1
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Świątek A, Kuczera K, Szoszkiewicz R. Effects of Proline on Internal Friction in Simulated Folding Dynamics of Several Alanine-Based α-Helical Peptides. J Phys Chem B 2024; 128:3856-3869. [PMID: 38606880 PMCID: PMC11056985 DOI: 10.1021/acs.jpcb.4c00623] [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: 01/29/2024] [Revised: 03/13/2024] [Accepted: 04/01/2024] [Indexed: 04/13/2024]
Abstract
We have studied in silico the effect of proline, a model cosolvent, on local and global friction coefficients in (un)folding of several typical alanine-based α-helical peptides. Local friction is related to dwell times of a single, ensemble-averaged hydrogen bond (HB) within each peptide. Global friction is related to energy dissipated in a series of configurational changes of each peptide experienced by increasing the number of HBs during folding. Both of these approaches are important in relation to future atomic force microscopic-based measurements of internal friction via force-clamp single-molecule force spectroscopy. Molecular dynamics (MD) simulations for six peptides, namely, ALA5, ALA8, ALA15, ALA21, (AAQAA)3, and H2N-GN(AAQAA)2G-COONH2, have been conducted at 2 and 5 M proline solutions in water. Using previously obtained MD data for these peptides in pure water as well as upgraded theoretical models, we obtained variations of local and global internal friction coefficients as a function of solution viscosity. The results showed the substantial role of proline in stabilizing the folded state and slowing the overall folding dynamics. Consequently, larger friction coefficients were obtained at larger viscosities. The local and global internal friction, i.e., respective, friction coefficients approximated to zero viscosity, was also obtained. The evolution of friction coefficients with viscosity was weakly dependent on the number of concurrent folding pathways but was rather dominated by a stabilizing effect of proline on the folded states. Obtained values of local and global internal friction showed qualitatively similar results and a clear dependency on the structure of the studied peptide.
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Affiliation(s)
- Adam Świątek
- Faculty of Chemistry,
Biological and Chemical Research Centre, University of Warsaw, Żwirki i Wigury 101, 02-089 Warsaw, Poland
| | - Krzysztof Kuczera
- Department
of Chemistry, The University of Kansas, Lawrence, Kansas 66045, United States
- Department of Molecular Biosciences, The
University of Kansas, Lawrence, Kansas 66045, United States
| | - Robert Szoszkiewicz
- Faculty of Chemistry,
Biological and Chemical Research Centre, University of Warsaw, Żwirki i Wigury 101, 02-089 Warsaw, Poland
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2
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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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3
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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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4
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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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5
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Rajput SS, Deopa SPS, Ajith VJ, Kamerkar SC, Patil S. Validity of point-mass model in off-resonance dynamic atomic force microscopy. NANOTECHNOLOGY 2021; 32:405702. [PMID: 34144547 DOI: 10.1088/1361-6528/ac0cb1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2021] [Accepted: 06/18/2021] [Indexed: 06/12/2023]
Abstract
The quantitative measurement of viscoelasticity of nano-scale entities is an important goal of nanotechnology research and there is considerable progress with advent of dynamic atomic force microscopy. The hydrodynamics of cantilever, the force sensor in AFM measurements, plays a pivotal role in quantitative estimates of nano-scale viscoelasticity. The point-mass (PM) model, wherein the AFM cantilever is approximated as a point-mass with mass-less spring is widely used in dynamic AFM analysis and its validity, particularly in liquid environments, is debated. It is suggested that the cantilever must be treated as a continuous rectangular beam to obtain accurate estimates of nano-scale viscoelasticity of materials it is probing. Here, we derived equations, which relate stiffness and damping coefficient of the material under investigation to measured parameters, by approximating cantilever as a point-mass and also considering the full geometric details. These equations are derived for both tip-excited as well as base-excited cantilevers. We have performed off-resonance dynamic atomic force spectroscopy on a single protein molecule to investigate the validity of widely used PM model. We performed measurements with AFMs equipped with different cantilever excitation methods as well as detection schemes to measure cantilever response. The data was analyzed using both, continuous beam model and the PM model. We found that both models yield same results when the experiments are performed in truly off-resonance regime with small amplitudes and the cantilever stiffness is much higher than the interaction stiffness. Our findings suggest that a simple PM approximation based model is adequate to describe the dynamics, provided care is taken while performing experiments so that the approximations used in these models are valid.
