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Voliotis M, Rosko J, Pilizota T, Liverpool TB. Steady-state running rate sets the speed and accuracy of accumulation of swimming bacteria. Biophys J 2022; 121:3435-3444. [PMID: 36045575 PMCID: PMC9515231 DOI: 10.1016/j.bpj.2022.08.012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Revised: 07/31/2022] [Accepted: 08/15/2022] [Indexed: 11/21/2022] Open
Abstract
We study the chemotaxis of a population of genetically identical swimming bacteria undergoing run and tumble dynamics driven by stochastic switching between clockwise and counterclockwise rotation of the flagellar rotary system, where the steady-state rate of the switching changes in different environments. Understanding chemotaxis quantitatively requires that one links the measured steady-state switching rates of the rotary system, as well as the directional changes of individual swimming bacteria in a gradient of chemoattractant/repellant, to the efficiency of a population of bacteria in moving up/down the gradient. Here we achieve this by using a probabilistic model, parametrized with our experimental data, and show that the response of a population to the gradient is complex. We find the changes to the steady-state switching rate in the absence of gradients affect the average speed of the swimming bacterial population response as well as the width of the distribution. Both must be taken into account when optimizing the overall response of the population in complex environments.
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Affiliation(s)
- Margaritis Voliotis
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom.
| | - Jerko Rosko
- School of Life Sciences, University of Warwick, Coventry, United Kingdom
| | - Teuta Pilizota
- Centre for Synthetic and Systems Biology, University of Edinburgh, Edinburgh, United Kingdom.
| | - Tanniemola B Liverpool
- School of Mathematics, University of Bristol, Bristol, United Kingdom; BrisSynBio, Life Sciences Building, University of Bristol, Bristol, United Kingdom.
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2
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Statistics and topology of fluctuating ribbons. Proc Natl Acad Sci U S A 2022; 119:e2122907119. [PMID: 35917354 PMCID: PMC9371672 DOI: 10.1073/pnas.2122907119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, for example, it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques. We show that these ribbons exhibit a range of topologically and geometrically complex morphologies exemplified by three phases-a twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and an entangled phase-that arise as the applied torque and force are varied. Furthermore, the transition from HW to HT phases is characterized by the spontaneous breaking of parity symmetry and the disappearance of perversions (that correspond to chirality-reversing localized defects). This leads to a universal response curve of a topological quantity, the link, as a function of the applied torque that is similar to magnetization curves in second-order phase transitions.
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Orientational Fluctuations and Bimodality in Semiflexible Nunchucks. Polymers (Basel) 2021; 13:polym13122031. [PMID: 34205822 PMCID: PMC8233940 DOI: 10.3390/polym13122031] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Revised: 06/14/2021] [Accepted: 06/14/2021] [Indexed: 11/16/2022] Open
Abstract
Semiflexible nunchucks are block copolymers consisting of two long blocks with high bending rigidity jointed by a short block of lower bending stiffness. Recently, the DNA nanotube nunchuck was introduced as a simple nanoinstrument that mechanically magnifies the bending angle of short double-stranded (ds) DNA and allows its measurement in a straightforward way [Fygenson et al., Nano Lett. 2020, 20, 2, 1388-1395]. It comprises two long DNA nanotubes linked by a dsDNA segment, which acts as a hinge. The semiflexible nunchuck geometry also appears in dsDNA with a hinge defect (e.g., a quenched denaturation bubble or a nick), and in end-linked stiff filaments. In this article, we theoretically investigate various aspects of the conformations and the tensile elasticity of semiflexible nunchucks. We analytically calculate the distribution of bending fluctuations of a wormlike chain (WLC) consisting of three blocks with different bending stiffness. For a system of two weakly bending WLCs end-jointed by a rigid kink, with one end grafted, we calculate the distribution of positional fluctuations of the free end. For a system of two weakly bending WLCs end-jointed by a hinge modeled as harmonic bending spring, with one end grafted, we calculate the positional fluctuations of the free end. We show that, under certain conditions, there is a pronounced bimodality in the transverse fluctuations of the free end. For a semiflexible nunchuck under tension, under certain conditions, there is bimodality in the extension as a function of the hinge position. We also show how steric repulsion affects the bending fluctuations of a rigid-rod nunchuck.
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4
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Noh G, Benetatos P. Tensile elasticity of a freely jointed chain with reversible hinges. SOFT MATTER 2021; 17:3333-3345. [PMID: 33630011 DOI: 10.1039/d1sm00053e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Many biopolymers exhibit reversible conformational transitions within the chain, which affect their bending stiffness and their response to a stretching force. For example, double stranded DNA may have denatured "bubbles" of unzipped single strands which open and close randomly. In other polymers, the transitions may be due to the reversible attachment and detachment of ligands on ligand-receptor complexes along the backbone. Semiflexible bundles under tension formed by the reversible attachment of cross-linkers, on a coarse-grained level, exhibit similar behaviour. The simplest theoretical model which captures what the above mentioned systems have in common is a freely jointed chain (FJC) with reversible hinges. Each hinge can be open, as in the usual FJC, or closed forcing the adjacent segments to align (stretch). In this article, we analyse it in the Gibbs ensemble. Remarkably, even though the usual FJC in the thermodynamic limit exhibits ensemble equivalence, the reversible FJC exhibits ensemble inequivalence. Even though a mean field treatment suggests a continuous phase transition to a fully hinged state at a certain force, the generating function method ("necklace model") shows that there is no phase transition. However, there is a crossover between the two states with clearly different responses. In the low force (linear response) regime, the reversible FJC has higher tensile compliance than its usual counterpart. In contrast, in the strong force regime, the tensile compliance of the reversible FJC is much lower than that of the usual FJC.
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Affiliation(s)
- Geunho Noh
- Department of Physics, Kyungpook National University, Bukgu, 80 Daehakro, Daegu 41566, Korea.
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5
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Bergues-Pupo AE, Lipowsky R, Vila Verde A. Unfolding mechanism and free energy landscape of single, stable, alpha helices at low pull speeds. SOFT MATTER 2020; 16:9917-9928. [PMID: 33030193 DOI: 10.1039/d0sm01166e] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Single alpha helices (SAHs) stable in isolated form are often found in motor proteins where they bridge functional domains. Understanding the mechanical response of SAHs is thus critical to understand their function. The quasi-static force-extension relation of a small number of SAHs is known from single-molecule experiments. Unknown, or still controversial, are the molecular scale details behind those observations. We show that the deformation mechanism of SAHs pulled from the termini at pull speeds approaching the quasi-static limit differs from that of typical helices found in proteins, which are stable only when interacting with other protein domains. Using molecular dynamics simulations with atomistic resolution at low pull speeds previously inaccessible to simulation, we show that SAHs start unfolding from the termini at all pull speeds we investigated. Unfolding proceeds residue-by-residue and hydrogen bond breaking is not the main event determining the barrier to unfolding. We use the molecular simulation data to test the cooperative sticky chain model. This model yields excellent fits of the force-extension curves and quantifies the distance, xE = 0.13 nm, to the transition state, the natural frequency of bond vibration, ν0 = 0.82 ns-1, and the height, V0 = 2.9 kcal mol-1, of the free energy barrier associated with the deformation of single residues. Our results demonstrate that the sticky chain model could advantageously be used to analyze experimental force-extension curves of SAHs and other biopolymers.
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Affiliation(s)
- Ana Elisa Bergues-Pupo
- Max Planck Institute of Colloids and Interfaces, Department of Theory & Bio-Systems, Am Mühlenberg 1, 14476 Potsdam, Germany.
| | - Reinhard Lipowsky
- Max Planck Institute of Colloids and Interfaces, Department of Theory & Bio-Systems, Am Mühlenberg 1, 14476 Potsdam, Germany.
| | - Ana Vila Verde
- Max Planck Institute of Colloids and Interfaces, Department of Theory & Bio-Systems, Am Mühlenberg 1, 14476 Potsdam, Germany.
