A general model for the dynamics of cell volume,global stability,and optimal control

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.     

Role of solute drag in intestinal transport

This study presents experiments related to the role of solvent drag and solute drag in the transmembrane movement of nonelectrolytes in a perfused rat intestine preparation. Conditions were chosen to simulate the effects of luminal hyperosmolarity on the permeability of tracer solutes. Data are presented on net water flux, transepithelial potentials, and lumen-to-blood and blood-to-lumen tracer solute movements during control electrolyte perfusion and after making the perfusate hyperosmotic. The results indicate that both solvent drag and solute drag can play significant roles in the transepithelial movement of solute and solute permeabilities in the rat ileum preparation. It is suggested that the potential roles of solvent drag and solute drag should be accounted for or considered during the characterization of the mechanisms of biological membrane function.     

The possible influence of osmotic poration on cell membrane water permeability

It has been hypothesized that pores in the plasma membrane form under conditions of rapid water efflux, allowing extracellular ice to grow into the cytoplasm under conditions of rapid freezing. When cells with intracellular ice are thawed slowly, the transmembrane ice crystal expands through recrystallization causing the cell to lyse. One of the implications of this hypothesis is that osmotic pores will provide an alternative route for water movement under conditions of osmotically induced flow. We show that the plasma membrane water permeability of a fibroblast cell changes as a function of the osmotic pressure gradient that is used to drive water movement. It is further shown that cell volume is more important than the magnitude of water flux in causing this departure from a uniform water permeability. We suggest that these data provide evidence of a transient route for water movement across cell membranes.     

The volume dependence of the erythrocyte water diffusion permeability

The product of the water diffusion permeability and the membrane area of a human erythrocyte has been found to be nearly independent of the cell volume. The product was measured by an NMR technique. This result conflicts with previous flow tube determinations but is in accord with recent measurements of the hydraulic permeability and various solute permeabilities. The results are consistent with the major part of the water fllux traversing the membrane through a fixed number of pores. There may also be a minor non-pore flux. It appears to be practicable to follow volume changes in the red blood cell by an NMR technique.     

Epithelial water transport in a balanced gradient system.

The relationship between epithelial fluid transport, standing osmotic gradients, and standing hydrostatic pressure gradients has been investigated using a perturbation expansion of the governing equations. The assumptions used in the expansion are: (a) the volume of lateral intercellular space per unit volume of epithelium is small; (b) the membrane osmotic permeability is much larger than the solute permeability. We find that the rate of fluid reabsorption is set by the rate of active solute transport across lateral membranes. The fluid that crosses the lateral membranes and enters the intercellular cleft is driven longitudinally by small gradients in hydrostatic pressure. The small hydrostatic pressure in the intercellular space is capable of causing significant transmembrane fluid movement, however, the transmembrane effect is countered by the presence of a small standing osmotic gradient. Longitudinal hydrostatic and osmotic gradients balance such that their combined effect on transmembrane fluid flow is zero, whereas longitudinal flow is driven by the hydrostatic gradient. Because of this balance, standing gradients within intercellular clefts are effectively uncoupled from the rate of fluid reabsorption, which is driven by small, localized osmotic gradients within the cells. Water enters the cells across apical membranes and leaves across the lateral intercellular membranes. Fluid that enters the intercellular clefts can, in principle, exit either the basal end or be secreted from the apical end through tight junctions. Fluid flow through tight junctions is shown to depend on a dimensionless parameter, which scales the resistance to solute flow of the entire cleft relative to that of the junction. Estimates of the value of this parameter suggest that an electrically leaky epithelium may be effectively a tight epithelium in regard to fluid flow.     

Structural Determinants of Oligomerization of the Aquaporin-4 Channel

The aquaporin (AQP) family of integral membrane protein channels mediate cellular water and solute flow. Although qualitative and quantitative differences in channel permeability, selectivity, subcellular localization, and trafficking responses have been observed for different members of the AQP family, the signature homotetrameric quaternary structure is conserved. Using a variety of biophysical techniques, we show that mutations to an intracellular loop (loop D) of human AQP4 reduce oligomerization. Non-tetrameric AQP4 mutants are unable to relocalize to the plasma membrane in response to changes in extracellular tonicity, despite equivalent constitutive surface expression levels and water permeability to wild-type AQP4. A network of AQP4 loop D hydrogen bonding interactions, identified using molecular dynamics simulations and based on a comparative mutagenic analysis of AQPs 1, 3, and 4, suggest that loop D interactions may provide a general structural framework for tetrameric assembly within the AQP family.     