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Affiliation(s)
- Shatruhan Singh Rajput
- Department of Physics, Indian Institute of Science Education and Research Pune, Dr Homi Bhabha Road, Pashan, Pune 411008, India
| | - Surya Pratap S Deopa
- Department of Physics, Indian Institute of Science Education and Research Pune, Dr Homi Bhabha Road, Pashan, Pune 411008, India
| | - V J Ajith
- Department of Physics, Indian Institute of Science Education and Research Pune, Dr Homi Bhabha Road, Pashan, Pune 411008, India
| | - Sukrut C Kamerkar
- Department of Biology, Indian Institute of Science Education and Research Pune, Dr Homi Bhabha Road, Pashan, Pune 411008, India
| | - Shivprasad Patil
- Department of Physics, Indian Institute of Science Education and Research Pune, Dr Homi Bhabha Road, Pashan, Pune 411008, India
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6
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Rajput SS, Deopa SPS, Yadav J, Ahlawat V, Talele S, Patil S. The nano-scale viscoelasticity using atomic force microscopy in liquid environment. NANOTECHNOLOGY 2021; 32:085103. [PMID: 33120375 DOI: 10.1088/1361-6528/abc5f3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We measured viscoelasticity of two nanoscale systems, single protein molecules and molecular layers of water confined between solid walls. In order to quantify the viscoelastic response of these nanoscale systems in liquid environment, the measurements are performed using two types of atomic force microscopes (AFMs), which employ different detection schemes to measure the cantilever response. We used a deflection detection scheme, available in commercial AFMs, that measures cantilever bending and a fibre-interferometer based detection which measures cantilever displacement. The hydrodynamics of the cantilever is modelled using Euler-Bernoulli equation with appropriate boundary conditions which accommodate both detection schemes. In a direct contradiction with many reports in the literature, the dissipation coefficient of a single octomer of titin I278 is found to be immeasurably low. The upper bound on the dissipation coefficient is 5 × 10-7 kg s-1, which is much lower than the reported values. The entropic stiffness of single unfolded domains of protein measured using both methods is in the range of 10 mN m-1. We show that in a conventional deflection detection measurement, the phase of the bending signal can be a primary source of artefacts in the dissipation estimates. It is recognized that the measurement of cantilever displacement, which has negligibly small phase lag due to hydrodynamics of the cantilever at low excitation frequencies, is better suited for ensuring artefact-free measurement of viscoelasticity compared to the measurement of the cantilever bending. Further, it was possible to measure dissipation in molecular layers of water confined between the tip and the substrate using fibre interferometer based AFM with similar experimental parameters. It confirms that the dissipation coefficient of a single I278 is below the detection limit of AFM. The results shed light on the discrepancy observed in the measured diffusional dynamics of protein collapse measured using Force spectroscopic techniques and single-molecule optical techniques.
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Affiliation(s)
- Shatruhan Singh Rajput
- Department of Physics, Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
| | - Surya Pratap S Deopa
- Department of Physics, Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
| | - Jyoti Yadav
- Department of Chemistry, Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
| | - Vikhyaat Ahlawat
- Department of Physics, Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
| | - Saurabh Talele
- Department of Physics, Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
| | - Shivprasad Patil
- Department of Physics, Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
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7
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Lee YR, Kwon S, Sung BJ. The non-classical kinetics and the mutual information of polymer loop formation. J Chem Phys 2020; 152:184905. [PMID: 32414275 DOI: 10.1063/5.0005453] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
The loop formation of a single polymer chain has served as a model system for various biological and chemical processes. Theories based on the Smoluchowski equation proposed that the rate constant (kloop) of the loop formation would be inversely proportional to viscosity (η), i.e., kloop ∼ η-1. Experiments and simulations showed, however, that kloop showed the fractional viscosity dependence of kloop ∼ η-β with β < 1 either in glasses or in low-viscosity solutions. The origin of the fractional viscosity dependence remains elusive and has been attributed to phenomenological aspects. In this paper, we illustrate that the well-known failure of classical kinetics of the loop formation results from the breakdown of the local thermal equilibrium (LTE) approximation and that the mutual information can quantify the breakdown of the LTE successfully.
