation on the dielectric spectrum. For this, we project long equilibrium trajectories into folded and unfolded states and thereby obtain dielectric spectra representative for disordered as well α-helical conformations without the need to change any other system parameter such as pH or temperature. The absorption spectrum in the α-helical state exhibits a feature in the sub-GHz range that is significantly stronger than in the unfolded state. As we show by an additional decomposition into peptide and water contributions, this slow dielectric mode, the relaxation time of which matches the independently determined peptide rotational relaxation time, is mostly caused by peptide polarization correlations, but also contains considerable contributions from peptide-water correlations. In contrast, the peptide spectral contribution shows no features in the GHz range where bulk water absorbs, not even in the peptide-water correlation part, we conclude that hydration water around Ala8 is more influenced by peptide polarization relaxation effects than the other way around. A further decomposition into water-self and water-collective polarization correlations shows that the dielectric response of hydration water is, in contrast to electrolyte solutions, retarded and that this retardation is mostly due to collective effects, the self relaxation of hydration water molecules is only slightly slowed down compared to bulk water. We find the dynamic peptide-water polarization cross correlations to be rather long-ranged and to extend more than one nanometer away from the peptide-water interface into the water hydration shell, in qualitative agreement with previous simulation studies and recent THz absorption experiments.
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Affiliation(s)
- Klaus F Rinne
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | | | - Roland R Netz
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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45
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Kaiser A, Babel S, ten Hagen B, von Ferber C, Löwen H. How does a flexible chain of active particles swell? J Chem Phys 2016; 142:124905. [PMID: 25833607 DOI: 10.1063/1.4916134] [Citation(s) in RCA: 72] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study the swelling of a flexible linear chain composed of active particles by analytical theory and computer simulation. Three different situations are considered: a free chain, a chain confined to an external harmonic trap, and a chain dragged at one end. First, we consider an ideal chain with harmonic springs and no excluded volume between the monomers. The Rouse model of polymers is generalized to the case of self-propelled monomers and solved analytically. The swelling, as characterized by the spatial extension of the chain, scales with the monomer number defining a Flory exponent ν which is ν = 1/2, 0, 1 in the three different situations. As a result, we find that activity does not change the Flory exponent but affects the prefactor of the scaling law. This can be quantitatively understood by mapping the system onto an equilibrium chain with a higher effective temperature such that the chain swells under an increase of the self-propulsion strength. We then use computer simulations to study the effect of self-avoidance on active polymer swelling. In the three different situations, the Flory exponent is now ν = 3/4, 1/4, 1 and again unchanged under self-propulsion. However, the chain extension behaves non-monotonic in the self-propulsion strength.
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Affiliation(s)
- Andreas Kaiser
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Sonja Babel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Borge ten Hagen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Christian von Ferber
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
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46
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Chung HS, Piana-Agostinetti S, Shaw DE, Eaton WA. Structural origin of slow diffusion in protein folding. Science 2015; 349:1504-10. [PMID: 26404828 DOI: 10.1126/science.aab1369] [Citation(s) in RCA: 152] [Impact Index Per Article: 16.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Experimental, theoretical, and computational studies of small proteins suggest that interresidue contacts not present in the folded structure play little or no role in the self-assembly mechanism. Non-native contacts can, however, influence folding kinetics by introducing additional local minima that slow diffusion over the global free-energy barrier between folded and unfolded states. Here, we combine single-molecule fluorescence with all-atom molecular dynamics simulations to discover the structural origin for the slow diffusion that markedly decreases the folding rate for a designed α-helical protein. Our experimental determination of transition path times and our analysis of the simulations point to non-native salt bridges between helices as the source, which provides a quantitative glimpse of how specific intramolecular interactions influence protein folding rates by altering dynamics and not activation free energies.
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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, Bethesda, MD, 20892-0520, USA.
| | | | - David E Shaw
- D. E. Shaw Research, New York, NY 10036, USA. Department of Biochemistry and Molecular Biophysics, Columbia University, New York, NY 10032, USA.
| | - William A Eaton
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD, 20892-0520, USA.
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47
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Waldauer SA, Stucki-Buchli B, Frey L, Hamm P. Effect of viscogens on the kinetic response of a photoperturbed allosteric protein. J Chem Phys 2015; 141:22D514. [PMID: 25494785 DOI: 10.1063/1.4897975] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
By covalently binding a photoswitchable linker across the binding groove of the PDZ2 domain, a small conformational change can be photo-initiated that mimics the allosteric transition of the protein. The response of its binding groove is investigated with the help of ultrafast pump-probe IR spectroscopy from picoseconds to tens of microseconds. The temperature dependence of that response is compatible with diffusive dynamics on a rugged energy landscape without any prominent energy barrier. Furthermore, the dependence of the kinetics on the concentration of certain viscogens, sucrose, and glycerol, has been investigated. A pronounced viscosity dependence is observed that can be best fit by a power law, i.e., a fractional viscosity dependence. The change of kinetics when comparing sucrose with glycerol as viscogen, however, provides strong evidence that direct interactions of the viscogen molecule with the protein do play a role as well. This conclusion is supported by accompanying molecular dynamics simulations.
