1
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Gironella-Torrent M, Bergamaschi G, Sorkin R, Wuite GJL, Ritort F. Viscoelastic phenotyping of red blood cells. Biophys J 2024; 123:770-781. [PMID: 38268191 PMCID: PMC10995428 DOI: 10.1016/j.bpj.2024.01.019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Revised: 12/21/2023] [Accepted: 01/18/2024] [Indexed: 01/26/2024] Open
Abstract
Red blood cells (RBCs) are the simplest cell types with complex dynamical and viscoelastic phenomenology. While the mechanical rigidity and the flickering noise of RBCs have been extensively investigated, an accurate determination of the constitutive equations of the relaxational kinetics is lacking. Here we measure the force relaxation of RBCs under different types of tensional and compressive extension-jump protocols by attaching an optically trapped bead to the RBC membrane. Relaxational kinetics follows linear response from 60 pN (tensional) to -20 pN (compressive) applied forces, exhibiting a triple exponential function with three well-separated timescales over four decades (0.01-100 s). While the fast timescale (τF∼0.02(1)s) corresponds to the relaxation of the membrane, the intermediate and slow timescales (τI=4(1)s; τS=70(8)s) likely arise from the cortex dynamics and the cytosol viscosity. Relaxation is highly heterogeneous across the RBC population, yet the three relaxation times are correlated, showing dynamical scaling. Finally, we find that glucose depletion and laser illumination of RBCs lead to faster triple exponential kinetics and RBC rigidification. Viscoelastic phenotyping is a promising dynamical biomarker applicable to other cell types and active systems.
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Affiliation(s)
- Marta Gironella-Torrent
- Small Biosystems Lab, Condensed Matter Physics Department, University of Barcelona, Barcelona, Spain; Department of Medical Biochemistry and Cell Biology, Institute of Biomedicine, The Sahlgrenska Academy, University of Gothenburg, Gothenburg, Sweden.
| | - Giulia Bergamaschi
- Department of Physics and Astronomy and LaserLab, Vrije Universiteit Amsterdam, Amsterdam, the Netherlands
| | - Raya Sorkin
- Raymond and Beverly Sackler Faculty of Exact Sciences, School of Chemistry, Tel Aviv University, Tel Aviv, Israel
| | - Gijs J L Wuite
- Department of Physics and Astronomy and LaserLab, Vrije Universiteit Amsterdam, Amsterdam, the Netherlands
| | - Felix Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, University of Barcelona, Barcelona, Spain; Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, Barcelona, Spain
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2
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Di Terlizzi I, Gironella M, Herraez-Aguilar D, Betz T, Monroy F, Baiesi M, Ritort F. Variance sum rule for entropy production. Science 2024; 383:971-976. [PMID: 38422150 DOI: 10.1126/science.adh1823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 01/09/2024] [Indexed: 03/02/2024]
Abstract
Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule (VSR) for displacement and force variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. We then apply the VSR to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements. The VSR paves the way to derive σ using force spectroscopy and time-resolved imaging in living and active matter.
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Affiliation(s)
- I Di Terlizzi
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - M Gironella
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
- Department of Medical Biochemistry and Cell Biology, Institute of Biomedicine, The Sahlgrenska Academy, University of Gothenburg, 40530 Gothenburg, Sweden
| | - D Herraez-Aguilar
- Facultad de Ciencias Experimentales, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1,800, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - T Betz
- Third Institute of Physics, Georg August Universität Göttingen, Göttingen, Germany
- Cluster of Excellence "Multiscale Bioimaging: from Molecular Machines to Networks of Excitable Cells" (MBExC), University of Göttingen, Göttingen, Germany
| | - F Monroy
- Departamento de Química Física, Facultad de Química, Universidad Complutense, 28040 Madrid, Spain
- Translational Biophysics, Instituto de Investigación Sanitaria Hospital Doce de Octubre (IMAS12), Av. Andalucía, 28041 Madrid, Spain
| | - M Baiesi
- Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - F Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
- Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028 Barcelona, Spain
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3
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Ter Burg C, Rissone P, Rico-Pasto M, Ritort F, Wiese KJ. Experimental Test of Sinai's Model in DNA Unzipping. Phys Rev Lett 2023; 130:208401. [PMID: 37267556 DOI: 10.1103/physrevlett.130.208401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Accepted: 04/04/2023] [Indexed: 06/04/2023]
Abstract
The experimental measurement of correlation functions and critical exponents in disordered systems is key to testing renormalization group (RG) predictions. We mechanically unzip single DNA hairpins with optical tweezers, an experimental realization of the diffusive motion of a particle in a one-dimensional random force field, known as the Sinai model. We measure the unzipping forces F_{w} as a function of the trap position w in equilibrium and calculate the force-force correlator Δ_{m}(w), its amplitude, and correlation length, finding agreement with theoretical predictions. We study the universal scaling properties since the effective trap stiffness m^{2} decreases upon unzipping. Fluctuations of the position of the base pair at the unzipping junction u scales as u∼m^{-ζ}, with a roughness exponent ζ=1.34±0.06, in agreement with the analytical prediction ζ=4/3. Our study provides a single-molecule test of the functional RG approach for disordered elastic systems in equilibrium.
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Affiliation(s)
- Cathelijne Ter Burg
- Laboratoire de Physique de l'Ećole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 24 rue Lhomond, 75005 Paris, France
| | - Paolo Rissone
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, Carrer de Martí i Franquès 1, 08028 Barcelona, Spain
| | - Marc Rico-Pasto
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, Carrer de Martí i Franquès 1, 08028 Barcelona, Spain
| | - Felix Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, Carrer de Martí i Franquès 1, 08028 Barcelona, Spain
- Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028 Barcelona, Spain
| | - Kay Jörg Wiese
- Laboratoire de Physique de l'Ećole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 24 rue Lhomond, 75005 Paris, France
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4
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Schmitt RK, Potts PP, Linke H, Johansson J, Samuelsson P, Rico-Pasto M, Ritort F. Information-to-work conversion in single-molecule experiments: From discrete to continuous feedback. Phys Rev E 2023; 107:L052104. [PMID: 37329008 DOI: 10.1103/physreve.107.l052104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2021] [Accepted: 04/10/2023] [Indexed: 06/18/2023]
Abstract
We theoretically investigate the extractable work in single molecule unfolding-folding experiments with applied feedback. Using a simple two-state model, we obtain a description of the full work distribution from discrete to continuous feedback. The effect of the feedback is captured by a detailed fluctuation theorem, accounting for the information aquired. We find analytical expressions for the average work extraction as well as an experimentally measurable bound thereof, which becomes tight in the continuous feedback limit. We further determine the parameters for maximal power or rate of work extraction. Although our two-state model only depends on a single effective transition rate, we find qualitative agreement with Monte Carlo simulations of DNA hairpin unfolding-folding dynamics.
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Affiliation(s)
- Regina K Schmitt
- Department of Physics and NanoLund, Lund University, Box 188, SE-221 00 Lund, Sweden
| | - Patrick P Potts
- Department of Physics and NanoLund, Lund University, Box 188, SE-221 00 Lund, Sweden
| | - Heiner Linke
- Department of Physics and NanoLund, Lund University, Box 188, SE-221 00 Lund, Sweden
| | - Jonas Johansson
- Department of Physics and NanoLund, Lund University, Box 188, SE-221 00 Lund, Sweden
| | - Peter Samuelsson
- Department of Physics and NanoLund, Lund University, Box 188, SE-221 00 Lund, Sweden
| | - Marc Rico-Pasto
- Department of Condensed Matter Physics, Small Biosystems Laboratory, Universitat de Barcelona, C/Marti i Franques 1, 08028 Barcelona, Spain
| | - Felix Ritort
- Department of Condensed Matter Physics, Small Biosystems Laboratory, Universitat de Barcelona, C/Marti i Franques 1, 08028 Barcelona, Spain
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5
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Garrahan JP, Ritort F. Generalized continuous Maxwell demons. Phys Rev E 2023; 107:034101. [PMID: 37072943 DOI: 10.1103/physreve.107.034101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2021] [Accepted: 02/16/2023] [Indexed: 04/20/2023]
Abstract
We introduce a family of generalized continuous Maxwell demons (GCMDs) operating on idealized single-bit equilibrium devices that combine the single-measurement Szilard and the repeated measurements of the continuous Maxwell demon protocols. We derive the cycle distributions for extracted work, information content, and time and compute the power and information-to-work efficiency fluctuations for the different models. We show that the efficiency at maximum power is maximal for an opportunistic protocol of continuous type in the dynamical regime dominated by rare events. We also extend the analysis to finite-time work extracting protocols by mapping them to a three-state GCMD. We show that dynamical finite-time correlations in this model increase the information-to-work conversion efficiency, underlining the role of temporal correlations in optimizing information-to-energy conversion. The effect of finite-time work extraction and demon memory resetting is also analyzed. We conclude that GCMD models are thermodynamically more efficient than the single-measurement Szilard and preferred for describing biological processes in an information-redundant world.