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Affiliation(s)
- Young-Ro Lee
- Department of Chemistry, Sogang University, Seoul 04107, South Korea
| | - Seulki Kwon
- Department of Chemistry, Sogang University, Seoul 04107, South Korea
| | - Bong June Sung
- Department of Chemistry, Sogang University, Seoul 04107, South Korea
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8
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Pierce A, Zheng Y, Wagner WL, Scheller HV, Mohnen D, Tsuda A, Ackermann M, Mentzer SJ. Pectin biopolymer mechanics and microstructure associated with polysaccharide phase transitions. J Biomed Mater Res A 2020; 108:246-253. [PMID: 31595695 PMCID: PMC7238754 DOI: 10.1002/jbm.a.36811] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2019] [Revised: 09/11/2019] [Accepted: 09/16/2019] [Indexed: 01/01/2023]
Abstract
Polysaccharide polymers like pectin can demonstrate striking and reversible changes in their physical properties depending upon relatively small changes in water content. Recent interest in using pectin polysaccharides as mesothelial sealants suggests that water content, rather than nonphysiologic changes in temperature, may be a practical approach to optimize the physical properties of the pectin biopolymers. Here, we used humidified environments to manipulate the water content of dispersed solution of pectins with a high degree of methyl esterification (high-methoxyl pectin; HMP). The gel phase transition was identified by a nonlinear increase in compression resistance at a water content of 50% (w/w). The gel phase was associated with a punched-out fracture pattern and scanning electron microscopy (SEM) images that revealed a cribiform (Swiss cheese-like) pectin microstructure. The glass phase transition was identified by a marked increase in resilience and stiffness. The glass phase was associated with a star-burst fracture pattern and SEM images that demonstrated a homogeneous pectin microstructure. In contrast, the burst strength of the pectin films was largely independent of water content over a range from 5 to 30% (w/w). These observations indicate the potential to use water content in the selective regulation of the physical properties of HMP biopolymers.
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Affiliation(s)
- Aidan Pierce
- Laboratory of Adaptive and Regenerative Biology, Brigham & Women’s Hospital, Harvard Medical School, Boston MA
| | - Yifan Zheng
- Laboratory of Adaptive and Regenerative Biology, Brigham & Women’s Hospital, Harvard Medical School, Boston MA
| | - Willi L. Wagner
- Laboratory of Adaptive and Regenerative Biology, Brigham & Women’s Hospital, Harvard Medical School, Boston MA
- Department of Diagnostic and Interventional Radiology, Translational Lung Research Center, University of Heidelberg, Heidelberg, Germany
| | - Henrik V. Scheller
- Joint BioEnergy Institute, Emeryville CA and the Environmental Genomics and Systems Biology Division, Lawrence Berkeley National Laboratory, Berkeley, CA
| | - Debra Mohnen
- Complex Carbohydrate Research Center and Department of Biochemistry and Molecular Biology, University of Georgia, Athens, GA
| | - Akira Tsuda
- Molecular and Integrative Physiological Sciences, Harvard School of Public Health, Boston, MA
| | - Maximilian Ackermann
- Institute of Functional and Clinical Anatomy, University Medical Center of the Johannes Gutenberg-University, Mainz, Germany
| | - Steven J. Mentzer
- Laboratory of Adaptive and Regenerative Biology, Brigham & Women’s Hospital, Harvard Medical School, Boston MA
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9
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Conformational entropy of a single peptide controlled under force governs protease recognition and catalysis. Proc Natl Acad Sci U S A 2018; 115:11525-11530. [PMID: 30341218 DOI: 10.1073/pnas.1803872115] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
Abstract
An immense repertoire of protein chemical modifications catalyzed by enzymes is available as proteomics data. Quantifying the impact of the conformational dynamics of the modified peptide remains challenging to understand the decisive kinetics and amino acid sequence specificity of these enzymatic reactions in vivo, because the target peptide must be disordered to accommodate the specific enzyme-binding site. Here, we were able to control the conformation of a single-molecule peptide chain by applying mechanical force to activate and monitor its specific cleavage by a model protease. We found that the conformational entropy impacts the reaction in two distinct ways. First, the flexibility and accessibility of the substrate peptide greatly increase upon mechanical unfolding. Second, the conformational sampling of the disordered peptide drives the specific recognition, revealing force-dependent reaction kinetics. These results support a mechanism of peptide recognition based on conformational selection from an ensemble that we were able to quantify with a torsional free-energy model. Our approach can be used to predict how entropy affects site-specific modifications of proteins and prompts conformational and mechanical selectivity.
