Osmosis and solute—Solvent drag

In 1903, George Hulett explained how solute alters water in an aqueous solution to lower the vapor pressure of its water. Hulett also explained how the same altered water causes osmosis and osmotic pressure when the solution is separated from liquid water by a membrane permeable to the water only. Hulett recognized that the solute molecules diffuse toward all boundaries of the solution containing the solute. Solute diffusion is stopped at all boundaries, at an open-unopposed surface of the solution, at a semipermeable membrane, at a container wall, or at the boundary of a solid or gaseous inclusion surrounded by solution but not dissolved in it. At each boundary of the solution, the solute molecules are reflected, they change momentum, and the change of momentum of all reflected molecules is a pressure, a solute pressure (i.e., a force on a unit area of reflecting boundary). When a boundary of the solution is open and unopposed, the solute pressure alters the internal tension in the force bonding the water in its liquid phase, namely, the hydrogen bond. All altered properties of the water in the solution are explained by the altered internal tension of the water in the solution. We acclaim Hulett's explanation of osmosis, osmotic pressure, and lowering of the vapor pressure of water in an aqueous solution. His explanation is self-evident. It is the necessary, sufficient, and inescapable explanation of all altered properties of the water in the solution relative to the same property of pure liquid water at the same externally applied pressure and the same temperature. We extend Hulett's explanation of osmosis to include the osmotic effects of solute diffusing through solvent and dragging on the solvent through which it diffuses. Therein lies the explanations of (1) the extravasation from and return of interstitial fluid to capillaries, (2) the return of luminal fluid in the proximal and distal convoluted tubules of a kidney nephron to their peritubular capillaries, (3) the return of interstitial fluid to the vasa recta, (4) return of aqueous humor to the episcleral veins, and (5) flow of phloem from source to sink in higher plants and many more examples of fluid transport and fluid exchange in animal and plant physiology. When a membrane is permeable to water only and when it separates differing aqueous solutions, the flow of water is from the solution with the lower osmotic pressure to the solution with the higher osmotic pressure.     

Modeling of neutral solute transport in a dynamically loaded porous permeable gel: implications for articular cartilage biosynthesis and tissue engineering

A primary mechanism of solute transport in articular cartilage is believed to occur through passive diffusion across the articular surface, but cyclical loading has been shown experimentally to enhance the transport of large solutes. The objective of this study is to examine the effect of dynamic loading within a theoretical context, and to investigate the circumstances under which convective transport induced by dynamic loading might supplement diffusive transport. The theory of incompressible mixtures was used to model the tissue (gel) as a mixture of a gel solid matrix (extracellular matrix/scaffold), and two fluid phases (interstitial fluid solvent and neutral solute), to solve the problem of solute transport through the lateral surface of a cylindrical sample loaded dynamically in unconfined compression with frictionless impermeable platens in a bathing solution containing an excess of solute. The resulting equations are governed by nondimensional parameters, the most significant of which are the ratio of the diffusive velocity of the interstitial fluid in the gel to the solute diffusivity in the gel (Rg), the ratio of actual to ideal solute diffusive velocities inside the gel (Rd), the ratio of loading frequency to the characteristic frequency of the gel (f), and the compressive strain amplitude (epsilon 0). Results show that when Rg > 1, Rd < 1, and f > 1, dynamic loading can significantly enhance solute transport into the gel, and that this effect is enhanced as epsilon 0 increases. Based on representative material properties of cartilage and agarose gels, and diffusivities of various solutes in these gels, it is found that the ranges Rg > 1, Rd < 1, correspond to large solutes, whereas f > 1 is in the range of physiological loading frequencies. These theoretical predictions are thus in agreement with the limited experimental data available in the literature. The results of this study apply to any porous hydrated tissue or material, and it is therefore plausible to hypothesize that dynamic loading may serve to enhance solute transport in a variety of physiological processes.     

Effects of dynamic loading on solute transport through the human cartilage endplate