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6
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Sluysmans D, Willet N, Thevenot J, Lecommandoux S, Duwez AS. Single-molecule mechanical unfolding experiments reveal a critical length for the formation of α-helices in peptides. NANOSCALE HORIZONS 2020; 5:671-678. [PMID: 32226978 DOI: 10.1039/d0nh00036a] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
α-Helix is the most predominant secondary structure in proteins and supports many functions in biological machineries. The conformation of the helix is dictated by many factors such as its primary sequence, intramolecular interactions, or the effect of the close environment. Several computational studies have proposed that there is a critical maximum length for the formation of intact compact helical structures, supporting the fact that most intact α-helices in proteins are constituted of a small number of amino acids. To obtain a detailed picture on the formation of α-helices in peptides and their mechanical stability, we have synthesized a long homopolypeptide of about 90 amino acids, poly(γ-benzyl-l-glutamate), and investigated its mechanical behaviour by AFM-based single-molecule force spectroscopy. The characteristic plateaus observed in the force-extension curves reveal the unfolding of a series of small helices (from 1 to 4) of about 20 amino acid residues connected to each other, rather than a long helix of 90 residues. Our results suggest the formation of a tertiary structure made of short helices with kinks, instead of an intact compact helical structure for sequences of more than 20 amino acid residues. To our knowledge, this is the first experimental evidence supporting the concept of a helical critical length previously proposed by several computational studies.
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Affiliation(s)
- Damien Sluysmans
- Molecular Systems Research Unit, University of Liège, Sart-Tilman B6a, 4000 Liège, Belgium.
| | - Nicolas Willet
- Molecular Systems Research Unit, University of Liège, Sart-Tilman B6a, 4000 Liège, Belgium. and Univ. Bordeaux, CNRS, Bordeaux INP, LCPO, UMR 5629, F-33600, Pessac, France
| | - Julie Thevenot
- Univ. Bordeaux, CNRS, Bordeaux INP, LCPO, UMR 5629, F-33600, Pessac, France
| | | | - Anne-Sophie Duwez
- Molecular Systems Research Unit, University of Liège, Sart-Tilman B6a, 4000 Liège, Belgium.
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7
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Kuo CC, Kachan D, Levine AJ, Dennin M. Bubble-raft collapse and the nonequilibrium dynamics of two-state elastica. Phys Rev E 2016; 93:032613. [PMID: 27078420 DOI: 10.1103/physreve.93.032613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2015] [Indexed: 11/07/2022]
Abstract
We report on the collapse of bubble rafts under compression in a closed rectangular geometry. A bubble raft is a single layer of bubbles at the air-water interface. A collapse event occurs when bubbles submerge beneath the neighboring bubbles under compression, causing the structure of the bubble raft to go from single-layer to multilayer. We studied the collapse dynamics as a function of compression velocity. At higher compression velocity we observe a more uniform distribution of collapse events, whereas at lower compression velocities the collapse events accumulate at the system boundaries. We propose that this system can be understood in terms of a linear elastic sheet coupled to a local internal (Ising) degree of freedom. The two internal states, which represent one bubble layer versus two, couple to the elasticity of the sheet by locally changing the reference state of the material. By exploring the collapse dynamics of the bubble raft, one may address the basic nonlinear mechanics of a number of complex systems in which elastic stress is coupled to local internal variables.
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Affiliation(s)
- Chin-Chang Kuo
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
| | - Devin Kachan
- Department of Physics & Astronomy, University of California, Los Angeles, California 90095, USA
| | - Alex J Levine
- Department of Physics & Astronomy, University of California, Los Angeles, California 90095, USA.,Department of Chemistry & Biochemistry, University of California, Los Angeles, California 90095, USA.,Department of Biomathematics, University of California, Los Angeles, California 90095, USA
| | - Michael Dennin
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA.,Institute for Complex Adaptive Matter, University of California, Irvine, California 92697, USA
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8
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Abstract
The treatment of bending and buckling of stiff biopolymer filaments by the popular worm-like chain model does not provide adequate understanding of these processes at the microscopic level. Thus, we have used the atomistic molecular-dynamic simulations and the Amber03 force field to examine the compression buckling of α-helix (AH) filaments at room temperature. It was found that the buckling instability occurs in AHs at the critical force f(c) in the range of tens of pN depending on the AH length. The decrease of the force f(c) with the contour length follows the prediction of the classic thin rod theory. At the force f(c) the helical filament undergoes the swift and irreversible transition from the smoothly bent structure to the buckled one. A sharp kink in the AH contour arises at the transition, accompanied by the disruption of the hydrogen bonds in its vicinity. The kink defect brings in an effective softening of the AH molecule at buckling. Nonbonded interactions between helical branches drive the rearrangement of a kinked AH into the ultimate buckled structure of a compact helical hairpin described earlier in the literature.