Gravitational Effects in a Passive Transmembrane Transport: The Flux Graviosmotic and Gravidiffusive Effects in Non-Electrolytes

In this paper the classification ofthe gravitational effects in a passive transmembranetransport is presented. Among these effects there arethe flux and force gravitational effects (fluxgraviosmotic effect, osmotic pressure graviosmoticeffect, flux gravidiffusive effect, osmotic pressuregravidiffusive effect, voltage gravielectric effectand current gravielectric effect). The volume fluxgraviosmotic and solute flux gravidiffusive effectsmodel equations for a single-membrane system areelaborated. These models for binary and ternarynon-electrolyte solutions have been verified using anexperimental data volume and solute fluxes forosmotic-diffusion cell with horizontally mountedmembrane. In the experimental set-up, water was placedon one side of the membrane. The opposite side of themembrane was exposed to binary or ternary solutions ofdensities greater than that of water (aqueous glucoseor glucose-0.2 mole/l aqueous ethanol) and binary andternary solutions of densities larger than that ofwater (aqueous ethanol or ethanol-0.05 mole/l aqueousglucose). These experimental results are interpretedin terms of the convective instability that increasesthe diffusive permeability coefficient of junction:boundary layer/membrane/boundary layer.     

Transmembrane potential and ionic content of rat alveolar macrophages

The cell volume, cell water, intracellular ionic concentrations, and transmembrane potential of rat alveolar macrophages were determined. The measurements were made on cells which had been separated from the medium by centrifugation through dibutyl phthalate in order to greatly reduce the trapped extracellular space. The mean cell volume of the alveolar macrophages is 1,525 cubic microns and 72% of this volume is water. The intracellular fluid is high in Na+ (97 mM) and lower in K+ (50 mM) and the intracellular Cl- concentration in 64 mM. The transmembrane potential, as measured from the equilibrium distribution of tritiated triphenylmethyl phosphonium and by using the fluorescent probe, Di-S-C3(5), is approximately -37 millivolts. Neither Na+, K+, nor Cl- is distributed at equilibrium. However, the K+ permeability of alveolar macrophage membranes appears to be greater than Na+ permeability.     

A Biomechanical Triphasic Approach to the Transport of Nondilute Solutions in Articular Cartilage

Biomechanical models for biological tissues such as articular cartilage generally contain an ideal, dilute solution assumption. In this article, a biomechanical triphasic model of cartilage is described that includes nondilute treatment of concentrated solutions such as those applied in vitrification of biological tissues. The chemical potential equations of the triphasic model are modified and the transport equations are adjusted for the volume fraction and frictional coefficients of the solutes that are not negligible in such solutions. Four transport parameters, i.e., water permeability, solute permeability, diffusion coefficient of solute in solvent within the cartilage, and the cartilage stiffness modulus, are defined as four degrees of freedom for the model. Water and solute transport in cartilage were simulated using the model and predictions of average concentration increase and cartilage weight were fit to experimental data to obtain the values of the four transport parameters. As far as we know, this is the first study to formulate the solvent and solute transport equations of nondilute solutions in the cartilage matrix. It is shown that the values obtained for the transport parameters are within the ranges reported in the available literature, which confirms the proposed model approach.     

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.     

The point of maximum cell water volume excursion in case of presence of an impermeable solute

A relativistic permeability model of cell osmotic response (Cryobiology 40:64-83; 41:366-367) is applied to a two-solute system with one impermeable solute. The use of the normalized water volume (w), and the amount of intracellular permeable solute (x), which is the product of the water volume and intracellular osmolality (y), as the main variables allowed us to obtain a homogeneous differential equation dx(Delta)/dw(Delta)=f(x(Delta)/w(Delta)), where w(Delta)=w-w(f), x(Delta)=x-x(f), and f refers to the final (equilibrium) values. The solution of this equation is an explicit function, w(Delta)=g(x(Delta)), which is given in the text. This approach allows us to obtain an analytical (exact) expression of the water volume at the moment of the maximum excursion (water extremum w(m)). Results are compared with numeration of basic osmotic equations and with approximation given in (Cryobiology 40:64-83). Assumption that, dw/dt approximately 0 gives good approximations of the kinetics of water and permeable CPA after the point of maximum volume excursion (the slow phase of osmotic response). Practical aspects of the relativistic permeability approach are also discussed.     