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Affiliation(s)
- Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, England, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, England, United Kingdom
| | - Felix Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/Martí i Franquès 1, E-08028 Barcelona, Spain
- Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, E-08028 Barcelona, Spain
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6
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Abstract
Maxwell's demon is a famous thought experiment and a paradigm of the thermodynamics of information. It is related to Szilard's engine, a two-state information-to-work conversion device in which the demon performs single measurements and extracts work depending on the state measurement outcome. A variant of these models, the continuous Maxwell demon (CMD), was recently introduced by Ribezzi-Crivellari and Ritort where work was extracted after multiple repeated measurements every time that τ is in a two-state system. The CMD was able to extract unbounded amounts of work at the cost of an unbounded amount of information storage. In this work, we built a generalization of the CMD to the N-state case. We obtained generalized analytical expressions for the average work extracted and the information content. We show that the second law inequality for information-to-work conversion is fulfilled. We illustrate the results for N-states with uniform transition rates and for the N = 3 case.
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Affiliation(s)
- Paul Raux
- Université Paris Cité, CNRS, UMR 8236-LIED, 75013 Paris, France
- Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
| | - Felix Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, University of Barcelona, 08028 Barcelona, Spain
- Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028 Barcelona, Spain
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7
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Abstract
Knowledge of the elastic properties, e.g., the persistence length or interphosphate distance, of single-stranded (ss) and double-stranded (ds) DNA under different experimental conditions is critical to characterizing molecular reactions studied with single-molecule techniques. While previous experiments have addressed the dependence of the elastic parameters upon varying ionic strength and contour length, temperature-dependent effects are less studied. Here, we examine the temperature-dependent elasticity of ssDNA and dsDNA in the range 5°C-50°C using a temperature-jump optical trap. We find a temperature softening for dsDNA and a temperature stiffening for ssDNA. Our results highlight the need for a general theory explaining the phenomenology observed.
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Affiliation(s)
- Marc Rico-Pasto
- Small Biosystems Lab, Condensed Matter Physics Department, University of Barcelona, Barcelona, Spain
| | - Felix Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, University of Barcelona, Barcelona, Spain
- Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, Barcelona, Spain
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8
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Martinez-Monge A, Pastor I, Bustamante C, Manosas M, Ritort F. Measurement of the specific and non-specific binding energies of Mg 2+ to RNA. Biophys J 2022; 121:3010-3022. [PMID: 35864738 PMCID: PMC9463699 DOI: 10.1016/j.bpj.2022.07.020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022] Open
Abstract
Determining the non-specific and specific electrostatic contributions of magnesium binding to RNA is a challenging problem. We introduce a single-molecule method based on measuring the folding energy of a native RNA in magnesium and at its equivalent sodium concentration. The latter is defined so that the folding energy in sodium equals the non-specific electrostatic contribution in magnesium. The sodium equivalent can be estimated according to the empirical 100/1 rule (1 M NaCl is equivalent to 10 mM MgCl2), which is a good approximation for most RNAs. The method is applied to an RNA three-way junction (3WJ) that contains specific Mg2+ binding sites and misfolds into a double hairpin structure without binding sites. We mechanically pull the RNA with optical tweezers and use fluctuation theorems to determine the folding energies of the native and misfolded structures in magnesium (10 mM MgCl2) and at the equivalent sodium condition (1 M NaCl). While the free energies of the misfolded structure are equal in magnesium and sodium, they are not for the native structure, the difference being due to the specific binding energy of magnesium to the 3WJ, which equals ΔG≃ 10 kcal/mol. Besides stabilizing the 3WJ, Mg2+ also kinetically rescues it from the misfolded structure over timescales of tens of seconds in a force-dependent manner. The method should generally be applicable to determine the specific binding energies of divalent cations to other tertiary RNAs.
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Affiliation(s)
- A Martinez-Monge
- Small Biosystems Lab, Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Carrer de Martí i Franquès, 1, 08028 Barcelona, Spain
| | - Isabel Pastor
- Small Biosystems Lab, Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Carrer de Martí i Franquès, 1, 08028 Barcelona, Spain; Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028 Barcelona, Spain
| | - Carlos Bustamante
- Departments of Chemistry, Physics and Molecular and Cell Biology, University of California Berkeley, Berkeley, California; Howard Hughes Medical Institute University of California Berkeley, Berkeley, California; Kavli Energy Nanosciences Institute, University of California Berkeley, Berkeley, California
| | - Maria Manosas
- Small Biosystems Lab, Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Carrer de Martí i Franquès, 1, 08028 Barcelona, Spain; Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028 Barcelona, Spain.
| | - Felix Ritort
- Small Biosystems Lab, Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Carrer de Martí i Franquès, 1, 08028 Barcelona, Spain; Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028 Barcelona, Spain.
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9
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Rissone P, Ritort F. Nucleic Acid Thermodynamics Derived from Mechanical Unzipping Experiments. Life (Basel) 2022; 12:1089. [PMID: 35888177 PMCID: PMC9320087 DOI: 10.3390/life12071089] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2022] [Revised: 07/18/2022] [Accepted: 07/19/2022] [Indexed: 12/02/2022] Open
Abstract
Force-spectroscopy techniques have led to significant progress in studying the physicochemical properties of biomolecules that are not accessible in bulk assays. The application of piconewton forces with laser optical tweezers to single nucleic acids has permitted the characterization of molecular thermodynamics and kinetics with unprecedented accuracy. Some examples are the hybridization reaction between complementary strands in DNA and the folding of secondary, tertiary, and other heterogeneous structures, such as intermediate and misfolded states in RNA. Here we review the results obtained in our lab on deriving the nearest-neighbor free energy parameters in DNA and RNA duplexes from mechanical unzipping experiments. Remarkable nonequilibrium effects are also observed, such as the large irreversibility of RNA unzipping and the formation of non-specific secondary structures in single-stranded DNA. These features originate from forming stem-loop structures along the single strands of the nucleic acid. The recently introduced barrier energy landscape model quantifies kinetic trapping effects due to stem-loops being applicable to both RNA and DNA. The barrier energy landscape model contains the essential features to explain the many behaviors observed in heterogeneous nucleic-acid folding.
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Affiliation(s)
| | - Felix Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, University of Barcelona, Carrer de Martí i Franqués 1, 08028 Barcelona, Spain;
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10
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Aspas-Caceres J, Rico-Pasto M, Pastor I, Ritort F. Folding Free Energy Determination of an RNA Three-Way Junction Using Fluctuation Theorems. Entropy 2022; 24:e24070895. [PMID: 35885118 PMCID: PMC9320289 DOI: 10.3390/e24070895] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/16/2022] [Revised: 06/23/2022] [Accepted: 06/24/2022] [Indexed: 11/16/2022]
Abstract
Nonequilibrium work relations and fluctuation theorems permit us to extract equilibrium information from nonequilibrium measurements. They find application in single-molecule pulling experiments where molecular free energies can be determined from irreversible work measurements by using unidirectional (e.g., Jarzynski’s equality) and bidirectional (e.g., Crooks fluctuation theorem and Bennet’s acceptance ratio (BAR)) methods. However, irreversibility and the finite number of pulls limit their applicability: the higher the dissipation, the larger the number of pulls necessary to estimate ΔG within a few kBT. Here, we revisit pulling experiments on an RNA three-way junction (3WJ) that exhibits significant dissipation and work-distribution long tails upon mechanical unfolding. While bidirectional methods are more predictive, unidirectional methods are strongly biased. We also consider a cyclic protocol that combines the forward and reverse work values to increase the statistics of the measurements. For a fixed total experimental time, faster pulling rates permit us to efficiently sample rare events and reduce the bias, compensating for the increased dissipation. This analysis provides a more stringent test of the fluctuation theorem in the large irreversibility regime.
