A mixture theory for charged-hydrated soft tissues containing multi-electrolytes: passive transport and swelling behaviors.

A new mixture theory was developed to model the mechano-electrochemical behaviors of charged-hydrated soft tissues containing multi-electrolytes. The mixture is composed of n + 2 constituents (1 charged solid phase, 1 noncharged solvent phase, and n ion species). Results from this theory show that three types of force are involved in the transport of ions and solvent through such materials: (1) a mechanochemical force (including hydraulic and osmotic pressures); (2) an electrochemical force; and (3) an electrical force. Our results also show that three types of material coefficients are required to characterize the transport rates of these ions and solvent: (1) a hydraulic permeability; (2) mechano-electrochemical coupling coefficients; and (3) an ionic conductance matrix. Specifically, we derived the fundamental governing relationships between these forces and material coefficients to describe such mechano-electrochemical transduction effects as streaming potential, streaming current, diffusion (membrane) potential, electro-osmosis, and anomalous (negative) osmosis. As an example, we showed that the well-known formula for the resting cell membrane potential (Hodgkin and Huxley, 1952a, b) could be derived using our new n + 2 mixture model (a generalized triphasic theory). In general, the n + 2 mixture theory is consistent with and subsumes all previous theories pertaining to specific aspects of charged-hydrated tissues. In addition, our results provided the stress, strain, and fluid velocity fields within a tissue of finite thickness during a one-dimensional steady diffusion process. Numerical results were provided for the exchange of Na+ and Ca++ through the tissue. These numerical results support our hypothesis that tissue fixed charge density (CF) plays a significant role in modulating kinetics of ions and solvent transport through charged-hydrated soft tissues.     

Statistical-mechanical theory of passive transport through semipermeable membranes.

The first general multicomponent equations for transport through semipermeable membranes are derived from basic statistical-mechanical principles. The procedure follows that used earlier for open membranes, but semipermeability is modelled mathematically by the introduction of external forces on the impermeant species. Gases are treated first in order to clarify the problems involved, but the final results apply to general nonideal solutions of any concentration. The mixed-solvent effect is treated rigorously, and a mixed-solvent osmotic pressure is defined. A useful specific identification of so-called osmotic flow is given, along with a demonstration that such an identification cannot be unique. Results are obtained both for discontinuous membrane models, and for a continuous model.     

Occurrence of passive furosemide-sensitive transmembrane potassium transport in cultured cells

Furosemide ($\text{1 · 10}{}^{\mathrm{?4}}\text{M}$) inhibits a proportion of the total passive (ouabain-insensitive) K⁺ influx into primary chick heart cell cultures (85%), BC₃H1 cells (75%), MDCK cells (40%) and HeLa cells (57%). This action of furosemide upon K⁺ influx is independent of ($\text{Na}{}^{\mathrm{+}}\text{+}\text{K}{}^{\mathrm{+}}\text{)-}\text{pump}$ inhibition since the furosemide-sensitive component of the K⁺ influx is identical in the presence and absence of ouabain ($\text{1 · 10}{}^{\mathrm{?3}}\text{M}$). For HeLa cells the passive, furosemide-sensitive component of K⁺ influx is markedly dependent upon the external K⁺, Na⁺ and Cl^? content. Acetate, iodide and nitrate are ineffective as substitutes for Cl^?, whereas Br^? is partially effective. Partial Cl^? replacement by NO₃^? gave an apparent affinity of 100 mM [Cl]. Na⁺ replacement by choline⁺ abolishes the furosemide-sensitive component, whereas Li⁺ replacement reduces this component by 48%. Partial Na⁺ replacement by choline⁺ gives an apparent affinity of 25 mM [Na⁺]. Variation in the external K⁺ content gives an affinity for the furosemide-sensitive component of approx. 1.0 mM. Furosemide inhibition of the passive K⁺ inflúx is of high affinity, half-maximal inhibition being observed at $\text{5 · 10}{}^{\mathrm{?6}}\text{M}$ furosemide. Piretanide ($\text{1 · 10}{}^{\mathrm{?4}}\text{M}$) and phloretin ($\text{1 · 10}{}^{\mathrm{?4}}\text{M}$) inhibit the same component of passive K⁺ influx as furosemide; ethacrynic acid and amiloride ($\text{both}\text{1 · 10}{}^{\mathrm{?4}}\text{M}$) partially so. The stilbene, SITS ($\text{1 · 10}{}^{\mathrm{?6}}\text{M}$), was ineffective as an inhibitor of the furosemide-sensitive component.     

