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Easyworm: an open-source software tool to determine the mechanical properties of worm-like chains Lamour, Guillaume; Kirkegaard, Julius B; Li, Hongbin; Knowles, Tuomas P; Gsponer, Jörg Jul 10, 2014

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BRIEF REPORTSEasyworm: an open-sourcelTuurlictieinpetheir mechanical properties that is also accessible to version to be installed. Source code (.m) files along withLamour et al. Source Code for Biology and Medicine 2014, 9:16http://www.scfbm.org/content/9/1/16the software are provided in the Additional file 1 of thispaper (Easyworm_SuppInfo.pdf).1Z1, CanadaFull list of author information is available at the end of the articlenon-specialists. Here we present a new software tool,Easyworm [6], for the determination of the persistencelength of polymer chains and derivation of their axialelastic modulus. This open-source software provides ac-curate measurements of the persistence length variedGUIDE .fig files will also work under a MATLAB envir-onment. They can also be deployed as stand-alone exe-cutables or shell scripts, providing the MATLABcompiler toolbox is installed on the development ma-chine. MCR versions, executable files, shell scripts andthe source code are freely available at http://www.chibi.ubc.ca/faculty/joerg-gsponer/gsponer-lab/software/easyworm.Detailed installation notes are provided on the same web-page. In addition, step-by-step instructions of how to use* Correspondence: lamour@chibi.ubc.ca1Centre for High-Throughput Biology, University of British Colombia,Vancouver, BC V6T 1Z4, Canada2Department of Chemistry, University of British Columbia, Vancouver, BC V6TDNA [4,5] asks for a fast and easy way to determineset of tools that, amongst others, allow the persistence length of single chains and the Young’s modulus of elasticity tobe calculated in multiple ways from images of polymers obtained by a variety of techniques (e.g. atomic forcemicroscopy, electron, contrast-phase, or epifluorescence microscopy).Conclusions: Easyworm thus provides a simple and efficient tool for specialists and non-specialists alike to solve acommon problem in (bio)polymer science. Stand-alone executables and shell scripts are provided along with sourcecode for further development.Keywords: Matlab, GUI, Polymer, Worm-like chain model, Persistence length, Young’s modulus, AFMIntroductionAlthough different approaches have been developed overthe years to determine the nanomechanical properties ofdifferent biopolymers [1-3], it is mainly biophysicists andengineers with appropriate technical skills who havebeen able to use them. However, the growing number oftechnological applications for functional biopolymerssuch as modified cytoskeletal filaments or engineeredover 6 orders of magnitude (from nm to mm ranges)and can be used by specialists and non-specialists alike.ImplementationEasyworm consists of several graphical user interfaces(GUI) functioning as stand-alone applications for Micro-soft Windows or Linux operating systems. They requirethe appropriate MATLAB Compiler Runtime (MCR)determine the mechanicachainsGuillaume Lamour1,2,3*, Julius B Kirkegaard4, Hongbin Li3,AbstractBackground: A growing spectrum of applications for natbiomedical research, demands for fast and universally appvery diverse polymers. To date, determining these properengineers with appropriate technical skills.Findings: Easyworm is a user-friendly software suite codedpolymeric chains and the extraction of the mechanical pro© 2014 Lamour et al.; licensee BioMed CentraCommons Attribution License (http://creativecreproduction in any medium, provided the orDedication waiver (http://creativecommons.orunless otherwise stated.MATLAB that simplifies the image analysis of individualrties of these chains. Easyworm contains a comprehensiveOpen Accesssoftware tool toproperties of worm-likeomas PJ Knowles4 and Jörg Gsponer1,3al and synthetic polymers, whether in industry or forable tools to determine the mechanical properties ofs is the privilege of a limited circle of biophysicists andl Ltd. This is an Open Access article distributed under the terms of the Creativeommons.org/licenses/by/2.0), which permits unrestricted use, distribution, andiginal work is properly credited. The Creative Commons Public Domaing/publicdomain/zero/1.0/) applies to the data made available in this article,epifluorescence, or simple contrast-phase optical micros-copy). Minimal user input is required in order to fit thecontour of polymers to parametric splines (see