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Affiliation(s)
- Steven A Waldauer
- Department of Chemistry, University of Zurich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland
| | - Brigitte Stucki-Buchli
- Department of Chemistry, University of Zurich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland
| | - Lukas Frey
- Department of Chemistry, University of Zurich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland
| | - Peter Hamm
- Department of Chemistry, University of Zurich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland
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48
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Bhavaraju M, Hansmann UHE. Effect of single point mutations in a form of systemic amyloidosis. Protein Sci 2015; 24:1451-62. [PMID: 26105812 DOI: 10.1002/pro.2730] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2015] [Revised: 06/14/2015] [Accepted: 06/21/2015] [Indexed: 01/23/2023]
Abstract
Amyloid deposits of light-chain proteins are associated with the most common form of systemic amyloidosis. We have studied the effects of single point mutations on amyloid formation of these proteins using explicit solvent model molecular dynamics simulations. For this purpose, we compare the stability of the wild-type immunoglobulin light-chain protein REI in its native and amyloid forms with that of four mutants: R61N, G68D, D82I, and A84T. We argue that the experimentally observed differences in the propensity for amyloid formation result from two effects. First, the mutant dimers have a lower stability than the wild-type dimer due to increase exposure of certain hydrophobic residues. The second effect is a shift in equilibrium between monomers with amyloid-like structure and such with native structures. Hence, when developing drugs against light-chain associated systemic amyloidosis, one should look for components that either stabilize the dimer by binding to the dimer interface or reduce for the monomers the probability of the amyloid form.
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Affiliation(s)
- Manikanthan Bhavaraju
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma, 73019
| | - Ulrich H E Hansmann
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma, 73019
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49
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Alred EJ, Scheele EG, Berhanu WM, Hansmann UHE. Stability of Iowa mutant and wild type Aβ-peptide aggregates. J Chem Phys 2015; 141:175101. [PMID: 25381547 DOI: 10.1063/1.4900892] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
Recent experiments indicate a connection between the structure of amyloid aggregates and their cytotoxicity as related to neurodegenerative diseases. Of particular interest is the Iowa Mutant, which causes early-onset of Alzheimer's disease. While wild-type Amyloid β-peptides form only parallel beta-sheet aggregates, the mutant also forms meta-stable antiparallel beta sheets. Since these structural variations may cause the difference in the pathological effects of the two Aβ-peptides, we have studied in silico the relative stability of the wild type and Iowa mutant in both parallel and antiparallel forms. We compare regular molecular dynamics simulations with such where the viscosity of the samples is reduced, which, we show, leads to higher sampling efficiency. By analyzing and comparing these four sets of all-atom molecular dynamics simulations, we probe the role of the various factors that could lead to the structural differences. Our analysis indicates that the parallel forms of both wild type and Iowa mutant aggregates are stable, while the antiparallel aggregates are meta-stable for the Iowa mutant and not stable for the wild type. The differences result from the direct alignment of hydrophobic interactions in the in-register parallel oligomers, making them more stable than the antiparallel aggregates. The slightly higher thermodynamic stability of the Iowa mutant fibril-like oligomers in its parallel organization over that in antiparallel form is supported by previous experimental measurements showing slow inter-conversion of antiparallel aggregates into parallel ones. Knowledge of the mechanism that selects between parallel and antiparallel conformations and determines their relative stability may open new avenues for the development of therapies targeting familial forms of early-onset Alzheimer's disease.
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Affiliation(s)
- Erik J Alred
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, USA
| | - Emily G Scheele
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, USA
| | - Workalemahu M Berhanu
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, USA
| | - Ulrich H E Hansmann
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, USA
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50
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Sterpone F, Derreumaux P, Melchionna S. Protein Simulations in Fluids: Coupling the OPEP Coarse-Grained Force Field with Hydrodynamics. J Chem Theory Comput 2015; 11:1843-53. [PMID: 26574390 PMCID: PMC5242371 DOI: 10.1021/ct501015h] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
A novel simulation framework that integrates the OPEP coarse-grained (CG) model for proteins with the Lattice Boltzmann (LB) methodology to account for the fluid solvent at mesoscale level is presented. OPEP is a very efficient, water-free and electrostatic-free force field that reproduces at quasi-atomistic detail processes like peptide folding, structural rearrangements, and aggregation dynamics. The LB method is based on the kinetic description of the solvent in order to solve the fluid mechanics under a wide range of conditions, with the further advantage of being highly scalable on parallel architectures. The capabilities of the approach are presented, and it is shown that the strategy is effective in exploring the role of hydrodynamics on protein relaxation and peptide aggregation. The end result is a strategy for modeling systems of thousands of proteins, such as in the case of dense protein suspensions. The future perspectives of the multiscale approach are also discussed.
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Affiliation(s)
- Fabio Sterpone
- Laboratoire de Biochimie Théorique, IBPC, CNRS UPR9080, Univ. Paris Diderot, Sorbonne Paris Cité, 13 rue Pierre et Marie Curie, 75005, Paris, France
| | - Philippe Derreumaux
- Laboratoire de Biochimie Théorique, IBPC, CNRS UPR9080, Univ. Paris Diderot, Sorbonne Paris Cité, 13 rue Pierre et Marie Curie, 75005, Paris, France
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