Easyworm: an open-source software tool to determine the mechanical properties of worm-like chains
- Guillaume Lamour^{1, 2, 3}Email author,
- Julius B Kirkegaard^{4},
- Hongbin Li^{3},
- Tuomas PJ Knowles^{4} and
- Jörg Gsponer^{1, 3}
DOI: 10.1186/1751-0473-9-16
© Lamour et al.; licensee BioMed Central Ltd. 2014
Received: 23 December 2013
Accepted: 2 July 2014
Published: 10 July 2014
Abstract
Background
A growing spectrum of applications for natural and synthetic polymers, whether in industry or for biomedical research, demands for fast and universally applicable tools to determine the mechanical properties of very diverse polymers. To date, determining these properties is the privilege of a limited circle of biophysicists and engineers with appropriate technical skills.
Findings
Easyworm is a user-friendly software suite coded in MATLAB that simplifies the image analysis of individual polymeric chains and the extraction of the mechanical properties of these chains. Easyworm contains a comprehensive set of tools that, amongst others, allow the persistence length of single chains and the Young’s modulus of elasticity to be calculated in multiple ways from images of polymers obtained by a variety of techniques (e.g. atomic force microscopy, electron, contrast-phase, or epifluorescence microscopy).
Conclusions
Easyworm thus provides a simple and efficient tool for specialists and non-specialists alike to solve a common problem in (bio)polymer science. Stand-alone executables and shell scripts are provided along with source code for further development.
Keywords
Matlab GUI Polymer Worm-like chain model Persistence length Young’s modulus AFMIntroduction
Although different approaches have been developed over the years to determine the nanomechanical properties of different biopolymers[1–3], it is mainly biophysicists and engineers with appropriate technical skills who have been able to use them. However, the growing number of technological applications for functional biopolymers such as modified cytoskeletal filaments or engineered DNA[4, 5] asks for a fast and easy way to determine their mechanical properties that is also accessible to non-specialists. Here we present a new software tool, Easyworm[6], for the determination of the persistence length of polymer chains and derivation of their axial elastic modulus. This open-source software provides accurate measurements of the persistence length varied over 6 orders of magnitude (from nm to mm ranges) and can be used by specialists and non-specialists alike.
Implementation
Easyworm consists of several graphical user interfaces (GUI) functioning as stand-alone applications for Microsoft Windows or Linux operating systems. They require the appropriate MATLAB Compiler Runtime (MCR) version to be installed. Source code (.m) files along with GUIDE .fig files will also work under a MATLAB environment. They can also be deployed as stand-alone executables or shell scripts, providing the MATLAB compiler toolbox is installed on the development machine. MCR versions, executable files, shell scripts and the source code are freely available athttp://www.chibi.ubc.ca/faculty/joerg-gsponer/gsponer-lab/software/easyworm. Detailed installation notes are provided on the same webpage. In addition, step-by-step instructions of how to use the software are provided in the Additional file1 of this paper (Easyworm_SuppInfo.pdf).
Methods overview
Persistence length calculations
Uncertainties on persistence length calculations
Uncertainties in the calculated persistence lengths are determined via random resampling using the standard method of bootstrap with replacement[7]. In short, new chain samples (bootstrap samples) that contain k chains are randomly chosen from the available k chains. As the bootstrap samples are different from the original sample, any chain can be selected more than once (see Ref[7] for details). For each bootstrap sample < cos θ >, < R^{2} >, or < δ^{2} > values are binned at regular length intervals as in Figure 2. Different forms of the WLC model are then fitted to the data. n (default 10) bootstrapping operations are done, and the mean of the n values returned at each iteration is the persistence length of the polymer. The standard deviation on the n values is the uncertainty on P (to which the uncertainty on the fractional dimension is propagated when considering non-equilibrated polymers, see Additional file1: Methods).
Additional tools
The standard deviation of this normal distribution is$<{\mathrm{\theta}}^{2}{\left(\ell \right)>}_{2\mathrm{D}}\phantom{\rule{0.5em}{0ex}}=\phantom{\rule{0.5em}{0ex}}\sqrt{\ell /\mathrm{P}}$. Therefore, we generated n segments of length ℓ joined at each other’s ends and forming angles θ randomly chosen according to a normal distribution around a mean 0 and with a standard deviation equal to$\sqrt{\ell /\mathrm{P}}$. Such synthetic chains are illustrated in Additional file1: Figure S4. Refer to Additional file1: Note S4 for details on how synthetic chains were used in the different analyses contained in this study.
Equilibration on the 2D surface
Another function implemented in Easyworm allows for the fast determination of the slope of < R > as a function of ℓ on any given range of ℓ (Figure 3b). Provided the contour length interval defined by the user to calculate this slope (corresponding to a scaling or fractal exponent[8]) is located above the persistence length (i.e. for ℓ > P), the slope is equal to 0.75 for a self-avoiding random walk in 2D[8]. We note that for our software, in practice, this measurement is accurate only for contour length values comprised between P and ~3P, since above 3P the number of data points available are usually too low to produce a measurement that is statistically significant.
