Spectral analysis methods for the robust measurement of the flexural rigidity of biopolymers

The mechanical properties of biopolymers can be determined from a statistical analysis of the ensemble of shapes they exhibit when subjected to thermal forces. In practice, extracting information from fluorescence microscopy images can be challenging due to low signal/noise ratios and other artifacts. To address these issues, we develop a suite of tools for image processing and spectral data analysis that is based on a biopolymer contour representation expressed in a spectral basis of orthogonal polynomials. We determine biopolymer shape and stiffness using global fitting routines that optimize a utility function measuring the amount of fluorescence intensity overlapped by such contours. This approach allows for filtering of high-frequency noise and interpolation over sporadic gaps in fluorescence. We use benchmarking to demonstrate the validity of our methods, by analyzing an ensemble of simulated images generated using a simulated biopolymer with known stiffness and subjected to various types of image noise. We then use these methods to determine the persistence lengths of taxol-stabilized microtubules. We find that single microtubules are well described by the wormlike chain polymer model, and that ensembles of chemically identical microtubules show significant heterogeneity in bending stiffness, which cannot be attributed to sampling or fitting errors. We expect these approaches to be useful in the study of biopolymer mechanics and the effects of associated regulatory molecules.     

A Blind Spot in Confocal Reflection Microscopy: The Dependence of Fiber Brightness on Fiber Orientation in Imaging Biopolymer Networks

We investigate the dependence of fiber brightness on three-dimensional fiber orientation when imaging biopolymer networks with confocal reflection microscopy (CRM) and confocal fluorescence microscopy (CFM). We compare image data of fluorescently labeled type I collagen networks concurrently acquired using each imaging modality. For CRM, fiber brightness decreases for more vertically oriented fibers, leaving fibers above ∼50° from the imaging plane entirely undetected. As a result, the three-dimensional network structure appears aligned with the imaging plane. In contrast, CFM data exhibit little variation of fiber brightness with fiber angle, thus revealing an isotropic collagen network. Consequently, we find that CFM detects almost twice as many fibers as are visible with CRM, thereby yielding more complete structural information for three-dimensional fiber networks. We offer a simple explanation that predicts the detected fiber brightness as a function of fiber orientation in CRM.     

Estimating the 3D Pore Size Distribution of Biopolymer Networks from Directionally Biased Data

The pore size of biopolymer networks governs their mechanical properties and strongly impacts the behavior of embedded cells. Confocal reflection microscopy and second harmonic generation microscopy are widely used to image biopolymer networks; however, both techniques fail to resolve vertically oriented fibers. Here, we describe how such directionally biased data can be used to estimate the network pore size. We first determine the distribution of distances from random points in the fluid phase to the nearest fiber. This distribution follows a Rayleigh distribution, regardless of isotropy and data bias, and is fully described by a single parameter—the characteristic pore size of the network. The bias of the pore size estimate due to the missing fibers can be corrected by multiplication with the square root of the visible network fraction. We experimentally verify the validity of this approach by comparing our estimates with data obtained using confocal fluorescence microscopy, which represents the full structure of the network. As an important application, we investigate the pore size dependence of collagen and fibrin networks on protein concentration. We find that the pore size decreases with the square root of the concentration, consistent with a total fiber length that scales linearly with concentration.     

Estimating the 3D Pore Size Distribution of Biopolymer Networks from Directionally Biased Data

The pore size of biopolymer networks governs their mechanical properties and strongly impacts the behavior of embedded cells. Confocal reflection microscopy and second harmonic generation microscopy are widely used to image biopolymer networks; however, both techniques fail to resolve vertically oriented fibers. Here, we describe how such directionally biased data can be used to estimate the network pore size. We first determine the distribution of distances from random points in the fluid phase to the nearest fiber. This distribution follows a Rayleigh distribution, regardless of isotropy and data bias, and is fully described by a single parameter—the characteristic pore size of the network. The bias of the pore size estimate due to the missing fibers can be corrected by multiplication with the square root of the visible network fraction. We experimentally verify the validity of this approach by comparing our estimates with data obtained using confocal fluorescence microscopy, which represents the full structure of the network. As an important application, we investigate the pore size dependence of collagen and fibrin networks on protein concentration. We find that the pore size decreases with the square root of the concentration, consistent with a total fiber length that scales linearly with concentration.     

