Osmotic water permeability of plasma and vacuolar membranes in protoplasts I. High osmotic water permeability in radish (<Emphasis Type="Italic">Raphanus sativus</Emphasis>) root cells as measured by a new method

Intra- and transcellular water movements in plants are regulated by the water permeability of the plasma membrane (PM) and vacuolar membrane (VM) in plant cells. In the present study, we investigated the osmotic water permeability of both PM (P ( f1)) and VM (P ( f2)), as well as the bulk osmotic water permeability of a protoplast (P ( f(bulk))) isolated from radish (Raphanus sativus) roots. The values of P ( f(bulk)) and P ( f2) were determined from the swelling/shrinking rate of protoplasts and isolated vacuoles under hypo- or hypertonic conditions. In order to minimize the effect of unstirred layer, we monitored dropping or rising protoplasts (vacuoles) in sorbitol solutions as they swelled or shrunk. P ( f1) was calculated from P ( f(bulk)) and P ( f2) by using the 'three-compartment model', which describes the theoretical relationship between P ( f1), P ( f2) and P ( f(bulk)) (Kuwagata and Murai-Hatano in J Plant Res, 2007). The time-dependent changes in the volume of protoplasts and isolated vacuoles fitted well to the theoretical curves, and solute permeation of PM and VM was able to be neglected for measuring the osmotic water permeability. High osmotic water permeability of more than 500 mum s(-1), indicating high activity of aquaporins (water channels), was observed in both PM and VM in radish root cells. This method has the advantage that P ( f1) and P ( f2) can be measured accurately in individual higher plant cells.     

Amicus Plato, sed magis amica veritas: plots must obey the laws they refer to and models shall describe biophysical reality!

In the companion paper, we discussed in details proper linearization, calculation of the inactive osmotic volume, and analysis of the results on the Boyle-vant’ Hoff plots. In this Letter, we briefly address some common errors and misconceptions in osmotic modeling and propose some approaches, namely: (1) inapplicability of the Kedem–Katchalsky formalism model in regards to the cryobiophysical reality, (2) calculation of the membrane hydraulic conductivity L_p in the presence of permeable solutes, (3) proper linearization of the Arrhenius plots for the solute membrane permeability, (4) erroneous use of the term “toxicity” for the cryoprotective agents, and (5) advantages of the relativistic permeability approach (RP) developed by us vs. traditional (“classic”) 2-parameter model.     

Osmotic mass transfer in the yeast Saccharomyces cerevisiae.

This paper reviews the passive mechanisms involved in the response of a yeast to changes in medium concentration and osmotic pressure. The results presented here were collected in our laboratory during the last decade and are experimentally based on the measurement of cell volume variations in response to changes in the medium composition. In the presence of isoosmotic concentration gradients of solutes between intracellular and extracellular media, mass transfers were found to be governed by the diffusion rate of the solutes through the cell membrane and were achieved within a few seconds. In the presence of osmotic gradients, mass transfers mainly consisting in a water flow were found to be rate limited by the mixing systems used to generate a change in the medium osmotic pressure. The use of ultra-rapid mixing systems allowed us to show that yeast cells respond to osmotic upshifts within a few milliseconds and to determine a very high hydraulic permeability for yeast membrane (Lp>6.10(-11) m x sec)-1) x Pa(-1)). This value suggested that yeast membrane may contain facilitators for water transfers between intra and extracellular media, i.e. aquaporins. Cell volume variation in response to osmotic gradients was only observed for osmotic gradients that exceeded the cell turgor pressure and the maximum cell volume decrease, observed during an hyperosmotic stress, corresponded to 60% of the initial yeast volume. These results showed that yeast membrane is highly permeable to water and that an important fraction of the intracellular content was rapidly transferred between intracellular and extracellular media in order to restore water balance after hyperosmotic stresses. Mechanisms implied in cell death resulting from these stresses are then discussed.     

Analytical solution for the extremums of cell water volume and cell volume using a two-parameter model

Based on a two-parameter model [Cryobiology 37 (1998) 271-289], the analytical solution for the extremums of cell water volume and cell volume for a two-solute system are obtained. Compared with the numerical solution, the analytical solution offers an accurate but simple choice. The approximate solution [Cryobiology 40 (2000) 64-83] for the extremum of cell water volume is also discussed, the reason for the deviation is presented.     

