A model of NaCl and water flow through paracellular pathways of renal proximal tubules.

To explain how hydrostatic pressure differences between tubule lumen and interstitium modulate isotonic reabsorption rates, we developed a model of NaCl and water flow through paracellular pathways of the proximal tubule. Structural elements of the model are a tight junction membrane, an intercellular channel whose walls transport NaCl actively at a constant rate, and a basement membrane. Equations of change were derived for the channel, boundary conditions were formulated from irreversible thermodynamics, and a pressure-area relationship typical of thin-walled tubing was assumed. The boundary value problem was solved numerically. The principal conclusions are: 1) channel NaCl concentration must remain within a few mOsm of isotonic values for reabsorption rates to be modulated by transtubular pressure differences known to affect this system: 2) basement membrane and channel wall parameters determine reabsorbate tonicity; tight junction parameters affect the sensitivity of reabsorption to transmural pressure; 3) channel NaCl concentration varies inversely with transmural pressure difference; this concentration variation controls NaCl diffusion through the tight junction; 4) modulation of NaCl diffusion through the tight junction controls the rate of isotonic reabsorption; modulation of water flow can increase sensitivity to transmural pressure; 5) no pressure-induced change in permeability of the tight junction or basement membrane is needed for pressure to modulate reabsorption; and 6) system performance is indifferent to the distribution of active transport sites, to the numerical value of the compliance function, and to the relationship between lumen and cell pressures.     

Isosmotic volume reabsorption in rat proximal tubule

A theoretical model incorporation both active and passive forces has been developed for fluid reabsorption from split oil droplets in rat intermediate and late proximal tubule. Of necessity, simplifying assumptions have been introduced; we have assumed that the epithelium can be treated as a single membrane and that the membrane "effective" HCO3 permeability is near zero. Based on this model with its underlying assumptions, the following conclusions are drawn. Regardless of the presence or absence of active NaCl transport, fluid reabsorption from the split oil droplet is isosmotic. The reabsorbate osmolarity can be affected by changes in tubular permeability parameters and applied forces but is not readily altered from an osmolarity essentially equal to that of plasma. In a split droplet, isosmotic flow need not be a special consequence of active Na transport, is not the result of a particular set of permeability properties, and is not merely a trivial consequence of a very high hydraulic conductivity; isosmotic flow can be obtained with hydraulic conductivity nearly an order of magnitude lower than that previously measured in the rat proximal convoluted tubule. Isosmotic reabsorption is, in part, the result of the interdependence of salt and water flows, their changing in parallel, and thus their ratio, the reabsorbate concentration being relatively invariant. Active NaCl transport can cause osmotic water flow by reducing the luminal fluid osmolarity. In the presence of passive forces the luminal fluid can be hypertonic to plasma, and active NaCl transport can still exert its osmotic effect on volume flow. There are two passive forces for volume flow: the Cl gradient and the difference in effective osmotic pressure; they have an approximately equivalent effect on volume flow. Experimentally, we have measured volume changes in a droplet made hyperosmotic by the addition of 50 mM NaCl; the experimental results are predicted reasonably well by our theoretical model.     

Analysis of standing droplets in rat proximal tubules

Volume, osmolality, and concentrations for Na, Cl, and raffinose have been measured as a function of time in standing droplets within rat intermediate and late proximal tubules. Standing droplet reabsorption proceeds without the development of a measurable osmotic difference across the epithelium. After 140 s of tubular exposure, droplet-to- plasma concentration differences are observed for raffinose, Na, and Cl with the observed Na concentration difference, usually referred to as limiting gradient, being approximately 9 mM. It is possible that a smaller or even no limiting difference would be attained with longer exposure times. Previous values measured for the limiting Na concentration in the rat proximal tubule were determined before the attainment of constant concentrations. Assuming that the Na concentration we measured is the limiting value, we estimate that active NaCl transport accounts for a very small fraction, less than 6%, of the volume reabsorption; using an alternative approach of fitting a theoretical model to our experimental data, active NaCl transport is again estimated to account for only 6% of the total reabsorbate. The previous interpretation that a limiting Na concentration gradient constitutes the most direct evidence for active Na transport may be in error; the gradient we measure can be modeled without incorporating active NaCl transport.     