Figure 1b)after uploading height maps in the first GUI, Easyworm1(for detailed instructions see Additional file 1: Figure S1and Note S1 in Easyworm_SuppInfo.pdf ). Then Easy-worm2 (second GUI; Additional file 1: Figure S2 andNote S2) is used to derive the mechanical propertiesfrom the data collected by Easyworm1.Persistence length calculationsThe persistence length P of a sample of individual poly-meric chains can be obtained via three distinct measuresall derived from the worm-like chain model (WLC) forsemi-flexible polymers. The choice of the measure tocalculate P is highly dependent on the value of P withregard to the contour length of the polymer. For in-stance, P can be much higher (e.g. microtubules) orLamour et al. Source Code for Biology and Medicine 2014, 9:16 Page 2 of 6http://www.scfbm.org/content/9/1/16Figure 1 Easyworm workflow. (a) Atomic force microscopy image ofan amyloid fibril. (b) Same image as in (a), in which the contour of thefibril has been fitted to a parametric spline (red line; see Additional fileMethods overviewEasyworm is optimized for analyzing images of individ-ual polymer chains taken by atomic force microscopy(AFM; Figure 1) but can also be used for analyzing im-ages taken by other methods (e.g. electron microscopy,1: Note S1). (c) Three distinct amyloid fibril samples plotted with theirinitial tangents aligned to facilitate visualization. P is the persistencelength of the fibrils, derived from the measures shown in Figure 2.Figure 2 Three distinct measures used to calculate the persistence le(a) cos θ, (b) mean square of the end-to-end distances R, and (c) mean sqmain text for details). Red diamonds, blue squares, and green circles represchain model to the data (according to the equations indicated in the mainFigure 1 (same color as the fitted curves).much lower (e.g. DNA) than the contour length. Forquite flexible polymers, it is recommended to monitorthe decay of tangent-tangent correlations (Figure 2a) ac-cording to [1]:< cos θ > ¼ e− ℓsP ð1Þwhere θ is the angle between two segments of thespline separated by a distance ℓ along the chain con-tour. s is a surface parameter that is set by the userto a value of 2 for chains that have equilibrated onthe 2D surface or to a value of 1.5 ± 0.5 for nonequili-brated chains (see Easyworm_SuppInfo.pdf for moredetails). Another available option [3] (Figure 2b) is thength. The data were generated from the fibrils plotted in Figure 1.uare of the deviations δ to secant midpoints, as a function of ℓ (seeent data for three different amyloid fibrils. Lines: fits of the worm-liketext). Persistence lengths (P) derived from the fits are indicated inmeasurement of the mean square of the end-to-enddistance R as a function of ℓ:< R2 > ¼ 2sPℓ 1− sPℓ1−e−ℓsP  ð2ÞIf the contour length of the fibrils is much lower thantheir persistence length, the user can choose anothermeasure [2] to derive P (Figure 2c):< δ2 > ¼ L324sPð3Þwhere δ is the deviation from the chain to the midpointof a secant of length L joining two knots of the splinefor each combination of knots over the chain contour.The fluctuation expressed in Eq. 3 is valid only for L < <P. In addition, L can be assimilated to ℓ (as defined inEqs. 1 and 2) for values of L lower than the persistencelength of the chain. All the functions described in Eqs. 1–3 assume that the chains are not self-avoiding.Uncertainties on persistence length calculationsUncertainties in the calculated persistence lengths aredetermined via random resampling using the standardmethod of bootstrap with replacement [7]. In short,new chain samples (bootstrap samples) that contain kchains are randomly chosen from the available kchains. As the bootstrap samples are different from theoriginal sample, any chain can be selected more thanonce (see Ref [7] for details). For each bootstrap sam-ple < cos θ >, < R2 >, or < δ2 > values are binned atregular length intervals as in Figure 2. Different formsof the WLC model are then fitted to the data. n (de-fault 10) bootstrapping operations are done, and themean of the n values returned at each iteration is thepersistence length of the polymer. The standard devi-ation on the n values is the uncertainty on P (to whichthe uncertainty on the fractional dimension is propa-gated when considering non-equilibrated polymers, seeAdditional file 1: Methods).Lamour et al. Source Code for Biology and Medicine 2014, 9:16 Page 3 of 6http://www.scfbm.org/content/9/1/16Figure 3 Two independent tests to determine whether thepolymers have fully equilibrated in 2 dimensions. (a) Kurtosis