An optimum method for the introduction or removal of permeable cryoprotectants: Isolated cells

On the basis of a nonequilibrium model for the transport of water and permeable solute across cell membranes, an optimum method has been devised for the introduction and the removal of a permeable cryoprotectant from single, isolated cells so that potentially lethal drastic alterations in cellular volume are minimized. The method involves the simultaneous variation of both the permeable (an initial step change, followed by a linear variation with time which overshoots the terminal value, and a final step change to the terminal value) and impermeable (an initial step change in the opposite direction of the permeable solute concentration change, followed by a period where the concentration remains constant, and a final step change back to the initial value) extracellular solute concentrations in a prescribed manner such that both the cellular water content and the intracellular electrolyte concentration remain constant as the intracellular permeable solute (CPA) concentration is either raised or lowered. The results of our theoretical analysis indicate that the osmotic stresses and strains usually imposed upon cells during the introduction and the removal of permeable cryoprotectants can be minimized and that the resulting protocols are clinically the most efficient.     

Transient breakdown in the selective permeability of the plasma membrane ofChlorella emersonii in response to hyperosmotic shock: Implications for cell water relations and osmotic adjustment

Summary In osmotic experiments involving cells of the euryhaline unicellular green algaChlorella emersonii exposed to hyperosmotic stress by immersion in a range of low molecular weight organic and inorganic solutes, a temporary breakdown in the selective permeability of the plasma membrane was observed during the initial phase of transfer to media of high osmotic strength (up to 2000 mosmol kg^–1). Thus, although the cells appeared to obey the Boyle-van't Hoff relationship in all cases, showing approximately linear changes in volume (at high salinity) as a function of the reciprocal of the external osmotic pressure, the extent of change was least for the triitols, propylene glycol and glycerol, intermediate for glucose, sorbitol, NaCl and KCl, with greatest changes in media containing the disaccharides sucrose and maltose. In NaCl-treated cells, uptake of external solute and loss of internal ions was observed in response to hyperosmotic treatment while sucrose-treated cells showed no significant uptake of external solute, although loss of intracellular K⁺ was observed. These observations suggest that the widely used technique of estimating cellular turgor, and osmotic/nonosmotic volume by means of the changes in volume that occur upon transfer to media containing increasing amounts of either a low molecular weight organic solute or an inorganic salt may be subject to error. The assumption that all algal cells behave as ideal osmometers, with outer membranes that are permeable to water but not to solutes, during the course of such experiments is therefore incorrect, and the data need to be adjusted to take account of hyperosmotically induced external solute penetration and/or loss of intracellular osmotica before meaningful estimates of cell turgor and osmotic volume can be obtained.     

Membrane water and solute permeability determined quantitatively by self-quenching of an entrapped fluorophore

Quantitative determination of rapid water and solute transport and solute reflection coefficients by light-scattering methods is complicated by dependence of vesicle or cell light scattering on nonvolume factors including solution refractive index, cell motion, and membrane aggregation. To overcome these difficulties, a fluorescence technique has been developed to measure accurately (1) osmotic water permeability (Pf), (2) solute permeability (Ps), and (3) solute reflection coefficient (sigma). The time course of vesicle volume is determined by the self-quenching of entrapped fluorescein sulfonate (FS), the best of a series of dyes screened for self-quenching, brightness, and vesicle loading/trapping. To validate the method, rabbit renal brush border vesicles (BBV) were loaded with 1-10 mM FS for 12 h at 4 degrees C and washed to remove extravesicular FS. FS leakage occurred over greater than 6 h at 4 degrees C and greater than 30 min at 23 degrees C. FS fluorescence vs vesicle volume was calibrated from the time course of fluorescence decrease (excitation 470 nm, emission greater than 515 nm) in response to a series of inward osmotic gradients in a stopped-flow apparatus. At 23 degrees C Pf was 0.005 +/- 0.001 cm/s, independent of osmotic gradient size, and inhibited 67% by 0.5 mM HgCl2. Urea Ps was 2 x 10(-6) cm/s with sigma 0.95-1.00 on the basis of the fluorescence time course analysis and the extravesicular [urea] required to obtain zero initial volume flow (null method) when vesicles were loaded with sucrose.(ABSTRACT TRUNCATED AT 250 WORDS)     

Exact solutions of a two parameter flux model and cryobiological applications

Solute-solvent transmembrane flux models are used throughout biological sciences with applications in plant biology, cryobiology (transplantation and transfusion medicine), as well as circulatory and kidney physiology. Using a standard two parameter differential equation model of solute and solvent transmembrane flux described by Jacobs [The simultaneous measurement of cell permeability to water and to dissolved substances, J. Cell. Comp. Physiol. 2 (1932) 427-444], we determine the functions that describe the intracellular water volume and moles of intracellular solute for every time t and every set of initial conditions. Here, we provide several novel biophysical applications of this theory to important biological problems. These include using this result to calculate the value of cell volume excursion maxima and minima along with the time at which they occur, a novel result that is of significant relevance to the addition and removal of permeating solutes during cryopreservation. We also present a methodology that produces extremely accurate sum of squares estimates when fitting data for cellular permeability parameter values. Finally, we show that this theory allows a significant increase in both accuracy and speed of finite element methods for multicellular volume simulations, which has critical clinical biophysical applications in cryosurgical approaches to cancer treatment.     