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Affiliation(s)
- Jaime Aspas-Caceres
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, Carrer de Martí i Franquès 1, 08028 Barcelona, Spain; (J.A.-C.); (M.R.-P.); (I.P.)
| | - Marc Rico-Pasto
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, Carrer de Martí i Franquès 1, 08028 Barcelona, Spain; (J.A.-C.); (M.R.-P.); (I.P.)
| | - Isabel Pastor
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, Carrer de Martí i Franquès 1, 08028 Barcelona, Spain; (J.A.-C.); (M.R.-P.); (I.P.)
| | - Felix Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, Carrer de Martí i Franquès 1, 08028 Barcelona, Spain; (J.A.-C.); (M.R.-P.); (I.P.)
- Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028 Barcelona, Spain
- Correspondence:
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11
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Abstract
Most single-molecule studies derive the kinetic rates of native, intermediate, and unfolded states from equilibrium hopping experiments. Here, we apply the Kramers kinetic diffusive model to derive the force-dependent kinetic rates of intermediate states from nonequilibrium pulling experiments. From the kinetic rates, we also extract the force-dependent kinetic barriers and the equilibrium folding energies. We apply our method to DNA hairpins with multiple folding pathways and intermediates. The experimental results agree with theoretical predictions. Furthermore, the proposed nonequilibrium single-molecule approach permits us to characterize kinetic and thermodynamic properties of native, unfolded, and intermediate states that cannot be derived from equilibrium hopping experiments.
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Affiliation(s)
- Marc Rico-Pasto
- Small
Biosystems Lab, Condensed Matter Physics Department, University of Barcelona, C/Martí i Franqués 1, Barcelona, 08028, Spain
| | - Anna Alemany
- Department
of Anatomy and Embryology, Leiden University
Medical Center, Leiden, 2333ZC, The Netherlands
| | - Felix Ritort
- Small
Biosystems Lab, Condensed Matter Physics Department, University of Barcelona, C/Martí i Franqués 1, Barcelona, 08028, Spain
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12
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Rissone P, Bizarro CV, Ritort F. Stem-loop formation drives RNA folding in mechanical unzipping experiments. Proc Natl Acad Sci U S A 2022; 119:e2025575119. [PMID: 35022230 PMCID: PMC8784153 DOI: 10.1073/pnas.2025575119] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2020] [Accepted: 11/29/2021] [Indexed: 12/22/2022] Open
Abstract
Accurate knowledge of RNA hybridization is essential for understanding RNA structure and function. Here we mechanically unzip and rezip a 2-kbp RNA hairpin and derive the 10 nearest-neighbor base pair (NNBP) RNA free energies in sodium and magnesium with 0.1 kcal/mol precision using optical tweezers. Notably, force-distance curves (FDCs) exhibit strong irreversible effects with hysteresis and several intermediates, precluding the extraction of the NNBP energies with currently available methods. The combination of a suitable RNA synthesis with a tailored pulling protocol allowed us to obtain the fully reversible FDCs necessary to derive the NNBP energies. We demonstrate the equivalence of sodium and magnesium free-energy salt corrections at the level of individual NNBP. To characterize the irreversibility of the unzipping-rezipping process, we introduce a barrier energy landscape of the stem-loop structures forming along the complementary strands, which compete against the formation of the native hairpin. This landscape correlates with the hysteresis observed along the FDCs. RNA sequence analysis shows that base stacking and base pairing stabilize the stem-loops that kinetically trap the long-lived intermediates observed in the FDC. Stem-loops formation appears as a general mechanism to explain a wide range of behaviors observed in RNA folding.
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Affiliation(s)
- Paolo Rissone
- Small Biosystems Laboratory, Condensed Matter Physics Department, University of Barcelona, Barcelona 08028, Spain
| | - Cristiano V Bizarro
- Instituto Nacional de Ciência e Tecnologia em Tuberculose, Centro de Pesquisas em Biologia Molecular e Funcional, Pontifícia Universidade Católica do Rio Grande do Sul, 90616-900 Porto Alegre, Brazil
| | - Felix Ritort
- Small Biosystems Laboratory, Condensed Matter Physics Department, University of Barcelona, Barcelona 08028, Spain;
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13
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Sundar Rajan V, Viader-Godoy X, Lin YL, Dutta U, Ritort F, Westerlund F, Wilhelmsson LM. Mechanical characterization of base analogue modified nucleic acids by force spectroscopy. Phys Chem Chem Phys 2021; 23:14151-14155. [PMID: 34180930 PMCID: PMC8261857 DOI: 10.1039/d1cp01985f] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
We use mechanical unfolding of single DNA hairpins with modified bases to accurately assess intra- and intermolecular forces in nucleic acids. As expected, the modification stabilizes the hybridized hairpin, but we also observe intriguing stacking interactions in the unfolded hairpin. Our study highlights the benefit of using base-modified nucleic acids in force-spectroscopy.
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Affiliation(s)
- Vinoth Sundar Rajan
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, Sweden. and Department of Biology and Biological Engineering, Chalmers University of Technology, Sweden.
| | - Xavier Viader-Godoy
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/Marti i Franques 1, Barcelona 08028, Spain
| | - Yii-Lih Lin
- Department of Biology and Biological Engineering, Chalmers University of Technology, Sweden.
| | - Uttama Dutta
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, Sweden. and Department of Biology and Biological Engineering, Chalmers University of Technology, Sweden.
| | - Felix Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/Marti i Franques 1, Barcelona 08028, Spain
| | - Fredrik Westerlund
- Department of Biology and Biological Engineering, Chalmers University of Technology, Sweden.
| | - L Marcus Wilhelmsson
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, Sweden.
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14
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Viader-Godoy X, Manosas M, Ritort F. Sugar-Pucker Force-Induced Transition in Single-Stranded DNA. Int J Mol Sci 2021; 22:4745. [PMID: 33947069 PMCID: PMC8124619 DOI: 10.3390/ijms22094745] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Revised: 04/23/2021] [Accepted: 04/26/2021] [Indexed: 01/16/2023] Open
Abstract
The accurate knowledge of the elastic properties of single-stranded DNA (ssDNA) is key to characterize the thermodynamics of molecular reactions that are studied by force spectroscopy methods where DNA is mechanically unfolded. Examples range from DNA hybridization, DNA ligand binding, DNA unwinding by helicases, etc. To date, ssDNA elasticity has been studied with different methods in molecules of varying sequence and contour length. A dispersion of results has been reported and the value of the persistence length has been found to be larger for shorter ssDNA molecules. We carried out pulling experiments with optical tweezers to characterize the elastic response of ssDNA over three orders of magnitude in length (60-14 k bases). By fitting the force-extension curves (FECs) to the Worm-Like Chain model we confirmed the above trend:the persistence length nearly doubles for the shortest molecule (60 b) with respect to the longest one (14 kb). We demonstrate that the observed trend is due to the different force regimes fitted for long and short molecules, which translates into two distinct elastic regimes at low and high forces. We interpret this behavior in terms of a force-induced sugar pucker conformational transition (C3'-endo to C2'-endo) upon pulling ssDNA.
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Affiliation(s)
| | - Maria Manosas
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, Carrer de Martí i Franquès 1, 08028 Barcelona, Spain;
| | - Felix Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, Carrer de Martí i Franquès 1, 08028 Barcelona, Spain;
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15
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Thorneywork AL, Gladrow J, Qing Y, Rico-Pasto M, Ritort F, Bayley H, Kolomeisky AB, Keyser UF. Direct detection of molecular intermediates from first-passage times. Sci Adv 2020; 6:eaaz4642. [PMID: 32494675 PMCID: PMC7195145 DOI: 10.1126/sciadv.aaz4642] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2019] [Accepted: 02/04/2020] [Indexed: 05/05/2023]
Abstract
All natural phenomena are governed by energy landscapes. However, the direct measurement of this fundamental quantity remains challenging, particularly in complex systems involving intermediate states. Here, we uncover key details of the energy landscapes that underpin a range of experimental systems through quantitative analysis of first-passage time distributions. By combined study of colloidal dynamics in confinement, transport through a biological pore, and the folding kinetics of DNA hairpins, we demonstrate conclusively how a short-time, power-law regime of the first-passage time distribution reflects the number of intermediate states associated with each of these processes, despite their differing length scales, time scales, and interactions. We thereby establish a powerful method for investigating the underlying mechanisms of complex molecular processes.