Nutrient and metabolite transport through the cartilage endplate (CEP) is important for maintaining proper disc nutrition, but the mechanisms of solute transport remain unclear. One unresolved issue is the role of dynamic loading. In comparison to static loading, dynamic loading is thought to enhance transport by increasing convection. However, the CEP has a high resistance to fluid flow, which could limit solute convection. Here we measure solute transport through site-matched cadaveric human lumbar CEP tissues under static vs. dynamic loading, and we determine how the degree of transport enhancement from dynamic loading depends on CEP porosity and solute size. We found that dynamic loading significantly increased small and large solute transport through the CEP: on average, dynamic loading increased the transport of sodium fluorescein (376 Da) by a factor of 1.85 ± 0.64 and the transport of a large dextran (4000 Da) by a factor of 4.97 ± 3.05. Importantly, CEP porosity (0.65 ± 0.07; range: 0.47–0.76) strongly influenced the degree of transport enhancement. Specifically, for both solutes, transport enhancement was greater for CEPs with low porosity than for CEPs with high porosity. This is because the CEPs with low porosity were susceptible to larger improvements in fluid flow under dynamic loading. The CEP becomes less porous and less hydrated with aging and as disc degeneration progresses. Together, these findings suggest that as those changes occur, dynamic loading has a greater effect on solute transport through the CEP compared to static loading, and thus may play a larger role in disc nutrition.     

The Mechanism of Isotonic Water Transport

The mechanism by which active solute transport causes water transport in isotonic proportions across epithelial membranes has been investigated. The principle of the experiments was to measure the osmolarity of the transported fluid when the osmolarity of the bathing solution was varied over an eightfold range by varying the NaCl concentration or by adding impermeant non-electrolytes. An in vitro preparation of rabbit gall bladder was suspended in moist oxygen without an outer bathing solution, and the pure transported fluid was collected as it dripped off the serosal surface. Under all conditions the transported fluid was found to approximate an NaCl solution isotonic to whatever bathing solution used. This finding means that the mechanism of isotonic water transport in the gall bladder is neither the double membrane effect nor co-diffusion but rather local osmosis. In other words, active NaCl transport maintains a locally high concentration of solute in some restricted space in the vicinity of the cell membrane, and water follows NaCl in response to this local osmotic gradient. An equation has been derived enabling one to calculate whether the passive water permeability of an organ is high enough to account for complete osmotic equilibration of actively transported solute. By application of this equation, water transport associated with active NaCl transport in the gall bladder cannot go through the channels for water flow under passive conditions, since these channels are grossly too impermeable. Furthermore, solute-linked water transport fails to produce the streaming potentials expected for water flow through these passive channels. Hence solute-linked water transport does not occur in the passive channels but instead involves special structures in the cell membrane, which remain to be identified.     

Corneal endothelium transports fluid in the absence of net solute transport

The corneal endothelium transports fluid from the corneal stroma to the aqueous humor, thus maintaining stromal transparency by keeping it relatively dehydrated. This fluid transport mechanism is thought to be driven by the transcellular transports of HCO(3)(-) and Cl(-) in the same direction, from stroma to aqueous. In parallel to these anion movements, for electroneutrality, there are paracellular Na(+) and transcellular K(+) transports in the same direction. The resulting net flow of solute might generate local osmotic gradients that drive fluid transport. However, there are reports that some 50% residual fluid transport remains in nominally HCO(3)(-) free solutions. We have examined the driving force for this residual fluid transport. We confirm that in nominally HCO(3)(-) free solutions, 48% of control fluid transport remains. When in addition Cl(-) channels are inhibited, 30% of control fluid movement still remains. Addition of a carbonic anhydrase inhibitor has no further effect. These manipulations combined inhibit the transcellular transport of all anions, without which there cannot be any net transport of solute and consequently no local osmotic gradients, yet there is residual fluid movement. Only the further addition of benzamil, an inhibitor of epithelial Na(+) channels, abolishes fluid transport completely. Our data are inconsistent with transcellular local osmosis and instead support the paradigm of paracellular fluid transport driven by electro-osmotic coupling.     

Sustained high-pressure in the spinal subarachnoid space while arterial expansion is low may be linked to syrinx development

Syringomyelia (a spinal cord cyst) usually develops as a result of conditions that cause cerebrospinal fluid (CSF) obstruction. The mechanism of syrinx formation and enlargement remains unclear, though previous studies suggest that the fluid enters via the perivascular spaces (PVS) of the penetrating arteries of the spinal cord, and that alterations in the CSF pulse timing and pressure could contribute to enhanced PVS inflow. This study uses an idealised computational model of the PVS to investigate the factors that influence peri-arterial fluid flow. First, we used three sample patient-specific models to explore whether changes in subarachnoid space (SAS) pressures in individuals with and without syringomyelia could influence PVS inflow. Second we conducted a parametric study to determine how features of the CSF pulse altered perivascular fluid, including alterations to timing and magnitude of the peak SAS pressure, the timing of reversal from high to low pressure (diastolic phase), and the area under the pressure–time curve. The model for the patient with syringomyelia had higher net CSF inflow to the PVS than the two subjects without syringomyelia. In the parametric study, only increasing the area under the high pressure region of the SAS pulse substantially increased PVS inflow, when coupled with a temporal shift in arterial and SAS pulses. This suggests that a period of sustained high SAS pressure while arterial diameter is low may increase net CSF pumping into the PVS.     