Determinants of epithelial cell volume

Epithelial cell volume is determined by the concentration of intracellular, osmotically active solutes. The high water permeability of the cell membrane of most epithelia prevents the establishment of large osmotic gradients between the cell and the bathing solutions. Steady-state cell volume is determined by the relative rates of solute entry and exit across the cell membranes. Inhibition of solute exit leads to cell swelling because solute entry continues; inhibition of solute entry leads to cell shrinkage because solute exit continues. Cell volume is then a measure of the rate and direction of net solute movements. Epithelial cells are also capable of regulation of the rate of solute entry and exit to maintain intracellular composition. Feedback control of NaCl entry into Necturus gallbladder epithelial cells is demonstrable after inhibition of the Na,K-ATPase or reduction in the NaCl concentration of the serosal bath. Necturus gallbladder cells respond to a change in the osmolality of the perfusion solution by rapidly regulating their volume to control values. This regulatory behavior depends on the transient activation of quiescent transport systems. These transport systems are responsible for the rapid readjustments of cell volume that follow osmotic perturbation. These powerful transporters may also play a role in steady-state volume regulation as well as in the control of cell pH.     

Osmotic water permeability of Necturus gallbladder epithelium

An electrophysiological technique that is sensitive to small changes in cell water content and has good temporal resolution was used to determine the hydraulic permeability (Lp) of Necturus gallbladder epithelium. The epithelial cells were loaded with the impermeant cation tetramethylammonium (TMA+) by transient exposure to the pore-forming ionophore nystatin in the presence of bathing solution TMA+. Upon removal of the nystatin a small amount of TMA+ is trapped within the cell. Changes in cell water content result in changes in intracellular TMA+ activity which are measured with intracellular ion-sensitive microelectrodes. We describe a method that allows us to determine the time course for the increase or decrease in the concentration of osmotic solute at the membrane surface, which allows for continuous monitoring of the difference in osmolality across the apical membrane. We also describe a new method for the determination of transepithelial hydraulic permeability (Ltp). Apical and basolateral membrane Lp's were assessed from the initial rates of change in cell water volume in response to anisosmotic mucosal or serosal bathing solutions, respectively. The corresponding values for apical and basolateral membrane Lp's were 0.66 x 10(-3) and 0.38 x 10(-3) cm/s.osmol/kg, respectively. This method underestimates the true Lp values because the nominal osmotic differences (delta II) cannot be imposed instantaneously, and because it is not possible to measure the true initial rate of volume change. A model was developed that allows for the simultaneous determination of both apical and basal membrane Lp's from a unilateral exposure to an anisosmotic bathing solution (mucosal). The estimates of apical and basal Lp with this method were 1.16 x 10(-3) and 0.84 x 10(-3) cm/s.osmol/kg, respectively. The values of Lp for the apical and basal cell membranes are sufficiently large that only a small (less than 3 mosmol/kg) transepithelial difference in osmolality is required to drive the observed rate of spontaneous fluid absorption by the gallbladder. Furthermore, comparison of membrane and transepithelial Lp's suggests that a large fraction of the transepithelial water flow is across the cells rather than across the tight junctions.     

Predicted permeability parameters of human ovarian tissue cells to various cryoprotectants and water

