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.     

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.     

Robust pore size analysis of filamentous networks from three-dimensional confocal microscopy

We describe a robust method for determining morphological properties of filamentous biopolymer networks, such as collagen or other connective tissue matrices, from confocal microscopy image stacks. Morphological properties including pore size distributions and percolation thresholds are important for transport processes, e.g., particle diffusion or cell migration through the extracellular matrix. The method is applied to fluorescently labeled fiber networks prepared from rat-tail tendon and calf-skin collagen, at concentrations of 1.2, 1.6, and 2.4 mg/ml. The collagen fibers form an entangled and branched network. The medial axes, or skeletons, representing the collagen fibers are extracted from the image stack by threshold intensity segmentation and distance-ordered homotopic thinning. The size of the fluid pores as defined by the radii of largest spheres that fit into the cavities between the collagen fibers is derived from Euclidean distance maps and maximal covering radius transforms of the fluid phase. The size of the largest sphere that can traverse the fluid phase between the collagen fibers across the entire probe, called the percolation threshold, was computed for both horizontal and vertical directions. We demonstrate that by representing the fibers as the medial axis the derived morphological network properties are both robust against changes of the value of the segmentation threshold intensity and robust to problems associated with the point-spread function of the imaging system. We also provide empirical support for a recent claim that the percolation threshold of a fiber network is close to the fiber diameter for which the Euler index of the networks becomes zero.     

Fast Two-Dimensional Bubble Analysis of Biopolymer Filamentous Networks Pore Size from Confocal Microscopy Thin Data Stacks

The average pore size ξ₀ of filamentous networks assembled from biological macromolecules is one of the most important physical parameters affecting their biological functions. Modern optical methods, such as confocal microscopy, can noninvasively image such networks, but extracting a quantitative estimate of ξ₀ is a nontrivial task. We present here a fast and simple method based on a two-dimensional bubble approach, which works by analyzing one by one the (thresholded) images of a series of three-dimensional thin data stacks. No skeletonization or reconstruction of the full geometry of the entire network is required. The method was validated by using many isotropic in silico generated networks of different structures, morphologies, and concentrations. For each type of network, the method provides accurate estimates (a few percent) of the average and the standard deviation of the three-dimensional distribution of the pore sizes, defined as the diameters of the largest spheres that can be fit into the pore zones of the entire gel volume. When applied to the analysis of real confocal microscopy images taken on fibrin gels, the method provides an estimate of ξ₀ consistent with results from elastic light scattering data.     

Fiber finding algorithm using stepwise tracing to identify biopolymer fibers in noisy 3D images

We present a novel fiber finding algorithm (FFA) that will permit researchers to detect and return traces of individual biopolymers. Determining the biophysical properties and structural cues of biopolymers can permit researchers to assess the progression and severity of disease. Confocal microscopy images are a useful method for observing biopolymer structures in three dimensions, but their utility for identifying individual biopolymers is impaired by noise inherent in the acquisition process, including convolution from the point spread function (PSF). The new, iterative FFA we present here 1) measures a microscope’s PSF and uses it as a metric for identifying fibers against the background; 2) traces each fiber within a cone angle; and 3) blots out the identified trace before identifying another fiber. Blotting out the identified traces in each iteration allows the FFA to detect and return traces of single fibers accurately and efficiently—even within fiber bundles. We used the FFA to trace unlabeled collagen type I fibers—a biopolymer used to mimic the extracellular matrix in in vitro cancer assays—imaged by confocal reflectance microscopy in three dimensions, enabling quantification of fiber contour length, persistence length, and three-dimensional (3D) mesh size. Based on 3D confocal reflectance microscopy images and the PSF, we traced and measured the fibers to confirm that colder gelation temperatures increased fiber contour length, persistence length, and 3D mesh size—thereby demonstrating the FFA’s use in quantifying biopolymers’ structural and physical cues from noisy microscope images.     

Brain Size and Number of Neurons: An Exercise in Synthetic Neuroanatomy

Certain remarkable invariances have long been known in comparative neuroanatomy, such as the proportionality between neuronal density and the inverse of the cubic root of brain volume or that between the square root of brain weight and the cubic root of body weight. Very likely these quantitative relations reflect some general principles of the architecture of neuronal networks. Under the assumption that most of brain volume is due to fibers, we propose four abstract models: I, constant fiber length per neuron; II, fiber length proportionate to brain diameter; III, complete set of connections between all neurons; IV, complete set of connections between compartments each containing the square root of the total number of neurons. Model I conforms well to the cerebellar cortex. Model II yields the observed comparative invariances between number of neurons and brain size. Model III is totally unrealistic, while Model IV is compatible with the volume of the hemispheric white substance in different mammalian species.     