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Affiliation(s)
- Alice L. Thorneywork
- Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK
- Corresponding author.
| | - Jannes Gladrow
- Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK
| | - Yujia Qing
- Department of Chemistry, University of Oxford, Oxford OX1 3TA, UK
| | - Marc Rico-Pasto
- Department de Fisica de la Materia Condensada, Universitat de Barcelona, C/Marti i Franques 1, 08028 Barcelona, Spain
| | - Felix Ritort
- Department de Fisica de la Materia Condensada, Universitat de Barcelona, C/Marti i Franques 1, 08028 Barcelona, Spain
- CIBER BNN, Instituto de Salud Carlos III, 28029 Madrid, Spain
| | - Hagan Bayley
- Department of Chemistry, University of Oxford, Oxford OX1 3TA, UK
| | - Anatoly B. Kolomeisky
- Department of Chemistry and Department of Chemical and Biomolecular Engineering Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
| | - Ulrich F. Keyser
- Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK
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16
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Landuzzi F, Viader-Godoy X, Cleri F, Pastor I, Ritort F. Detection of single DNA mismatches by force spectroscopy in short DNA hairpins. J Chem Phys 2020; 152:074204. [PMID: 32087630 DOI: 10.1063/1.5139284] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Identification of defective DNA structures is a difficult task, since small differences in base-pair bonding are hidden in the local structural variability of a generally random base-pair sequence. Defects, such as base mismatches, missing bases, crosslinks, and so on, occur in DNA with high frequency and must be efficiently identified and repaired to avoid dire consequences such as genetic mutations. Here, we focus on the detection of base mismatches, which is local deviations from the ideal Watson-Crick pairing rule, which may typically originate from DNA replication process, foreign chemical attack, or ionizing radiation. Experimental detection of a mismatch defect demands the ability to measure slight deviations in the free energy and molecular structure. We introduce different mismatches in short DNA hairpins (10 or 20 base pairs plus a 4-base loop) sandwiched between dsDNA handles to be used in single-molecule force spectroscopy with optical tweezers. We perform both hopping and force-pulling experiments to measure the excess free energies and deduce the characteristic kinetic signatures of the mismatch from the force-distance curves. All-atom molecular dynamics simulations lend support to the detailed interpretation of the experimental data. Such measurements, at the lowest sensitivity limits of this experimental technique, demonstrate the capability of identifying the presence of mismatches in a random complementary dsDNA sequence and provide lower bounds for the ability to distinguish different structural defects.
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Affiliation(s)
- F Landuzzi
- Department of Physics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Japan
| | - X Viader-Godoy
- Small Biosystems Lab., Univ. de Barcelona, Diagonal 647, 08028 Barcelona, Spain
| | - F Cleri
- I.E.M.N. (UMR Cnrs 8520), 59652 Villeneuve d'Ascq, France
| | - I Pastor
- Small Biosystems Lab., Univ. de Barcelona, Diagonal 647, 08028 Barcelona, Spain
| | - F Ritort
- Small Biosystems Lab., Univ. de Barcelona, Diagonal 647, 08028 Barcelona, Spain
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17
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Sundar Rajan VEJ, Viader X, Lin YL, Ritort F, Westerlund F, Wilhelmsson M. Studying the Intramolecular Forces of Base-Modified Nucleic Acids using Optical Tweezers. Biophys J 2020. [DOI: 10.1016/j.bpj.2019.11.1298] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022] Open
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18
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Sorkin R, Bergamaschi G, Kamsma D, Brand G, Dekel E, Ofir-Birin Y, Rudik A, Gironella M, Ritort F, Regev-Rudzki N, Roos WH, Wuite GJL. Probing cellular mechanics with acoustic force spectroscopy. Mol Biol Cell 2018; 29:2005-2011. [PMID: 29927358 PMCID: PMC6232971 DOI: 10.1091/mbc.e18-03-0154] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
A large number of studies demonstrate that cell mechanics and pathology are intimately linked. In particular, deformability of red blood cells (RBCs) is key to their function and is dramatically altered in the time course of diseases such as anemia and malaria. Due to the physiological importance of cell mechanics, many methods for cell mechanical probing have been developed. While single-cell methods provide very valuable information, they are often technically challenging and lack the high data throughput needed to distinguish differences in heterogeneous populations, while fluid-flow high-throughput methods miss the accuracy to detect subtle differences. Here we present a new method for multiplexed single-cell mechanical probing using acoustic force spectroscopy (AFS). We demonstrate that mechanical differences induced by chemical treatments of known effect can be measured and quantified. Furthermore, we explore the effect of extracellular vesicles (EVs) uptake on RBC mechanics and demonstrate that EVs uptake increases RBC deformability. Our findings demonstrate the ability of AFS to manipulate cells with high stability and precision and pave the way to further new insights into cellular mechanics and mechanobiology in health and disease, as well as potential biomedical applications.
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Affiliation(s)
- Raya Sorkin
- Department of Physics and Astronomy and LaserLab, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands.,Department of Molecular Biophysics, Zernike Instituut, Rijksuniversiteit Groningen, 9747 AG Groningen, The Netherlands
| | - Giulia Bergamaschi
- Department of Physics and Astronomy and LaserLab, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Douwe Kamsma
- Department of Physics and Astronomy and LaserLab, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Guy Brand
- Department of Physics and Astronomy and LaserLab, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Elya Dekel
- Department of Biomolecular Sciences, Weizmann Institute of Science, Rehovot 761000, Israel
| | - Yifat Ofir-Birin
- Department of Biomolecular Sciences, Weizmann Institute of Science, Rehovot 761000, Israel
| | - Ariel Rudik
- Department of Biomolecular Sciences, Weizmann Institute of Science, Rehovot 761000, Israel
| | - Marta Gironella
- Small Biosystems Lab, Departament de Fsica de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, 08028 Barcelona, Spain
| | - Felix Ritort
- Small Biosystems Lab, Departament de Fsica de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, 08028 Barcelona, Spain
| | - Neta Regev-Rudzki
- Department of Biomolecular Sciences, Weizmann Institute of Science, Rehovot 761000, Israel
| | - Wouter H Roos
- Department of Molecular Biophysics, Zernike Instituut, Rijksuniversiteit Groningen, 9747 AG Groningen, The Netherlands
| | - Gijs J L Wuite
- Department of Physics and Astronomy and LaserLab, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
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19
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Crisanti A, Picco M, Ritort F. Derivation of the spin-glass order parameter from stochastic thermodynamics. Phys Rev E 2018; 97:052103. [PMID: 29906861 DOI: 10.1103/physreve.97.052103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2017] [Indexed: 06/08/2023]
Abstract
A fluctuation relation is derived to extract the order parameter function q(x) in weakly ergodic systems. The relation is based on measuring and classifying entropy production fluctuations according to the value of the overlap q between configurations. For a fixed value of q, entropy production fluctuations are Gaussian distributed allowing us to derive the quasi-FDT so characteristic of aging systems. The theory is validated by extracting the q(x) in various types of glassy models. It might be generally applicable to other nonequilibrium systems and experimental small systems.
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Affiliation(s)
- A Crisanti
- Dipartimento di Fisica, Università di Roma "La Sapienza", and Istituto dei Sistemi Complessi ISC-CNR, P.le Aldo Moro 2, 00185 Roma, Italy
| | - M Picco
- Sorbonne Université, CNRS, Université Pierre et Marie Curie, LPTHE, F-75005 Paris, France
| | - F Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/ Martí i Franquès, E-08028, Barcelona, Spain
- CIBER-BBN Center for Bioengineering, Biomaterials and Nanomedicine, Instituto de Salud Carlos III, Madrid, Spain
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20
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Affiliation(s)
- M. Rico-Pasto
- Departament de Fisica de la Materia Condensada, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
| | - I. Pastor
- Departament de Fisica de la Materia Condensada, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
- CIBER_BNN, Instituto de Salud Carlos III, 28029 Madrid, Spain
| | - F. Ritort
- Departament de Fisica de la Materia Condensada, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
- CIBER_BNN, Instituto de Salud Carlos III, 28029 Madrid, Spain
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21
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Huguet JM, Ribezzi-Crivellari M, Bizarro CV, Ritort F. Derivation of nearest-neighbor DNA parameters in magnesium from single molecule experiments. Nucleic Acids Res 2018; 45:12921-12931. [PMID: 29177444 PMCID: PMC5728412 DOI: 10.1093/nar/gkx1161] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2017] [Accepted: 11/08/2017] [Indexed: 12/17/2022] Open
Abstract
DNA hybridization is an essential molecular reaction in biology with many applications. The nearest-neighbor (NN) model for nucleic acids predicts DNA thermodynamics using energy values for the different base pair motifs. These values have been derived from melting experiments in monovalent and divalent salt and applied to predict melting temperatures of oligos within a few degrees. However, an improved determination of the NN energy values and their salt dependencies in magnesium is still needed for current biotechnological applications seeking high selectivity in the hybridization of synthetic DNAs. We developed a methodology based on single molecule unzipping experiments to derive accurate NN energy values and initiation factors for DNA. A new set of values in magnesium is derived, which reproduces unzipping data and improves melting temperature predictions for all available oligo lengths, in a range of temperature and salt conditions where correlation effects between the magnesium bound ions are weak. The NN salt correction parameters are shown to correlate to the GC content of the NN motifs. Our study shows the power of single-molecule force spectroscopy assays to unravel novel features of nucleic acids such as sequence-dependent salt corrections.