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10
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Kailasham R, Chakrabarti R, Prakash JR. Rheological consequences of wet and dry friction in a dumbbell model with hydrodynamic interactions and internal viscosity. J Chem Phys 2018; 149:094903. [DOI: 10.1063/1.5040397] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Affiliation(s)
- R. Kailasham
- IITB-Monash Research Academy, Indian Institute of Technology Bombay, Mumbai, Maharashtra 400076, India
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai, Maharashtra 400076, India
- 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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11
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Echeverria I, Makarov DE, Papoian GA. Concerted Dihedral Rotations Give Rise to Internal Friction in Unfolded Proteins. J Am Chem Soc 2014; 136:8708-13. [DOI: 10.1021/ja503069k] [Citation(s) in RCA: 80] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ignacia Echeverria
- Department
of Chemistry and Biochemistry and Institute for Physical Science and
Technology, University of Maryland, College Park, Maryland 20742, United States
| | - Dmitrii E. Makarov
- Department
of Chemistry and Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, United States
| | - Garegin A. Papoian
- Department
of Chemistry and Biochemistry and Institute for Physical Science and
Technology, University of Maryland, College Park, Maryland 20742, United States
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12
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Cheng RR, Hawk AT, Makarov DE. Exploring the role of internal friction in the dynamics of unfolded proteins using simple polymer models. J Chem Phys 2013; 138:074112. [DOI: 10.1063/1.4792206] [Citation(s) in RCA: 51] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Miserez A, Guerette PA. Phase transition-induced elasticity of α-helical bioelastomeric fibres and networks. Chem Soc Rev 2013; 42:1973-95. [DOI: 10.1039/c2cs35294j] [Citation(s) in RCA: 46] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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14
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Mochrie SGJ, Mack AH, Schlingman DJ, Collins R, Kamenetska M, Regan L. Unwinding and rewinding the nucleosome inner turn: force dependence of the kinetic rate constants. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012710. [PMID: 23410362 PMCID: PMC3902847 DOI: 10.1103/physreve.87.012710] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2012] [Revised: 10/11/2012] [Indexed: 06/01/2023]
Abstract
A simple model for the force-dependent unwinding and rewinding rates of the nucleosome inner turn is constructed and quantitatively compared to the results of recent measurements [A. H. Mack et al., J. Mol. Biol. 423, 687 (2012)]. First, a coarse-grained model for the histone-DNA free-energy landscape that incorporates both an elastic free-energy barrier and specific histone-DNA bonds is developed. Next, a theoretical expression for the rate of transitions across a piecewise linear free-energy landscape with multiple minima and maxima is presented. Then, the model free-energy landscape, approximated as a piecewise linear function, and the theoretical expression for the transition rates are combined to construct a model for the force-dependent unwinding and rewinding rates of the nucleosome inner turn. Least-mean-squares fitting of the model rates to the rates observed in recent experiments rates demonstrates that this model is able to well describe the force-dependent unwinding and rewinding rates of the nucleosome inner turn, observed in the recent experiments, except at the highest forces studied, where an additional ad hoc term is required to describe the data, which may be interpreted as an indication of an alternate high-force nucleosome disassembly pathway, that bypasses simple unwinding. The good agreement between the measurements and the model at lower forces demonstrates that both specific histone-DNA contacts and an elastic free-energy barrier play essential roles for nucleosome winding and unwinding, and quantifies their relative contributions.
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Affiliation(s)
- S G J Mochrie
- Integrated Graduate Program in Physical and Engineering Biology, Yale University, New Haven, Connecticut 06520, USA.