Elastic Behavior and Platelet Retraction in Low- and High-Density Fibrin?Gels

Fibrin is a biopolymer that gives thrombi the mechanical strength to withstand the forces imparted on them by blood flow. Importantly, fibrin is highly extensible, but strain hardens at low deformation rates. The density of fibrin in clots, especially arterial clots, is higher than that in gels made at plasma concentrations of fibrinogen (3–10 mg/mL), where most rheology studies have been conducted. Our objective in this study was to measure and characterize the elastic regimes of low (3–10 mg/mL) and high (30–100 mg/mL) density fibrin gels using shear and extensional rheology. Confocal microscopy of the gels shows that fiber density increases with fibrinogen concentration. At low strains, fibrin gels act as thermal networks independent of fibrinogen concentration. Within the low-strain regime, one can predict the mesh size of fibrin gels by the elastic modulus using semiflexible polymer theory. Significantly, this provides a link between gel mechanics and interstitial fluid flow. At moderate strains, we find that low-density fibrin gels act as nonaffine mechanical networks and transition to affine mechanical networks with increasing strains within the moderate regime, whereas high-density fibrin gels only act as affine mechanical networks. At high strains, the backbone of individual fibrin fibers stretches for all fibrin gels. Platelets can retract low-density gels by >80% of their initial volumes, but retraction is attenuated in high-density fibrin gels and with decreasing platelet density. Taken together, these results show that the nature of fibrin deformation is a strong function of fibrin fiber density, which has ramifications for the growth, embolization, and lysis of thrombi.     

Silica nanocasts of wood fibers: a study of cell-wall accessibility and structure

The porosity and the available surface area of a lignocellulosic fiber can influence the accessibility and reactivity in derivatization and modification reactions because the porous cell-wall network determines the upper size limit for molecules that can penetrate and react with the interior of the wall. To obtain information concerning the accessibility of the porous cell wall of wood fibers, surfactant-templated sol-gel mineralization has been examined. Wood and kraft pulp samples of Norway spruce were impregnated with a silica sol-gel and subsequently heated (calcined) and transformed into structured mesoporous silica. Microscopy studies (environmental scanning electron microscopy, transmission electron microsopy, TEM) on the silica casts showed that the three-dimensional architecture of the wood and pulp fiber cell wall was revealed down to the nanometer level. Image analysis of TEM micrographs of silica fragments from the never-dried pulp revealed complete infiltration of the cell-wall voids and microcavities (mean pore width 4.7 +/- 2 nm) by the sol-gel and the presence of cellulose fibrils with a width of 3.6 +/- 1 nm. Cellulose fibrils of the same width as that shown by image analysis were also identified by nitrogen adsorption measurements of the pore size distribution in the replicas.     

Pore and matrix distribution in the fiber wall revealed by atomic force microscopy and image analysis

A method for the ultrastructural investigation of fiber cross-sections based on atomic force microscopy in combination with image analysis is presented. A uniform distribution of pores across the matrix material within the fiber wall was revealed by impregnation of pulp fibers with poly(ethylene glycol). The effects of chemical and mechanical processing on the pore and matrix structure and on the arrangement of the cellulose fibril aggregates were investigated. During chemical processing, changes in the fiber ultrastructure occur: a broadening of the pore and matrix lamella widths in combination with a reduction in their number and an enlargement of the cellulose fibril aggregates. It was found that pores formed during pulping are evenly distributed across the fiber wall in the transverse direction. In contrast, refining increases the pore and matrix lamella width in the fiber wall closest to the middle lamella an effect which gradually decrease in size toward the lumen side.     

Effect of some factors on fabrication of poly(L-lactic acid) microporous foams by thermally induced phase separation using N,N-dimethylacetamide as solvent

