Asymptotic behavior of osmotic volume changes induced by a permeant solute (original) (raw)
Related papers
Osmosis is essential for the living organisms. In biological systems the process usually occurs in confined volumes and may express specific features. The osmotic pressure in aqueous solutions was studied here experimentally as a function of solute concentration (0.05-0.5 M) in two different regimes: of constant and variable solution volume. Sucrose, a biologically active substance, was chosen as a reference solute for the complex tests. A custom made osmotic cell was used. A novel operative experimental approach, employing limited variation of the solution volume, was developed and applied for the purpose. The established equilibrium values of the osmotic pressure are in agreement with the theoretical expectations and do not exhibit any evident differences for both regimes. In contrast, the obtained kinetic dependences reveal striking divergence in the rates of the process at constant and varied solution volume for the respective solute concentrations. The rise of pressure is much faster at constant solution volume, while the solvent influx is many times greater in the regime of variable volume. The results obtained suggest a feasible mechanism for the way in which the living cells rapidly achieve osmotic equilibrium upon changes in the environment.
Mathematical Modeling of Cell Volume Alterations under Different Osmotic Conditions
Biophysics and Medical Physics Computing, 2014
Cell volume, together with membrane potential and intracellular hydrogen ion concentration, is an essential biophysical parameter for normal cellular activity. Cell volumes can be altered by osmotically active compounds and extracellular tonicity. In this study, a simple mathematical model of osmotically induced cell swelling and shrinking is presented. Emphasis is given to water diffusion across the membrane. The mathematical description of the cellular behavior consists in a system of coupled ordinary differential equations. We compare experimental data of cell volume alterations driven by differences in osmotic pressure with mathematical simulations under hypotonic and hypertonic conditions. Implications for a future model are also discussed. Keywords: eukaryotic cell, mathematical modeling, osmosis, volume alterations
On the non-linearity of osmotic flow
Experimental Thermal and Fluid Science, 2004
The osmotic water flow and the solute flow through three different commercial cellulose acetate membranes were measured with different NaCl concentrations, hydrostatic pressures and module flow conditions. Based on the measurements, the concentrations on the surfaces of the selective layer of the membrane were theoretically calculated and the results applied to fit equations whose derivation is based on the theory of dimensional analysis. The results show that the frequently used linear forms of the osmotic transport equation do not satisfactorily describe the phenomenon. The proposed forms of a new transport equation for water flux are Aw DxsÀBw Dpr 1þU xs or A w D ffiffiffiffi x s p À B w D ffiffiffiffi p r p where A w , B w and U are the transport coefficients, x s is the molar fraction of the solute, x s is the mean molar fraction and p r is the dimensionless pressure. The question of whether the non-linear phenomenon of osmotic water transport is much more general than hitherto expected, is raised. Criticism is provided on the assumption of internal concentration polarisation as an explanation of the apparent non-linearities appearing in the experiments. The two-coefficient linear equation was found sufficient to describe the measured solute flux. The one-coefficient linear equation for solute flux, relating the flux only to the solute concentration difference or molar fraction difference, was found to be inadequate.
The effect of cell size distribution on predicted osmotic responses of cells
Cryo letters
An understanding of the kinetics of the osmotic response of cells is important in understanding permeability properties of cell membranes and predicting cell responses during exposure to anisotonic conditions. Traditionally, a mathematical model of cell osmotic response is obtained by applying mass transport and Boyle-vant Hoff equations using numerical methods. In the usual application of these equations, it is assumed that all cells are the same size equal to the mean or mode of the population. However, biological cells (even if they had identical membranes and hence identical permeability characteristics--which they do not) have a distribution in cell size and will therefore shrink or swell at different rates when exposed to anisotonic conditions. A population of cells may therefore exhibit a different average osmotic response than that of a single cell. In this study, a mathematical model using mass transport and Boyle-van't Hoff equations was applied to measured size distri...
The Osmotic Migration of Cells in a Solute Gradient
Biophysical Journal, 1999
The effect of a nonuniform solute concentration on the osmotic transport of water through the boundaries of a simple model cell is investigated. A system of two ordinary differential equations is derived for the motion of a single cell in the limit of a fast solute diffusion, and an analytic solution is obtained for one special case. A two-dimensional finite element model has been developed to simulate the more general case (finite diffusion rates, solute gradient induced by a solidification front). It is shown that the cell moves to regions of lower solute concentration due to the uneven flux of water through the cell boundaries. This mechanism has apparently not been discussed previously. The magnitude of this effect is small for red blood cells, the case in which all of the relevant parameters are known. We show, however, that it increases with cell size and membrane permeability, so this effect could be important for larger cells. The finite element model presented should also have other applications in the study of the response of cells to an osmotic stress and for the interaction of cells and solidification fronts. Such investigations are of major relevance for the optimization of cryopreservation processes.
Theoretical framework for microscopic osmotic phenomena
Physical Review E, 2007
The basic ingredients of osmotic pressure are a solvent fluid with a soluble molecular species which is restricted to a chamber by a boundary which is permeable to the solvent fluid but impermeable to the solute molecules. For macroscopic systems at equilibrium, the osmotic pressure is given by the classical van't Hoff Law, which states that the pressure is proportional to the product of the temperature and the difference of the solute concentrations inside and outside the chamber. For microscopic systems the diameter of the chamber may be comparable to the length-scale associated with the solute-wall interactions or solute molecular interactions. In each of these cases, the assumptions underlying the classical van't Hoff Law may no longer hold. In this paper we develop a general theoretical framework which captures corrections to the classical theory for the osmotic pressure under more general relationships between the size of the chamber and the interaction length scales. We also show that notions of osmotic pressure based on the hydrostatic pressure of the fluid and the mechanical pressure on the bounding walls of the chamber must be distinguished for microscopic systems. To demonstrate how the theoretical framework can be applied, numerical results are presented for the osmotic pressure associated with a polymer of N monomers confined in a spherical chamber as the bond strength is varied.