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15
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Affiliation(s)
- Charles E. Sing
- Department
of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139,
United States
| | - Alfredo Alexander-Katz
- Department
of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139,
United States
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16
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Schulz JCF, Schmidt L, Best RB, Dzubiella J, Netz RR. Peptide chain dynamics in light and heavy water: zooming in on internal friction. J Am Chem Soc 2012; 134:6273-9. [PMID: 22414068 DOI: 10.1021/ja211494h] [Citation(s) in RCA: 76] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Frictional effects due to the chain itself, rather than the solvent, may have a significant effect on protein dynamics. Experimentally, such "internal friction" has been investigated by studying folding or binding kinetics at varying solvent viscosity; however, the molecular origin of these effects is hard to pinpoint. We consider the kinetics of disordered glycine-serine and α-helix forming alanine peptides and a coarse-grained protein folding model in explicit-solvent molecular dynamics simulations. By varying the solvent mass over more than two orders of magnitude, we alter only the solvent viscosity and not the folding free energy. Folding dynamics at the near-vanishing solvent viscosities accessible by this approach suggests that solvent and internal friction effects are intrinsically entangled. This finding is rationalized by calculation of the polymer end-to-end distance dynamics from a Rouse model that includes internal friction. An analysis of the friction profile along different reaction coordinates, extracted from the simulation data, demonstrates that internal as well as solvent friction varies substantially along the folding pathways and furthermore suggests a connection between friction and the formation of hydrogen bonds upon folding.
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17
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Borgogna M, Bellich B, Cesàro A. Marine polysaccharides in microencapsulation and application to aquaculture: "from sea to sea". Mar Drugs 2011; 9:2572-2604. [PMID: 22363241 PMCID: PMC3280570 DOI: 10.3390/md9122572] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2011] [Revised: 11/18/2011] [Accepted: 11/22/2011] [Indexed: 12/15/2022] Open
Abstract
This review's main objective is to discuss some physico-chemical features of polysaccharides as intrinsic determinants for the supramolecular structures that can efficiently provide encapsulation of drugs and other biological entities. Thus, the general characteristics of some basic polysaccharides are outlined in terms of their conformational, dynamic and thermodynamic properties. The analysis of some polysaccharide gelling properties is also provided, including the peculiarity of the charged polysaccharides. Then, the way the basic physical chemistry of polymer self-assembly is made in practice through the laboratory methods is highlighted. A description of the several literature procedures used to influence molecular interactions into the macroscopic goal of the encapsulation is given with an attempt at classification. Finally, a practical case study of specific interest, the use of marine polysaccharide matrices for encapsulation of vaccines in aquaculture, is reported.
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Affiliation(s)
| | | | - Attilio Cesàro
- Department of Life Sciences, University of Trieste, Via L. Giorgieri, 1-I-34127 Trieste, Italy; (M.B.); (B.B.)
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18
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Einert TR, Sing CE, Alexander-Katz A, Netz RR. Conformational dynamics and internal friction in homopolymer globules: equilibrium vs. non-equilibrium simulations. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2011; 34:1-16. [PMID: 22167584 DOI: 10.1140/epje/i2011-11130-8] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2011] [Accepted: 11/03/2011] [Indexed: 05/31/2023]
Abstract
We study the conformational dynamics within homopolymer globules by solvent-implicit Brownian dynamics simulations. A strong dependence of the internal chain dynamics on the Lennard-Jones cohesion strength ε and the globule size N (G) is observed. We find two distinct dynamical regimes: a liquid-like regime (for ε < ε(s) with fast internal dynamics and a solid-like regime (for ε > ε(s) with slow internal dynamics. The cohesion strength ε(s) of this freezing transition depends on N (G) . Equilibrium simulations, where we investigate the diffusional chain dynamics within the globule, are compared with non-equilibrium simulations, where we unfold the globule by pulling the chain ends with prescribed velocity (encompassing low enough velocities so that the linear-response, viscous regime is reached). From both simulation protocols we derive the internal viscosity within the globule. In the liquid-like regime the internal friction increases continuously with ε and scales extensive in N (G) . This suggests an internal friction scenario where the entire chain (or an extensive fraction thereof) takes part in conformational reorganization of the globular structure.
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Affiliation(s)
- T R Einert
- Physik Department, Technische Universität München, James-Franck-Straße, Garching, Germany.