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Affiliation(s)
- Josep Maria Huguet
- Condensed Matter Physics Department, University of Barcelona, C/Marti i Franques s/n, 08028 Barcelona, Spain.,MINTRADA, Plaça de la Font 4B, 25344 St. Martí de Maldà., Lleida, Spain
| | - Marco Ribezzi-Crivellari
- Laboratoire de Biochimie, Institute of Chemistry, Biology and Innovation (CBI), UMR 8231, ESPCI Paris/CNRS, PSL Research University, 10 rue Vauquelin, 75231 Paris Cedex 05, France
| | - Cristiano Valim Bizarro
- Pontifícia Universidade Católica do Rio Grande do Sul, Avenida Ipiranga, 6681, 90619900 Porto Alegre, Brazil
| | - Felix Ritort
- Condensed Matter Physics Department, University of Barcelona, C/Marti i Franques s/n, 08028 Barcelona, Spain.,CIBER-BBN de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Sanidad Carlos III, Madrid, Spain
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22
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Camunas-Soler J, Alemany A, Ritort F. Experimental measurement of binding energy, selectivity, and allostery using fluctuation theorems. Science 2017; 355:412-415. [PMID: 28126820 DOI: 10.1126/science.aah4077] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2016] [Accepted: 12/16/2016] [Indexed: 12/13/2022]
Abstract
Thermodynamic bulk measurements of binding reactions rely on the validity of the law of mass action and the assumption of a dilute solution. Yet, important biological systems such as allosteric ligand-receptor binding, macromolecular crowding, or misfolded molecules may not follow these assumptions and may require a particular reaction model. Here we introduce a fluctuation theorem for ligand binding and an experimental approach using single-molecule force spectroscopy to determine binding energies, selectivity, and allostery of nucleic acids and peptides in a model-independent fashion. A similar approach could be used for proteins. This work extends the use of fluctuation theorems beyond unimolecular folding reactions, bridging the thermodynamics of small systems and the basic laws of chemical equilibrium.
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Affiliation(s)
- Joan Camunas-Soler
- Small Biosystems Lab, Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Barcelona, Spain.,Centro de Investigación Biomédica en Red (CIBER) de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, Madrid, Spain
| | - Anna Alemany
- Small Biosystems Lab, Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Barcelona, Spain.,Centro de Investigación Biomédica en Red (CIBER) de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, Madrid, Spain
| | - Felix Ritort
- Small Biosystems Lab, Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Barcelona, Spain. .,Centro de Investigación Biomédica en Red (CIBER) de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, Madrid, Spain
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23
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Abstract
For fluctuating currents in nonequilibrium steady states, the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving. We show that this relation holds not only for the long-time limit of fluctuations, as described by large deviation theory, but also for fluctuations on arbitrary finite time scales. This generalization facilitates applying the thermodynamic uncertainty relation to single molecule experiments, for which infinite time scales are not accessible. Importantly, often this finite-time variant of the relation allows inferring a bound on the entropy production that is even stronger than the one obtained from the long-time limit. We illustrate the relation for the fluctuating work that is performed by a stochastically switching laser tweezer on a trapped colloidal particle.
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Affiliation(s)
- Patrick Pietzonka
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Felix Ritort
- Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
- CIBER-BBN de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, 28029 Madrid, Spain
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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24
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Abstract
Biomolecules diffusively explore their energy landscape overcoming energy barriers via thermally activated processes to reach the biologically relevant conformation. Mechanically induced unfolding and folding reactions offer an excellent playground to feature these processes at the single-molecule level by monitoring changes in the molecular extension. Here we investigate two-state DNA hairpins designed to have the transition states at different locations. We use optical tweezers to characterize the force-dependent behavior of the kinetic barrier from nonequilibrium pulling experiments by using the continuous effective barrier approach (CEBA). We introduce the mechanical fragility and the molecular transition-state susceptibility, both useful quantities to characterize the response of the transition state to an applied force. Our results demonstrate the validity of the Leffler-Hammond postulate where the transition state approaches the folded state as force increases, implying monotonically decreasing fragility with force and a non-negative transition state susceptibility at all forces.
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Affiliation(s)
- Anna Alemany
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona , Diagonal 647, 080028 Barcelona, Spain
| | - Felix Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona , Diagonal 647, 080028 Barcelona, Spain
- Ciber-BBN, Networking Research Center of Bioengineering, Biomaterials and Nanomedicine, Instituto Carlos III , 28029 Madrid, Spain
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25
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Dieterich E, Camunas-Soler J, Ribezzi-Crivellari M, Seifert U, Ritort F. Control of force through feedback in small driven systems. Phys Rev E 2016; 94:012107. [PMID: 27575077 DOI: 10.1103/physreve.94.012107] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/29/2016] [Indexed: 06/06/2023]
Abstract
Controlling a time-dependent force applied to single molecules or colloidal particles is crucial for many types of experiments. Since in optical tweezers the primary controlled variable is the position of the trap, imposing a target force requires an active feedback process. We analyze this feedback process for the paradigmatic case of a nonequilibrium steady state generated by a dichotomous force protocol, first theoretically for a colloidal particle in a harmonic trap and then with both simulations and experiments for a long DNA hairpin. For the first setup, we find there is an optimal feedback gain separating monotonic from oscillatory response, whereas a too strong feedback leads to an instability. For the DNA molecule, reaching the target force requires substantial feedback gain since weak feedback cannot overcome the tendency to relax towards the equilibrium force.
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Affiliation(s)
- E Dieterich
- II. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - J Camunas-Soler
- Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
- CIBER-BBN de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, 28029 Madrid, Spain
| | - M Ribezzi-Crivellari
- Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
- CIBER-BBN de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, 28029 Madrid, Spain
| | - U Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - F Ritort
- Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
- CIBER-BBN de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, 28029 Madrid, Spain
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26
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Alemany A, Ritort F. Determination of the elastic properties of short ssDNA molecules by mechanically folding and unfolding DNA hairpins. Biopolymers 2016; 101:1193-9. [PMID: 25091120 DOI: 10.1002/bip.22533] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2014] [Revised: 07/30/2014] [Accepted: 07/31/2014] [Indexed: 01/15/2023]
Abstract
The characterization of elastic properties of biopolymers is crucial to understand many molecular reactions determined by conformational bending fluctuations of the polymer. Direct measurement of such elastic properties using single-molecule methods is usually hindered by the intrinsic tendency of such biopolymers to form high-order molecular structures. For example, single-stranded deoxyribonucleic acids (ssDNA) tend to form secondary structures such as local double helices that prevent the direct measurement of the ideal elastic response of the ssDNA. In this work, we show how to extract the ideal elastic response in the entropic regime of short ssDNA molecules by mechanically pulling two-state DNA hairpins of different contour lengths. This is achieved by measuring the force dependence of the molecular extension and stiffness on mechanically folding and unfolding the DNA hairpin. Both quantities are fit to the worm-like chain elastic model giving values for the persistence length and the interphosphate distance. This method can be used to unravel the elastic properties of short ssDNA and RNA sequences and, more generally, any biopolymer that can exhibit a cooperative two-state transition between mechanically folded and unfolded states (such as proteins).