A mathematical model of solute coupled water transport in toad intestine incorporating recirculation of the actively transported solute

A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2-4) in agreement with experiments. The virtual solute concentration of fluid emerging from lis is then significantly larger than the concentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emerging downstream lis is taken up by cells through the serosal membrane and pumped back into lis, i.e., the solute would have to be recirculated. With input variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Ussing, J. Membr. Biol. 168:241-251), computations predict that 60-80% of the pumped flux stems from serosal bath in agreement with the experimental estimate of the recirculation flux. Robust solutions are obtained with realistic concentrations and pressures of lis, and with the following features. Rate of fluid absorption is governed by the solute permeability of mucosal membrane. Maximum fluid flow is governed by density of pumps on lis-membranes. Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux of water through cells exceeds inward water flux between cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water, i.e., the model generates pseudo-solvent drag. The associated flux-ratio equation is derived.     

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.     

Diffusive transport in Stokeslet flow and its application to plankton ecology

In this paper we consider the advective/diffusive transport of a solute near a hovering zooplankter. We approximate the fluid flow with that of a Stokeslet, corresponding to the plankter exerting a point force on the water, and assume that the plankter acts as a point source for the transported solute, located at the same point as the force. We find an analytical expression in closed form for the steady-state concentration of the solute. We also discuss the situation where the plankter performs Brownian motion. Finally we apply the results to the courtship of the marine copepod Pseudocalanus elongatus, where the male performs a mating dance below the hovering female. For this situation, our model supports the hypothesis that the mating dance is guided by the plume of a signalling pheromone.     

Concentration wave of a solute in an artery: the influence of curvature

Mass transport and diffusion phenomena in the arterial lumen are studied through a mathematical model. Blood flow is described by the unsteady Navier-Stokes equation and solute dynamics by an advection-diffusion equation, the convective field being provided by the fluid velocity. A linearization procedure over the steady state solution is carried out and an asymptotic analysis is used to study the effect of a small curvature with respect to the straight tube. Analytical and numerical solutions are found: the results show the characteristics of the long wave propagation and the role played by the geometry on the solute distribution and demonstrate the strong influence of curvature induced by the fluid dynamics.     

Selective antibody precipitation using polyelectrolytes: A novel approach to the purification of monoclonal antibodies

We evaluated the potential for polyelectrolyte induced precipitation of antibodies to replace traditional chromatography purification. We investigated the impact of solution pH, solution ionic strength and polyelectrolyte molecular weight on the degree of precipitation using the anionic polyelectrolytes polyvinylsulfonic acid (PVS), polyacrylic acid (PAA), and polystyrenesulfonic acid (PSS). As we approached the pI of the antibody, charge neutralization of the antibody reduced the antibody–polyelectrolyte interaction, reducing antibody precipitation. At a given pH, increasing solution ionic strength prevented the ionic interaction between the polyelectrolyte and the antibody, reducing antibody precipitation. With increasing pH of precipitation, there was an increase in impurity clearance. Increasing polyelectrolyte molecular weight allowed the precipitation to be performed under conditions of higher ionic strength. PVS was selected as the preferred polyelectrolyte based on step yield following resolubilization, purification performance, as well as the nature of the precipitate. We evaluated PVS precipitation as a replacement for the initial capture step, as well as an intermediate polishing step in the purification of a humanized monoclonal antibody. PVS precipitation separated the antibody from host cell impurities such as host cell proteins (HCP) and DNA, process impurities such as leached protein A, insulin and gentamicin, as well as antibody fragments and aggregates. PVS was subsequently removed from antibody pools to <1 µg/mg using anion exchange chromatography. PVS precipitation did not impact the biological activity of the resolubilized antibody. Biotechnol. Bioeng. 2009;102: 1141–1151. © 2008 Wiley Periodicals, Inc.     