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19
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Hinczewski M, Netz RR. Anisotropic Hydrodynamic Mean-Field Theory for Semiflexible Polymers under Tension. Macromolecules 2011. [DOI: 10.1021/ma2009645] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Affiliation(s)
- Michael Hinczewski
- Department of Physics, Technical University of Munich, 85748 Garching, Germany
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
| | - Roland R. Netz
- Department of Physics, Technical University of Munich, 85748 Garching, Germany
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
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20
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Abstract
Time-resolved single-molecule biophysical experiments yield data that contain a wealth of dynamic information, in addition to the equilibrium distributions derived from histograms of the time series. In typical force spectroscopic setups the molecule is connected via linkers to a readout device, forming a mechanically coupled dynamic network. Deconvolution of equilibrium distributions, filtering out the influence of the linkers, is a straightforward and common practice. We have developed an analogous dynamic deconvolution theory for the more challenging task of extracting kinetic properties of individual components in networks of arbitrary complexity and topology. Our method determines the intrinsic linear response functions of a given object in the network, describing the power spectrum of conformational fluctuations. The practicality of our approach is demonstrated for the particular case of a protein linked via DNA handles to two optically trapped beads at constant stretching force, which we mimic through Brownian dynamics simulations. Each well in the protein free energy landscape (corresponding to folded, unfolded, or possibly intermediate states) will have its own characteristic equilibrium fluctuations. The associated linear response function is rich in physical content, because it depends both on the shape of the well and its diffusivity-a measure of the internal friction arising from such processes as the transient breaking and reformation of bonds in the protein structure. Starting from the autocorrelation functions of the equilibrium bead fluctuations measured in this force clamp setup, we show how an experimentalist can accurately extract the state-dependent protein diffusivity using a straightforward two-step procedure.
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21
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Taniguchi Y, Khatri BS, Brockwell DJ, Paci E, Kawakami M. Dynamics of the coiled-coil unfolding transition of myosin rod probed by dissipation force spectrum. Biophys J 2010; 99:257-62. [PMID: 20655854 DOI: 10.1016/j.bpj.2010.04.007] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2010] [Revised: 03/23/2010] [Accepted: 04/01/2010] [Indexed: 01/27/2023] Open
Abstract
The motor protein myosin II plays a crucial role in muscle contraction. The mechanical properties of its coiled-coil region, the myosin rod, are important for effective force transduction during muscle function. Previous studies have investigated the static elastic response of the myosin rod. However, analogous to the study of macroscopic complex fluids, how myosin will respond to physiological time-dependent loads can only be understood from its viscoelastic response. Here, we apply atomic force microscopy using a magnetically driven oscillating cantilever to measure the dissipative properties of single myosin rods that provide unique dynamical information about the coiled-coil structure as a function of force. We find that the friction constant of the single myosin rod has a highly nontrivial variation with force; in particular, the single-molecule friction constant is reduced dramatically and increases again as it passes through the coiled-uncoiled transition. This is a direct indication of a large free-energy barrier to uncoiling, which may be related to a fine-tuned dynamic mechanosignaling response to large and unexpected physiological loads. Further, from the critical force at which the minimum in friction occurs we determine the asymmetry of the bistable landscape that controls uncoiling of the coiled coil. This work highlights the sensitivity of the dissipative signal in force unfolding to dynamic molecular structure that is hidden to the elastic signal.
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Affiliation(s)
- Yukinori Taniguchi
- School of Materials Science, Japan Advanced Institute of Science and Technology, Ishikawa, Japan
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22
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Hiraiwa T, Ohta T. Linear viscoelasticity of a single semiflexible polymer with internal friction. J Chem Phys 2010; 133:044907. [PMID: 20687686 DOI: 10.1063/1.3463427] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The linear viscoelastic behaviors of single semiflexible chains with internal friction are studied based on the wormlike-chain model. It is shown that the frequency dependence of the complex compliance in the high frequency limit is the same as that of the Voigt model. This asymptotic behavior appears also for the Rouse model with internal friction. We derive the characteristic times for both the high frequency limit and the low frequency limit and compare the results with those obtained by Khatri et al.
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Affiliation(s)
- Tetsuya Hiraiwa
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
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23
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Khatri B, Yew ZT, Krivov S, McLeish T, Paci E. Fluctuation power spectra reveal dynamical heterogeneity of peptides. J Chem Phys 2010; 133:015101. [DOI: 10.1063/1.3456552] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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24
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Frases S, Pontes B, Nimrichter L, Rodrigues ML, Viana NB, Casadevall A. The elastic properties of the Cryptococcus neoformans capsule. Biophys J 2009; 97:937-45. [PMID: 19686640 DOI: 10.1016/j.bpj.2009.04.043] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2009] [Revised: 04/07/2009] [Accepted: 04/15/2009] [Indexed: 11/29/2022] Open
Abstract
Microbial capsules are important for virulence, but their architecture and physical properties are poorly understood. The human pathogenic fungus Cryptococcus neoformans has a large polysaccharide capsule that is necessary for virulence and is the target of protective antibody responses. To study the C. neoformans capsule we developed what we believe is a new approach whereby we probed the capsular elastic properties by applying forces using polystyrene beads manipulated with optical tweezers. This method allowed us to determine the Young's modulus for the capsule in various conditions that affect capsule growth. The results indicate that the Young's modulus of the capsule decreases with its size and increases with the Ca(2+) concentration in solution. Also, capsular polysaccharide manifests an unexpected affinity for polystyrene beads, a property that may function in attachment to host cells and environmental structures. Bead probing with optical tweezers provides a new, nondestructive method that may have wide applicability for studying the effects of growth conditions, immune components, and drugs on capsular properties.