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Affiliation(s)
- Anna Alemany
- Small Biosystems Lab, Departament de Física Fonamental, Universitat de Barcelona, C/ Martí i Franquès 1, 08028, Barcelona, Spain
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27
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Abstract
We review the current knowledge on the use of single-molecule force spectroscopy techniques to extrapolate the elastic properties of nucleic acids. We emphasize the lesser-known elastic properties of single-stranded DNA. We discuss the importance of accurately determining the elastic response in pulling experiments, and we review the simplest models used to rationalize the experimental data as well as the experimental approaches used to pull single-stranded DNA. Applications used to investigate DNA conformational transitions and secondary structure formation are also highlighted. Finally, we provide an overview of the effects of salt and temperature and briefly discuss the effects of contour length and sequence dependence.
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Affiliation(s)
- Joan Camunas-Soler
- Departament de Física Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain; .,CIBER-BBN de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, 28029 Madrid, Spain
| | - Marco Ribezzi-Crivellari
- Departament de Física Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain; .,CIBER-BBN de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, 28029 Madrid, Spain
| | - Felix Ritort
- Departament de Física Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain; .,CIBER-BBN de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, 28029 Madrid, Spain
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28
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de Lorenzo S, Ribezzi-Crivellari M, Arias-Gonzalez JR, Smith SB, Ritort F. A Temperature-Jump Optical Trap for Single-Molecule Manipulation. Biophys J 2016; 108:2854-64. [PMID: 26083925 DOI: 10.1016/j.bpj.2015.05.017] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2014] [Revised: 05/11/2015] [Accepted: 05/12/2015] [Indexed: 11/25/2022] Open
Abstract
To our knowledge, we have developed a novel temperature-jump optical tweezers setup that changes the temperature locally and rapidly. It uses a heating laser with a wavelength that is highly absorbed by water so it can cover a broad range of temperatures. This instrument can record several force-distance curves for one individual molecule at various temperatures with good thermal and mechanical stability. Our design has features to reduce convection and baseline shifts, which have troubled previous heating-laser instruments. As proof of accuracy, we used the instrument to carry out DNA unzipping experiments in which we derived the average basepair free energy, entropy, and enthalpy of formation of the DNA duplex in a range of temperatures between 5°C and 50°C. We also used the instrument to characterize the temperature-dependent elasticity of single-stranded DNA (ssDNA), where we find a significant condensation plateau at low force and low temperature. Oddly, the persistence length of ssDNA measured at high force seems to increase with temperature, contrary to simple entropic models.
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Affiliation(s)
- Sara de Lorenzo
- Departament de Física Fonamental, Universitat de Barcelona, Barcelona, Spain; Ciber-BBN de Bioingenería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, Madrid, Spain
| | | | - J Ricardo Arias-Gonzalez
- Instituto Madrileño de Estudios Avanzados en Nanociencia (IMDEA Nanociencia), Cantoblanco, Madrid, Spain; CNB-CSIC-IMDEA Nanociencia Associated Unit "Unidad de Nanobiotecnología", Madrid, Spain
| | | | - Felix Ritort
- Departament de Física Fonamental, Universitat de Barcelona, Barcelona, Spain; Ciber-BBN de Bioingenería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, Madrid, Spain.
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29
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Abstract
Optical tweezers (OTs) allow the measurement of fluctuations at the nanoscale, in particular fluctuations in the end-to-end distance in single molecules. Fluctuation spectra can yield valuable information, but they can easily be contaminated by instrumental effects. We identify axial fluctuations, i.e., fluctuations of the trapped beads in the direction of light propagation, as one of these instrumental effects. Remarkably, axial fluctuations occur on a characteristic timescale similar to that of conformational (folding) transitions, which may lead to misinterpretation of the experimental results. We show that a precise measurement of the effect of force on both axial and conformational fluctuations is crucial to disentangle them. Our results on axial fluctuations are captured by a simple and general formula valid for all OT setups and provide experimentalists with a general strategy to distinguish axial fluctuations from conformational transitions.
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30
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Camunas-Soler J, Manosas M, Frutos S, Tulla-Puche J, Albericio F, Ritort F. Single-molecule kinetics and footprinting of DNA bis-intercalation: the paradigmatic case of Thiocoraline. Nucleic Acids Res 2015; 43:2767-79. [PMID: 25690887 PMCID: PMC4357703 DOI: 10.1093/nar/gkv087] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
DNA bis-intercalators are widely used in molecular biology with applications ranging from DNA imaging to anticancer pharmacology. Two fundamental aspects of these ligands are the lifetime of the bis-intercalated complexes and their sequence selectivity. Here, we perform single-molecule optical tweezers experiments with the peptide Thiocoraline showing, for the first time, that bis-intercalation is driven by a very slow off-rate that steeply decreases with applied force. This feature reveals the existence of a long-lived (minutes) mono-intercalated intermediate that contributes to the extremely long lifetime of the complex (hours). We further exploit this particularly slow kinetics to determine the thermodynamics of binding and persistence length of bis-intercalated DNA for a given fraction of bound ligand, a measurement inaccessible in previous studies of faster intercalating agents. We also develop a novel single-molecule footprinting technique based on DNA unzipping and determine the preferred binding sites of Thiocoraline with one base-pair resolution. This fast and radiolabelling-free footprinting technique provides direct access to the binding sites of small ligands to nucleic acids without the need of cleavage agents. Overall, our results provide new insights into the binding pathway of bis-intercalators and the reported selectivity might be of relevance for this and other anticancer drugs interfering with DNA replication and transcription in carcinogenic cell lines.
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Affiliation(s)
- Joan Camunas-Soler
- Small Biosystems Lab, Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona, 08028 Barcelona, Spain CIBER de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, 28029 Madrid, Spain
| | - Maria Manosas
- Small Biosystems Lab, Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona, 08028 Barcelona, Spain CIBER de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, 28029 Madrid, Spain
| | - Silvia Frutos
- Small Biosystems Lab, Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona, 08028 Barcelona, Spain CIBER de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, 28029 Madrid, Spain
| | - Judit Tulla-Puche
- Institute for Research in Biomedicine (IRB Barcelona), Barcelona Science Park, Baldiri Reixac 10-12, 08028 Barcelona, Spain
| | - Fernando Albericio
- Institute for Research in Biomedicine (IRB Barcelona), Barcelona Science Park, Baldiri Reixac 10-12, 08028 Barcelona, Spain
| | - Felix Ritort
- Small Biosystems Lab, Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona, 08028 Barcelona, Spain CIBER de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, 28029 Madrid, Spain
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31
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Abstract
Fluctuation relations (FRs) are among the few existing general results in nonequilibrium systems. Their verification requires the measurement of the total work performed on a system. Nevertheless in many cases only a partial measurement of the work is possible. Here we consider FRs in dual-trap optical tweezers where two different forces (one per trap) are measured. With this setup we perform pulling experiments on single molecules by moving one trap relative to the other. We demonstrate that work should be measured using the force exerted by the trap that is moved. The force that is measured in the trap at rest fails to provide the full dissipation in the system, leading to a (incorrect) work definition that does not satisfy the FR. The implications to single-molecule experiments and free-energy measurements are discussed. In the case of symmetric setups a second work definition, based on differential force measurements, is introduced. This definition is best suited to measure free energies as it shows faster convergence of estimators. We discuss measurements using the (incorrect) work definition as an example of partial work measurement. We show how to infer the full work distribution from the partial one via the FR. The inference process does also yield quantitative information, e.g., the hydrodynamic drag on the dumbbell. Results are also obtained for asymmetric dual-trap setups. We suggest that this kind of inference could represent a previously unidentified and general application of FRs to extract information about irreversible processes in small systems.
