David A. Berk

Role of tumor–host interactions in interstitial diffusion of macromolecules: Cranial vs. subcutaneous tumors

The large size of many novel therapeutics impairs their transport through the tumor extracellular matrix and thus limits their therapeutic effectiveness. We propose that extracellular matrix composition, structure, and distribution determine the transport properties in tumors. Furthermore, because the characteristics of the extracellular matrix largely depend on the tumor–host interactions, we postulate that diffusion of macromolecules will vary with tumor type as well as anatomical location. Diffusion coefficients of macromolecules and liposomes in tumors growing in cranial windows (CWs) and dorsal chambers (DCs) were measured by fluorescence recovery after photobleaching. For the same tumor types, diffusion of large molecules was significantly faster in CW than in DC tumors. The greater diffusional hindrance in DC tumors was correlated with higher levels of collagen type I and its organization into fibrils. For molecules with diameters comparable to the interfibrillar space the diffusion was 5- to 10-fold slower in DC than in CW tumors. The slower diffusion in DC tumors was associated with a higher density of host stromal cells that synthesize and organize collagen type I. Our results point to the necessity of developing site-specific drug carriers to improve the delivery of molecular medicine to solid tumors.

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.

Hindered diffusion in agarose gels: test of effective medium model

The diffusivities of uncharged macromolecules in gels (D) are typically lower than in free solution (D infinity), because of a combination of hydrodynamic and steric factors. To examine these factors, we measured D and D infinity for dilute solutions of several fluorescein-labeled macromolecules, using an image-based fluorescence recovery after photobleaching technique. Test macromolecules with Stokes-Einstein radii (rs) of 2.1-6.2 nm, including three globular proteins (bovine serum albumin, ovalbumin, lactalbumin) and four narrow fractions of Ficoll, were studied in agarose gels with agarose volume fractions (phi) of 0.038-0.073. The gels were characterized by measuring the hydraulic permeability of supported agarose membranes, allowing calculation of the Darcy permeability (kappa) for each gel sample. It was found that kappa, which is a measure of the intrinsic hydraulic conductance of the gel, decreased by an order of magnitude as phi was increased over the range indicated. The diffusivity ratio D/D infinity, which varied from 0.20 to 0.63, decreased with increases in rs or phi. Thus as expected, diffusional hindrances were the most severe for large macromolecules and/or relatively concentrated gels. According to a recently proposed theory for hindered diffusion through fibrous media, the diffusivity ratio is given by the product of a hydrodynamic factor (F) and a steric factor (S). The functional form is D/D infinity = F(rs/k1/2) S(f), where f = [(rs+rf)/rf]2 phi and rf is the fiber radius. Values of D/D infinity calculated from this effective medium theory, without use of adjustable parameters, were in much better agreement with the measured values than were predictions based on other approaches. The strengths and limitations of the effective medium theory for predicting diffusivities in gels are discussed.

Fluorescence photobleaching with spatial Fourier analysis: measurement of diffusion in light-scattering media.

A new method for the measurement of diffusion in thick samples is introduced, based upon the spatial Fourier analysis of Tsay and Jacobson (Biophys. J. 60: 360-368, 1991) for the video image analysis of fluorescence recovery after photobleaching (FRAP). In this approach, the diffusion coefficient is calculated from the decay of Fourier transform coefficients in successive fluorescence images. Previously, the application of FRAP in thick samples has been confounded by the optical effects of out-of-focus light and scattering and absorption by the sample. The theory of image formation is invoked to show that the decay rate is the same for both the observed fluorescence intensity and the true concentration distribution in the tissue. The method was tested in a series of macromolecular diffusion measurements in aqueous solution, in agarose gel, and in simulated tissue consisting of tumor cells (45% v/v) and blood cells (5% v/v) in an agarose gel. For a range of fluorescently labeled proteins (MW = 14 to 600 kD) and dextrans (MW = 4.4 to 147.8 kD), the diffusion coefficients in aqueous solution were comparable to previously published values. A comparison of the spatial Fourier analysis with a conventional direct photometric method revealed that even for the weakly scattering agarose sample, the conventional method gives a result that is inaccurate and dependent on sample thickness whereas the diffusion coefficient calculated by the spatial Fourier method agreed with published values and was independent of sample thickness. The diffusion coefficient of albumin in the simulated tissue samples, as determined by the spatial Fourier analysis, varied slightly with sample thickness. In contrast, when the same video images were analyzed by direct photometric analysis, the calculated diffusion coefficients were grossly inaccurate and highly dependent on sample thickness. No simple correction could be devised to ensure the accuracy of the direct photometric method of analysis.These in vitro experiments demonstrate the advantage of our new analysis for obtaining an accurate measure of the local diffusion coefficient in microscopic samples that are thick (thickness greater than the microscope depth of focus) and scatter light.

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.

Lateral diffusion of small compounds in human stratum corneum and model lipid bilayer systems.