Some comments on recent discussion of the Boyle van't Hoff relationship

The estimation of several cellular biophysical parameters must be made in order to mathematically predict optimal cryopreservation protocols. These parameters include total cell volume, osmotically inactive volume, cell surface area, and relative water and solute permeabilities. Recent attention has been paid to the determination of the osmotically inactive volume and, specifically, an argument was made suggesting that this volume was incorrectly determined in the literature [4]. Here we show that this assertion is false.     

Membrane Permeability Modeling: Kedem–Katchalsky vs a Two-Parameter Formalism

The analysis of experiments for the purpose of determining cell membrane permeability parameters is often done using the Kedem–Katchalsky (KK) formalism (1958). In this formalism, three parameters, the hydraulic conductivity (L_p), the solute permeability (P_s), and a reflection coefficient (ς), are used to characterize the membrane. Sigma was introduced to characterize flux interactions when water and solute (cryoprotectant) cross the membrane through a common channel. However, the recent discovery and characterization of water channels (aquaporins) in biological membranes reveals that aquaporins are highly selective for water and do not typically cotransport cryoprotectants. In this circumstance, sigma is a superfluous parameter, as pointed out by Kedem and Katchalsky. When sigma is unneeded, a two-parameter model (2P) utilizing onlyL_pandP_sis sufficient, simpler to implement, and less prone to spurious results. In this paper we demonstrate that the 2P and KK formalism yield essentially the same result (L_pandP_s) when cotransporting channels are absent. This demonstration is accomplished using simulation techniques to compare the transport response of a model cell using a KK or 2P formalism. Sigma is often misunderstood, even when its use is appropriate. It is discussed extensively here and several simulations are used to illustrate and clarify its meaning. We also discuss the phenomenological nature of transport parameters in many experiments, especially when both bilayer and channel transport are present.     

Importance of intracellular water apparent diffusion to the measurement of membrane permeability

The exchange of water across biological membranes is of fundamental significance to both animal and plant physiology. Diffusional membrane permeability (P(d)) for the Xenopus oocyte, an important model system for water channel investigation, is typically calculated from intracellular water pre-exchange lifetime, cell volume, and cell surface area. There is debate, however, whether intracellular water motion affects water lifetime, and thereby P(d). Mathematical modeling of water transport is problematic because the intracellular water diffusion rate constant (D) for cells is usually unknown. The measured permeability may be referred to as the apparent diffusional permeability, P, to acknowledge this potential error. Herein, we show that magnetic resonance (MR) spectroscopy can be used to measure oocyte water exchange with greater temporal resolution and higher signal-to-noise ratio than other methods. MR imaging can be used to assess both oocyte geometry and intracellular water diffusion for the same single cells. MR imaging is used to confirm the dependence of intracellular water lifetime on intracellular diffusion. A model is presented to relate intracellular lifetime to true membrane diffusional permeability. True water diffusional permeability (2.7 +/- 0.4 microm/s) is shown to be 39 +/- 6% greater than apparent diffusional permeability for 8 oocytes. This discrepancy increases with cell size and permeability (such as after water channel expression) and decreases with increasing intracellular water D.     

The physico-chemical mechanism of mediated transport. II. Osmotic and isosmotic volume flow

The process of volume change of cells subject to osmotic shocks or isosmotic entrance of permeant solute is formulated on the basis of the accepted structure for the plasma membrane and a physico-chemical approach similar to that recently developed. The effect of relevant parameters is discussed and theoretical equilibrium values for the variables are calculated in connection with water and permeant solute permeability determinations. Although a sorption-diffusional mechanism for solute and/or water volume flow within the membrane is assumed in both cases, the kinetics of volume change is shown to be totally different between them. In the isosmotic process a fixed relationship, given by the total solute concentration, is shown to exist between the permeant solute and volume fluxes to the cell, thereby implying a definite value for the volume fraction of water in the migration pathway, higher than 90%. The bi-phase osmotic regulatory response caused by permeant solute is simulated on the basis of an osmotic and isosmotic processes in series, showing good agreement with general behavior. Finally, an explanation to the problem of volume flow and forces in connection with a diffusional mechanism in biological and artificial membranes, is presented.     