Regulation of paracellular Na and Cl conductances by hydrostatic pressure

The effect of hydrostatic pressure on the paracellular ion conductance (Gp) composed of the Na⁺ conductance (G_Na) and the Cl⁻ conductance (G_Cl) has been Investigated. Gp, G_Na and G_Cl were time-dependently increased after applying an osmotic gradient generated by NaCl with basolateral hypotonicity. Hydrostatic pressure (1-4 cm H₂O) applied from the basolateral side enhanced the osmotic gradient-induced increase in Gp, G_Na and G_Cl in a magnitude-dependent manner, while the hydrostatic pressure applied from the apical side diminished the osmotic gradient-induced increase in Gp, G_Na and G_Cl. How the hydrostatic pressure influences Gp, G_Na and G_Cl under an isosmotic condition was also investigated. Gp, G_Na and G_Cl were stably constant under a condition with basolateral application of sucrose canceling the NaCl-generated osmotic gradient (an isotonic condition). Even under this stable condition, the basolaterally applied hydrostatic pressure drastically elevated Gp, G_Na and G_Cl, while apically applied hydrostatic pressure had little effect on Gp, G_Na or G_Cl. Taken together, these observations suggest that certain factors controlled by the basolateral osmolality and the basolaterally applied hydrostatic pressure mainly regulate the Gp, G_Na and G_Cl.     

Nonlinear interactions in renal blood flow regulation

We have developed a model of tubuloglomerular feedback (TGF) and the myogenic mechanism in afferent arterioles to understand how the two mechanisms are coupled. This paper presents the model. The tubular model predicts pressure, flow, and NaCl concentration as functions of time and tubular length in a compliant tubule that reabsorbs NaCl and water; boundary conditions are glomerular filtration rate (GFR), a nonlinear outflow resistance, and initial NaCl concentration. The glomerular model calculates GFR from a change in protein concentration using estimates of capillary hydrostatic pressure, tubular hydrostatic pressure, and plasma flow rate. The arteriolar model predicts fraction of open K channels, intracellular Ca concentration (Ca(i)), potential difference, rate of actin-myosin cross bridge formation, force of contraction, and length of elastic elements, and was solved for two arteriolar segments, identical except for the strength of TGF input, with a third, fixed resistance segment representing prearteriolar vessels. The two arteriolar segments are electrically coupled. The arteriolar, glomerular, and tubular models are linked; TGF modulates arteriolar circumference, which determines vascular resistance and glomerular capillary pressure. The model couples TGF input to voltage-gated Ca channels. It predicts autoregulation of GFR and renal blood flow, matches experimental measures of tubular pressure and macula densa NaCl concentration, and predicts TGF-induced oscillations and a faster smaller vasomotor oscillation. There are nonlinear interactions between TGF and the myogenic mechanism, which include the modulation of the frequency and amplitude of the myogenic oscillation by TGF. The prediction of modulation is confirmed in a companion study (28).     

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.     

The mechanisms of refilling of xylem conduits and bleeding of tall birch during spring

Seasonal variations in osmolality and components of xylem sap in tall birch trees were determined using several techniques. Xylem sap was extracted from branch and trunk sections of 58 trees using the very rapid gas bubble-based jet-discharge method. The 5-cm long wood pieces were taken at short intervals over the entire tree height. The data show that large biphasic osmolality gradients temporarily exist within the conducting xylem conduits during leaf emergence (up to 272 mosmol x kg(-1) at the apex). These gradients (arising mainly from glucose and fructose) were clearly held within the xylem conduit as demonstrated by (1)H NMR imaging of intact twigs. Refilling experiments with benzene, sucrose infusion, electron and light microscopy, as well as (1)H NMR chemical shift microimaging provided evidence that the xylem of birch represents a compartment confined by solute-reflecting barriers (radial: lipid linings/lipid bodies; axial: presumably air-filled spaces). These features allow transformation of osmolality gradients into osmotic pressure gradients. Refilling of the xylem occurs by a dual mechanism: from the base (by root pressure) and from the top (by hydrostatic pressure generated by xylem-bound osmotic pressure). The generation of osmotic pressure gradients was accompanied by bleeding. Bleeding could be observed at a height of up to 21 m. Bleeding rates measured at a given height decreased exponentially with time. Evidence is presented that the driving force for bleeding is the weight of the static water columns above the bleeding point. The pressure exerted by the water columns and the bleeding volume depend on the water-filling status of (communicating) vessels.     