Glioma expansion in collagen I matrices: analyzing collagen concentration-dependent growth and motility patterns

We study the growth and invasion of glioblastoma multiforme (GBM) in three-dimensional collagen I matrices of varying collagen concentration. Phase-contrast microscopy studies of the entire GBM system show that invasiveness at early times is limited by available collagen fibers. At early times, high collagen concentration correlates with more effective invasion. Conversely, high collagen concentration correlates with inhibition in the growth of the central portion of GBM, the multicellular tumor spheroid. Analysis of confocal reflectance images of the collagen matrices quantifies how the collagen matrices differ as a function of concentration. Studying invasion on the length scale of individual invading cells with a combination of confocal and coherent anti-Stokes Raman scattering microscopy reveals that the invasive GBM cells rely heavily on cell-matrix interactions during invasion and remodeling.     

Image-adaptive deconvolution for three-dimensional deep biological imaging

Deconvolution algorithms are widely used in conventional fluorescence microscopy, but they remain difficult to apply to deep imaging systems such as confocal and two-photon microscopy, due to the practical difficulty of measuring the system's point spread function (PSF), especially in biological experiments. Since a separate PSF measurement performed under the design optical conditions of the microscope cannot reproduce the true experimental conditions prevailing in situ, the most natural approach to solve the problem is to extract the PSF from the images themselves. We investigate here the approach of cropping an approximate PSF directly from the images, by exploiting the presence of small structures within the samples under study. This approach turns out to be practical in many cases, allowing significantly better restorations than with a design PSF obtained by imaging fluorescent beads in gel. We demonstrate the advantages of this approach with a number of deconvolution experiments performed both on artificially blurred and noisy test images, and on real confocal images taken within an in vitro preparation of the mouse hearing organ.     

3D Visualization and Measurement of Capillaries Supplying Metabolically Different Fiber Types in the Rat Extensor Digitorum Longus Muscle During Denervation and Reinnervation

The aim of this study was to determine whether capillarity in the denervated and reinnervated rat extensor digitorum longus muscle (EDL) is scaled by muscle fiber oxidative potential. We visualized capillaries adjacent to a metabolically defined fiber type and estimated capillarity of fibers with very high oxidative potential (O) vs fibers with very low oxidative potential (G). Capillaries and muscle fiber types were shown by a combined triple immunofluorescent technique and the histochemical method for NADH-tetrazolium reductase. Stacks of images were captured by a confocal microscope. Applying the Ellipse program, fibers were outlined, and the diameter, perimeter, cross-sectional area, length, surface area, and volume within the stack were calculated for both fiber types. Using the Tracer plug-in module, capillaries were traced within the three-dimensional (3D) volume, the length of capillaries adjacent to individual muscle fibers was measured, and the capillary length per fiber length (Lcap/Lfib), surface area (Lcap/Sfib), and volume (Lcap/Vfib) were calculated. Furthermore, capillaries and fibers of both types were visualized in 3D. In all experimental groups, O and G fibers significantly differed in girth, Lcap/Sfib, and Lcap/Vfib, but not in Lcap/Lfib. We conclude that capillarity in the EDL is scaled by muscle fiber size and not by muscle fiber oxidative potential. (J Histochem Cytochem 57:437–447, 2009)     

Semi-automated methods for simulation and measurement of amyloid fiber distributions obtained from transmission electron microscopy experiments

Transmission electron microscopy (TEM) is the standard procedure for qualitatively confirming the presence of amyloid fibers in a protein aggregation reaction product. However, extracting quantitative information about the amyloid size distribution from the electron micrographs is a nontrivial problem. Here we describe methods for (i) the simulation of pseudo-TEM images of amyloid fiber distributions having known characteristic properties and (ii) the semi-automated processing of experimental TEM images of amyloid fibers to produce two-dimensional histogram plots reflecting either the distribution of amyloid length and width or, alternatively, the distribution of width and fiber rigidity/persistence. The processing method is fully automatic when the density of fibers on the grid is sufficiently low (such that the adsorbed fibers do not touch) and is semi-automatic (requiring some user decision making) when the fibers are overlapping. Termed "ADM" (for Amyloid Distribution Measurement), the program suite is written in MATLAB code and is available on request from the author.     

Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control

This protocol outlines a procedure for collecting and analyzing point spread functions (PSFs). It describes how to prepare fluorescent microsphere samples, set up a confocal microscope to properly collect 3D confocal image data of the microspheres and perform PSF measurements. The analysis of the PSF is used to determine the resolution of the microscope and to identify any problems with the quality of the microscope's images. The PSF geometry is used as an indicator to identify problems with the objective lens, confocal laser scanning components and other relay optics. Identification of possible causes of PSF abnormalities and solutions to improve microscope performance are provided. The microsphere sample preparation requires 2-3 h plus an overnight drying period. The microscope setup requires 2 h (1 h for laser warm up), whereas collecting and analyzing the PSF images require an additional 2-3 h.     

Bending dynamics of fluctuating biopolymers probed by automated high-resolution filament tracking

Microscope images of fluctuating biopolymers contain a wealth of information about their underlying mechanics and dynamics. However, successful extraction of this information requires precise localization of filament position and shape from thousands of noisy images. Here, we present careful measurements of the bending dynamics of filamentous (F-)actin and microtubules at thermal equilibrium with high spatial and temporal resolution using a new, simple but robust, automated image analysis algorithm with subpixel accuracy. We find that slender actin filaments have a persistence length of approximately 17 microm, and display a q(-4)-dependent relaxation spectrum, as expected from viscous drag. Microtubules have a persistence length of several millimeters; interestingly, there is a small correlation between total microtubule length and rigidity, with shorter filaments appearing softer. However, we show that this correlation can arise, in principle, from intrinsic measurement noise that must be carefully considered. The dynamic behavior of the bending of microtubules also appears more complex than that of F-actin, reflecting their higher-order structure. These results emphasize both the power and limitations of light microscopy techniques for studying the mechanics and dynamics of biopolymers.     

Image restoration for confocal microscopy: improving the limits of deconvolution, with application to the visualization of the mammalian hearing organ

Deconvolution algorithms have proven very effective in conventional (wide-field) fluorescence microscopy. Their application to confocal microscopy is hampered, in biological experiments, by the presence of important levels of noise in the images and by the lack of a precise knowledge of the point spread function (PSF) of the system. We investigate the application of wavelet-based processing tools to deal with these problems, in particular wavelet denoising methods, which turn out to be very effective in application to three-dimensional confocal images. When used in combination with more classical deconvolution algorithms, these methods provide a robust and efficient restoration scheme allowing one to deal with difficult imaging conditions. To make our approach applicable in practical situations, we measured the PSF of a Biorad-MRC1024 confocal microscope under a large set of imaging conditions, including in situ acquisitions. As a specific biological application, we present several examples of restorations of three-dimensional confocal images acquired inside an intact preparation of the hearing organ. We also provide a quantitative assessment of the gain in quality achieved by wavelet-aided restorations over classical deconvolution schemes, based on a set of numerical experiments that we performed with test images.     

Determination of the elastic properties of short ssDNA molecules by mechanically folding and unfolding DNA hairpins

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). © 2014 Wiley Periodicals, Inc. Biopolymers 101: 1193–1199, 2014.     

Anisotropy in sickle hemoglobin fibers from variations in bending and twist

We have studied the variations of twist and bend in sickle hemoglobin fibers. We find that these variations are consistent with an origin in equilibrium thermal fluctuations, which allows us to estimate the bending and torsional rigidities and effective corresponding material moduli. We measure bending by electron microscopy of frozen hydrated fibers and find that the bending persistence length, a measure of the length of fiber required before it starts to be significantly bent due to thermal fluctuations, is 130microm, somewhat shorter than that previously reported using light microscopy. The torsional persistence length, obtained by re-analysis of previously published experiments, is found to be only 2.5microm. Strikingly this means that the corresponding torsional rigidity of the fibers is only 6x10(-27)Jm, much less than their bending rigidity of 5x10(-25)Jm. For (normal) isotropic materials, one would instead expect these to be similar. Thus, we present the first quantitative evidence of a very significant material anisotropy in sickle hemoglobin fibers, as might arise from the difference between axial and lateral contacts within the fiber. We suggest that the relative softness of the fiber with respect to twist deformation contributes to the metastability of HbS fibers: HbS double strands are twisted in the fiber but not in the equilibrium crystalline state. Our measurements inform a theoretical model of the thermodynamic stability of fibers that takes account of both bending and extension/compression of hemoglobin (double) strands within the fiber.     