Biocompatible, highly interconnected microporous poly(L-lactic acid) (PLLA) foams or scaffolds with nano-fibrous structure, containing pores with diameters of 0.1-3.5 μm and fibers with diameters of 300-700 nm scale, were prepared through the thermally induced liquid-liquid phase separation (TIPS) method using N,N'-dimethyl acetamide (DMAc) as solvent. Various foam morphologies were obtained by changing parameters involved in the TIPS process, such as polymer concentration, solvent composition, and quenching temperatures. The morphology of different foams was examined by scanning electron microscopy, whereas the pore size and the pore size distribution were calculated. The results showed that most porous foams presented nano-fibrous structure with interconnected open pores. In the case of using DMAc as solvent, with increasing polymer concentration, either the average pore diameter or the pore size distribution exhibited a maximum value at 0.05 g/mL polymer concentration and quenching temperature of -30°C. It was found that all the pore size distribution fit the F-distribution equation. With increasing the quenching temperature from -30°C to -10°C, the maximum average pore diameter of the foams decreased and the pore size distribution became narrower, whereas the polymer concentration exhibiting the maximum pore size and widest pore size distribution increased from 0.05 g/mL to 0.07 g/mL. In the case of using the mixed solvent of DMAc/DOX (1,4-dioxane) from 9/1 to 7/3 (v/v) there appeared a maximum value of average pore diameter and a widest pore size distribution all at 0.05 g/mL PLLA concentration and quenching temperature of -30°C. The maximum pore size tends to increase with increasing DOX content.     

Preparation of biopolymer fibers by electrospinning from room temperature ionic liquids

Electrospinning is a versatile process used to prepare micro- and nano- sized fibers from various polymers dissolved in volatile solvents. In this report, cellulose and cellulose-heparin composite fibers are prepared from nonvolatile room temperature ionic liquid (RTIL) solvents by electrospinning. RTILs are extracted from the biopolymer fiber after the fiber formation using a cosolvent. Micron to nanometer sized, branched fibers were obtained from 10% (w/w) concentration of polysaccharide biopolymer in RTIL solution with an applied voltage of 15-20 kV. Cellulose-heparin composite fibers showed anticoagulant activity, demonstrating that the bioactivity of heparin remained unaffected even on exposure to a high voltage involved in electrospinning.     

S-nitrosoglutathione acts as a small molecule modulator of human fibrin clot architecture

Background

Altered fibrin clot architecture is increasingly associated with cardiovascular diseases; yet, little is known about how fibrin networks are affected by small molecules that alter fibrinogen structure. Based on previous evidence that S-nitrosoglutathione (GSNO) alters fibrinogen secondary structure and fibrin polymerization kinetics, we hypothesized that GSNO would alter fibrin microstructure.

Methodology/Principal Findings

Accordingly, we treated human platelet-poor plasma with GSNO (0.01–3.75 mM) and imaged thrombin induced fibrin networks using multiphoton microscopy. Using custom designed computer software, we analyzed fibrin microstructure for changes in structural features including fiber density, diameter, branch point density, crossing fibers and void area. We report for the first time that GSNO dose-dependently decreased fibrin density until complete network inhibition was achieved. At low dose GSNO, fiber diameter increased 25%, maintaining clot void volume at approximately 70%. However, at high dose GSNO, abnormal irregularly shaped fibrin clusters with high fluorescence intensity cores were detected and clot void volume increased dramatically. Notwithstanding fibrin clusters, the clot remained stable, as fiber branching was insensitive to GSNO and there was no evidence of fiber motion within the network. Moreover, at the highest GSNO dose tested, we observed for the first time, that GSNO induced formation of fibrin agglomerates.

Conclusions/Significance

Taken together, low dose GSNO modulated fibrin microstructure generating coarse fibrin networks with thicker fibers; however, higher doses of GSNO induced abnormal fibrin structures and fibrin agglomerates. Since GSNO maintained clot void volume, while altering fiber diameter it suggests that GSNO may modulate the remodeling or inhibition of fibrin networks over an optimal concentration range.     

Structure-Function Relations and Rigidity Percolation in the Shear Properties of Articular Cartilage

Among mammalian soft tissues, articular cartilage is particularly interesting because it can endure a lifetime of daily mechanical loading despite having minimal regenerative capacity. This remarkable resilience may be due to the depth-dependent mechanical properties, which have been shown to localize strain and energy dissipation. This paradigm proposes that these properties arise from the depth-dependent collagen fiber orientation. Nevertheless, this structure-function relationship has not yet been quantified. Here, we use confocal elastography, quantitative polarized light microscopy, and Fourier-transform infrared imaging to make same-sample measurements of the depth-dependent shear modulus, collagen fiber organization, and extracellular matrix concentration in neonatal bovine articular cartilage. We find weak correlations between the shear modulus |G^∗| and both the collagen fiber orientation and polarization. We find a much stronger correlation between |G^∗| and the concentration of collagen fibers. Interestingly, very small changes in collagen volume fraction v_c lead to orders-of-magnitude changes in the modulus with |G^∗| scaling as (v_c – v₀)^ξ. Such dependencies are observed in the rheology of other biopolymer networks whose structure exhibits rigidity percolation phase transitions. Along these lines, we propose that the collagen network in articular cartilage is near a percolation threshold that gives rise to these large mechanical variations and localization of strain at the tissue’s surface.     

