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- Elasticity of Short DNA Molecules: Theory and Experiment for...Elasticity of Short DNA Molecules: Theory and Experiment for Contour Lengths of 0.6–7μm
Biophysical Journal, Volume 93, Issue 12, 15 December 2007, Pages 4360-4373
Yeonee Seol, Jinyu Li, Philip C. Nelson, Thomas T. Perkins and M.D. Betterton
AbstractThe wormlike chain (WLC) model currently provides the best description of double-stranded DNA elasticity for micron-sized molecules. This theory requires two intrinsic material parameters—the contour length and the persistence length . We measured and then analyzed the elasticity of double-stranded DNA as a function of (632nm–7.03m) using the classic solution to the WLC model. When the elasticity data were analyzed using this solution, the resulting fitted value for the persistence length depended on ; even for moderately long DNA molecules (=1300nm), this apparent persistence length was 10% smaller than its limiting value for long DNA. Because is a material parameter, and cannot depend on length, we sought a new solution to the WLC model, which we call the “finite wormlike chain (FWLC),” to account for effects not considered in the classic solution. Specifically we accounted for the finite chain length, the chain-end boundary conditions, and the bead rotational fluctuations inherent in optical trapping assays where beads are used to apply the force. After incorporating these corrections, we used our FWLC solution to generate force-extension curves, and then fit those curves with the classic WLC solution, as done in the standard experimental analysis. These results qualitatively reproduced the apparent dependence of on seen in experimental data when analyzed with the classic WLC solution. Directly fitting experimental data to the FWLC solution reduces the apparent dependence of on by a factor of 3. Thus, the FWLC solution provides a significantly improved theoretical framework in which to analyze single-molecule experiments over a broad range of experimentally accessible DNA lengths, including both short (a few hundred nanometers in contour length) and very long (microns in contour length) molecules.
Abstract | Full Text | PDF (676 kb) - Inferring the Diameter of a Biopolymer from Its Stretching R...Inferring the Diameter of a Biopolymer from Its Stretching Response
Biophysical Journal, Volume 89, Issue 1, 1 July 2005, Pages 80-86
Ngo Minh Toan, Davide Marenduzzo and Cristian Micheletti
AbstractWe investigate the stretching response of a thick polymer model by means of extensive stochastic simulations. The computational results are synthesized in an analytic expression that characterizes how the force versus elongation curve depends on the polymer structural parameters: its thickness and granularity (spacing of the monomers). The expression is used to analyze experimental data for the stretching of various different types of biopolymers: polypeptides, polysaccharides, and nucleic acids. Besides recovering elastic parameters (such as the persistence length) that are consistent with those obtained from standard entropic models, the approach allows us to extract viable estimates for the polymers diameter and granularity. This shows that the basic structural polymer features have such a profound impact on the elastic behavior that they can be recovered with the sole input of stretching measurements.
Abstract | Full Text | PDF (154 kb) - Entropic Elasticity Controls Nanomechanics of Single Tropoco...Entropic Elasticity Controls Nanomechanics of Single Tropocollagen Molecules
Biophysical Journal, Volume 93, Issue 1, 1 July 2007, Pages 37-43
Markus J. Buehler and Sophie Y. Wong
AbstractWe report molecular modeling of stretching single molecules of tropocollagen, the building block of collagen fibrils and fibers that provide mechanical support in connective tissues. For small deformation, we observe a dominance of entropic elasticity. At larger deformation, we find a transition to energetic elasticity, which is characterized by first stretching and breaking of hydrogen bonds, followed by deformation of covalent bonds in the protein backbone, eventually leading to molecular fracture. Our force-displacement curves at small forces show excellent quantitative agreement with optical tweezer experiments. Our model predicts a persistence length ≈ 16nm, confirming experimental results suggesting that tropocollagen molecules are very flexible elastic entities. We demonstrate that assembly of single tropocollagen molecules into fibrils significantly decreases their bending flexibility, leading to decreased contributions of entropic effects during deformation. The molecular simulation results are used to develop a simple continuum model capable of describing an entire deformation range of tropocollagen molecules. Our molecular model is capable of describing different regimes of elastic and permanent deformation, without relying on empirical parameters, including a transition from entropic to energetic elasticity.