Microfluidic generation and selective degradation of biopolymer-based Janus microbeads

We describe a microfluidic approach for generating Janus microbeads from biopolymer hydrogels. A flow-focusing device was used to emulsify the coflow of aqueous solutions of one or two different biopolymers in an organic phase to synthesize homo or hetero Janus microbeads. Biopolymer gelation was initiated, in the chip, by diffusion-controlled ionic cross-linking of the biopolymers. Pectin-pectin (homo Janus) and, for the first time, pectin-alginate (hetero Janus) microbeads were produced. The efficiency of separation of the two hemispheres, which reflected mixing and convection phenomena, was investigated by confocal scanning laser microscopy (CSLM) of previously labeled biopolymers. The interface of the hetero Janus structure was clearly defined, whereas that of the homo Janus microbeads was poorly defined. The Janus structure was confirmed by subjecting each microbead hemisphere to specific enzymatic degradation. These new and original microbeads from renewable resources will open up opportunities for studying relationships between combined enzymatic hydrolysis and active compound release.     

AutoSmarTrace: Automated chain tracing and flexibility analysis of biological filaments

Single-molecule imaging is widely used to determine statistical distributions of molecular properties. One such characteristic is the bending flexibility of biological filaments, which can be parameterized via the persistence length. Quantitative extraction of persistence length from images of individual filaments requires both the ability to trace the backbone of the chains in the images and sufficient chain statistics to accurately assess the persistence length. Chain tracing can be a tedious task, performed manually or using algorithms that require user input and/or supervision. Such interventions have the potential to introduce user-dependent bias into the chain selection and tracing. Here, we introduce a fully automated algorithm for chain tracing and determination of persistence lengths. Dubbed “AutoSmarTrace,” the algorithm is built off a neural network, trained via machine learning to identify filaments within images recorded using atomic force microscopy. We validate the performance of AutoSmarTrace on simulated images with widely varying levels of noise, demonstrating its ability to return persistence lengths in agreement with input simulation parameters. Persistence lengths returned from analysis of experimental images of collagen and DNA agree with previous values obtained from these images with different chain-tracing approaches. Although trained on atomic-force-microscopy-like images, the algorithm also shows promise to identify chains in other single-molecule imaging approaches, such as rotary-shadowing electron microscopy and fluorescence imaging.     

The mechanical fingerprint of a parallel polyprotein dimer

We use the GCN4 oligomerization domain to engineer a covalently linked parallel polyprotein dimer based on the well-studied I27 domain of titin. We use single molecule atomic force microscopy techniques to stretch single polyprotein fibers and verify their mechanical properties. We find that the engineered polyprotein dimers extend in perfect register, doubling the unfolding force and halving the persistence length while keeping the contour length increase unchanged. These experiments directly confirm the mechanical scaling laws proposed for parallel bundles of modular proteins.     

Fiber alignment directs cell motility over chemotactic gradients

The ability of tissue engineered scaffolds to direct cell behavior is paramount for scaffold design. Cell migration can be directed by various methods including chemical, adhesive, mechanical, and topographical cues. Electrospinning has emerged as a popular method to control topography and create fibrous scaffolds similar to that found in extracellular matrix. One major hurdle is limited cell infiltration and several studies have explored methods to alter electrospun materials to increase scaffold porosity; however, uniform cell distributions within scaffolds is still limited. Towards this, we investigated the motility of HUVECs on a model system of electrospun hyaluronic acid fibers under a gradient of VEGF and found that topographical cues dominate cell motility direction. Using time‐lapse microscopy, cell aspect ratio, and migration angle were measured; cells were directed in a chemical gradient and/or on aligned electrospun fibers. Measurements of the persistence time demonstrated an additive effect of the chemical gradient and fiber alignment. However, when fibers were aligned perpendicular to a chemical gradient, cells were directed by fiber alignment and there was no effect of the chemical gradient. These results suggest that topographical cues may be more influential than chemical cues in directing cell motility and should be considered in material design. Biotechnol. Bioeng. 2013; 110: 1249–1254. © 2012 Wiley Periodicals, Inc.     