Statistical-mechanical theory of passive transport through partially sieving or leaky membranes

The basic equations for multicomponent transport through partially sieving or leaky membranes are discussed from a statistical-mechanical viewpoint. They have the same mathematical form as the corresponding equations for open membranes, but differ in a discontinuous way from the equations for semipermeable membranes (since a "leak" in a semipermeable membrane constitutes a discontinuous or singular perturbation). Partially sieving membranes can be made to mimic semipermeable behavior through the introduction of characteristic time scales. They may approximate semipermeable behavior at short times, but always deviate at longer times.     

A theory of osmotic lysis of lipid vesicles

Osmotic lysis of vesicles is shown to begin when the membrane expansion due to osmotic pressure exceeds its critical value, delta S, at which a membrane ruptures to form a pore. The dependence of delta S on the vesicle radius and respective osmotic pressures are obtained. It is found that osmotic pressure necessary for small (100 A) vesicles to rupture should exceed 30 atm, for large (10 000 A) vesicles it being as small as 10(-3) atm. In the case of large (greater than or approximately 1000 A) vesicles the value of relative expansion of the membrane at which its rupture occurs in a reasonable time only depends slightly on the vesicle radius. For instance, for 10 000 A vesicles it amounts to 3%. The tension of membrane rupture is about 8 dyn/cm for large vesicles. Membrane tension, although it decreases considerably as a result of rupture and pore formation, does not vanish completely. It supports the residual intravesicular pressure causing the efflux of vesicle (cell) contents. Simultaneously, osmotic influx of water through the membrane occurs that results in either complete rupture of the membrane with the efflux of the whole of the contents, or its gradual washout in either of two, quasi-steady or pulse-wise regimes. In the first case a pore is steadily open, whereas in the second case it alternately opens and closes, ejecting about 5% of internal solution each time. Lysis kinetics is analyzed. Pulse-wise regime of lysis is shown to be the most likely one.     

Applied osmotic loading for promoting development of engineered cartilage

This study investigated the potential use of static osmotic loading as a cartilage tissue engineering strategy for growing clinically relevant grafts from either synovium-derived stem cells (SDSCs) or chondrocytes. Bovine SDSCs and chondrocytes were individually encapsulated in 2% w/v agarose and divided into chondrogenic media of osmolarities 300 (hypotonic), 330 (isotonic), and 400 (hypertonic, physiologic) mOsM for up to 7 weeks. The application of hypertonic media to constructs comprised of SDSCs or chondrocytes led to increased mechanical properties as compared to hypotonic (300 mOsM) or isotonic (330 mOsM) media (p<0.05). Constant exposure of SDSC-seeded constructs to 400 mOsM media from day 0 to day 49 yielded a Young's modulus of 513±89 kPa and GAG content of 7.39±0.52%ww on day 49, well within the range of values of native, immature bovine cartilage. Primary chondrocyte-seeded constructs achieved almost as high a Young's modulus, reaching 487±187 kPa and 6.77±0.54%ww (GAG) for the 400 mOsM condition (day 42). These findings suggest hypertonic loading as a straightforward strategy for 3D cultivation with significant benefits for cartilage tissue engineering strategies. In an effort to understand potential mechanisms responsible for the observed response, cell volume measurements in response to varying osmotic conditions were evaluated in relation to the Boyle–van't Hoff (BVH) law. Results confirmed that chondrocytes behave as perfect osmometers; however SDSCs deviated from the BVH relation.     

