Mathematical Modeling of Cell Volume Alterations under Different Osmotic Conditions (original) (raw)
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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.
How erythrocyte volume is regulated, or what mathematical models can and cannot do for biology
Biochemistry (Moscow). Supplement. Series A, Membrane and cell biology, 2009
Modern concepts of the red blood cell (RBC) volume regulation are considered. It is shown that the system of ion pumps and channels in the cell membrane ensures the physiological value of volume with a precision of about 10% even at 5-to 7-fold variations of passive membrane permeability for ions. Particular attention is paid to mathematical models for evaluation of the role of different molecular mechanisms in the RBC volume control. It is shown that many questions, for example, 'why the Na + ,K +-ATPase pumps the ions in opposite directions' or 'what is the physiological role of Ca 2+-activated K +-channels', cannot be answered without adequate mathematical models of such complex control systems as cell volume control.
Asymptotic behavior of osmotic volume changes induced by a permeant solute
Mathematical Biosciences, 1976
The system of two non-linear differential equations used to describe the osmotic behavior of spherical cells immersed in saline containing a permeant solute cannot be solved analytically. On the other hand, numerical or perturbation techniques are insufficient to describe the exact behavior of the solutions around the equilibrium or critical point. In order to study the asymptotic behavior of the solutions, a classical linearization technique has been used. The conclusion is that the solutions will definitely lie below (or above) the equilibrium value and will not show asymptotic damped oscillations around it.
A general model for the dynamics of cell volume, global stability, and optimal control
Journal of Mathematical Biology, 2010
Cell volume and concentration regulation in the presence of changing extracellular environments has been studied for centuries, and recently a general nondimensional model was introduced that encompassed solute and solvent transmembrane flux for a wide variety of solutes and flux mechanisms. Moreover, in many biological applications it is of considerable interest to understand optimal controls for both volume and solute concentrations. Here we examine a natural extension of this general model to an arbitrary number of solutes or solute pathways, show that this system is globally asymptotically stable and controllable, define necessary conditions for time-optimal controls in the arbitrary-solute case, and using a theorem of Boltyanski prove sufficient conditions for these controls in the commonly encountered two-solute case. Keywords Cellular mass transport • optimization • stability • cryobiology • sufficiency theorem 1 Introduction Recently, a general model of cell volume regulation was introduced that accounts for active and passive transport of water and a solute across the cell membrane This work appeared as part of a doctoral dissertation [Benson(2009)]
Journal of Cellular Physiology, 1990
Experiments were done on fully grown Xenopus oocytes to determine the extent and the properties of cellular water of hydration. The studies involved the osmotic shrinking and swelling of the oocytes under known osmotic pressure as well as proton NMR spectral, titration, and free induction decay analyses. Studies were done both on whole oocytes and on subcellular fractions. The results show that little if any of the oocyte water in situ has the motional or osmotic properties expected of pure "bulk" water. Four distinct water of hydration compartments were found and defined on the basis of distinct hydrogen bounding mechanisms. Some ofthe water in yolk platelets was found not to be in fast exchange with other water compartments. Osmotic shrinkage of oocytes caused an adaptive decrease in the bound water of hydration compartments. This osmotically induced decrease is attributed to decreased surface area available for the hydrogen bounding of water molecules on cellular proteins
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.
Journal of Food Engineering, 1997
Part I of this communication described a mathematical model for mass transfer in cellular tissue subjected to osmotic dehydration and Part II presented the methodology for solving the model equation and vertfiing the model. This third part contains results of a parametric study on osmotic dehydration using the model. The parameters investigated included concentration of the osmotic solution, molecular weight of solute, permeability of cell membrane, and initial void ratio of tissue. It was shown that an increase of solute concentration in the osmotic solution resulted in an increase of the rate of osmotic dehydration as well as the final equilibrium state values. Relationships involved in the equilibrium conditions achieved in the tissue varied with the external solution concentration. Mass transfer in both the extracellular volume and across the ceil membrane were shown to be potentially rate-limiting factors in osmotic dehydration.
Poroelastic osmoregulation of living cell volume
iScience, 2021
Highlights Cell height changes can be finely captured by defocusing microscopy Water permeation and cellular deformability regulate dynamics of cell volume changes Poroelasticity describes the dynamics of cell volume changes The response of cell to hypo or hyperosmotic shocks are modeled by poroelasticity