ofthe θ distribution as a function of ℓ (blue circles). θ is the angleformed by two discrete chain segments separated by a distance ℓalong the chain contour. A kurtosis equal to 3 (broken line) indicatesthat the polymers have fully equilibrated on the 2D (see alsoFigure 4). (b) Mean end-to-end distance R as a function of ℓ. Forℓ > P where P is the persistence length, a slope of 0.75 indicates fullequilibration in 2D. The data displayed in (a) and (b) were collectedfor amyloid fibrils seeded on glass, where full equilibration in 2D isexpected [9].Figure 4 Precision of persistence length measurements byEasyworm. Persistence length P (of W sample, see Additional file 1:Table S1) is displayed as a function of the number of chains used toperform the analysis (black symbols). The coefficient of determinationCD associated with each fit realized is indicated in colored opensymbols and reveals how well the data fit the model. The contourlength of the chains analyzed here is ~1.0 ± 0.5 μm (mean ± SD). Alldata points and their associated error bars are the result of 10bootstrapping operations (see main text for details). Refer to main textfor the meaning of cos θ, R, and δ.Additional toolsA complementary set of tools is provided in severalgraphical user interfaces that serve detailed analyses ofthe data, including the plotting of polymers (Figure 1c)and the statistical treatment of polymer contour lengths(see Additional file 1: Figure S2 and Note S2). For in-stance, the user can plot a histogram of the distributionof polymer contour lengths, and Gaussian fitting of thedistribution can be done within the GUI. Also availableis the possibility to derive an axial elastic modulus fromthree distinct models for the cross-sectional geometry ofthe polymer. Importantly, multiple control functions areincluded. First, the ability to adapt the fitting of thechain contour by setting a user-defined “fitting param-eter” (see Additional file 1: Figure S1 and Note S1). Inpractice, this allows preserving the accuracy of the mea-surements at any given resolution providing it meetsminimum requirements (see Additional file 1: Note S1for details). Second, two independent tests [3,8] to deter-mine whether or not the polymers have fully equili-brated in 2D, which can influence the choice of themodel used to be fitted to data (see next section, wherethese two tests are described in detail). Third, a Monte-Carlo-based method described previously [3] was imple-mented into another graphical user interface (Synchains)to generate in silico polymers with user-defined persist-ence lengths (Additional file 1: Figure S3 and Note S3).In short, if P is the persistence length, then the small an-gles θ between discrete segments located at a distance ℓapart have a probability density P:P θ ℓð Þð Þ2D α e−Pθ22ℓ ð4ÞThe standard deviation of this normal distribution is< θ2ðℓÞ >2D ¼ffiffiffiffiffiffiffiℓ=Pp. Therefore, we generated n seg-ments of length ℓ joined at each other’s ends and form-ing angles θ randomly chosen according to a normaldistribution around a mean 0 and with a standard devi-ation equal toffiffiffiffiffiffiffiℓ=Pp. Such synthetic chains are illus-trated in Additional file 1: Figure S4. Refer to Additionalfile 1: Note S4 for details on how synthetic chains wereused in the different analyses contained in this study.Table 1 Evaluation of the measurement accuracy using synthetic polymers with known persistence lengths as testsamples*Sample N chainsPersistence length according to all 3 measures (nm) †(CD)‡[interval; nm]▲ < R2 > = f(ℓ) ▲ < cos θ > = f(ℓ) ▲ < δ2 > = f(ℓ)§SP50 38§68 ± 3 (0.996) §70 ± 6 (0.927)–[0; 500] [20; 500]is tnmR iswaans oLamour et al. Source Code for Biology and Medicine 2014, 9:16 Page 4 of 6http://www.scfbm.org/content/9/1/16SP750 78777 ± 114 (0.999)[0; 1900]¶SP2500-1 442867 ± 372 (0.999)[0; 600]¶SP2500-2 353047 ± 496 (0.999)[0; 2500]¤SP2500-2 352525 ± 191 (0.999)[0; 600]SP8000 417280 ± 1060 (0.999)[0; 1200]SP1e5 4864264 ± 5514 (0.999)[0; 3500]SP5.2e6 701.49e5 ± 0.13e5 (0.999)[0; 19500]Refer to Additional file 1: Note S4 and Table S1 for details on how the data in th*Each number in the sample names corresponds to the persistence length P (inP was set to 50 nm.†CD is the coefficient of determination (usually noted “R2” but not here because‡[interval] is the range of distance ℓ (along the chain contour) on which each fit▲Mean square of the end-to-end distance R, tangent-tangent correlations < cos θ >§We excluded chains displaying non-self-avoiding random walk from the analysiP was expected [3].