Diffusion anisotropy in collagen gels and tumors: the effect of fiber network orientation

The interstitial matrix is comprised of cross-linked collagen fibers, generally arranged in nonisotropic orientations. Spatial alignment of matrix components within the tissue can affect diffusion patterns of drugs. In this study, we developed a methodology for the calculation of diffusion coefficients of macromolecules and nanoparticles in collagenous tissues. The tissues are modeled as three-dimensional, stochastic, fiber networks with varying degrees of alignment. We employed a random walk approach to simulate diffusion and a Stokesian dynamics method to account for hydrodynamic hindrance. We performed our analysis for four different structures ranging from nearly isotropic to perfectly aligned. We showed that the overall diffusion coefficient is not affected by the orientation of the network. However, structural anisotropy results in diffusion anisotropy, which becomes more significant with increase in the degree of alignment, the size of the diffusing particle, and the fiber volume fraction. To test our model predictions we performed diffusion measurements in reconstituted collagen gels and tumor xenografts. We measured fiber alignment and diffusion with second harmonic generation and multiphoton fluorescent recovery after photobleaching techniques, respectively. The results showed for the first time in tumors that the structure and orientation of collagen fibers in the extracellular space leads to diffusion anisotropy.     

Diffusion in immobilized-cell gels

Summary The relationship between the diffusion coefficient, the effective diffusion coefficient and the partition coefficient for a solute in a cell-containing gel is discussed. The use of correlation equations that are based on some kind of physical model is recommended when the effect of cell concentration on diffusion is interpreted.     

Primary culture of mouse mammary tumor epithelial cells embedded in collagen gels

Summary Mammary tumor epithelial cells from BALB/cfC3H mice were dispersely embedded inside the collagen gels in Ham's F-12 medium containing horse serum. A sustained cell growth leading to a 5- to 10-fold increase in cell number over initial level was observed in less than 2 weeks. The extent of this growth was found to be dependent on serum concentration. However, addition of various protein and steroid hormones, both singly and in combination, to low-serum-containing medium failed to achieve a comparable level of growth to that promoted by higher serum concentration. Mammary tumor cells can now be consistently propagated in primary culture. This investigation was supported by Grants CA05388 and CA09041 awarded by the National Cancer Institute, Department of Health, Education and Welfare, and by cancer research funds of the University of California.     

Primary culture of mouse mammary tumor epithelial cells embedded in collagen gels

Mammary tumor epithelial cells from BALB/cfC3H mice were dispersely embedded inside the collagen gels in Ham's F-12 medium containing horse serum. A sustained cell growth leading to a 5- to 10-fold increase in cell number over initial level was observed in less than 2 weeks. The extent of this growth was found to be dependent on serum concentration. However, addition of various protein and steroid hormones, both singly and in combination, to low-serum-containing medium failed to achieve a comparable level of growth to that promoted by higher serum concentration. Mammary tumor cells can now be consistently propagated in primary culture.     

Phenotypic stability of mouse mammary tumor cells cultured on collagen gels

Summary This study demonstrates that phenotypic characteristics of androgen-responsive (AR) Shionogi mouse mammary tumors and androgen-independent (AI) derivatives can be maintained in culture. Cells were seeded onto collagen gels in medium containing 2% dextran-characoal-treated fetal bovine serum with or without 0.01 μg/ml dihydrotestosterone (DHT). Androgen-responsive tumors grew more rapidly than AI tumors in vivo and consequently, cells from AR tumors cultured in DHT-containing medium grew faster than cells in DHT-deprived medium and cells from AI tumors. Androgen-responsive tumors had a sheetlike growth pattern; AI tumors formed clumps or irregular cords of cells. Cells from AR tumors cultured in the presence of DHT formed confluent pavements, whereas cells maintained in the absence of DHT and cells from AI tumors formed clusters or cords of cells. Ultrastructurally, cells of AR tumors were elongated; cells of AI tumors were smaller and rounder. These cellular morphologies persisted in culture. Tumorigenicity of cells was assayed by injecting cells s.c. into host mice. Tumors arising from cells of freshly dissociated AR tumors and cells of AR tumors cultured in the presence of DHT appeared more rapidly and grew faster in intact males than in castrated males and intact females. Tumors arising from cells cultured in the absence of DHT and from freshly dissociated or cultured cells of AI tumors had identical rates of appearance and growth in all hosts. This culture system permits these cells to retain their state of malignant progression in vitro and should be a useful model for studying the origin of heterogeneity within tumors and its role in tumor behavior. This work was supported by a grant from the National Cancer Institute of Canada. J. T. E. is a Research Scholar of the National Cancer Institute of Canada.     