This study presents a generic numerical model to simulate the coupled solute and solvent transport in human ovarian tissue sections during addition and removal of chemical additives or cryoprotective agents (CPA). The model accounts for the axial and radial diffusion of the solute (CPA) as well as axial convection of the CPA, and a variable vascular surface area (A) during the transport process. In addition, the model also accounts for the radial movement of the solvent (water) into and out of the vascular spaces. Osmotic responses of various cells within an human ovarian tissue section are predicted by the numerical model with three model parameters: permeability of the tissue cell membrane to water (L(p)), permeability of the tissue cell membrane to the solute or CPA (omega) and the diffusion coefficient of the solute or CPA in the vascular space (D). By fitting the model results with published experimental data on solute/water concentrations within an human ovarian tissue section, I was able to determine the permeability parameters of ovarian tissue cells in the presence of 1.5M solutions of each of the following: dimethyl sulphoxide (DMSO), propylene glycol (PROH), ethylene glycol (EG), and glycerol (GLY), at two temperatures (4 degrees C and 27 degrees C). Modeling Approach 1: Assuming a constant value of solute diffusivity (D = 1.0 x 10(-9) m(2)/sec), the best fit values of L(p) ranged from 0.35 x 10(-14) to 1.43 x 10(-14) m(3)/N-sec while omega ranged from 2.57 x 10(-14) to 70.5 x 10(-14) mol/N-sec. Based on these values of L(p) and omega, the solute reflection coefficient, sigma defined as sigma = 1-omega v(CPA)/L(P) ranged from 0.9961 to 0.9996. Modeling Approach 2: The relative values of omega and sigma from our initial modeling suggest that the embedded ovarian tissue cells are relatively impermeable to all the CPAs investigated (or omega approximately 0 and sigma approximately 1.0). Consequently the model was modified and used to predict the values of L(p) and D assuming omega = 0 and sigma = 1.0. The best fit values of L(p) ranged from 0.44 x 10(-14) to 1.2 x 10(-14) m(3)/N-sec while D ranged from 0.85 x 10(-9) to 2.08 x 10(-9) m(2)/sec. Modeling Approach 3: Finally, the best fit values of D from modeling approach 2 were incorporated into model 1 to re-predict the values of L(p) and omega. It is hoped that the ovarian tissue cell parameters reported here will help to optimize chemical loading and unloading procedures for whole ovarian tissue sections and consequently, tissue cryopreservation procedures.     

Effect of cGMP-dependent signaling system in regulation of osmotic permeability in the frog urinary bladder

In frogs' isolated urinary bladders, contribution of cytosolic guanylate cyclase and cGMP-dependent protein kinase to regulation of osmotic permeability was studied. ODQ (25-100 microM), an inhibitor of cytosolic guanylate cyclase induced an increase of vasotocin-activated osmotic permeability but had no effect on the hormone-activated transepithelial urea transport. In isolated mucosal epithelial cells ODQ (50 microM) decreased the concentration of intracellular cGMP. In these cells L-NAME (0.5 nM), an inhibitor of NO synthase, also decreased the level of cGMP whereas cAMP was significantly increased. 8-pCPT-cGMP (25 and 50 microM), a permeable cGMP analogue which selectively activates protein kinase G, inhibited vasotocin-induced increase of water transport along osmotic gradient indicating that protein kinase G is involved in regulation of water reabsorption. The data obtained show that NO/cGMP signalling system in the frog urinary bladder appears to be a negative modulator of vasotocin-activated increase of osmotic permeability.     

Canine RBC osmotic tolerance and membrane permeability

The objective of this study was to determine the cryobiological characteristics of canine red blood cells (RBC). These included the hydraulic conductivity (L(p)), the permeability coefficients (P(s)) of common cryoprotectant agents (CPAs), the associated reflection coefficient (sigma), the activation energies (E(a)) of L(p) and P(s) and the osmotic tolerance limits. By using a stopped-flow apparatus, the changes of fluorescence intensity emitted by intracellularly entrapped 5-carboxyfluorescein diacetate (CFDA) were recorded when cells were experiencing osmotic volume changes. After the determination of the relationship between fluorescence intensity and cell volume, cell volume changes were calculated. These volume changes were used in three-parameter fitting calculations to determine the values of L(p), P(s), and sigma for common CPAs. These volume measurements and data analyses were repeated at three different temperatures (22, 14, 7 degrees C). Using the Arrhenius equation, the activation energies of L(p) and P(s) in the presence of CPAs were determined. The osmotic tolerance limits for canine RBC were determined by measuring the percentage of free hemoglobin in NaCl solutions with various osmolalities compared to that released by RBC incubated in double distilled water. The upper and lower osmotic tolerance limits were found to be 150mOsm (1.67V(iso)) and 1200mOsm (0.45V(iso)), respectively. These parameters were then used to calculate the amount of non-permeating solute needed to keep cell volume excursions within the osmotic tolerance limits during CPA addition and removal.     