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Affiliation(s)
- Susana Frases
- Department of Microbiology and Immunology, Albert Einstein College of Medicine, The Bronx, New York, USA.
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25
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Affiliation(s)
- Tetsuya Hiraiwa
- Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
| | - Takao Ohta
- Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
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26
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Alexander-Katz A, Wada H, Netz RR. Internal friction and nonequilibrium unfolding of polymeric globules. PHYSICAL REVIEW LETTERS 2009; 103:028102. [PMID: 19659248 DOI: 10.1103/physrevlett.103.028102] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2007] [Indexed: 05/28/2023]
Abstract
The stretching response of a single collapsed homopolymer is studied using Brownian dynamic simulations. The irreversibly dissipated work is found to be dominated by internal friction effects below the collapse temperature, and the internal viscosity grows exponentially with the effective cohesive strength between monomers. These results explain friction effects of globular DNA and are relevant for dissipation at intermediate stages of protein folding.
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Affiliation(s)
- Alfredo Alexander-Katz
- Department of Materials Science and Engineering, MIT, Cambridge, Massachusetts 02139, USA
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27
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Khatri BS, Byrne K, Kawakami M, Brockwell DJ, Smith DA, Radford SE, McLeish TCB. Internal friction of single polypeptide chains at high stretch. Faraday Discuss 2009; 139:35-51; discussion 105-28, 419-20. [PMID: 19048989 DOI: 10.1039/b716418c] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Experiments that measure the viscoelasticity of single molecules from the Brownian fluctuations of an atomic force microscope (AFM) have provided a new window onto their internal dynamics in an underlying conformational landscape. Here we develop and apply these methods to examine the internal friction of unfolded polypeptide chains at high stretch. The results reveal a power law dependence of internal friction with tension (exponent 1.3 +/- 0.5) and a relaxation time approximately independent of force. To explain these results we develop a frictional worm-like chain (FWLC) model based on the Rayleigh dissipation function of a stiff chain with dynamical resistance to local bending. We analyse the dissipation rate integrated over the chain length by its Fourier components to calculate an effective tension-dependent friction constant for the end-to-end vector of the chain. The result is an internal friction that increases as a power law with tension with an exponent 3/2, consistent with experiment. Extracting the intrinsic bending friction constant of the chain it is found to be approximately 7 orders of magnitude greater than expected from solvent friction alone; a possible explanation we offer is that the underlying energy landscape for bending amino acids and/or peptide bond is rough, consistent with recent results on both proteins and polysaccharides.
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Affiliation(s)
- Bhavin S Khatri
- Department of Physics & Astronomy, University of Leeds, Leeds, UK.
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28
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The effect of temperature on mechanical resistance of the native and intermediate states of I27. Biophys J 2008; 95:5296-305. [PMID: 18775959 DOI: 10.1529/biophysj.108.141275] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We investigated the effect of temperature on the mechanical unfolding of I27 from human cardiac titin, employing a custom-built temperature control device for single-molecule atomic force microscopy measurement. A sawtooth pattern was observed in the force curves where each force peak reports on the unfolding of an I27 domain. In early unfolding events, we observed a "hump-like" deviation due to the detachment of beta-strand A from each I27 domain. The force at which the humps appear was approximately 130 pN and showed no temperature dependence, at least in the temperature range of 2 degrees C-30 degrees C. The hump structure was successfully analyzed with a two-state worm-like chain model, and the Gibbs free energy difference of the detachment reaction was estimated to be 11.6 +/- 0.58 kcal/mol and found to be temperature independent. By contrast, upon lowering the temperature, the mean unfolding force from the partly unfolded intermediate state was found to markedly increase and the unfolding force distribution to broaden significantly, suggesting that the distance (x(u)) between the folded and transition states in the energy landscape along the pulling direction is decreased. These results suggest that the local structure of beta-strand A are stabilized by topologically simple local hydrogen-bond network and that the temperature does not affect the detachment reaction thermodynamically and kinetically, whereas the interaction between the beta-strands A' and G, which is a critical region for its mechanical stability, is strongly dependent on the temperature.