Revisiting the Münch pressure-flow hypothesis for long-distance transport of carbohydrates: modelling the dynamics of solute transport inside a semipermeable tube

A mathematical model of the Münch pressure-flow hypothesis for long-distance transport of carbohydrates via sieve tubes is constructed using the Navier-Stokes equation for the motion of a viscous fluid and the van't Hoff equation for osmotic pressure. Assuming spatial dimensions that are appropriate for a sieve tube and ensuring suitable initial profiles of the solute concentration and solution velocity lets the model become mathematically tractable and concise. In the steady-state case, it is shown via an analytical expression that the solute flux is diffusion-like with the apparent diffusivity coefficient being proportional to the local solute concentration and around seven orders of magnitude greater than a diffusivity coefficient for sucrose in water. It is also shown that, in the steady-state case, the hydraulic conductivity over one metre can be calculated explicitly from the tube radius and physical constants and so can be compared with experimentally determined values. In the time-dependent case, it is shown via numerical simulations that the solute (or water) can simultaneously travel in opposite directions at different locations along the tube and, similarly, change direction of travel over time at a particular location along the tube.     

PI3P signaling regulates receptor sorting but not transport in the endosomal pathway

While evidence is accumulating that phosphoinositide signaling plays a crucial role in growth factor and hormone receptor down-regulation, this signaling pathway has also been proposed to regulate endosomal membrane transport and multivesicular endosome biogenesis. Here, we have followed the fate of the down-regulated EGF receptor (EGFR) and bulk transport (fluid phase) markers in the endosomal pathway in vivo and in vitro. We find that bulk transport from early to late endosomes is not affected after inhibition of the phosphatidylinositol-3-phosphate (PI3P) signaling pathway, but that the EGFR then remains trapped in early endosomes. Similarly, we find that hepatocyte growth factor-regulated tyrosine kinase substrate (Hrs) is not directly involved in bulk solute transport, but is required for EGFR sorting. These observations thus show that transport and sorting can be uncoupled in the endosomal pathway. They also show that PI3P signaling does not regulate the core machinery of endosome biogenesis and transport, but controls the sorting of down-regulated receptor molecules in early endosomes via Hrs.     

Effects of SNP, ouabain, and amiloride on electrical potential profile of isolated sheep pleura.

The fluid and solute transport properties of pleural tissue were studied by using specimens of intact visceral and parietal pleura from adult sheep lungs. The samples were transferred to the laboratory in a Krebs-Ringer solution at 4 degrees C within 1 h from the death of the animal. The pleura was then mounted as a planar sheet in a Ussing-type chamber. The results that are presented in this study are the means of six different experiments. The spontaneous potential difference and the inhibitory effects of sodium nitroprusside (SNP), ouabain, and amiloride on transepithelial electrical resistance (R(TE)) were measured. The spontaneous potential difference across parietal pleura was 0.5 +/- 0.1 mV, whereas that across visceral pleura was 0.4 +/- 0.1 mV. R(TE) of both pleura was very low: 22.02 +/- 4.1 Omega. cm2 for visceral pleura and 22.02 +/- 3.5 Omega. cm2 for parietal pleura. There was an increase in the R(TE) when SNP was added to the serosal bathing solution of parietal pleura and to the serosal or mucosal bathing solution in visceral pleura. The same was observed when ouabain was added to the mucosal surface of visceral pleura and to either the mucosal or serosal surface of parietal pleura. Furthermore, there was an increase in R(TE) when amiloride was added to the serosal bathing solution of parietal pleura. Consequently, the sheep pleura appears to play a role in the fluid and solute transport between the pleural capillaries and the pleural space. There results suggest that there is a Na+ and K+ transport across both the visceral and parietal pleura.     

Measurement of the effective thickness of the mucosal unstirred layer in Necturus gallbladder epithelium

The effective thickness of the unstirred fluid layer (USL) adjacent to an epithelial barrier can be estimated from the time course for the accumulation or depletion of a solute at the membrane surface. In 1985 we reported an unstirred layer thickness of approximately 70 microns for Necturus gallbladder epithelium. In our earlier studies the delay caused by noninstantaneous bulk solution mixing was not taken into account and thus the USL thickness was systematically overestimated. In the present studies we describe an analysis of the time course of solute arrival at the membrane surface that takes into account noninstantaneous bulk solution mixing. We also describe a simple technique to monitor the accumulation or depletion of a solute at the membrane surface. The time course for the change in the concentration of either tetramethylammonium (TMA+) or tetrabutylammonium (TBA+) upon elevation of bulk solution concentration is sensed at the membrane surface with an ion-sensitive microelectrode. Because of the high selectivity of the ion-sensitive resin for TMA+ or TBA+ over other monovalent cations in the solution (Na+ and K+), a low concentration (1-2 mM) of the probe can be used. By measuring the time course of the arrival of first one probe and then the other, under identical superfusion conditions, sufficient information is obtained to eliminate multiple fits to the data, obtained when only one probe is used. Neglecting bulk solution mixing caused an error greater than 50% in estimated apparent USL thickness. The effective thickness of the USL depends critically upon chamber geometry, flow rate, and the position of superfusion and suction pipettes. Under our experimental conditions the effective USL at the mucosal surface of Necturus gallbladder epithelium was approximately 40 microns.     