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Affiliation(s)
| | - Felix Ritort
- Departament de Fisica Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain; andCentro de Investigacion Biomedica en Red-Bioingeneria, Biomateriales y Nanomedicina (CIBER-BBN), Instituto de Salud Carlos III, 28029 Madrid, Spain
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32
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Bosco A, Camunas-Soler J, Ritort F. Elastic properties and secondary structure formation of single-stranded DNA at monovalent and divalent salt conditions. Nucleic Acids Res 2014; 42:2064-74. [PMID: 24225314 PMCID: PMC3919573 DOI: 10.1093/nar/gkt1089] [Citation(s) in RCA: 96] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2013] [Revised: 10/16/2013] [Accepted: 10/17/2013] [Indexed: 11/16/2022] Open
Abstract
Single-stranded DNA (ssDNA) plays a major role in several biological processes. It is therefore of fundamental interest to understand how the elastic response and the formation of secondary structures are modulated by the interplay between base pairing and electrostatic interactions. Here we measure force-extension curves (FECs) of ssDNA molecules in optical tweezers set up over two orders of magnitude of monovalent and divalent salt conditions, and obtain its elastic parameters by fitting the FECs to semiflexible models of polymers. For both monovalent and divalent salts, we find that the electrostatic contribution to the persistence length is proportional to the Debye screening length, varying as the inverse of the square root of cation concentration. The intrinsic persistence length is equal to 0.7 nm for both types of salts, and the effectivity of divalent cations in screening electrostatic interactions appears to be 100-fold as compared with monovalent salt, in line with what has been recently reported for single-stranded RNA. Finally, we propose an analysis of the FECs using a model that accounts for the effective thickness of the filament at low salt condition and a simple phenomenological description that quantifies the formation of non-specific secondary structure at low forces.
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Affiliation(s)
- Alessandro Bosco
- SISSA - Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, Italy, Elettra-Sincrotrone Trieste S.C.p.A., Strada Statale 14 - km 163,5 in AREA Science Park, 34149 Basovizza Trieste, Italy, Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain and CIBER de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, Madrid, Spain
| | - Joan Camunas-Soler
- SISSA - Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, Italy, Elettra-Sincrotrone Trieste S.C.p.A., Strada Statale 14 - km 163,5 in AREA Science Park, 34149 Basovizza Trieste, Italy, Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain and CIBER de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, Madrid, Spain
| | - Felix Ritort
- SISSA - Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, Italy, Elettra-Sincrotrone Trieste S.C.p.A., Strada Statale 14 - km 163,5 in AREA Science Park, 34149 Basovizza Trieste, Italy, Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain and CIBER de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, Madrid, Spain
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33
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Alemany A, Sanvicens N, de Lorenzo S, Marco MP, Ritort F. Bond elasticity controls molecular recognition specificity in antibody-antigen binding. Nano Lett 2013; 13:5197-5202. [PMID: 24074342 DOI: 10.1021/nl402617f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Force-spectroscopy experiments make it possible to characterize single ligand-receptor pairs. Here we measure the spectrum of bond strengths and flexibilities in antibody-antigen interactions using optical tweezers. We characterize the mechanical evolution of polyclonal antibodies generated under infection and the ability of a monoclonal antibody to cross-react against different antigens. Our results suggest that bond flexibility plays a major role in remodeling antibody-antigen bonds in order to improve recognition during the maturation of the humoral immune system.
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Affiliation(s)
- Anna Alemany
- Small Biosystems Lab, Department Física Fonamental, Universitat de Barcelona , C/Martí i Franquès 1, 08028 Barcelona, Spain
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34
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Camunas-Soler J, Frutos S, Bizarro CV, de Lorenzo S, Fuentes-Perez ME, Ramsch R, Vilchez S, Solans C, Moreno-Herrero F, Albericio F, Eritja R, Giralt E, Dev SB, Ritort F. Electrostatic binding and hydrophobic collapse of peptide-nucleic acid aggregates quantified using force spectroscopy. ACS Nano 2013; 7:5102-5113. [PMID: 23706043 DOI: 10.1021/nn4007237] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Knowledge of the mechanisms of interaction between self-aggregating peptides and nucleic acids or other polyanions is key to the understanding of many aggregation processes underlying several human diseases (e.g., Alzheimer's and Parkinson's diseases). Determining the affinity and kinetic steps of such interactions is challenging due to the competition between hydrophobic self-aggregating forces and electrostatic binding forces. Kahalalide F (KF) is an anticancer hydrophobic peptide that contains a single positive charge that confers strong aggregative properties with polyanions. This makes KF an ideal model to elucidate the mechanisms by which self-aggregation competes with binding to a strongly charged polyelectrolyte such as DNA. We use optical tweezers to apply mechanical forces to single DNA molecules and show that KF and DNA interact in a two-step kinetic process promoted by the electrostatic binding of DNA to the aggregate surface followed by the stabilization of the complex due to hydrophobic interactions. From the measured pulling curves we determine the spectrum of binding affinities, kinetic barriers, and lengths of DNA segments sequestered within the KF-DNA complex. We find there is a capture distance beyond which the complex collapses into compact aggregates stabilized by strong hydrophobic forces and discuss how the bending rigidity of the nucleic acid affects this process. We hypothesize that within an in vivo context, the enhanced electrostatic interaction of KF due to its aggregation might mediate the binding to other polyanions. The proposed methodology should be useful to quantitatively characterize other compounds or proteins in which the formation of aggregates is relevant.
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Affiliation(s)
- Joan Camunas-Soler
- Small Biosystems Lab, Departament de Física Fonamental, Universitat de Barcelona, Avinguda Diagonal 647, 08028 Barcelona, Spain
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35
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Ribezzi-Crivellari M, Huguet JM, Ritort F. Counter-propagating dual-trap optical tweezers based on linear momentum conservation. Rev Sci Instrum 2013; 84:043104. [PMID: 23635178 DOI: 10.1063/1.4799289] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We present a dual-trap optical tweezers setup which directly measures forces using linear momentum conservation. The setup uses a counter-propagating geometry, which allows momentum measurement on each beam separately. The experimental advantages of this setup include low drift due to all-optical manipulation, and a robust calibration (independent of the features of the trapped object or buffer medium) due to the force measurement method. Although this design does not attain the high-resolution of some co-propagating setups, we show that it can be used to perform different single molecule measurements: fluctuation-based molecular stiffness characterization at different forces and hopping experiments on molecular hairpins. Remarkably, in our setup it is possible to manipulate very short tethers (such as molecular hairpins with short handles) down to the limit where beads are almost in contact. The setup is used to illustrate a novel method for measuring the stiffness of optical traps and tethers on the basis of equilibrium force fluctuations, i.e., without the need of measuring the force vs molecular extension curve. This method is of general interest for dual trap optical tweezers setups and can be extended to setups which do not directly measure forces.
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36
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Abstract
A fluctuation relation for aging systems is introduced and verified by extensive numerical simulations. It is based on the hypothesis of partial equilibration over phase-space regions in a scenario of entropy-driven relaxation. The relation provides a simple alternative method, amenable of experimental implementation, to measure replica symmetry breaking parameters in aging systems. The connection with the effective temperatures obtained from the fluctuation-dissipation theorem is discussed.
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Affiliation(s)
- A Crisanti
- Dipartimento di Fisica, Università di Roma La Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
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37
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Abstract
RNA duplex stability depends strongly on ionic conditions, and inside cells RNAs are exposed to both monovalent and multivalent ions. Despite recent advances, we do not have general methods to quantitatively account for the effects of monovalent and multivalent ions on RNA stability, and the thermodynamic parameters for secondary structure prediction have only been derived at 1M [Na(+)]. Here, by mechanically unfolding and folding a 20 bp RNA hairpin using optical tweezers, we study the RNA thermodynamics and kinetics at different monovalent and mixed monovalent/Mg(2+) salt conditions. We measure the unfolding and folding rupture forces and apply Kramers theory to extract accurate information about the hairpin free energy landscape under tension at a wide range of ionic conditions. We obtain non-specific corrections for the free energy of formation of the RNA hairpin and measure how the distance of the transition state to the folded state changes with force and ionic strength. We experimentally validate the Tightly Bound Ion model and obtain values for the persistence length of ssRNA. Finally, we test the approximate rule by which the non-specific binding affinity of divalent cations at a given concentration is equivalent to that of monovalent cations taken at 100-fold concentration for small molecular constructs.
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Affiliation(s)
- C V Bizarro
- Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
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38
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Palassini M, Ritort F. Improving free-energy estimates from unidirectional work measurements: theory and experiment. Phys Rev Lett 2011; 107:060601. [PMID: 21902307 DOI: 10.1103/physrevlett.107.060601] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2009] [Revised: 07/05/2011] [Indexed: 05/31/2023]
Abstract
We derive analytical expressions for the bias of the Jarzynski free-energy estimator from N nonequilibrium work measurements, for a generic work distribution. To achieve this, we map the estimator onto the random energy model in a suitable scaling limit parametrized by (logN)/μ, where μ measures the width of the lower tail of the work distribution, and then compute the finite-N corrections to this limit with different approaches for different regimes of (logN)/μ. We show that these expressions describe accurately the bias for a wide class of work distributions and exploit them to build an improved free-energy estimator from unidirectional work measurements. We apply the method to optical tweezers unfolding and refolding experiments on DNA hairpins of varying loop size and dissipation, displaying both near-Gaussian and non-Gaussian work distributions.
