# Cell Mechanics

## Modeling the Cell Response to Osmotic Loading Using Mixture Theory

The fundamental physical mechanisms of solute and water transport across the cell membrane have long been studied in the field of cell membrane biophysics, and there exist a number of formalisms aiming to characterize transport through membrane channels and/or lipid bilayers. These formalisms include a one-parameter (solute permeability) model, a classic two-parameter (water and solute permeability) model and a commonly used three-parameter model (water and solute permeability and a solute-solvent interaction term) developed by Kedem and Katchalsky. The parameters of interest (permeabilities) can be extracted from the formulation when the cell volume change is measured in the experiment, assuming that the cell volume change is due purely to the volume of the water (and solute) that enters or exudes from the cell. These formulations have been derived from the general theory of irreversible thermodynamics.

In more recent decades, the field of rational mechanics has addressed problems in the mixture of fluids (solvent and solutes) as well as the mixture of fluids and solids (deformable porous media). In our studies we have applied the theory of mixtures to the analysis of the passive response of cells to osmotic loading. We have generalized the formulation to incorporate partition coefficients for the solutes in the cytoplasm relative to the external solution, and accounts for cell membrane tension.

## Biomimetic Analysis of Alginate Beads in Dextran Solutions

To help assess whether this more elaborate model of the cell was justified, we performed a study to investigate the response of spherical gels to osmotic loading, both from experiments and theory. In the experimental component of the study alginate was used as the model gel, and it was osmotically loaded with dextran solutions of various concentrations and molecular weight, to verify the predictions from the theoretical analysis. Results showed that the mixture framework could accurately predict the transient and equilibrium response of alginate gels to osmotic loading with dextran solutions. It was 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. This study was the first to demonstrate that gels may exhibit a partial volume recovery when loaded osmotically. The validation of this framework facilitated our subsequent investigations of the role of the protoplasm in the response of cells to osmotic loading.

## Partitioning of Osmolytes by the Cytoplasm

Due to the dense organization of organelles, cytoskeletal elements, and protein complexes that make up the intracellular environment, we hypothesized that membrane-permeant solutes may be excluded from a fraction of the interstitial space of the cytoplasm via steric restrictions, electrostatic interactions and other long-range intermolecular forces. We performed experiments to investigate the hypothesis that the intracellular partitioning of membrane-permeant solutes manifests itself as a partial volume recovery in response to hyperosmotic loading, based on our prior theoretical and biomimetic experimental studies. Osmotic loading experiments were performed on immature bovine chondrocytes using culture conditions where regulatory volume responses were shown to be insignificant. Osmotic loading with membrane-permeant glycerol (92 Da) and urea (60 Da) were observed to produce partial volume recoveries consistent with the proposed hypothesis, whereas loading with 1,2-propanediol (76 Da) produced complete volume recovery. Combining these experimental results with the previous theoretical framework produced a measure for the intracellular partition coefficient of each of these solutes. The finding that intracellular partitioning of membrane-permeant solutes manifests itself as a partial volume recovery under osmotic loading offered a simple method for characterizing the partition coefficient. These measurements suggested that significant partitioning may occur even for small membrane-permeant osmolytes. Furthermore, a positive correlation was observed suggesting that a soluteâ€™s cytoplasmic partition coefficient increases with increasing hydrophobicity. The biomimetic studies of alginate in dextran and osmotic loading of chondrocytes represent a significant component of the dissertation of Michael Albro.

## Water Transport Through Chondrocytes

Because of the avascular nature of adult cartilage nutrients and waste products are transported to and from the chondrocytes by diffusion and convection through the extracellular matrix. The convective interstitial fluid flow within and around chondrocytes is poorly understood. From a theoretical study, we demonstrated that the incorporation of a semi-permeable membrane when modeling the chondrocyte leads to the following findings: Under mechanical loading of an isolated chondrocyte the intracellular fluid pressure is on the order of tens of Pascals and the transmembrane fluid outflow, on the order of picometers per second, takes several days to subside; consequently the chondrocyte behaves practically as an incompressible solid whenever the loading duration is on the order of minutes or hours. When embedded in its extracellular matrix, the chondrocyte response is substantially different. Mechanical loading of the tissue leads to a fluid pressure difference between intracellular and extracellular compartments on the order of tens of kilopascals and the transmembrane outflow, on the order of a nanometer per second, subsides in about one hour. The volume of the chondrocyte decreases concomitantly with that of the extracellular matrix. The interstitial fluid flow in the extracellular matrix is directed around the cell, with peak values on the order of tens of nanometers per second. The viscous fluid shear stress acting on the cell surface is orders of magnitude smaller than the solid matrix shear stresses resulting from the extracellular matrix deformation. These results provided new insight toward our understanding of water transport in chondrocytes.