Twisted architectures in cell-free assembled collagen gels: study of collagen substrates used for cultures

Reprecipitated fibrils from collagen solutions assemble into aggregates often showing a remarkable twisted structure. We first observed these aggregates in collagen gels prepared to facilitate culture of epithelial cells. We verified that these structures form in the absence of cells and correspond to a process of self-assembly. Studies on reconstructed fibrils of collagen are generally based on the examination of thin specimens mounted onto coated grids prepared for electron microscopy. We rather applied the classical methods of fixation, embedding and ultramicrotomy, which allowed us to analyze the structure of these aggregates, several microns in diameter. Our gels were prepared from 2.5 mg/ml tropocollagen solutions usually chosen for cell and organ cultures. The time required to obtain twisted architectures, in these aggregates, depends on temperature and the presence of factors such as fetal calf serum proteins. Twist is observed at two different levels of organization. Microfibrils are gathered into twisted bundles which condense into cross-striated fibrils. These fibrils themselves aggregate and show a mutual twist whose orientation is left-handed as is the twist observed within each microfibril bundle. Several models of these architectures are presented. Planar twist, cylindrical twist and toroidal twist are described and their relation to the structure of certain liquid crystals is considered. Examples of orthogonal packing also have been observed. These structures obtained in vitro are very close to patterns already described in vivo in numerous collagen matrices.     

Fibroblastic cell cycling in collagen gels

Abstract. Quiescent C3H10T1/2 mouse fibroblasts resume DNA synthesis and proliferation following incubation in medium containing fresh serum both when grown in monolayer and when grown in a collagen matrix. We observed that the rate of DNA synthesis is reduced at high initial cell densities and low initial collagen concentrations. In a collagen matrix, fibroblasts contract the matrix causing an increase in cell density and collagen concentration. We studied the chronological relationship between the kinetics of DNA synthesis and the collagen matrix contraction. The rate of collagen collection per cell changes in time, dependent on initial cell and collagen concentration. The kinetics of the collagen collection showed a positive correlation with the kinetics of DNA synthesis, 16 h later.     

Diffusion in gels containing immobilized cells: a critical review

Eleven experimental investigation of diffusion in gels containing immobilized cells are reviewed. The experimental data, which quantitatively express the diffusion coefficient as a function of the cell concentration, are compared with a number of well-known equations developed for mass transfer in heterogeneous media. Based on this comparison, a procedure for the theoretical prediction of effective diffusion coefficients in cell-containing gels is recommended.     

Diffusion in the slice microenvironment and implications for physiological studies

The brain cell microenvironment includes the extracellular space surrounding the cell together with the cellular elements that define the space. The dense packing of cells in the mammalian nervous system ensures that the extracellular space is narrow but highly complex in geometry. Recent studies with ion-selective micropipettes have revealed that the cerebellar slice can support changes in [K+]o that resemble those seen in the intact preparation. In the slice, [K+]o responses of individual cells can even be resolved. Studies with iontophoretic techniques and quantitative analysis in the slice have shown that the extracellular space has diffusion properties, characterized by a volume fraction and a tortuosity, that are very similar to those seen in the intact animal. These data confirm that the microenvironment in the slice is comparable to that in the intact animal. The diffusion parameters can be used to make predictions about the time necessary for substances to diffuse into slices under various conditions. Such estimates, together with other studies, indicate that it is probably inadvisable to use slices with thicknesses in excess of 300--400 micrometers, and that the bathing conditions can be critical in maintaining slice viability.     

Contraction of fibroblast-containing collagen gels: Initial collagen concentration regulates the degree of contraction and cell survival

Remodeling of extracellular matrix involves a number of steps including the recruitment, accumulation, and eventual apoptosis of parenchymal cells as well as the production, organization, and rearrangement of extracellular matrix produced by these cells. The culture of fibroblasts in three-dimensional gels made of type I collagen has been used as a model of tissue contraction which characterizes both wound repair and fibrosis. The current study was designed to determine the effect of initial collagen concentration on the ability of fibroblasts to contract collagen gels and on cell survival. Native type I collagen was extracted from rat tail tendons and used to prepare collagen gels with varying collagen concentrations (0.75-2.0 mg/ml). Human lung fibroblasts (HFL-1) were cast into the gels and cultured in Dulbecco modified Eagle medium with 0.1% fetal calf serum for 2 wk. The gel size, collagen content, and deoxyribonucleic acid (DNA) content were determined. Gels prepared with an initial concentration of 0.75 mg/ml contracted more rapidly and to a smaller final size than gels prepared from 2 mg/ml initial collagen concentration (final size 7.1 versus 36.4% of initial size, P < 0.01). There was no significant degradation of the collagen in the gels under either condition. Hence, the dramatically increased contraction of the lower density gels resulted in a higher final density (P < 0.01). Cell density was estimated from DNA content. In low initial density gels, the final DNA content was significantly less than that in higher initial density gels (0.73 versus 1.88 microg/gel, P < 0.05). This was accompanied by an increased percentage of apoptotic cells at day 14 (43.3 versus 34.1%, P < 0.05). If the gels were maintained in the attached state which largely prevents contraction, apoptosis was significantly reduced, suggesting that contraction rather than matrix composition was a requirement for the increased apoptosis. In summary, these findings indicate that the initial matrix composition can lead to differing outcomes during fibroblast-mediated wound contraction.     