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Affiliation(s)
- Matteo Palassini
- Departament de Física Fonamental, Universitat de Barcelona, Spain
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39
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Forns N, de Lorenzo S, Manosas M, Hayashi K, Huguet JM, Ritort F. Improving signal/noise resolution in single-molecule experiments using molecular constructs with short handles. Biophys J 2011; 100:1765-74. [PMID: 21463590 DOI: 10.1016/j.bpj.2011.01.071] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2010] [Revised: 01/25/2011] [Accepted: 01/31/2011] [Indexed: 11/30/2022] Open
Abstract
We investigate unfolding/folding force kinetics in DNA hairpins exhibiting two and three states with newly designed short dsDNA handles (29 bp) using optical tweezers. We show how the higher stiffness of the molecular setup moderately enhances the signal/noise ratio (SNR) in hopping experiments as compared to conventional long-handled constructs (≅700 bp). The shorter construct results in a signal of higher SNR and slower folding/unfolding kinetics, thereby facilitating the detection of otherwise fast structural transitions. A novel analysis, as far as we are aware, of the elastic properties of the molecular setup, based on high-bandwidth measurements of force fluctuations along the folded branch, reveals that the highest SNR that can be achieved with short handles is potentially limited by the marked reduction of the effective persistence length and stretch modulus of the short linker complex.
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Affiliation(s)
- N Forns
- Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona, Barcelona, Spain
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40
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41
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Abstract
We unzip DNA molecules using optical tweezers and determine the sizes of the cooperatively unzipping and zipping regions separating consecutive metastable intermediates along the unzipping pathway. Sizes are found to be distributed following a power law, ranging from one base pair up to more than a hundred base pairs. We find that a large fraction of unzipping regions smaller than 10 bp are seldom detected because of the high compliance of the released single stranded DNA. We show how the compliance of a single nucleotide sets a limit value around 0.1 N/m for the stiffness of any local force probe aiming to discriminate one base pair at a time in DNA unzipping experiments.
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Affiliation(s)
- J M Huguet
- Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
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42
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Affiliation(s)
- Andrea Crisanti
- a Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 1-00185 Roma, and Istituto Nazionale per la Fisica della Materia, Unità di Roma , Roma, Italy
| | - Felix Ritort
- b Departamento de Física Fondamental , Facultat de Física, Universitat de Barcelona , Diagonal 647, 08028 Barcelona, Spain
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43
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Joanny JF, Metzler R, Ritort F, Weitz D. Polymer physics of the cell. Preface. Phys Biol 2009; 6:020301. [PMID: 19581700 DOI: 10.1088/1478-3975/6/2/020301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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44
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45
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Abstract
We analyze fluctuation-dissipation relations in the backgammon model: a system that displays glassy behavior at zero temperature due to the existence of entropy barriers. We study local and global fluctuation relations for the different observables in the model. For the case of a global perturbation we find a unique negative fluctuation-dissipation ratio that is independent of the observable and which diverges linearly with the waiting time. This result suggests that a negative effective temperature can be observed in glassy systems even in the absence of thermally activated processes.
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Affiliation(s)
- A Garriga
- Fundació Centre Pitiús d'Estudis Avançats, Palau de Congressos, 07840 Sta. Eulària, Ibiza, Spain
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46
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47
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Sunyer R, Ritort F, Farré R, Navajas D. Thermal activation and ATP dependence of the cytoskeleton remodeling dynamics. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 79:051920. [PMID: 19518493 DOI: 10.1103/physreve.79.051920] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2008] [Revised: 02/12/2009] [Indexed: 05/27/2023]
Abstract
The cytoskeleton (CSK) is a nonequilibrium polymer network that uses hydrolyzable sources of free energy such as adenosine triphosphate (ATP) to remodel its internal structure. As in inert nonequilibrium soft materials, CSK remodeling has been associated with structural rearrangements driven by energy-activated processes. We carry out particle tracking and traction microscopy measurements of alveolar epithelial cells at various temperatures and ATP concentrations. We provide the first experimental evidence that the remodeling dynamics of the CSK is driven by structural rearrangements over free-energy barriers induced by thermally activated forces mediated by ATP. The measured activation energy of these forces is approximately 40k_{B}T_{r} ( k_{B} being the Boltzmann constant and T_{r} being the room temperature). Our experiments provide clues to understand the analogy between the dynamics of the living CSK and that of inert nonequilibrium soft materials.
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Affiliation(s)
- R Sunyer
- Unitat de Biofísica i Bioenginyeria, Universitat de Barcelona and CIBER-Enfermedades Respiratorias, 08036 Barcelona, Spain and Institut de Bioenginyeria de Catalunya, 08028 Barcelona, Spain
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48
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Junier I, Mossa A, Manosas M, Ritort F. Recovery of free energy branches in single molecule experiments. Phys Rev Lett 2009; 102:070602. [PMID: 19257655 DOI: 10.1103/physrevlett.102.070602] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2008] [Revised: 01/19/2009] [Indexed: 05/27/2023]
Abstract
We present a method for determining the free energy of coexisting states from irreversible work measurements. Our approach is based on a fluctuation relation that is valid for dissipative transformations in partially equilibrated systems. To illustrate the validity and usefulness of the approach, we use optical tweezers to determine the free energy branches of the native and unfolded states of a two-state molecule as a function of the pulling control parameter. We determine, within 0.6kBT accuracy, the transition point where the free energies of the native and the unfolded states are equal.
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Affiliation(s)
- Ivan Junier
- Programme d'Epigénomique, 523 Terrasses de l'Agora, 91034 Evry, France
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49
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Abstract
RNA folding is a kinetic process governed by the competition of a large number of structures stabilized by the transient formation of base pairs that may induce complex folding pathways and the formation of misfolded structures. Despite its importance in modern biophysics, the current understanding of RNA folding kinetics is limited by the complex interplay between the weak base pair interactions that stabilize the native structure and the disordering effect of thermal forces. The possibility of mechanically pulling individual molecules offers a new perspective to understand the folding of nucleic acids. Here we investigate the folding and misfolding mechanism in RNA secondary structures pulled by mechanical forces. We introduce a model based on the identification of the minimal set of structures that reproduce the patterns of force-extension curves obtained in single molecule experiments. The model requires only two fitting parameters: the attempt frequency at the level of individual base pairs and a parameter associated to a free-energy correction that accounts for the configurational entropy of an exponentially large number of neglected secondary structures. We apply the model to interpret results recently obtained in pulling experiments in the three-helix junction S15 RNA molecule (RNAS15). We show that RNAS15 undergoes force-induced misfolding where force favors the formation of a stable non-native hairpin. The model reproduces the pattern of unfolding and refolding force-extension curves, the distribution of breakage forces, and the misfolding probability obtained in the experiments.
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Affiliation(s)
- M Manosas
- Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
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50
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Maragakis P, Ritort F, Bustamante C, Karplus M, Crooks GE. Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise. J Chem Phys 2008; 129:024102. [PMID: 18624511 DOI: 10.1063/1.2937892] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Jarzynski equality and the fluctuation theorem relate equilibrium free energy differences to nonequilibrium measurements of the work. These relations extend to single-molecule experiments that have probed the finite-time thermodynamics of proteins and nucleic acids. The effects of experimental error and instrument noise have not been considered previously. Here, we present a Bayesian formalism for estimating free energy changes from nonequilibrium work measurements that compensates for instrument noise and combines data from multiple driving protocols. We reanalyze a recent set of experiments in which a single RNA hairpin is unfolded and refolded using optical tweezers at three different rates. Interestingly, the fastest and farthest-from-equilibrium measurements contain the least instrumental noise and, therefore, provide a more accurate estimate of the free energies than a few slow, more noisy, near-equilibrium measurements. The methods we propose here will extend the scope of single-molecule experiments; they can be used in the analysis of data from measurements with atomic force microscopy, optical, and magnetic tweezers.
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Affiliation(s)
- Paul Maragakis
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA.
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