Results and performance evaluation
Evaluation of the measurement accuracy using synthetic polymers with known persistence lengths as test samples
^{*}Sample | N chains | Persistence length according to all 3 measures (nm)^{†}(C_{D})^{‡}[interval; nm] | ||
---|---|---|---|---|
^{▲} < R^{2} > = f(ℓ) | ^{▲} < cos θ > = f(ℓ) | ^{▲} < δ^{2} > = f(ℓ) | ||
^{§}SP50 | 38 | ^{§}68 ± 3 (0.996) | ^{§}70 ± 6 (0.927) | – |
[0; 500] | [20; 500] | |||
SP750 | 78 | 777 ± 114 (0.999) | 728 ± 32 (0.968) | 538 ± 28 (0.961) |
[0; 1900] | [50; 1000] | [0; 300] | ||
^{¶}SP2500-1 | 44 | 2867 ± 372 (0.999) | 2599 ± 506 (0.947) | 2986 ± 914 (0.923) |
[0; 600] | [20; 500] | [0; 600] | ||
^{¶}SP2500-2 | 35 | 3047 ± 496 (0.999) | 3015 ± 590 (0.966) | 2894 ± 608 (0.991) |
[0; 2500] | [40; 2500] | [0; 1200] | ||
^{¤}SP2500-2 | 35 | 2525 ± 191 (0.999) | 2542 ± 214 (0.960) | 2441 ± 318 (0.966) |
[0; 600] | [40; 600] | [0; 600] | ||
SP8000 | 41 | 7280 ± 1060 (0.999) | 6669 ± 494 (0.789) | 8262 ± 1083 (0.949) |
[0; 1200] | [20; 700] | [0; 800] | ||
SP1e5 | 48 | 64264 ± 5514 (0.999) | – | 86475 ± 14480 (0.985) |
[0; 3500] | [0; 3500] | |||
SP5.2e6 | 70 | 1.49e5 ± 0.13e5 (0.999) | – | 5.64e6 ± 0.85e6 (0.994) |
[0; 19500] | [0; 18000] |
Conclusions
Easyworm is a tool for researchers in need of a fast and ready-to-use program in order to determine the persistence length and derive the elastic modulus of their polymers, whether these are amyloid fibrils[9] or any nano- or micro-filaments. In addition to determining the mechanical properties, Easyworm also provides complementary tools to analyze polymer contour lengths, create synthetic polymers, visualize polymers and generate output files for plotting purposes.
Authors’ information
GL is a postdoctoral research fellow in the laboratories of JG and HBL at the University of British Columbia (Canada). JBK is a student in TPJK’s laboratory at the University of Cambridge (UK). HBL is an associate professor in Chemistry, TPJK a lecturer in Physical Chemistry, and JG an assistant professor in Biochemistry.
Declarations
Acknowledgments
This work was financially supported by PrioNet Canada, the Canadian Institutes of Health Research (CIHR), and the Natural Sciences and Engineering Research Council of Canada (NSERC). We thank anonymous reviewers for their helpful comments.
Authors’ Affiliations
References
- Doi M, Edwards SF: The Theory of Polymer Dynamics. 1986, New York: Oxford University Press Inc.Google Scholar
- Gittes F, Mickey B, Nettleton J, Howard J: Flexural rigidity of microtubules and actin-filaments measured from thermal fluctuations in shape. J Cell Biol. 1993, 120: 923-934. 10.1083/jcb.120.4.923.View ArticlePubMedGoogle Scholar
- Rivetti C, Guthold M, Bustamante C: Scanning force microscopy of DNA deposited onto mica: Equilibration versus kinetic trapping studied by statistical polymer chain analysis. J Mol Biol. 1996, 264: 919-932. 10.1006/jmbi.1996.0687.View ArticlePubMedGoogle Scholar
- Grinthal A, Kang SH, Epstein AK, Aizenberg M, Khan M, Aizenberg J: Steering nanofibers: An integrative approach to bio-inspired fiber fabrication and assembly. Nano Today. 2012, 7: 35-52. 10.1016/j.nantod.2011.12.005.View ArticleGoogle Scholar
- Knowles TPJ, Buehler MJ: Nanomechanics of functional and pathological amyloid materials. Nat Nanotechnol. 2011, 6: 469-479. 10.1038/nnano.2011.102.View ArticlePubMedGoogle Scholar
- Easyworm free software. [http://www.chibi.ubc.ca/faculty/joerg-gsponer/gsponer-lab/software/easyworm].
- Efron B, Gong G: A leisurely look at the bootstrap, the jackknife, and cross-validation. Am Stat. 1983, 37: 36-48.Google Scholar
- Valle F, Favre M, De Los Rios P, Rosa A, Dietler G: Scaling exponents and probability distributions of DNA end-to-end distance. Phys Rev Lett. 2005, 95: 158105.View ArticlePubMedGoogle Scholar
- Lamour G, Yip CK, Li H, Gsponer J: High Intrinsic Mechanical Flexibility of Mouse Prion Nanofibrils Revealed by Measurements of Axial and Radial Young’s Moduli. ACS Nano. 2014, 8: 3851-3861. 10.1021/nn5007013.View ArticlePubMedGoogle Scholar
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