A method for the isolation and culture of human colonic crypts in collagen gels

Summary Little is known concerning the biological factors that control the proliferation of the stem cells of the colonic mucosa. In part this is due to a lack of systems suitable for studying the proliferation of this mucosa in vitro. We describe a simple technique for the isolation of single viable intact crypts which are free of stroma and which can then be cultured for periods of at least 16 d using a collagen gel culture method. This method of crypt isolation was efficient with the mean yield of viable intact crypts being 1.4 ±1.2×10⁴ ( ± SD) crypts/cm² of mucosa. In culture, mucosal cells only survived for extended periods when the crypts were cultured in collagen gels over a feeder layer of bovine aortic endothelial cells. Cells containing mucus were present in the cultured crypts at all stages of the culture; however we have not been able to demonstrate alkaline phosphatase activity in these crypts. Studies of DNA synthesis after 7 d in culture, using a 18-h pulse label with bromodeoxyuridine (BUdR) has shown that DNA synthesis, as measured by incorporation of BUdR into nuclei, is still occurring in these cultured crypts.     

Physical and chemical modifications of collagen gels: impact on diffusion

The extracellular matrix (ECM) represents a major barrier for delivery of therapeutic drugs, and the transport is determined by the ECM composition, structure, and distribution. Because of the high interstitial fluid pressure in tumors, diffusion becomes the main transport mechanism through ECM. The purpose of this work was to study the impact of the structure of the collagen network on diffusion, by studying to what extent the orientation and chemical modification of the collagen network influenced diffusion. Collagen gels with a concentration of 0.2-2.0% that is comparable with the amount of collagen in the tumor ECM were used as a model system for ECM. Collagen gels were aligned in a low-strength magnetic field and geometrical confinement, and chemically modified by adding decorin or hyaluronan. Diffusion of dextran 2-MDa molecules in the collagen gels was measured using fluorescence recovery after photobleaching. Alignment of the collagen fibers in our gels was found to have no impact on the diffusion coefficient. Adding decorin reduced the diameter of the collagen fibers, but no effect on diffusion was observed. Hyaluronan also reduced the fiber diameter, and high concentration of hyaluronan (2.5 mg/ml) increased the diffusion coefficient. The results indicate that the structure of the collagen network is not a major factor in determining the diffusion through the ECM. Rather, increasing the concentration of collagen was found to reduce the diffusion coefficient. Concentration of the collagen network is more important than the structure in determining the diffusion coefficient.     

Behaviour of Duchenne dystrophy fibroblasts in collagen gels

In order to clarify the possible involvement of the cell surface in the pathogenesis of Duchenne muscular dystrophy, we have examined the behaviour of fibroblasts cultured from Duchenne patients in hydrated collagen lattices. No differences could be found between Duchenne and normal skin fibroblasts, either after initial seeding or following prolonged culture within the collagen gel.     

Diffusion and partitioning of proteins in charged agarose gels.

The effects of electrostatic interactions on the diffusion and equilibrium partitioning of fluorescein-labeled proteins in charged gels were examined using fluorescence recovery after photobleaching and gel chromatography, respectively. Measurements were made with BSA, ovalbumin, and lactalbumin in SP-Sepharose (6% sulfated agarose), in phosphate buffers at pH 7 and ionic strengths ranging from 0.01 to 1.0 M. Diffusivities in individual gel beads (D) and in the adjacent bulk solution (D infinity) were determined from the spatial Fourier transform of the digitized two-dimensional fluorescence recovery images. Equilibrium partition coefficients (phi) were measured by recirculating protein solutions through a gel chromatography column until equilibrium was reached, and using a mass balance. Diffusion in the gel beads was hindered noticeably, with D/D infinity = 0.4-0.5 in each case. There were no effects of ionic strength on BSA diffusivities, but with the smaller proteins (ovalbumin and lactalbumin) D infinity increased slightly and D decreased at the lowest ionic strength. In contrast to the modest changes in diffusivity, there were marked effects of ionic strength on the partition coefficients of these proteins. We conclude that for diffusion of globular proteins through gel membranes of like charge, electrostatic effects on the effective diffusivity (Deff = phi D) are likely to result primarily from variations in phi with only small contributions from the intramembrane diffusivity.     