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Affiliation(s)
- Peter Palenčár
- Polymer Institute, Slovak Academy of Sciences, 845 41 Bratislava, Slovakia
| | - Tomáš Bleha
- Polymer Institute, Slovak Academy of Sciences, 845 41 Bratislava, Slovakia
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9
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Sharma GP, Reshetnyak YK, Andreev OA, Karbach M, Müller G. Coil-helix transition of polypeptide at water-lipid interface. JOURNAL OF STATISTICAL MECHANICS (ONLINE) 2015; 2015:P01034. [PMID: 31456824 PMCID: PMC6711616 DOI: 10.1088/1742-5468/2015/01/p01034] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We present the exact solution of a microscopic statistical mechanical model for the transformation of a long polypeptide between an unstructured coil conformation and an α-helix conformation. The polypeptide is assumed to be adsorbed to the interface between a polar and a non-polar environment such as realized by water and the lipid bilayer of a membrane. The interfacial coil-helix transformation is the first stage in the folding process of helical membrane proteins. Depending on the values of model parameters, the conformation changes as a crossover, a discontinuous transition, or a continuous transition with helicity in the role of order parameter. Our model is constructed as a system of statistically interacting quasiparticles that are activated from the helix pseudo-vacuum. The particles represent links between adjacent residues in coil conformation that form a self-avoiding random walk in two dimensions. Explicit results are presented for helicity, entropy, heat capacity, and the average numbers and sizes of sboth coil and helix segments.
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Affiliation(s)
- Ganga P Sharma
- Department of Physics, University of Rhode Island, Kingston RI 02881, USA
| | - Yana K Reshetnyak
- Department of Physics, University of Rhode Island, Kingston RI 02881, USA
| | - Oleg A Andreev
- Department of Physics, University of Rhode Island, Kingston RI 02881, USA
| | - Michael Karbach
- Fachgruppe Physik, Bergische Universität Wuppertal, D-42097 Wuppertal, Germany
| | - Gerhard Müller
- Department of Physics, University of Rhode Island, Kingston RI 02881, USA
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10
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Massucci FA, Pérez Castillo I, Pérez Vicente CJ. Cavity approach for modeling and fitting polymer stretching. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052708. [PMID: 25493817 DOI: 10.1103/physreve.90.052708] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2014] [Indexed: 06/04/2023]
Abstract
The mechanical properties of molecules are today captured by single molecule manipulation experiments, so that polymer features are tested at a nanometric scale. Yet devising mathematical models to get further insight beyond the commonly studied force-elongation relation is typically hard. Here we draw from techniques developed in the context of disordered systems to solve models for single and double-stranded DNA stretching in the limit of a long polymeric chain. Since we directly derive the marginals for the molecule local orientation, our approach allows us to readily calculate the experimental elongation as well as other observables at wish. As an example, we evaluate the correlation length as a function of the stretching force. Furthermore, we are able to fit successfully our solution to real experimental data. Although the model is admittedly phenomenological, our findings are very sound. For single-stranded DNA our solution yields the correct (monomer) scale and yet, more importantly, the right persistence length of the molecule. In the double-stranded case, our model reproduces the well-known overstretching transition and correctly captures the ratio between native DNA and overstretched DNA. Also in this case the model yields a persistence length in good agreement with consensus, and it gives interesting insights into the bending stiffness of the native and overstretched molecule, respectively.