An image-based technique of fluorescence recovery after photobleaching (video-FRAP) was used to measure the lateral diffusion coefficients of a series of nine fluorescent probes in two model lipid bilayer systems, dimyristoylphosphatidylcholine (DMPC) and DMPC/cholesterol (40 mol%), as well as in human stratum corneum-extracted lipids. The probes were all lipophilic, varied in molecular weight from 223 to 854 Da, and were chosen to characterize the lateral diffusion of small compounds in these bilayer systems. A clear molecular weight dependence of the lateral diffusion coefficients in DMPC bilayers was observed. Values ranged from 6.72 x 10(-8) to 16.2 x 10(-8) cm2/s, with the smaller probes diffusing faster than the larger ones. Measurements in DMPC/cholesterol bilayers, which represent the most thorough characterization of small-solute diffusion in this system, exhibited a similar molecular weight dependence, although the diffusion coefficients were lower, ranging from 1.62 x 10(-8) to 5.60 x 10(-8) cm2/s. Lateral diffusion measurements in stratum corneum-extracted lipids, which represent a novel examination of diffusion in this unique lipid system, also exhibited a molecular weight dependence, with values ranging from 0.306 x 10(-8) to 2.34 x 10(-8) cm2/s. Literature data showed that these strong molecular weight dependencies extend to even smaller compounds than those examined in this study. A two-parameter empirical expression is presented that describes the lateral diffusion coefficient in terms of the solutes molecular weight and captures the size dependence over the range examined. This study illustrates the degree to which small-molecule lateral diffusion in stratum corneum-extracted lipids can be represented by diffusion in DMPC and DMPC/cholesterol bilayer systems, and may lead to a better understanding of small-solute transport across human stratum corneum.

Comparison of IgG diffusion and extracellular matrix composition in rhabdomyosarcomas grown in mice versus in vitro as spheroids reveals the role of host stromal cells

The tumour extracellular matrix acts as a barrier to the delivery of therapeutic agents. To test the hypothesis that extracellular matrix composition governs the penetration rate of macromolecules in tumour tissue, we measured the diffusion coefficient of nonspecific IgG in three rhabdomyosarcoma subclones growing as multicellular spheroids in vitro or as subcutaneous tumours in dorsal windows in vivo. In subcutaneous tumours, the diffusion coefficient decreased with increasing content of collagen and sulphated glycosaminoglycans. When grown as multicellular spheroids, no differences in either extracellular matrix composition or diffusion coefficient were found. Comparison of in vitro vs in vivo results suggests an over-riding role of host stromal cells in extracellular matrix production subjected to modulation by tumour cells. Penetration of therapeutic macromolecules through tumour extracellular matrix might thus be largely determined by the host organ. Hence, caution must be exercised in extrapolating drug penetrability from spheroids and multilayer cellular sandwiches consisting of only tumour cells to tumours in vivo.

Lateral mobility of integral proteins in red blood cell tethers

The red blood cell membrane is a complex material that exhibits both solid- and liquidlike behavior. It is distinguished from a simple lipid bilayer capsule by its mechanical properties, particularly its shear viscoelastic behavior and by the long-range mobility of integral proteins on the membrane surface. Subject to sufficiently large extension, the membrane loses its shear rigidity and flows as a two-dimensional fluid. These experiments examine the change in integral protein mobility that accompanies the mechanical phenomenon of extensional failure and liquidlike flow. A flow channel apparatus is used to create red cell tethers, hollow cylinders of greatly deformed membrane, up to 36-microns long. The diffusion of proteins within the surface of the membrane is measured by the technique of fluorescence redistribution after photobleaching (FRAP). Integral membrane proteins are labeled directly with a fluorescein dye (DTAF). Mobility in normal membrane is measured by photobleaching half of the cell and measuring the rate of fluorescence recovery. Protein mobility in tether membrane is calculated from the fluorescence recovery rate after the entire tether has been bleached. Fluorescence recovery rates for normal membrane indicate that more than half the labeled proteins are mobile with a diffusion coefficient of approximately 4 x 10(-11) cm2/s, in agreement with results from other studies. The diffusion coefficient for proteins in tether membrane is greater than 1.5 x 10(-9) cm2/s. This dramatic increase in diffusion coefficient indicates that extensional failure involves the uncoupling of the lipid bilayer from the membrane skeleton.

Quantitative analysis of angiogenesis and growth of bone: effect of indomethacin exposure in a combined in vitro-in vivo approach

Nonsteroidal anti-inflammatory agents have been used experimentally and clinically to suppress a variety of physiological events, including angiogenesis and formation of bone. The exact mechanisms by which indomethacin alters skeletal tissue generation are unknown, due in part to methodological limitations. By the use of an organ culture assay and an animal model using intravital microscopy in mice bearing dorsal skinfold chambers, the effect of indomethacin on growth and angiogenesis of neonatal femora was characterized over 16 days. In both assays, femora significantly elongated with time (P<0.05). The in vitro growth rate was more rapid than in vivo and dependent on the serum concentration, culture medium and age of mice. Although enthancing the serum content promoted cellular proliferation in organ culture, it dose-dependently suppressed femoral elongation, leading at 20% fetal calf serum to growth rates identical to those observed in vivo. Indomethacin supplementation (2 and 10 mg l−1) significantly accelerated longitudinal femoral growth in organ culture (P<0.05), whereas in vivo indomethacin (2 mg kg−1) did not modulate either angiogenesis or elongation of bone. Our in vitro data propose a central role of serum in the regulation of bone formation. Although indomethacin altered femoral gowth in vitro, our findings do not suggest that indomethacin suppresses angiogenesis or growth of bone in vivo. The complexity of physiological events in vivo may be obscuring a detectable effect.

Heating or freezing bone: Effects on angiogenesis induction and growth potential in mice

We have characterized the effect of bone graft treatment by heating or freezing (with or without dimethyl sulfoxide (DMSO)). Tissue culture and dorsal skin-fold chambers in mice were used as sites to quantify the effect on angiogenesis, growth and calcification of neonatal femora. Fresh femora increased in both length and cartilage diameter (calcification in vivo only), but cryopreservation or heating abolished the increase in femoral dimensions. In vivo, femora of all experimental groups elicited an angiogenic response from the host tissue, which was most pronounced for fresh femora, weaker for DMSO-preserved frozen bone and poor for unprotected frozen bone and boiled femora. Freezing in the presence of a cryopreservative (DMSO) was found to preserve the angiogenic potential of frozen bone, whereas unprotected heating or freezing significantly impaired angiogenesis induction and growth potential.