Characterization of the Concentration-Dependence of Solute Diffusivity and Partitioning in a Model Dextran-Agarose Transport System

Abstract

This study reports experimental measurements of solute diffusivity and partition coefficient for various solute concentrations and gel porosities, and proposes novel constitutive relations to describe these observed values. The longer-term aim is to explore the theoretical ramifications of accommodating variations in diffusivity and partition coefficient with solute concentration and tissue porosity, and investigate whether they might suggest novel mechanisms not previously recognized in the field of solute transport in deformable porous media. The study implements a model transport system of agarose hydrogels to investigate the effect of solute concentration and hydrogel porosity on the transport of dextran polysaccharides. The proposed phenomenological constitutive relations are shown to provide better fits of experimental results than prior models proposed in the literature based on the microstructure of the gel. While these constitutive models were developed for the transport of dextran in agarose hydrogels, it is expected that they may also be applied to the transport of similar molecular weight solutes in other porous media. This quantification can assist in the application of biophysical models that describe biological transport in deformable tissues, as well as the cell cytoplasm.

Fig. 1

(A) Representative intensity profiles of recovery of bleached line during FRAP, at four selected time points. Solid curves represent curve-fits of Eq.(1) to each profile, producing a value for w² at each time point. (B) Plot of w² versus time for the same FRAP test. The slope of the line is proportional to the diffusion coefficient according to Eq.(2).

Fig. 2

(A) Diffusion coefficient versus dextran concentration for 70 kDa dextran. Solid curves represent curve-fit of Eq.(6) to the experimental data. (B) Diffusion coefficient versus dextran concentration for 10 kDa dextran. Solid curves represent curve-fit of Eq.(6) to the experimental data.

Fig. 3

(A) Partition coefficient versus dextran concentration for 70 kDa dextran. Solid curves represent curve-fit of Eqs.(7)–(8) to the experimental data. (B) Partition coefficient versus dextran concentration for 10 kDa dextran. Solid curves represent curve-fit of Eqs.(7)–(8) to the experimental data.

Fig. 4

Comparison of experimental results and model fits for the partition coefficient in the limit of dilute (κ₀) and high solute concentrations (κ_∞), as a function of agarose gel solid content (1−ϕ_w ) for the 70 kDa dextran. Solid lines represent the sigmoidal models of Eq.(8) and dashed lines represent the exponential model of Ogston as used by Tong and Anderson .

Fig. 5

Representative case of normalized concentration uptake for 2% agarose exposed to 70 kDa dextran at 7 μM. Solid curves represent curve-fit of Eq.(5) to the experimental data.

Fig. 6

Comparison of experimental results and various models for the hindrance to solute diffusion, D/D₀ , in the limit of dilute dextran concentrations. (A) 70 kDa dextran, and (B) 10 kDa dextran. See text for description of various models.

Fig. 7

Comparison of diffusivities of 10 kDa and 70 kDa dextran as measured from FRAP (Fig. 1) and disk absorption (Fig. 5), in the case of dilute concentrations in 2% agarose. No statistical differences were observed between the two methods (p>0.16).