Osmotic Transport across Cell Membranes in Nondilute Solutions: A New Nondilute Solute Transport Equation

The fundamental physical mechanisms of water and solute transport across cell membranes have long been studied in the field of cell membrane biophysics. Cryobiology is a discipline that requires an understanding of osmotic transport across cell membranes under nondilute solution conditions, yet many of the currently-used transport formalisms make limiting dilute solution assumptions. While dilute solution assumptions are often appropriate under physiological conditions, they are rarely appropriate in cryobiology. The first objective of this article is to review commonly-used transport equations, and the explicit and implicit assumptions made when using the two-parameter and the Kedem-Katchalsky formalisms. The second objective of this article is to describe a set of transport equations that do not make the previous dilute solution or near-equilibrium assumptions. Specifically, a new nondilute solute transport equation is presented. Such nondilute equations are applicable to many fields including cryobiology where dilute solution conditions are not often met. An illustrative example is provided. Utilizing suitable transport equations that fit for two permeability coefficients, fits were as good as with the previous three-parameter model (which includes the reflection coefficient, σ). There is less unexpected concentration dependence with the nondilute transport equations, suggesting that some of the unexpected concentration dependence of permeability is due to the use of inappropriate transport equations.     

Osmotic flow caused by polyelectrolytes

Osmotic flow of water caused by high concentrations of anionic polyelectrolytes across semipermeable membranes, permeable only to solvent and simple electrolyte, has been measured in a newly designed flow cell. The flow cell features small solution and solvent compartments and an efficient stirring mechanism. We have demonstrated that, while the osmotic pressure of the anionic polyelectrolytes is determined primarily by micro-counterions, the osmotic flow is determined by solution-dependent properties as embodied in the hydrodynamic frictional coefficient which is determined by the polymer backbone segment of the polyelectrolyte. The variation of the osmotic permeability coefficient, L(p)(o), with concentration and osmotic pressure closely correlated with the concentration dependence of this frictional coefficient. These studies confirm previous work that the kinetics of osmotic flow across a membrane impermeable to the osmotically active solute is primarily determined by the diffusive mobility of the solute.     

Single Water Channels of Aquaporin-1 Do not Obey the Kedem-Katchalsky Equations

The Kedem-Katchalsky (KK) equations are often used to obtain information about the osmotic properties and conductance of channels to water. Using human red cell membranes, in which the osmotic flow is dominated by Aquaporin-1, we show here that compared to NaCl the reflexion coefficient of the channel for methylurea, when corrected for solute volume exchange and for the water permeability of the lipid membrane, is 0.54. The channels are impermeable to these two solutes which would seem to rule out flow interaction and require a reflexion coefficient close to 1.0 for both. Thus, two solutes can give very different osmotic flow rates through a semi-permeable pore, a result at variance with both classical theory and the KK formulation. The use of KK equations to analyze osmotic volume changes, which results in a single hybrid reflexion coefficient for each solute, may explain the discrepancy in the literature between such results and those where the equations have not been employed. Osmotic reflexion coefficients substantially different from 1.0 cannot be ascribed to the participation of other 'hidden' parallel aqueous channels consistently with known properties of the membrane. Furthermore, we show that this difference cannot be due to second-order effects, such as a solute-specific interaction with water in only part of the channel, because the osmosis is linear with driving force down to zero solute concentration, a finding which also rules out the involvement of unstirred-layer effects. Reflexion coefficients smaller than 1.0 do not necessitate water-solute flow interaction in permeable aqueous channels; rather, the osmotic behaviour of impermeable molecular-sized pores can be explained by differences in the fundamental nature of water flow in regions either accessible or inaccessible to solute, created by a varying cross-section of the channel.     

Permeation of water through the KcsA K+ channel

Previous studies have reported that the KcsA potassium channel has an osmotic permeability coefficient of 4.8 x 10(-12) cm3/s, giving it a significantly higher osmotic permeability coefficient than that of some membrane channels specialized in water transport. This high osmotic permeability is proposed to occur when the channel is depleted of potassium ions, the presence of which slow down the water permeation process. The atomic structure of the potassium-depleted KcsA channel and the mechanisms of water permeation have not been well characterized so far. Here, all-atom molecular dynamics simulations, in conjunction with an umbrella sampling strategy and a nonequilibrium approach to simulate pressure gradients are employed to illustrate the permeation of water in the absence of ions through the KcsA K+ channel. Equilibrium molecular dynamics simulations (95 ns combined total length) identified a possible structure of the potassium-depleted KcsA channel, and umbrella sampling calculations (160 ns combined total length) revealed that this structure is not permeable by water molecules moving along the channel axis. The simulation of a pressure gradient across the channel (30 ns combined total length) identified an alternative permeation pathway with a computed osmotic permeability of approximately (2.7 +/- 0.9) x 10(-13) cm3/s. Water fluxes along this pathway did not proceed through collective water motions or transitions to vapor state. All of the major results of this study were robust against variations in a wide set of simulation parameters (force field, water model, membrane model, and channel conformation).