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29
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Staple DB, Hanke F, Kreuzer HJ. Dynamics of single-molecule force-ramp experiments: The role of fluctuations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:021801. [PMID: 18352043 DOI: 10.1103/physreve.77.021801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2007] [Revised: 12/06/2007] [Indexed: 05/26/2023]
Abstract
In the force-ramp mode of the atomic force microscope, the force with which a macromolecule is stretched is increased linearly in time by properly controlling the motion of the cantilever through a feedback loop. Using a master equation approach for the coupled cantilever-macromolecule system, we mimic such a feedback loop, to study nonequilibrium effects in the measurements of force-extension curves and fluctuations. In particular, it is shown that the fluctuations are the same for force-ramp experiments and for the more commonly used constant velocity experiments. Thus the exact same statistics suffice for the explanation of either experiment. Specific results are presented for the stretching of Dextran.
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Affiliation(s)
- Douglas B Staple
- Department of Physics and Atmospheric Science, Dalhousie University, Halifax, NS, Canada.
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30
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Haverkamp RG, Marshall AT, Williams MAK. Entropic and Enthalpic Contributions to the Chair−Boat Conformational Transformation in Dextran under Single Molecule Stretching. J Phys Chem B 2007; 111:13653-7. [DOI: 10.1021/jp076052t] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Richard G. Haverkamp
- Institute of Technology and Engineering, Massey University, Private Bag 11222, Palmerston North, New Zealand
| | - Aaron T. Marshall
- Institute of Technology and Engineering, Massey University, Private Bag 11222, Palmerston North, New Zealand
| | - Martin A. K. Williams
- Institute of Fundamental Sciences, Massey University, Private Bag 11222, Palmerston North, New Zealand
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31
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Khatri BS, McLeish TCB. Rouse Model with Internal Friction: A Coarse Grained Framework for Single Biopolymer Dynamics. Macromolecules 2007. [DOI: 10.1021/ma071175x] [Citation(s) in RCA: 69] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Bhavin S. Khatri
- Polymer and Complex Fluids Group, School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, U.K
| | - Tom C. B. McLeish
- Polymer and Complex Fluids Group, School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, U.K
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32
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Williams MAK, Marshall AT, Anjukandi P, Haverkamp RG. Investigation of the effects of fine structure on the nanomechanical properties of pectin. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:021927. [PMID: 17930085 DOI: 10.1103/physreve.76.021927] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2007] [Indexed: 05/25/2023]
Abstract
Pectin is an important structural polysaccharide found in the cell walls of all land plants. While in detail its composition and its organization in muro are complex, it is predominantly a copolymer of galacturonic acid and its methylesterified counterpart. Previous single-molecule stretching studies carried out on a sparsely methylesterified pectin sample indicated the importance of force-induced conformational transitions of the pyranose ring during extension, and the possible biological role of such transitions was discussed. More heavily methylesterified samples are better biomimetic models of the polymeric components as found in the plant cell wall, in particular being less restricted by the shackles of the significant intermolecular interactions expected to constrain the behavior of bare galacturonic acid sequences. Density functional theory calculations revealed that upon extending galacturonic acid monomers, whether methylesterified or not, the initial ((4)C1) chair structure is transformed to a ((3)S5) skew boat and that subsequently upon further elongation, via an intermediate inverted skew boat ((5)S3), the inverted chair ((1)C4) is reached. Experimentally, the force-extension curve of highly methylesterified pectin was found to be solvent dependent in the same manner as the un-esterified sample, indicating that minimal changes in the strength of interring hydrogen bonding result from such a substitution, and finally, as only subtle changes in the force-extension behavior of pectin resulted from changes in the degree of methylesterification, previous speculations about the role of force-induced transformations in vivo are supported.
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Affiliation(s)
- M A K Williams
- Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand
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