Elastic Moduli of Collagen Gels Can Be Predicted from Two-Dimensional Confocal Microscopy

We quantitatively compare data obtained from imaging two-dimensional slices of three-dimensional unlabeled and fluorescently labeled collagen gels with confocal reflectance microscopy (CRM) and/or confocal fluorescence microscopy (CFM). Different network structures are obtained by assembling the gels over a range of concentrations at various temperatures. Comparison between CRM and CFM shows that the techniques are not equally sensitive to details of network structure, with CFM displaying higher fidelity in imaging fibers parallel to the optical axis. Comparison of CRM of plain and labeled collagen gels shows that labeling itself induces changes in gel structure, chiefly through inhibition of fibril bundling. Despite these differences, image analyses carried out on two-dimensional CFM and CRM slices of collagen gels reveal identical trends in structural parameters as a function of collagen concentration and gelation temperature. Fibril diameter approximated from either CRM or CFM is in good accord with that determined via electron microscopy. Two-dimensional CRM images are used to show that semiflexible polymer theory can relate network structural properties to elastic modulus successfully. For networks containing bundled fibrils, it is shown that average structural diameter, rather than fibril diameter, is the length scale that sets the magnitude of the gel elastic modulus.     

Native fibrin gel networks observed by 3D microscopy, permeation and turbidity

Native fully hydrated fibrin gels formed at different fibrinogen and thrombin concentrations and at different ionic strengths were studied by confocal laser 3D microscopy, liquid permeation and turbidity. The gels were found to be composed of straight rod-like fiber elements that often came together at denser nodes. In gels formed at high fibrinogen concentrations, or with high amounts of thrombin, the spaces between the fibers decreased, indicating a decrease of gel porosity. The fiber strands were also shorter. Gel porosity decreased dramatically in gels formed at the high ionic strengths. Shorter fibers were observed and fiber swelling occurred at ionic strengths above 0.24. Quantitative parameters for gel porosity, fiber mass/length ratio and diameter were also derived by liquid permeation and turbidometric analyses of the gels. Permeation analysis showed that gel porosity (measured as Ks) decreased in gels formed at higher fibrin and thrombin concentrations in agreement with the porosity observed by microscopy. The turbidometric analysis showed good agreement with the permeation data for gels formed at various thrombin concentrations, but supported the permeation data more poorly in gels formed at different fibrinogen concentrations, especially above 2.5 mg/ml. Turbidometric analysis showed that the fiber mass/length ratio and diameter decreased in gels formed at ionic strength up to 0.24, as was seen in the permeation study. However, at higher ionic strengths swelling of the fibers was suggested from the gel turbidity data and this was also indicated by microscopy. These findings are discussed in relation to previous hydrodynamic and electron microscopic studies of fibrin gels.     

A Pulse Coupled Neural Network Segmentation Algorithm for Reflectance Confocal Images of Epithelial Tissue

Automatic segmentation of nuclei in reflectance confocal microscopy images is critical for visualization and rapid quantification of nuclear-to-cytoplasmic ratio, a useful indicator of epithelial precancer. Reflectance confocal microscopy can provide three-dimensional imaging of epithelial tissue in vivo with sub-cellular resolution. Changes in nuclear density or nuclear-to-cytoplasmic ratio as a function of depth obtained from confocal images can be used to determine the presence or stage of epithelial cancers. However, low nuclear to background contrast, low resolution at greater imaging depths, and significant variation in reflectance signal of nuclei complicate segmentation required for quantification of nuclear-to-cytoplasmic ratio. Here, we present an automated segmentation method to segment nuclei in reflectance confocal images using a pulse coupled neural network algorithm, specifically a spiking cortical model, and an artificial neural network classifier. The segmentation algorithm was applied to an image model of nuclei with varying nuclear to background contrast. Greater than 90% of simulated nuclei were detected for contrast of 2.0 or greater. Confocal images of porcine and human oral mucosa were used to evaluate application to epithelial tissue. Segmentation accuracy was assessed using manual segmentation of nuclei as the gold standard.