An analogue computer simulation of cloacal resorption of salt and water from ureteral urine in birds

The transmural flow of NaCl and water occurring during the retrograde flow of ureteral urine into the coprodeum and large intestine of birds has been simulated by analogue computation. The purpose was to estimate whether a fraction of the urine (water) which in the dehydrated state is hyperosmotic to plasma can, in spite of this, be absorbed from the narrow space between the epithelium and the central faeces core. The values of urine flow, urine osmolality, osmotic permeability, net NaCl absorption rate, and solute-linked water flow determined by in vivo perfusion studies in the domestic fowl were used in the calculation. The cloacal sojourn of ureteral urine was found to result in a net water gain but at the expense of a hyperosmotic NaCl absorption. The model was further used to evaluate the quantitative influence of the system's parameters upon the fractional water absorption. This was found very sensitive to the urine osmolality, moderately sensitive to the urine flow and NaCl absorption rate and almost unaffected by the osmotic permeability of the coprodeum and large intestine within a reasonable physiological range. The change of the epithelial transport parameters from the normally hydrated to the dehydrated state resulted in a marked increase in water absorption.     

Study in the anuran amphibian Xenopus laevis, some blood characteristics and nitrogen excretion based on changes in the water osmolarity]

The pH, the osmolality and the urea and ammonia concentrations in blood, as well as the net urea and ammonia excretions, were studied in the amphibian Xenopus laevis exposed for several weeks to increased osmotic pressure (OP) of the ambient water, as a result of the addition of either NaCl or mannitol to the water. The pH and the ammonia concentration of the blood were independent of the variations of the ambient osmolarity. On the contrary, the blood osmolality and its urea concentration increased markedly when the ambient OP was augmented. The increase of ambient OP by NaCl addition to the medium augmented the urea net excretion and slightly decreased the ammonia excretion. When the increase of ambient OP resulted from the addition of mannitol in the water, excretions of urea and ammonia became negligible.     

Apoplastic transport across young maize roots: effect of the exodermis

The uptake of water and of the fluorescent apoplastic dye PTS (trisodium 3-hydroxy-5,8,10-pyrenetrisulfonate) by root systems of young maize (Zea mays L.) seedlings (age: 11–21 d) has been studied with plants which either developed an exodermis (Casparian band in the hypodermis) or were lacking it. Steady-state techniques were used to measure water uptake across excised roots. Either hydrostatic or osmotic pressure gradients were applied to induce water flows. Roots without an exodermis were obtained from plants grown in hydroponic culture. Roots which developed an exodermis were obtained using an aeroponic (=mist) cultivation method. When the osmotic concentration of the medium was varied, the hydraulic conductivity of the root (Lp _r in m³ · m⁻² · MPa⁻¹ · s⁻¹) depended on the osmotic pressure gradient applied between root xylem and medium. Increasing the gradient (i.e. decreasing the osmotic concentration of the medium; range: zero to 40 mM of mannitol), increased the osmotic Lp _r. In the presence of hydrostatic pressure gradients applied by a pressure chamber, root Lp _r was constant over the entire range of pressures (0–0.4 MPa). The presence of an exodermis reduced root Lp _r in hydrostatic experiments by a factor of 3.6. When the osmotic pressure of the medium was low (i.e. in the presence of a strong osmotic gradient between xylem sap and medium), the presence of an exodermis caused the same reduction of root Lp _r in osmotic experiments as in hydrostatic ones. However, when the osmotic concentration of the medium was increased (i.e. the presence of low gradients of osmotic pressure), no marked effect of growth conditions on osmotic root Lp _r was found. Under these conditions, the absolute value of osmotic root Lp _r was lower by factors of 22 (hydroponic culture) and 9.7 (aeroponic culture) than in the corresponding experiments at low osmotic concentration. Apoplastic flow of PTS was low. In hydrostatic experiments, xylem exudate contained only 0.3% of the PTS concentration of the bathing medium. In the presence of osmotic pressure gradients, the apoplastic flow of PTS was further reduced by one order of magnitude. In both types of experiments, the development of an exodermis did not affect PTS flow. In osmotic experiments, the effect of the absolute value of the driving force cannot be explained in terms of a simple dilution effect (Fiscus model). The results indicate that the radial apoplastic flows of water and PTS across the root were affected differently by apoplastic barriers (Casparian bands) in the exodermis. It is concluded that, unlike water, the apoplastic flow of PTS is rate-limited at the endodermis rather than at the exodermis. The use of PTS as a tracer for apoplastic water should be abandoned. Received: 9 October 1997 / Accepted: 5 February 1998     