Control of Cell Volume in Skeletal Muscle

Regulation of cell volume is a fundamental property of all animal cells and is of particular importance in skeletal muscle where exercise is associated with a wide range of cellular changes that would be expected to influence cell volume. These complex electrical, metabolic and osmotic changes, however, make rigorous study of the consequences of individual factors on muscle volume difficult despite their likely importance during exercise. Recent charge-difference modelling of cell volume distinguishes three major aspects to processes underlying cell volume control: (i) determination by intracellular impermeant solute; (ii) maintenance by metabolically dependent processes directly balancing passive solute and water fluxes that would otherwise cause cell swelling under the influence of intracellular membrane-impermeant solutes; and (iii) volume regulation often involving reversible short-term transmembrane solute transport processes correcting cell volumes towards their normal baselines in response to imposed discrete perturbations. This review covers, in turn, the main predictions from such quantitative analysis and the experimental consequences of comparable alterations in extracellular pH, lactate concentration, membrane potential and extracellular tonicity. The effects of such alterations in the extracellular environment in resting amphibian muscles are then used to reproduce the intracellular changes that occur in each case in exercising muscle. The relative contributions of these various factors to the control of cell volume in resting and exercising skeletal muscle are thus described.     

Computational modeling of coupled blood-wall mass transport of LDL: effects of local wall shear stress

The work herein represents a novel approach for the modeling of low-density lipoprotein (LDL) transport from the artery lumen into the arterial wall, taking into account the effects of local wall shear stress (WSS) on the endothelial cell layer and its pathways of volume and solute flux. We have simulated LDL transport in an axisymmetric representation of a stenosed coronary artery, where the endothelium is represented by a three-pore model that takes into account the contributions of the vesicular pathway, normal junctions, and leaky junctions also employing the local WSS to yield the overall volume and solute flux. The fraction of leaky junctions is calculated as a function of the local WSS based on published experimental data and is used in conjunction with the pore theory to determine the transport properties of this pathway. We have found elevated levels of solute flux at low shear stress regions because of the presence of a larger number of leaky junctions compared with high shear stress regions. Accordingly, we were able to observe high LDL concentrations in the arterial wall in these low shear stress regions despite increased filtration velocity, indicating that the increase in filtration velocity is not sufficient for the convective removal of LDL.     

Regulation of plant aquaporin activity

Accumulating evidence indicates that aquaporins play a key role in plant water relations. Plant aquaporins are part of a large and highly divergent protein family that can be divided into four subfamilies according to amino acid sequence similarity. As in other organisms, plant aquaporins facilitate the transcellular movement of water, but, in some cases, also the flux of small neutral solutes across a cellular membrane. Plant cell membranes are characterized by a large range of osmotic water permeabilities, and recent data indicate that plant aquaporin activity might be regulated by gating mechanisms. The factors affecting the gating behaviour possibly involve phosphorylation, heteromerization, pH, Ca2+, pressure, solute gradients and temperature. Regulation of aquaporin trafficking may also represent a way to modulate membrane water permeability. The aim of this review is to integrate recent molecular and biophysical data on the mechanisms regulating aquaporin activity in plant membranes and to relate them to putative changes in protein structure.     

The relationship between membrane fluidity and permeabilities to water,solutes, ammonia,and protons

Several barrier epithelia such as renal collecting duct, urinary bladder, and gastric mucosa maintain high osmotic pH and solute gradients between body compartments and the blood by means of apical membranes of exceptionally low permeabilities. Although the mechanisms underlying these low permeabilities have been only poorly defined, low fluidity of the apical membrane has been postulated. The solubility diffusion model predicts that lower membrane fluidity will reduce permeability by reducing the ability of permeant molecules to diffuse through the lipid bilayer. However, little data compare membrane fluidity with permeability properties, and it is unclear whether fluidity determines permeability to all, or only some substances. We therefore studied the permeabilities of a series of artificial large unilamellar vesicles (LUV) of eight different compositions, exhibiting a range of fluidities encountered in biological membranes. Cholesterol and sphingomyelin content and acyl chain saturation were varied to create a range of fluidities. LUV anisotropy was measured as steady state fluorescence polarization of the lipophilic probe DPH. LUV permeabilities were determined by monitoring concentration-dependent or pH-sensitive quenching of entrapped carboxyfluorescein on a stopped- flow fluorimeter. The relation between DPH anisotropy and permeability to water, urea, acetamide, and NH3 was well fit in each instance by single exponential functions (r > 0.96), with lower fluidity corresponding to lower permeability. By contrast, proton permeability correlated only weakly with fluidity. We conclude that membrane fluidity determines permeability to most nonionic substances and that transmembrane proton flux occurs in a manner distinct from flux of other substances.