An overview of oxygen transport in plants: diffusion and convection

The movement of gases within plants is crucial for species that live in flood-prone areas with limited soil oxygen. These plants adapt to hypoxia/anoxia not by using oxygen more efficiently, but by ensuring a steady oxygen supply to their cells. Wetland plants typically form gas-filled spaces (aerenchyma) in their tissues, providing a low-resistance pathway for gas movement between shoots and roots, especially when the shoots are above water, and the roots are submerged. Oxygen movement in plant roots is mainly through diffusion. However, in certain species, such as emergent and floating-leaved plants, pressurized flows can also facilitate the movement of gases within their stems and rhizomes. Three types of pressurized (convective) flows have been identified: humidity-induced pressurization (positive pressure), thermal osmosis (positive pressure with air flow against the heat gradient), and venturi-induced suction (negative pressure) caused by wind passing over broken culms. A clear diel variation in pressurized flows exists, with higher pressures and flows during the day and negligible pressures and flows during the night. This article discusses some key aspects of these mechanisms for oxygen movement.     

Formulating gels for decreased mucociliary transport using rheologic properties: Polyacrylic acids

The purpose of these studies was to identify the rheologic properties of polyacrylic acid gels necessary for optimal reductions in mucociliary clearance. The mucociliary transport of 2 bioadhesive polyacrylic acid polymers, polycarbophil and carbopol, was assessed in vitro by measuring their clerance rates across explants of ciliated bovine tracheal tissue. The viscoelastic properties of polymer gels were measured in the presence of mucus using controlled stress rheometry. Combinations of apparent viscosity (η) and complex modulus (G^*) were found to be the most useful parameters in the identification of polyacrylic acid formulations capable of decreasing mucociliary transport rate (MTR). A narrow range of η and G^* values suitable for reducing mucociliary clearance, while remaining sufficiently fluid for intranasal administration, were identified. The correlations between the rheologic parameters of the polycarbophil gels and their mucociliary transport rates were used to identify other polyacrylic acid gels that also had suitable mucociliary clearance properties, demonstrating that these parameters can be used to direct the optimization of formulations using simple in vitro rheologic testing. Published: April 20, 2007     

Diffusion of macromolecules in agarose gels: comparison of linear and globular configurations.

The diffusion coefficients (D) of different types of macromolecules (proteins, dextrans, polymer beads, and DNA) were measured by fluorescence recovery after photobleaching (FRAP) both in solution and in 2% agarose gels to compare transport properties of these macromolecules. Diffusion measurements were conducted with concentrations low enough to avoid macromolecular interactions. For gel measurements, diffusion data were fitted according to different theories: polymer chains and spherical macromolecules were analyzed separately. As chain length increases, diffusion coefficients of DNA show a clear shift from a Rouse-like behavior (DG congruent with N0-0.5) to a reptational behavior (DG congruent with N0-2.0). The pore size, a, of a 2% agarose gel cast in a 0.1 M PBS solution was estimated. Diffusion coefficients of the proteins and the polymer beads were analyzed with the Ogston model and the effective medium model permitting the estimation of an agarose gel fiber radius and hydraulic permeability of the gels. Not only did flexible macromolecules exhibit greater mobility in the gel than did comparable-size rigid spherical particles, they also proved to be a more useful probe of available space between fibers.     

ATP reduces gel compaction in osteoblast-populated collagen gels.

Bone remodeling is a localized process, but regulated by systemic signals such as hormones, cytokines, and mechanical loading. The mechanism by which bone cells convert these systemic signals into local signals is not completely understood. It is broadly accepted that the "prestress" in cytoskeleton of cells affects the magnitude of cellular responses to mechanical stimuli. Prestress derives from stiff cytoskeletal proteins and their connections within the cell and from cell contractility upon attaching to matrix. In an in vitro model of three-dimensional gel compaction, the relative cellular prestress levels in the same matrix environment were determined by matrix compaction rate: a greater compaction rate resulted in a higher level of prestress. In the present study, the effects of ATP on the prestress of osteoblasts were studied using mouse MC3T3-E1 cells grown in three-dimensional bioartificial tissues (BATs). ATP (> or =100 microM) reduced the compaction rate of BATs in a dose-dependent manner. ADP, 2'-(or 3')-O-(4-benzoylbenzoyl) ATP, and UTP, but not alpha,beta-methylene ATP, also reduced the compaction rate but to a lesser extent. Pyridoxal-phosphate-6-azophenyl-2',4'-disulfonic acid tetrasodium did not block the effect of ATP on BAT compaction rate. These results indicate that both P2X and P2Y receptors are involved in ATP-induced reduction of BAT compaction rate. Steady fluid flow and RT-PCR results showed that ATP reduced cell attachment on type I collagen by downregulating the expression of integrin alpha(1). These results suggest a potential role for P2 receptors in matrix remodeling and repair and as a potential drug target in treatment of bone diseases.