STUDIES OF EXCITABLE MEMBRANES : I. Macromolecular Specializations of the Neuromuscular Junction and the Nonjunctional Sarcolemma

The neuromuscular junctions and nonjunctional sarcolemmas of mammalian skeletal muscle fibers were studied by conventional thin-section electron microscopy and freeze-fracture techniques. A modified acetylcholinesterase staining procedure that is compatible with light microscopy, conventional thin-section electron microscopy, and freeze-fracture techniques is described. Freeze-fracture replicas were utilized to visualize the internal macromolecular architecture of the nerve terminal membrane, the chemically excitable neuromuscular junction postsynaptic folds, and the electrically excitable nonjunctional sarcolemma. The nerve terminal membrane is characterized by two parallel rows of 100–110-Å particles which may be associated with synpatic vesicle fusion and release. On the postsynpatic folds, irregular rows of densely packed 110–140-Å particles were observed and evidence is assembled which indicates that these large transmembrane macromolecules may represent the morphological correlate for functional acetylcholine receptor activity in mammalian motor endplates. Differences in the size and distribution of particles in mammalian as compared with amphibian and fish postsynaptic junctional membranes are correlated with current biochemical and electron micrograph autoradiographic data. Orthogonal arrays of 60-Å particles were observed in the split postsynaptic sarcolemmas of many diaphragm myofibers. On the basis of differences in the number and distribution of these "square" arrays within the sarcolemmas, two classes of fibers were identified in the diaphragm. Subsequent confirmation of the fiber types as fast- and slow-twitch fibers (Ellisman et al. 1974. J. Cell Biol. 63[2, Pt. 2]:93 a. [Abstr.]) may indicate a possible role for the square arrays in the electrogenic mechanism. Experiments in progress involving specific labeling techniques are expected to permit positive identification of many of these intriguing transmembrane macromolecules.     

Mechanisms of Plastic Deformation in Collagen Networks Induced by Cellular Forces

Contractile cells can reorganize fibrous extracellular matrices and form dense tracts of fibers between neighboring cells. These tracts guide the development of tubular tissue structures and provide paths for the invasion of cancer cells. Here, we studied the mechanisms of the mechanical plasticity of collagen tracts formed by contractile premalignant acinar cells and fibroblasts. Using fluorescence microscopy and second harmonic generation, we quantified the collagen densification, fiber alignment, and strains that remain within the tracts after cellular forces are abolished. We explained these observations using a theoretical fiber network model that accounts for the stretch-dependent formation of weak cross-links between nearby fibers. We tested the predictions of our model using shear rheology experiments. Both our model and rheological experiments demonstrated that increasing collagen concentration leads to substantial increases in plasticity. We also considered the effect of permanent elongation of fibers on network plasticity and derived a phase diagram that classifies the dominant mechanisms of plasticity based on the rate and magnitude of deformation and the mechanical properties of individual fibers. Plasticity is caused by the formation of new cross-links if moderate strains are applied at small rates or due to permanent fiber elongation if large strains are applied over short periods. Finally, we developed a coarse-grained model for plastic deformation of collagen networks that can be employed to simulate multicellular interactions in processes such as morphogenesis, cancer invasion, and fibrosis.     

Influence of ionic strength on the dichroism properties of polynucleosomal fibers

We report electric-dichroism and electron-microscopic studies of chromatin fibers fixed by protein–protein crosslinking at salt concentrations ranging from 10 to 100 mM. The results confirm a progressive disorganization of the fiber as the salt concentration is lowered. The positive dichroism and large polarizability anisotropy characteristic of the 300-Å diameter fiber found in 100 mM salt are replaced by negative dichroism and smaller effective polarizability anisotropy or dipole moment for samples fixed at lower salt concentration. We interpret the results in terms of segmental, field-induced orientation of the disorganized structure which is present in low salt concentrations. We also observed a field-induced absorbance decrease in chromatin fibers fixed at salt concentration at and below 100 mM. All three optical effects, namely overall orientation of the high-salt fixed fiber, segmental orientation of the low-salt fixed fiber, and field-induced absorbance decrease, occur on roughly the same time scale, 20–100 μs for 50 nucleosome polynucleosomes. The polarizability anisotropy of fibers fixed in 100 mM salt was found to be proportional to the length of the fragment and to the reciprocal square root of the conductivity of the solution used for electric-dichroism measurements. Addition of Mg²⁺ to the measurement buffer affected the dichroism amplitude of samples fixed below 100 mM salt but not those fixed at 100 mM salt. The results reinforce the need for caution in interpreting electric-dichroism measurements on chromatin fibers because of possible field-induced distortion effects.     