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Affiliation(s)
| | - Isaac Pérez Castillo
- Department of Mathematics, King's College London, London WC2R 2LS, United Kingdom and Instituto de Física, Universidad Nacional Autónoma de México, P.O. Box 20-364, México DF 01000, México
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11
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Mishra A, Panwar AS, Chakrabarti B. Equilibrium Morphologies and Force Extension Behavior for Polymers with Hydrophobic Patches: Role of Quenched Disorder. MACROMOL THEOR SIMUL 2014. [DOI: 10.1002/mats.201300154] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Ankur Mishra
- Department of Metallurgical Engineering and Materials Science; Indian Institute of Technology Bombay; Powai, Mumbai 400076 India
- Department of Mathematical Sciences; Durham University; Durham DH1 3LE UK
- Isaac Newton Institute of Mathematical Sciences; 20 Clarkson Road Cambridge CB3 0EH UK
| | - Ajay Singh Panwar
- Department of Metallurgical Engineering and Materials Science; Indian Institute of Technology Bombay; Powai, Mumbai 400076 India
- Department of Mathematical Sciences; Durham University; Durham DH1 3LE UK
- Isaac Newton Institute of Mathematical Sciences; 20 Clarkson Road Cambridge CB3 0EH UK
| | - Buddhapriya Chakrabarti
- Department of Metallurgical Engineering and Materials Science; Indian Institute of Technology Bombay; Powai, Mumbai 400076 India
- Department of Mathematical Sciences; Durham University; Durham DH1 3LE UK
- Isaac Newton Institute of Mathematical Sciences; 20 Clarkson Road Cambridge CB3 0EH UK
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12
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van Buul AM, Schwartz E, Brocorens P, Koepf M, Beljonne D, Maan JC, Christianen PCM, Kouwer PHJ, Nolte RJM, Engelkamp H, Blank K, Rowan AE. Stiffness versus architecture of single helical polyisocyanopeptides. Chem Sci 2013. [DOI: 10.1039/c3sc50552a] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
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13
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Evans AA, Levine AJ. High-energy deformation of filaments with internal structure and localized torque-induced melting of DNA. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:051915. [PMID: 23004795 DOI: 10.1103/physreve.85.051915] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2012] [Indexed: 06/01/2023]
Abstract
We develop a continuum elastic approach to examining the bending mechanics of semiflexible filaments with a local internal degree of freedom that couples to the bending modulus. We apply this model to study the nonlinear mechanics of a double-stranded DNA oligomer (shorter than its thermal persistence length) whose free ends are linked by a single-stranded DNA chain. This construct, studied by H. Qu and G. Zocchi [Europhys. Lett. 94, 18003 (2011)], displays nonlinear strain softening associated with the local melting of the double-stranded DNA under applied torque and serves as a model system with which to study the nonlinear elasticity of DNA under large energy deformations. We show that one can account quantitatively for the observed bending mechanics using an augmented wormlike chain model, the helix-coil wormlike chain. We also predict that the highly bent and partially molten dsDNA should exhibit particularly large end-to-end fluctuations associated with the fluctuation of the length of the molten region, and propose appropriate experimental tests. We suggest that the augmented wormlike chain model discussed here is a useful analytic approach to the nonlinear mechanics of DNA or other biopolymer systems.