Regulation of the paracellular Na+ and Cl- conductances by the NaCl-generated osmotic gradient in a manner dependent on the direction of osmotic gradients

In the present study, we investigated the effect of osmolality on the paracellular ion conductance (Gp) composed of the Na⁺ conductance (G_Na) and the Cl⁻ conductance (G_Cl). An osmotic gradient generated by NaCl with relatively apical hypertonicity (NaCl-absorption-direction) induced a large increase in the G_Na associated with a small increase in the G_Cl, whereas an osmotic gradient generated by NaCl with relatively basolateral hypertonicity (NaCl-secretion-direction) induced small increases in the G_Na and the G_Cl. These increases in the Gp caused by NaCl-generated osmotic gradients were diminished by the application of sucrose canceling the NaCl-generated osmotic gradient. The osmotic gradient generated by basolateral application of sucrose without any NaCl gradients had little effects on the Gp. However, this basolateral application of sucrose produced a precondition drastically quickening the time course of the action of the NaCl-generated osmotic gradient on the Gp. Further, we found that application of the basolateral hypotonicity generated by reduction of NaCl concentration shifted the localization of claudin-1 to the apical from the basolateral side. These results indicate that the osmotic gradient regulates the paracellular ion conductive pathway of tight junctions via a mechanism dependent on the direction of NaCl gradients associated with a shift of claudin-1 localization to the apical side in renal A6 epithelial cells.     

Pseudo-streaming potentials in Necturus gallbladder epithelium. II. The mechanism is a junctional diffusion potential

The mechanisms of apparent streaming potentials elicited across Necturus gallbladder epithelium by addition or removal of sucrose from the apical bathing solution were studied by assessing the time courses of: (a) the change in transepithelial voltage (Vms). (b) the change in osmolality at the cell surface (estimated with a tetrabutylammonium [TBA+]-selective microelectrode, using TBA+ as a tracer for sucrose), and (c) the change in cell impermeant solute concentration ([TMA+]i, measured with an intracellular double-barrel TMA(+)-selective microelectrode after loading the cells with TMA+ by transient permeabilization with nystatin). For both sucrose addition and removal, the time courses of Vms were the same as the time courses of the voltage signals produced by [TMA+]i, while the time courses of the voltage signals produced by [TBA+]o were much faster. These results suggest that the apparent streaming potentials are caused by changes of [NaCl] in the lateral intercellular spaces, whose time course reflects the changes in cell water volume (and osmolality) elicited by the alterations in apical solution osmolality. Changes in cell osmolality are slow relative to those of the apical solution osmolality, whereas lateral space osmolality follows cell osmolality rapidly, due to the large surface area of lateral membranes and the small volume of the spaces. Analysis of a simple mathematical model of the epithelium yields an apical membrane Lp in good agreement with previous measurements and suggests that elevations of the apical solution osmolality elicit rapid reductions in junctional ionic selectivity, also in good agreement with experimental determinations. Elevations in apical solution [NaCl] cause biphasic transepithelial voltage changes: a rapid negative Vms change of similar time course to that of a Na+/TBA+ bi-ionic potential and a slow positive Vms change of similar time course to that of the sucrose-induced apparent streaming potential. We conclude that the Vms changes elicited by addition of impermeant solute to the apical bathing solution are pseudo-streaming potentials, i.e., junctional diffusion potentials caused by salt concentration changes in the lateral intercellular spaces secondary to osmotic water flow from the cells to the apical bathing solution and from the lateral intercellular spaces to the cells. Our results do not support the notion of junctional solute-solvent coupling during transepithelial osmotic water flow.     