Abstract | Full Text | PDF (488 kb) - …more
Copyright © 2007 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 93, Issue 12, 4099, 15 December 2007
doi:10.1529/biophysj.107.117572
New and Notable
The Great Hunt For Extra Compliance
Jan Liphardt
, 
Physics Department, University of California, Berkeley, California
Address reprint requests to Jan Liphardt, Tel.: 510-642-3578.Every field has skeletons in their closet. One of the skeletons of single molecule biophysics is the persistence length of short DNA molecules. Loosely speaking, the persistence length, P, is a statement about the elasticity of a polymer; an infinitely stiff polymer has an infinite P. Knowledge of the persistence length of DNA and RNA is essential to design and interpret single-molecule experiments. Two models of polymer elasticity constitute the theoretical bedrock of the field: the freely-jointed chain and the wormlike chain (WLC). In this issue, Seol et al. 1 extend the classic WLC model in a way that will be immediately useful to experimentalists working on a multitude of systems.
The story starts in the early 1990s, when it became possible to experimentally characterize the elasticity of single DNA molecules. In 1994, Bustamante et al. 2 reported that force extension curves of λ-DNA beautifully fit the WLC model. Despite λ-DNA having a finite length (97kb) and clearly not being an ideal polymer, a continuum elastic theory such as the WLC captured its elasticity surprisingly well. Right from the beginning, however, it was apparent that we should not expect the WLC to faithfully represent all DNAs in all situations. Even in the first article there were hints of the stretchable solid regime at forces above ∼10 pN, and at even higher forces the DNA suddenly overstretched 3, another clear departure from the WLC model.
Nonetheless, one thing was sacred: the persistence length of DNA. The persistence length certainly did depend on ionic strength, pH, and intercalators 3,4,5, but incoming graduate students were told that P captured an intrinsic property of DNA and did not depend on the polymer’s length. Most practitioners suspected that this was not true, since the concept of a persistence length becomes ill-defined when the polymer is not much longer than P. Moreover, many experimental studies of short pieces of DNA revealed that it was more compliant than predicted from the classic WLC parameterized with the canonical value of P, 50nm.
What we did not know was how P depends on the contour length, and when we need to explicitly incorporate finite L effects in our models and experiments. This is what makes the finite-WLC of Seol et al. so useful—this extension of the classic WLC includes three effects critical to experiments: the finite length of the chain, rotational fluctuations of the bead, and the boundary conditions at the polymer’s anchor points.
As described by Seol et al., there are two equivalent ways of applying the finite-WLC to force-extension curves. Experimental data can be fit directly to the finite-WLC, or the data can be fit to the classic WLC, and all the complexity can be dealt with by correcting P for the effects discussed above. The former approach is conceptually more elegant, and the latter approach is mathematically simpler and is easy to plug into existing data-processing scripts.
Out of curiosity, I compared the performance of the classic WLC to the finite-WLC using some single-molecule RNA unfolding data 6, and I found that the finite-WLC does rather well. The article of Seol et al. contains extensive experimental results that establish the performance of their finite-WLC.
Is the finite-WLC the end of the story? Fortunately not—a multitude of essential biological processes take place on length scales far below one persistence length, and we are only beginning to understand the intricacies of DNA and RNA elasticity on short and very short scales. Nonetheless, the finite-WLC gives us a glimpse of what future models of DNA elasticity will look like. Not only that, but Seol et al. also gives us a blueprint for constructing elasticity models for specific experimental geometries and length scales.
References
1. (2007). Elasticity of short DNA molecules: theory and experiment for contour lengths of 0.6–7μm. Biophys. J. 93, 4360–4373. Abstract | Full Text | PDF (676 kb) | CrossRef | PubMed
2. (1994). Entropic elasticity of λ-phage DNA. Science 265, 1599–1600. PubMed
3. (1996). Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules. Science 271, 795–799. PubMed
4. (1997). Ionic effects on the elasticity of single DNA molecules. Proc. Natl. Acad. Sci. USA 94, 6185–6190. CrossRef | PubMed
5. (2001). The effect of pH on the overstretching transition of double-stranded DNA: evidence of force-induced DNA melting. Biophys. J. 80, 874–881. Abstract | Full Text | PDF (179 kb) | PubMed
6. (2001). Reversible unfolding of single RNA molecules by mechanical force. Science 292, 733–737. CrossRef | PubMed
Publication Information
Received: August 2, 2007
Accepted: August 14, 2007