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Affiliation(s)
- Arthur A Evans
- Department of Chemistry & Biochemistry, University of California, Los Angeles, California 90095, USA
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14
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Tensile Mechanics of α-Helical Coil Springs. Biopolymers 2010. [DOI: 10.1007/12_2009_41] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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15
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Montana V, Liu W, Mohideen U, Parpura V. Single molecule measurements of mechanical interactions within ternary SNARE complexes and dynamics of their disassembly: SNAP25 vs. SNAP23. J Physiol 2009; 587:1943-60. [PMID: 19273577 DOI: 10.1113/jphysiol.2009.168575] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
Regulated exocytosis is a crucial event for intercellular communication between neurons and astrocytes within the CNS. The soluble N-ethylmaleimide-sensitive fusion protein attachment protein receptor (SNARE) complex, composed of synaptobrevin 2, syntaxin and synaptosome-associated protein of 25 kDa or 23 kDa (SNAP25 or SNAP23), is essential in this process. It was reported that SNAP25 and SNAP23 have distinct roles in exocytotic release, where SNAP25, but not SNAP23, supports an exocytotic burst. It is not clear, however, whether this is due to the intrinsic properties of the ternary SNARE complex, containing either SNAP25 or SNAP23, or perhaps due to the differential association of these proteins with ancillary proteins to the complex. Here, using force spectroscopy, we show from single molecule investigations of the SNARE complex, that SNAP23A created a local interaction at the ionic layer by cuffing syntaxin 1A and synaptobrevin 2, similar to the action of SNAP25B; thus either of the ternary complexes would allow positioning of vesicles at a maximal distance of approximately 13 nm from the plasma membrane. However, the stability of the ternary SNARE complex containing SNAP23A is less than half of that for the complex containing SNAP25B. Thus, differences in the stability of the two different ternary complexes could underlie some of the SNAP25/23 differential ability to control the exocytotic burst.
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Affiliation(s)
- Vedrana Montana
- Department of Neurobiology, University of Alabama, Birmingham, AL 35294, USA
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16
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Zegarra FC, Peralta GN, Coronado AM, Gao YQ. Free energies and forces in helix-coil transition of homopolypeptides under stretching. Phys Chem Chem Phys 2009; 11:4019-24. [PMID: 19440631 DOI: 10.1039/b820021a] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We show here that constant velocity steered molecular dynamics (SMD) simulations of alpha-helices in a vacuum present a well defined plateau in the force-extension relationship for homopolypeptides having more than (approximately) twenty residues. With the processes being far away from equilibrium, the energies strongly depend on the stretching velocity. Importantly, for a given velocity variation, the energy variation depends also on the helix sequence. Additionally, our observations show that homopolypeptides made of ten different amino acids (Ala, Cys, Gln, Ile, Leu, Met, Phe, Ser, Thr and Val) present a linear helix-coil transition.
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Affiliation(s)
- Fabio C Zegarra
- Facultad de Ingeniería Mecánica, Universidad Nacional de Ingeniería, Lima, Peru
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17
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Abstract
Single molecule experiments have opened promising new avenues of investigations in biology, but the quantitative interpretation of results remains challenging. In particular, there is a need for a comparison of such experiments with theoretical methods. We experimentally determine the activation free energy for single molecule interactions between two synaptic proteins syntaxin 1A and synaptobrevin 2, using an atomic force microscope and the Jarzynski equality of nonequilibrium thermodynamics. The value obtained is shown to be reasonably consistent with that from single molecule reaction rate theory. The temperature dependence of the spontaneous dissociation lifetime along with different pulling speeds is used to confirm the approach to the adiabatic limit. This comparison of the Jarzynski equality for intermolecular interactions extends the procedure for calculation of activation energies in nonequilibrium processes.
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18
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Chakrabarti B, Levine AJ. Nonlinear elasticity of an alpha-helical polypeptide: Monte Carlo studies. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:031903. [PMID: 17025663 DOI: 10.1103/physreve.74.031903] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2004] [Revised: 06/12/2006] [Indexed: 05/12/2023]
Abstract
We report on Monte Carlo studies of the elastic properties of the helix-coil wormlike chain model of alpha-helical polypeptides. In this model the secondary structure enters as a scalar (Ising-like) variable that controls the local chain bending modulus. We characterize the nonlinear elastic properties of these molecules including their response to applied tensile forces and bending torques both individually and in combination. We find a pronounced effect of applied torque on the extensional compliance of the molecule and a similar effect of tension on the bending compliance. Finally we speculate that the strongly nonlinear response of alpha-helical polypeptides to combinations of torque and force plays a role in allosteric transitions in proteins.