The influence and interactions of hydrostatic and osmotic pressures on the intracellular milieu of chondrocytes

The intracellular milieu of chondroctyes is regulated by an array of proteins in the cell membrane which operate as transport pathways, allowing ions and nutrients such as glucose and amino acids and metabolites such as lactate to cross the plasma membrane. Here we investigated the influence of hydrostatic pressure on intracellular calcium concentrations ([Ca(2+)](i)) in isolated bovine articular chondrocytes. We found that short applications of high hydrostatic pressures led to a significant increase in [Ca(2+)](i). The pressure-induced rise was abolished for long (240 sec) but not short (30 sec) pressure applications by removal of extracellular Ca(2+). The rise in pressure was also blocked by the inhibitors neomycin and thapsigargin confirming that pressure, by generating IP(3), led to an increase in [Ca(2+)](i) by mobilising the pool of Ca(2+) ions contained within intracellular stores. We also found that intracellular [Na(+)] was affected by a rise in osmotic pressure and further affected by application of hydrostatic pressure. The effect of hydrostatic pressure on sulphate incorporation depended strongly on extracellular osmolality. Since significant gradients in extracellular osmolality exist across intact cartilage, the results imply that responses of chondrocytes to the same pressure will vary depending on location in the joint. The results also indicate that hydrostatic pressures can affect several different transporter systems thus influencing the intracellular milieu and chondrocyte metabolism.     

Amniotic fluid and hemodynamic model in monochorionic twin pregnancies and twin-twin transfusion syndrome

We developed a mathematical model of monochorionic twin pregnancies and twin-twin transfusion syndrome (TTTS), combining both fetal fluid dynamics and fetoplacental growth and circulation alterations and assuming that transplacental fluid flow from mother to fetus accounts for normal fetal and amniotic fluid volumes. Ten coupled differential equations, describing fetal total body and amniotic fluid volumes, their osmolalities, and fetal blood colloid osmotic pressure, for both donor and recipient twins, were solved numerically. Amniotic flows are controlled by fetal plasma osmolality and hydrostatic and colloid osmotic pressures. We included varying placental anastomoses and placental sharing of the circulations. Consistent with clinical experience, model predictions are: fetofetal transfusion from unidirectional arteriovenous anastomoses cause oligo-polyhydramnios, a normal size recipient but hypovolemic donor; compensating oppositely directed deep and superficial anastomoses moderate discordant development; and anhydramnios results from mild and severe TTTS, where milder forms may even present earlier in gestation than severe TTTS. Unequal placental circulatory sharing may exacerbate discordant development. In conclusion, our model simulates a wide variety of realistic manifestations of amniotic fluid volume and fetal growth in TTTS related to placental angioarchitecture. The model may allow an assessment of the efficacy of current therapeutic interventions for TTTS.     

Life under pressure: hydrostatic pressure in cell growth and function

H(2)O is one of the most essential molecules for cellular life. Cell volume, osmolality and hydrostatic pressure are tightly controlled by multiple signaling cascades and they drive crucial cellular functions ranging from exocytosis and growth to apoptosis. Ion fluxes and cell shape restructuring induce asymmetries in osmotic potential across the plasma membrane and lead to localized hydrodynamic flow. Cells have evolved fascinating strategies to harness the potential of hydrodynamic flow to perform crucial functions. Plants exploit hydrodynamics to drive processes including gas exchange, leaf positioning, nutrient acquisition and growth. This paradigm is extended by recent work that reveals an important role for hydrodynamics in pollen tube growth.     

Effects of changes in the composition of the mucosal solution on the electrical properties of the toad urinary bladder epithelium

Summary By the use of microelectrode techniques, the potential profile and the electrical resistances of the cellular and shunt pathways across the toad urinary bladder epithelium were measured under control conditions and after exposing the mucosal side to solutions of low and high NaCl concentrations and osmolatities. The resistance of the shunt pathway increases at low NaCl concentration (even if the osmolality is kept constant), and decreases at high NaCl concentration (by a nonspecific osmotic mechanism). The inverse relationship between mucosal NaCl concentration and shunt resistance suggests a regulatory mechanism of net sodium transport by reduction of the passive blood-to-urine sodium flux at low urinary sodium concentrations. In addition, the transepithelial potential and the potentials at both cell borders fall in both low and high mucosal NaCl, and the magnitude of these changes is such that they cannot be explained by changes in the shunt pathway alone.     