An update on passive transport in and out of plant cells

Transport across membranes is critical for plant survival. Membranes are the interfaces at which plants interact with their environment. The transmission of energy and molecules into cells provides plants with the source material and power to grow, develop, defend, and move. An appreciation of the physical forces that drive transport processes is thus important for understanding the plant growth and development. We focus on the passive transport of molecules, describing the fundamental concepts and demonstrating how different levels of abstraction can lead to different interpretations of the driving forces. We summarize recent developments on quantitative frameworks for describing diffusive and bulk flow transport processes in and out of cells, with a more detailed focus on plasmodesmata, and outline open questions and challenges.

New insights enhance our understanding of the physical forces that drive passive transport across plant membranes highlights.     

Active and passive transport of potassium in cells of excised pea epicotyls

The Ussing-Theorell equation, which provides a fundamental test for the independent passive movement of ions under conditions of nonequilibrium, has been used to assess the active and passive components of K⁺ uptake by segments of pea epicotyl (Pisum sativum L. cultivar Alaska), incubated for 24 hours in both 1-fold and 10-fold concentrations of a complete nutrient solution. Measurements of the rates at which ⁴²K diffused out of the segments provided data from which were estimated the K⁺ content of, and the fluxes to and from, the nonfree space compartments, interpreted as being cytoplasm and vacuole. For this analysis the serial model of MacRobbie and Dainty and Pitman for the spatial arrangement of cell compartments was used. On the basis of these values, and measurements of electrical potential across the cell membranes, the vacuolar K⁺ concentration was found to be fairly close to that expected as a result of passive diffusion between the cytoplasm and vacuole provided that no potential exists across the tonoplast. Cytoplasmic K⁺ concentration, however, was much too high in both treatments to be accounted for in passive terms. It was concluded, therefore, that, on the basis of the model, the high ratio of influx to efflux was maintained in the cells by an active K⁺ pump located at the plasmalemma. There is some reason to question the applicability of this model for flux analysis to the conditions of high net influx as encountered here; nonetheless, it provides a first approach to an over-all flux analysis in pea stem tissue.     

A molecular framework for coupling cellular volume and osmotic solute transport control

Eukaryotic cells expand using vesicle traffic to increase membrane surface area. Expansion in walled eukaryotes is driven by turgor pressure which depends fundamentally on the uptake and accumulation of inorganic ions. Thus, ion uptake and vesicle traffic must be controlled coordinately for growth. How this coordination is achieved is still poorly understood, yet is so elemental to life that resolving the underlying mechanisms will have profound implications for our understanding of cell proliferation, development, and pathogenesis, and will find applications in addressing the mineral and water use by plants in the face of global environmental change. Recent discoveries of interactions between trafficking and ion transport proteins now open the door to an entirely new approach to understanding this coordination. Some of the advances to date in identifying key protein partners in the model plant Arabidopsis and in yeast at membranes vital for cell volume and turgor control are outlined here. Additionally, new evidence is provided of a wider participation among Arabidopsis Kv-like K(+) channels in selective interaction with the vesicle-trafficking protein SYP121. These advances suggest some common paradigms that will help guide further exploration of the underlying connection between ion transport and membrane traffic and should transform our understanding of cellular homeostasis in eukaryotes.     