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19
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Allemand JF, Cocco S, Douarche N, Lia G. Loops in DNA: an overview of experimental and theoretical approaches. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2006; 19:293-302. [PMID: 16554978 DOI: 10.1140/epje/i2005-10073-y] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2005] [Accepted: 02/02/2006] [Indexed: 05/07/2023]
Abstract
DNA loop formation plays a central role in many cellular processes. The aim of this paper is to present the state of the art and open problems regarding the experimental and theoretical approaches to DNA looping. A particular attention is devoted to the effects of the protein bridge size and of protein induced sharp DNA bending on DNA loop formation enhancement.
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Affiliation(s)
- J-F Allemand
- Laboratoire de Physique Statistique de l'ENS, CNRS, 24 rue Lhomond, 75005, Paris, France
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20
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Ziv G, Haran G, Thirumalai D. Ribosome exit tunnel can entropically stabilize alpha-helices. Proc Natl Acad Sci U S A 2005; 102:18956-61. [PMID: 16357202 PMCID: PMC1323178 DOI: 10.1073/pnas.0508234102] [Citation(s) in RCA: 115] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Several experiments have suggested that newly synthesized polypeptide chains can adopt helical structures deep within the ribosome exit tunnel. We hypothesize that confinement in the roughly cylindrical tunnel can entropically stabilize alpha-helices. The hypothesis is validated by using theory and simulations of coarse-grained off-lattice models. The model helix, which is unstable in the bulk, is stabilized in a cylindrical cavity provided the diameter (D) of the cylinder exceeds a critical value D*. When D < D* both the helical content and the helix-coil transition temperature (T(f)) decrease abruptly. Surprisingly, we find that the stability of the alpha-helix depends on the number (N) of amino acid residues. Entropic stabilization, as measured by changes in T(f), increases nonlinearly as N increases. The simulation results are in quantitative agreement with a standard helix-coil theory that takes into account entropy cost of confining a polypeptide chain in a cylinder. The results of this work are in qualitative accord with most of the findings of a recent experiment in which N-dependent ribosome-induced helix stabilization of transmembrane sequences was measured by fluorescence resonance energy transfer.
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Affiliation(s)
- Guy Ziv
- Department of Chemical Physics, Weizmann Institute of Science, POB 26, Rehovot 76100, Israel
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Douarche N, Cocco S. Protein-mediated DNA loops: effects of protein bridge size and kinks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:061902. [PMID: 16485969 DOI: 10.1103/physreve.72.061902] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2005] [Indexed: 05/06/2023]
Abstract
This paper focuses on the probability that a portion of DNA closes on itself through thermal fluctuations. We investigate the dependence of this probability upon the size of a protein bridge and/or the presence of a kink at half DNA length. The DNA is modeled by the wormlike chain model, and the probability of loop formation is calculated in two ways: exact numerical evaluation of the constrained path integral and the extension of the Shimada and Yamakawa saddle point approximation. For example, we find that the looping free energy of a 100-base-pairs DNA decreases from 24 kBT to 13 kBT when the loop is closed by a protein of r=10 length. It further decreases 5 kBT to when the loop has a kink of 120 degrees at half-length.
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Affiliation(s)
- Nicolas Douarche
- CNRS-Laboratoire de Physique Statistique de l'ENS, 24 rue Lhomond, 75005 Paris, France
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Prasad A, Hori Y, Kondev J. Elasticity of semiflexible polymers in two dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:041918. [PMID: 16383431 DOI: 10.1103/physreve.72.041918] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2005] [Indexed: 05/05/2023]
Abstract
We study theoretically the entropic elasticity of a semiflexible polymer, such as DNA, confined to two dimensions. Using the worm-like-chain model we obtain an exact analytical expression for the partition function of the polymer pulled at one end with a constant force. The force-extension relation for the polymer is computed in the long chain limit in terms of Mathieu characteristic functions. We also present applications to the interaction between a semiflexible polymer and a nematic field, and derive the nematic order parameter and average extension of the polymer in a strong field.
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Affiliation(s)
- Ashok Prasad
- Martin Fisher School of Physics, Brandeis University, Mailstop 057, Waltham, Massachusetts 02454-9110, USA.
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