Hydrogenation of nitrotoluene using palladium supported on chitosan hollow fiber: catalyst characterization and influence of operative parameters studied by experimental design methodology

The strong affinity of chitosan for metal ions and more specifically for precious metals such as palladium and platinum has focused the interest on using this biopolymer as a support for catalytic metals. The manufacturing of hollow chitosan fibers, softly cross-linked with glutaraldehyde, followed by palladium sorption at pH 2 in HCl solutions and further reduction using hydrogen gas, opened the route for the design of a new continuous catalytic system. This material was used for the hydrogenation of nitrotoluene, which was converted into o-toluidine, in methanol solutions. The substrate was circulated inside the lumen of the fiber, while the hydrogen donor (hydrogen gas) was maintained at constant pressure in the outlet compartment of the reactor. Several parameters (substrate concentration, metal content in the fiber, and flow rate) have been tested for their impact on catalytic performance, measured by the turnover frequency (TOF), conversion yield or o-toluidine production, using a surface response methodology for the optimization of the process. Metal content in the fiber revealed a critical parameter; the influence of this parameter was extensively studied through the structural characterization of the fibers using XPS analysis (oxidation state of Pd), X-ray diffraction analysis (size of Pd crystals), TEM analysis (size and distribution of Pd crystals), and diffusion profiles (porosity) in order to correlate catalytic performance to fiber characterization.     

Fiber depolymerization

Depolymerization is, by definition, a crucial process in the reversible assembly of various biopolymers. It may also be an important factor in the pathology of sickle cell disease. If sickle hemoglobin fibers fail to depolymerize fully during passage through the lungs then they will reintroduce aggregates into the systemic circulation and eliminate or shorten the protective delay (nucleation) time for the subsequent growth of fibers. We study how depolymerization depends on the rates of end- and side-depolymerization, k(end) and k(side), which are, respectively, the rates at which fiber length is lost at each end and the rate at which new breaks appear per unit fiber length. We present both an analytic mean field theory and supporting simulations showing that the characteristic fiber depolymerization time tau= square root 1/k(end)k(side) depends on both rates, but not on the fiber length L, in a large intermediate regime 1 < k(side)L(2)/k(end) < (L/d)(2), with d the fiber diameter. We present new experimental data which confirms that both mechanisms are important and shows how the rate of side depolymerization depends strongly on the concentration of CO, acting as a proxy for oxygen. Our theory remains rather general and could be applied to the depolymerization of an entire class of linear aggregates, not just sickle hemoglobin fibers.     

Morphological analysis of pore size and connectivity in a thick mixed‐culture biofilm

Morphological parameters are commonly used to predict transport and metabolic kinetics in biofilms. Yet, quantification of biofilm morphology remains challenging because of imaging technology limitations and lack of robust analytical approaches. We present a novel set of imaging and image analysis techniques to estimate internal porosity, pore size distributions, and pore network connectivity to a depth of 1 mm at a resolution of 10 µm in a biofilm exhibiting both heterotrophic and nitrifying activities. Optical coherence tomography (OCT) scans revealed an extensive pore network with diameters as large as 110 µm directly connected to the biofilm surface and surrounding fluid. Thin‐section fluorescence in situ hybridization microscopy revealed that ammonia‐oxidizing bacteria (AOB) distributed through the entire thickness of the biofilm. AOB were particularly concentrated in the biofilm around internal pores. Areal porosity values estimated from OCT scans were consistently lower than those estimated from multiphoton laser scanning microscopy, though the two imaging modalities showed a statistically significant correlation (r = 0.49, p < 0.0001). Estimates of areal porosity were moderately sensitive to gray‐level threshold selection, though several automated thresholding algorithms yielded similar values to those obtained by manually thresholding performed by a panel of environmental engineering researchers (±25% relative error). These findings advance our ability to quantitatively describe the geometry of biofilm internal pore networks at length scales relevant to engineered biofilm reactors and suggest that internal pore structures provide crucial habitat for nitrifier growth.