¶SP2500-1 and SP2500-2 differ by their contour length (respectively 0.4 ± 0.2 and 5.¤The calculated value for P is closer to the theoretical value than in the same sampthe shortest ℓ distances, hence rendering statistical analysis more reliable.728 ± 32 (0.968) 538 ± 28 (0.961)[50; 1000] [0; 300]2599 ± 506 (0.947) 2986 ± 914 (0.923)[20; 500] [0; 600]3015 ± 590 (0.966) 2894 ± 608 (0.991)[40; 2500] [0; 1200]2542 ± 214 (0.960) 2441 ± 318 (0.966)[40; 600] [0; 600]6669 ± 494 (0.789) 8262 ± 1083 (0.949)[20; 700] [0; 800]–86475 ± 14480 (0.985)[0; 3500]–5.64e6 ± 0.85e6 (0.994)[0; 18000]able was generated with Synchains and analyzed with Easyworm.) that was used to generate one particular synthetic polymer (SP), e.g. for SP50,already used to refer to the end-to-end distance).s made.d mean square of the deviations δ to secant midpoint, as described in Eqs. 1–3.f SP50 chains (see Additional file 1: Figure S5). Therefore the value of 70 nm for3 ± 2.8 μm).le in the above line. This is probably due a larger amount of data available forefficient as monitoring the deviations δ from the poly-mer to secant midpoints (see Table 1).ConclusionsEasyworm is a tool for researchers in need of a fast andready-to-use program in order to determine the persist-ence length and derive the elastic modulus of their poly-mers, whether these are amyloid fibrils [9] or any nano- ormicro-filaments. In addition to determining the mechan-ical properties, Easyworm also provides complementarytools to analyze polymer contour lengths, create syntheticpolymers, visualize polymers and generate output files forplotting purposes.Additional fileAdditional file 1: (Easyworm_SuppInfo.pdf) is available with theonline version of this article. It contains Additional file Methods, TableS1, Figures S1-S5, Notes S1-S4 (including step-by-step instructions to usethe software), and a list of References.Additional file 1: Table S1. Light blue markers represent the samples forwhich the most reliable calculations of persistence length are achievedby measuring < cos θ > and/or < R2 >, whereas purple markers indicatesamples for which measuring < δ2 > provides the best estimation ofthe persistence length. Black markers indicate samples for which allmeasures provided reliable results. Therefore, the light blue regionindicates where measures of < cos θ > and/or < R2 > should be used toprovide the most reliable value for the persistence length, whereas thepink region indicates where measure of < δ2 > should be used. Notethat background coloring serves as a guide only and that the frontierbetween light blue and pink regions (indicated by the blackarrowhead) is strongly correlated to the image size available foranalysis (typically, in the orders of 1–10 μm).Lamour et al. Source Code for Biology and Medicine 2014, 9:16 Page 5 of 6http://www.scfbm.org/content/9/1/16Equilibration on the 2D surfaceEasyworm2 contains two functions that can help to de-termine whether or not the chains fully equilibrate in 2D(Figure 3). The first one calculates the ratio of the evenmoments, i.e. the kurtosis of the distribution of the θangle (Figure 3a). If the chains fully equilibrate in 2D,then the θ distribution is Gaussian [3], and in the rangewhere angles θ are still fully correlated (i.e., ℓ ≤ P and< cos θ > ≥ 0.6, see Figure 4), the kurtosis results in:< θ4 ℓð Þ>2D< θ2 ℓð Þ >22D¼ 3 ð5ÞFor distances ℓ greater than P, the kurtosis does notequal to 3 anymore and starts decreasing. When the θ an-gles become completely uncorrelated (i.e., < cos θ > = 0),then the distribution of θ is uniform, that is, all θ anglesare equiprobable. Only when this condition is fully metthe kurtosis equals 1.8 (see Additional file 1: Figure S4 formore details).Another function implemented in Easyworm allowsfor the fast determination of the slope of < R > as a func-tion of ℓ on any given range of ℓ (Figure 3b). Providedthe contour length interval defined by the user to calcu-late this slope (corresponding to a scaling or fractal ex-ponent [8]) is located above the persistence length (i.e.for ℓ > P), the slope is equal to 0.75 for a self-avoidingrandom walk in 2D [8]. We note that for our software,in practice, this measurement is accurate only for con-tour length values comprised between P and ~3P, sinceabove 3P the number of data points available are usuallytoo low to produce a measurement that is statisticallysignificant.Results and performance evaluationWe used in silico polymers (see Additional tools section)in order to test the accuracy of the measurements madeby Easyworm. The benchmarks (see Table 1) indicatethat