Renal blood flow, early distal sodium, and plasma renin concentrations during osmotic diuresis

Inconsistencies in previous reports regarding changes in early distal NaCl concentration (ED(NaCl)) and renin secretion during osmotic diuresis motivated our reinvestigation. After intravenous infusion of 10% mannitol, ED(NaCl) fell from 42.6 to 34.2 mM. Proximal tubular pressure increased by 12.6 mmHg. Urine flow increased 10-fold, and sodium excretion increased by 177%. Plasma renin concentration (PRC) increased by 58%. Renal blood flow and glomerular filtration rate decreased, however end-proximal flow remained unchanged. After a similar volume of hypotonic glucose (152 mM), ED(NaCl) increased by 3.6 mM, (P < 0.01) without changes in renal hemodynamics, urine flow, sodium excretion rate, or PRC. Infusion of 300 micromol NaCl in a smaller volume caused ED(NaCl) to increase by 6.4 mM without significant changes in PRC. Urine flow and sodium excretion increased significantly. There was a significant inverse relationship between superficial nephron ED(NaCl) and PRC. We conclude that ED(Na) decreases during osmotic diuresis, suggesting that the increase in PRC was mediated by the macula densa. The results suggest that the natriuresis during osmotic diuresis is a result of impaired sodium reabsorption in distal tubules and collecting ducts.     

A Physiological Approach to Perfusion-Flxation of Tissues with Formalin

A method of perfusion-fixation with formalin is here presented which is based upon well established physiological principles. It represents an attempt to preserve more accurately the structure and relationships of nervous tissue found in the living state. The essential points include the following: (1) Perfusion at an hydrostatic pressure equivalent to the mean arterial pressure of the animal to be fixed to maintain the normal patency of the vascular bed. For the guinea pig, it is approximately 70 mm. Hg; for the cat and monkey, it is approximately 120 mm. Hg. (2) The addition of a colloid to the perfusion fluid which will exert an osmotic pressure equal to the hydrostatic pressure in the capillaries and thus prevent edema. Gum acacia is used in this method. Its concentration depends upon the hydrostatic pressure to be used: for 70 mm. Hg, in the guinea pig it is 2.4%; for 122 mm. Hg, in the cat and the monkey, it is 5.6% gum acacia. (3) The addition of an electrolyte to the perfusion fluid to make it isotonic to the tissue fluid and thus prevent a disturbance in the distribution of water in the animal with resultant tissue distortion. NaCl (0.9%) is used in this method. (4) For further fixation or for preservation of the tissues, they are placed in a solution of 10% formalin which contains 0.9% NaCl to minimize swelling.     

Root hydraulic properties of spruce measured with the pressure probe

The root pressure probe was used for the first time to measure the hydraulic properties of entire root systems of youngPicea abies. Hydraulic conductance was measured by osmotic and hydrostatic pressure relaxation techniques. Osmotic experiments were conducted by changing the nutrient solution and hydrostatic experiments by causing flow across the root with the pressure probe and with external pressure applied to the root system or to the cut stem of the excised root system. Usually,Picea abies root systems did not develop appreciable root pressure (< 0.02 MPA) and could be induced to reach a root pressure of 0.07 MPa by treating with KNO₃. In general, hydraulic conductance of the root system was large, but it was much smaller in the osmotic than in the hydrostatic experiments. Both hydrostatic techniques gave similar results. The results were explainable by a composite transport model of the root.     

Osmotic Flow of Water across Permeable Cellulose Membranes

Direct measurements have been made of the net volume flow through cellulose membranes, due to a difference in concentration of solute across the membrane. The aqueous solutions used included solutes ranging in size from deuterated water to bovine serum albumin. For the semipermeable membrane (impermeable to the solute) the volume flow produced by the osmotic gradient is equal to the flow produced by the hydrostatic pressure RT ΔC, as given by the van't Hoff relationship. In the case in which the membrane is permeable to the solute, the net volume flow is reduced, as predicted by the theory of Staverman, based on the thermodynamics of the steady state. A means of establishing the amount of this reduction is given, depending on the size of the solute molecule and the effective pore radius of the membrane. With the help of these results, a hypothetical biological membrane moving water by osmotic and hydrostatic pressure gradients is discussed.