Osmotic loading of spherical gels: a biomimetic study of hindered transport in the cell protoplasm

Abstract

Osmotic loading of cells has been used to investigate their physicochemical properties as well as their biosynthetic activities. The classical Kedem-Katchalsky framework for analyzing cell response to osmotic loading, which models the cell as a fluid-filled membrane, does not generally account for the possibility of partial volume recovery in response to loading with a permeating osmolyte, as observed in some experiments. The cell may be more accurately represented as a hydrated gel surrounded by a semi-permeable membrane, with the gel and membrane potentially exhibiting different properties. To help assess whether this more elaborate model of the cell is justified, this study investigates the response of spherical gels to osmotic loading, both from experiments and theory. The spherical gel is described using the framework of mixture theory. In the experimental component of the study alginate is used as the model gel, and is osmotically loaded with dextran solutions of various concentrations and molecular weight, to verify the predictions from the theoretical analysis. Results show that the mixture framework can accurately predict the transient and equilibrium response of alginate gels to osmotic loading with dextran solutions. It is found that the partition coefficient of dextran in alginate regulates the equilibrium volume response and can explain partial volume recovery based on passive transport mechanisms. The validation of this theoretical framework facilitates future investigations of the role of the protoplasm in the response of cells to osmotic loading.

Figure 1

Schematic of testing apparatus for osmotic loading of alginate beads.

Figure 2

Normalized volume response of osmotically-loaded alginate beads: (a) Means and standard deviations for osmotic loading with 40 kDa dextran (4, 5, 6 and 7 mM). (b) Mean and standard deviation for osmotic loading with 75 kDa dextran (3 mM).

Figure 2

Normalized volume response of osmotically-loaded alginate beads: (a) Means and standard deviations for osmotic loading with 40 kDa dextran (4, 5, 6 and 7 mM). (b) Mean and standard deviation for osmotic loading with 75 kDa dextran (3 mM).

Figure 3

Permeability of alginate to dextran solutions (k̃), obtained from curve-fitting of the volume response of alginate beads to osmotic loading with dextran solutions, and from direct permeation measurements on alginate disks. Within each set, numbers above bars indicate the concentrations against which differences were statistically significant (p<0.0001).

Figure 4

Representative theoretical curvefits (solid curves) of experimental results (symbols) shown for each dextran concentration and molecular weight (symbols).

Figure 5

Diffusivity of dextran in free solution (D₀₎ and in alginate (D), obtained from curve-fitting of the volume response of alginate beads to osmotic loading with dextran solutions. Numbers above bars indicate the concentrations against which differences were statistically significant (p<0.005).

Figure 6

Partition coefficient of dextran in alginate (κ), obtained from curve-fitting of the volume response of alginate beads to osmotic loading with dextran solutions: (a) As a function of dextran concentration and molecular weight (numbers above bars indicate the concentrations against which differences were statistically significant, p<0.0001); (b) as a function of gel dilatation at equilibrium (40 kDa dextran only).

Figure 6

Partition coefficient of dextran in alginate (κ), obtained from curve-fitting of the volume response of alginate beads to osmotic loading with dextran solutions: (a) As a function of dextran concentration and molecular weight (numbers above bars indicate the concentrations against which differences were statistically significant, p<0.0001); (b) as a function of gel dilatation at equilibrium (40 kDa dextran only).

Figure 7

Viscosity η of 40 kDa dextran solutions of various concentrations, measured using a glass capillary viscometer.

Figure 8

Hydraulic permeability (k) of alginate to 40 kDa dextran solutions of various concentrations, as a function of alginate gel dilatation at equilibrium (tr E ≈ 1− V_eq/V_r).

Figure 9

Volume response of bovine articular cartilage chondrocytes to osmotic loading with 1.4 M glycerol at 21°C. Adapted from Figure 7 of Xu et al. [26], with permission.