Easyworm is able to provide reliable results over avery wide range of persistence lengths P from that ofDNA (P ≈ 50 nm [3]) to that of microtubules (P ≈5.2 mm [2]). In another test performed on amyloid fi-brils generated in vitro, we determined that relativelygood precision on the measurements of P can be ob-tained with a minimum of 50–60 chains that have con-tour length CL ~1.0 ± 0.5 nm (Figure 4). The number ofchains required will be higher if CL is lower. As Easy-worm can be used to derive persistence lengths varyingover several orders of magnitude, we included a graph-ical guide that provides the user with indications onwhich measure to use depending on the persistencelength of the sample (Figure 5). For instance, when con-sidering fibrils having P > 5 μm, monitoring the end-to-end distance R along the polymer contour is not asFigure 5 Graphical guide indicating which measure should beused to derive the persistence length. The crosses (syntheticchains of known persistence length) and circles (experimentalpolymers) correspond to data points that are given in Table 1 andCompeting interestsThe authors declare no competing interests.Authors’ contributionsGL developed the software from TPJK’s initial code. GL and JBK tested thesoftware. HBL and JG advised on the methods. GL wrote the manuscript. Allauthors commented and edited the manuscript. All authors have read andapproved the final manuscript.Authors’ informationSubmit your next manuscript to BioMed Centraland take full advantage of: • Convenient online submission• Thorough peer review• No space constraints or color figure charges• Immediate publication on acceptance• Inclusion in PubMed, CAS, Scopus and Google Scholar• Research which is freely available for redistributionLamour et al. Source Code for Biology and Medicine 2014, 9:16 Page 6 of 6http://www.scfbm.org/content/9/1/16GL is a postdoctoral research fellow in the laboratories of JG and HBL at theUniversity of British Columbia (Canada). JBK is a student in TPJK’s laboratoryat the University of Cambridge (UK). HBL is an associate professor inChemistry, TPJK a lecturer in Physical Chemistry, and JG an assistantprofessor in Biochemistry.AcknowledgmentsThis work was financially supported by PrioNet Canada, the CanadianInstitutes of Health Research (CIHR), and the Natural Sciences andEngineering Research Council of Canada (NSERC). We thank anonymousreviewers for their helpful comments.Author details1Centre for High-Throughput Biology, University of British Colombia,Vancouver, BC V6T 1Z4, Canada. 2Department of Chemistry, University ofBritish Columbia, Vancouver, BC V6T 1Z1, Canada. 3Department ofBiochemistry & Molecular Biology, University of British Colombia, Vancouver,BC V6T 2A1, Canada. 4Department of Chemistry, University of Cambridge,Cambridge CB2 1EW, UK.Received: 23 December 2013 Accepted: 2 July 2014Published: 10 July 2014References1. Doi M, Edwards SF: The Theory of Polymer Dynamics. New York: OxfordUniversity Press Inc.; 1986.2. Gittes F, Mickey B, Nettleton J, Howard J: Flexural rigidity of microtubulesand actin-filaments measured from thermal fluctuations in shape. J CellBiol 1993, 120:923–934.3. Rivetti C, Guthold M, Bustamante C: Scanning force microscopy of DNAdeposited onto mica: Equilibration versus kinetic trapping studied bystatistical polymer chain analysis. J Mol Biol 1996, 264:919–932.4. Grinthal A, Kang SH, Epstein AK, Aizenberg M, Khan M, Aizenberg J:Steering nanofibers: An integrative approach to bio-inspired fiberfabrication and assembly. Nano Today 2012, 7:35–52.5. Knowles TPJ, Buehler MJ: Nanomechanics of functional and pathologicalamyloid materials. Nat Nanotechnol 2011, 6:469–479.6. Easyworm free software. [http://www.chibi.ubc.ca/faculty/joerg-gsponer/gsponer-lab/software/easyworm]7. Efron B, Gong G: A leisurely look at the bootstrap, the jackknife, andcross-validation. Am Stat 1983, 37:36–48.8. Valle F, Favre M, De Los Rios P, Rosa A, Dietler G: Scaling exponents andprobability distributions of DNA end-to-end distance. Phys Rev Lett 2005,95:158105.9. Lamour G, Yip CK, Li H, Gsponer J: High Intrinsic Mechanical Flexibility ofMouse Prion Nanofibrils Revealed by Measurements of Axial and RadialYoung’s Moduli. ACS Nano 2014, 8:3851–3861.doi:10.1186/1751-0473-9-16Cite this article as: Lamour et al.: Easyworm: an open-source softwaretool to determine the mechanical properties of worm-like chains. SourceCode for Biology and Medicine 2014 9:16.Submit your manuscript at www.biomedcentral.com/submit


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