A Moment Dead, a Moment Alive: How a Situational Personhood Emerges in the Vegetative State in an Israeli Hospital Unit

ABSTRACT  Here we address the personhood of patients in a permanent vegetative state (PVS), who fall outside categories of "alive" or "dead" and "subject" or "object." Drawing on fieldwork in an Israeli hospital, we examine multiple and shifting approaches to PVS patients, which are articulated in the course of caring for and living with them. We argue that, alongside the institutional definition of these patients as being in a PVS, which, as Kaufman showed, evokes irresolvable confusion as to their ontological nature, there appear and disappear other senses of their personhood. Allying with other studies of cognitively impaired patients (e.g., those with dementia and Alzheimer's), we explore this relational person-concept while demonstrating its situational nature. We analyze patients' admission to the hospital, showing how their essentialistic personhood is "emptied" and how and when their fluid, relational personhood appears and disappears, further showing how this personhood is reified by imagined life stories.     

Contribution of solvent drag through intercellular junctions to absorption of nutrients by the small intestine of the rat

The lumen of the small intestine in anesthetized rats was recirculated with 50 ml perfusion fluid containing normal salts, 25 mM glucose and low concentrations of hydrophilic solutes ranging in size from creatinine (mol wt 113) to Inulin (mol wt 5500). Ferrocyanide, a nontoxic, quadrupally charged anion was not absorbed; it could therefore be used as an osmotically active solute with reflection coefficient of 1.0 to adjust rates of fluid absorption, Jv, and to measure the coefficient of osmotic flow, Lp. The clearances from the perfusion fluid of all other test solutes were approximately proportional to Jv. From Lp and rates of clearances as a function of Jv and molecular size we estimate (a) the fraction of fluid absorption which passes paracellularly (approx. 50%), (b) coefficients of solvent drag of various solutes within intercellular junctions, (c) the equivalent pore radius of intercellular junctions (50 A) and their cross sectional area per unit path length (4.3 cm per cm length of intestine). Glucose absorption also varied as a function of Jv. From this relationship and the clearances of inert markers we calculate the rate of active transport of glucose, the amount of glucose carried paracellularly by solvent drag or back-diffusion at any given Jv and luminal glucose concentration and the concentration of glucose in the absorbate. The results indicate that solvent drag through paracellular channels is the principal route for intestinal transport of glucose or amino acids at physiological rates of fluid absorption and concentration. In the absence of luminal glucose the rate of fluid absorption and the clearances of all inert hydrophilic solutes were greatly reduced. It is proposed that Na-coupled transport of organic solutes from lumen to intercellular spaces provides the principal osmotic force for fluid absorption and triggers widening of intercellular junctions, thus promoting bulk absorption of nutrients by solvent drag. Further evidence for regulation of channel width is provided in accompanying papers on changes in electrical impedance and ultrastructure of junctions during Na-coupled solute transport.     

Physiological significance of the structure and components of the apoplast canal system for water absorption in plants

The non-linear differential equation that describes the coupling between water transport and solute transport in the apoplast canal system in plants was proposed by Katou and Furumoto in 1986. In the present paper, we analytically solved the equation in order to find the law describing the canal system. In the canal system, water transport is regulated linearly by solute transport under physiological conditions. The approximate solution of the differential equations defines the conditions of the structure and components of the apoplast canal for optimal water absorption. Water absorption during cell elongation in plants requires that the apoplast canal be composed of a cell wall with an appropriate diffusion coefficient for solute.     

The effect of cyclic deformation and solute binding on solute transport in cartilage

Diffusive transport must play an important role in transporting nutrients into cartilage due to its avascular nature. Recent theoretical studies generally support the idea that cyclic loading enhances large molecule transport through advection. However, to date, reactive transport, i.e. the effects of solute binding, has not yet been taken into consideration in cyclically deformed cartilage. In the present study, we develop a reactive transport model to describe the potential role of binding of solute within cyclically deformed cartilage. Our results show that binding does have a significant effect on transport, particularly for the low IGF-I concentrations typical of synovial fluid. A dynamic loading regime of high strain magnitudes (up to 10%) in combination with high frequencies (e.g. 1 Hz) was seen to produce the most dramatic results with enhanced total uptake ratio as high as 25% averaged over the first 5h of cyclic loading.