Dataset Information

Estimating the 3D pore size distribution of biopolymer networks from directionally biased data.

ABSTRACT: 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.

SUBMITTER: Lang NR

PROVIDER: S-EPMC3824714 | biostudies-literature | 2013 Nov

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Estimating the 3D pore size distribution of biopolymer networks from directionally biased data.

Lang Nadine R NR Münster Stefan S Metzner Claus C Krauss Patrick P Schürmann Sebastian S Lange Janina J Aifantis Katerina E KE Friedrich Oliver O Fabry Ben B

Biophysical journal 20131101 9

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 ...[more]

PMID: 24209841

Similar Datasets

Project description:BACKGROUND: Cellular metabolism is one of the most investigated system of biological interactions. While the topological nature of individual reactions and pathways in the network is quite well understood there is still a lack of comprehension regarding the global functional behavior of the system. In the last few years flux-balance analysis (FBA) has been the most successful and widely used technique for studying metabolism at system level. This method strongly relies on the hypothesis that the organism maximizes an objective function. However only under very specific biological conditions (e.g. maximization of biomass for E. coli in reach nutrient medium) the cell seems to obey such optimization law. A more refined analysis not assuming extremization remains an elusive task for large metabolic systems due to algorithmic limitations. RESULTS: In this work we propose a novel algorithmic strategy that provides an efficient characterization of the whole set of stable fluxes compatible with the metabolic constraints. Using a technique derived from the fields of statistical physics and information theory we designed a message-passing algorithm to estimate the size of the affine space containing all possible steady-state flux distributions of metabolic networks. The algorithm, based on the well known Bethe approximation, can be used to approximately compute the volume of a non full-dimensional convex polytope in high dimensions. We first compare the accuracy of the predictions with an exact algorithm on small random metabolic networks. We also verify that the predictions of the algorithm match closely those of Monte Carlo based methods in the case of the Red Blood Cell metabolic network. Then we test the effect of gene knock-outs on the size of the solution space in the case of E. coli central metabolism. Finally we analyze the statistical properties of the average fluxes of the reactions in the E. coli metabolic network. CONCLUSION: We propose a novel efficient distributed algorithmic strategy to estimate the size and shape of the affine space of a non full-dimensional convex polytope in high dimensions. The method is shown to obtain, quantitatively and qualitatively compatible results with the ones of standard algorithms (where this comparison is possible) being still efficient on the analysis of large biological systems, where exact deterministic methods experience an explosion in algorithmic time. The algorithm we propose can be considered as an alternative to Monte Carlo sampling methods.

Project description:3D printed scaffolds can be used, for example, in medical applications for simulating body tissues or for manufacturing prostheses. However, it is difficult to print porous structures of specific porosity and pore size values with fused deposition modelling (FDM) technology. The present paper provides a methodology to design porous structures to be printed. First, a model is defined with some theoretical parallel planes, which are bounded within a geometrical figure, for example a disk. Each plane has randomly distributed points on it. Then, the points are joined with lines. Finally, the lines are given a certain volume and the structure is obtained. The porosity of the structure depends on three geometrical variables: the distance between parallel layers, the number of columns on each layer and the radius of the columns. In order to obtain mathematical models to relate the variables with three responses, the porosity, the mean of pore diameter and the variance of pore diameter of the structures, design of experiments with three-level factorial analysis was used. Finally, multiobjective optimization was carried out by means of the desirability function method. In order to favour fixation of the structures by osseointegration, porosity range between 0.5 and 0.75, mean of pore size between 0.1 and 0.3 mm, and variance of pore size between 0.000 and 0.010 mm² were selected. Results showed that the optimal solution consists of a structure with a height between layers of 0.72 mm, 3.65 points per mm² and a radius of 0.15 mm. It was observed that, given fixed height and radius values, the three responses decrease with the number of points per surface unit. The increase of the radius of the columns implies the decrease of the porosity and of the mean of pore size. The decrease of the height between layers leads to a sharper decrease of both the porosity and the mean of pore size. In order to compare calculated and experimental values, scaffolds were printed in polylactic acid (PLA) with FDM technology. Porosity and pore size were measured with X-ray tomography. Average value of measured porosity was 0.594, while calculated porosity was 0.537. Average value of measured mean of pore size was 0.372 mm, while calculated value was 0.434 mm. Average value of variance of pore size was 0.048 mm², higher than the calculated one of 0.008 mm². In addition, both round and elongated pores were observed in the printed structures. The current methodology allows designing structures with different requirements for porosity and pore size. In addition, it can be applied to other responses. It will be very useful in medical applications such as the simulation of body tissues or the manufacture of prostheses.

Dataset Information

Estimating the 3D pore size distribution of biopolymer networks from directionally biased data.

Publications

Estimating the 3D pore size distribution of biopolymer networks from directionally biased data.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure