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.

Modeling the two-way feedback between contractility and matrix realignment reveals a nonlinear mode of cancer cell invasion

“…To include the steric hindrance effects associated with the decrease in interfibrillar pore size (d) at high concentrations of collagen, we use the experimental data that suggest that permeability is proportional to the area of the voids, M ∝ d 2 (37). Given that the pore size scales with collagen concentration (ρ) such that d ∝ ρ −1=2 (38), and the matrix stiffness scales with collagen concentration such that E m ∝ ρ 1.7 (39), we assume that the permeability at high matrix stiffnesses ðE m > 0.6 kPaÞ decreases with the matrix stiffness, M ∝ ðE m Þ −0.6…”

Micromechanics of cellularized biopolymer networks

“…Despite its lack of biochemical complexity compared with live tissue, reconstituted type I collagen gel has been successfully used to provide mechanistic insights into processes such as morphogenesis (7), wound repair (8), and cell migration (9). In particular, the rheology and especially the rigidity of collagen gel have been shown to tune the growth and migratory phenotypes of cancer cells in vitro (10, 11).Structurally, collagen gels are formed by fibrous networks and typically have pore sizes of a few to tens of microns (12)(13)(14). The typical size of these structural discontinuities is comparable to the size of cells and is much larger than cell-ECM adhesion complexes (15,16).…”

“…Structurally, collagen gels are formed by fibrous networks and typically have pore sizes of a few to tens of microns (12)(13)(14). The typical size of these structural discontinuities is comparable to the size of cells and is much larger than cell-ECM adhesion complexes (15,16).…”

Automated analysis of collagen networks via microscopy

“…The blind spot affecting the confocal reflection microscopy images introduces an error in the estimation of the pore size. However, if the cutoff angle for the missing fibers is known, it is possible to compute a correction as was done in [6] for collagen hydrogels polymerized in culture wells. Currently, we are implementing this correction for the estimation of the pore size in both platforms.…”

“…Three-dimensional collagen networks are typically acquired using either confocal reflection microscopy or confocal fluorescence microscopy [6]. The former is the modality chosen to imaging in this work due to its simplicity and lower cost.…”