Water transport in aquaporins: osmotic permeability matrix analysis of molecular dynamics simulations

Single-channel osmotic water permeability (p(f)) is a key quantity for investigating the transport capability of the water channel protein, aquaporin. However, the direct connection between the single scalar quantity p(f) and the channel structure remains unclear. In this study, based on molecular dynamics simulations, we propose a p(f)-matrix method, in which p(f) is decomposed into contributions from each local region of the channel. Diagonal elements of the p(f) matrix are equivalent to the local permeability at each region of the channel, and off-diagonal elements represent correlated motions of water molecules in different regions. Averaging both diagonal and off-diagonal elements of the p(f) matrix recovers p(f) for the entire channel; this implies that correlated motions between distantly-separated water molecules, as well as adjacent water molecules, influence the osmotic permeability. The p(f) matrices from molecular dynamics simulations of five aquaporins (AQP0, AQP1, AQP4, AqpZ, and GlpF) indicated that the reduction in the water correlation across the Asn-Pro-Ala region, and the small local permeability around the ar/R region, characterize the transport efficiency of water. These structural determinants in water permeation were confirmed in molecular dynamics simulations of three mutants of AqpZ, which mimic AQP1.     

Optical measurement of osmotic water transport in cultured cells. Role of glucose transporters

Methodology was developed to measure osmotic water permeability in monolayer cultured cells and applied to examine the proposed role of glucose transporters in the water pathway (1989. Proc. Natl. Acad. Sci. USA. 86:8397-8401). J774 macrophages were grown on glass coverslips and mounted in a channel-type perfusion chamber for rapid fluid exchange without cell detachment. Relative cell volume was measured by 45 degrees light scattering using an inverted microscope; measurement accuracy was validated by confocal imaging microscopy. The time required for greater than 90% fluid exchange was less than 1 s. In response to a decrease in perfusate osmolality from 300 to 210 mosM, cells swelled without lag at an initial rate of 4.5%/s, corresponding to a water permeability coefficient of (6.3 +/- 0.4) x 10(-3) cm/s (SE, n = 20, 23 degrees C), assuming a cell surface-to-volume ratio of 4,400 cm-1. The initial rate of cell swelling was proportional to osmotic gradient size, independent of perfusate viscosity, and increased by amphotericin B (25 micrograms/ml), and had an activation energy of 10.0 +/- 1 kcal/mol (12-39 degrees C). The compounds phloretin (20 microM) and cytochalasin B (2.5 micrograms/ml) inhibited glucose transport by greater than 85% but did not influence Pf in paired experiments in which Pf was measured before and after inhibitor addition. The mercurials HgCl2 (0.1 mM) and p-chloromercuribenzoate (1 mM) did not inhibit Pf. A stopped-flow light scattering technique was used to measure Pf independently in J774 macrophages grown in suspension culture. Pf in suspended cells was (4.4 +/- 0.3) x 10(-3) cm/s (assuming a surface-to-volume ratio of 8,800 cm-1), increased more than threefold by amphotericin B, and not inhibited by phloretin and cytochalasin B under conditions of strong inhibition of glucose transport. The glucose reflection coefficient was 0.98 +/- 0.03 as measured by induced osmosis, assuming a unity reflection coefficient for sucrose. These results establish a quantitative method for measurement of osmotic water transport in adherent cultured cells and provide evidence that glucose transporters are not involved in the water transporting pathway.     

Effect of thiourea on PCMBS inhibition of osmotic water transport in human red cells

The organomercurial reagent p-chloromercuribenzene sulfonate (PCMBS) is an inhibitor of osmotic water permeability in the human red cell membrane. We have found that thiourea, when added along with PCMBS to a red cell suspension, interferes with this inhibition and at high enough concentrations prevents the inhibition from developing altogether. For a 2 mM PCMBS concentration K_i = ; 3 ± 1 mM. When thiourea is added at a later time, the PCMBS inhibition, which normally takes about 20 min to develop fully, is halted and remains fixed at the value attained by that time. Thiourea also inhibits the reversal of PCMBS inhibition by a 10 mM concentration of cysteine, the half-time for reversal increasing by more than an order of magnitude when [thiourea] = ; 50 mM. Possible implications for the nature of the water and urea transport pathways across the red cell membrane are discussed.