Permeability-surface Product Research Articles

Influence of pH on the Uptake and Pharmacodynamics of Quinidine in the Isolated Perfused Rat Heart

Using the single-pass isolated perfused rat heart preparation we examined the effect of perfusate pH (pH 7.05, 7.46, 7.71, 7.92) on quinidine output concentration (C(out)) and delta QT. Eight hearts were perfused at 2.5 ml/min. with quinidine (20 microM) for 35 min. followed by a 35-40 min. washout period with drug-free perfusate. This procedure was repeated four times in each preparation with the pH sequence varied and the same pH used in the first and last phases. Increasing pH slowed the rate of equilibration of C(out), the equilibration rate constant (k) decreasing from 0.273 min.-1 at pH 7.05 to 0.095 min.-1 at pH 7.92. A modified Kety-Renkin-Crone equation was fitted to the C(out) versus time data for each pH. The estimated volume of distribution (V) increased significantly with pH from 11.5 +/- 1.1 to 32.5 +/- 2.9 ml/g, but the permeability surface product did not change with pH (mean 17.7 ml/min./g). There was a linear relationship between V and calculated un-ionised quinidine C(out), with an intercept of 5.70 ml/g corresponding to the V of ionised drug. This indicates that ionised and un-ionised drug readily enter the heart and that the slower equilibration with pH is due to the increased V which results from increased partitioning of un-ionised quinidine into myocardial tissue. Perfusion pH did not directly affect baseline QT interval, but the rate of attainment of maximum delta QT decreased with increasing perfusate pH. Plots of delta QT versus calculated coronary output quinidine concentration did not change with pH, showing that this drug effect was due to both ionised and un-ionised moieties. This study shows that myocardial permeability and pharmacodynamic effect (delta QT) of quinidine are not influenced by perfusion pH over the range 7.0 to 7.9, although rate of equilibration of both C(out) and effect vary with pH.

Handling of tracer norepinephrine by the dog liver.

Norepinephrine handling by the dog liver was appraised by carrying out tracer-transient, multiple-indicator-dilution studies within steady-state conditions in a basal situation, during norepinephrine infusion and after the uptake inhibitor desipramine. In controls, tracer norepinephrine extraction averaged 61%, whereas bulk norepinephrine extraction was approximately 31%; intrahepatic secretion of unlabeled norepinephrine accounted for the difference. Infusion of norepinephrine, raising arterial levels more than an order of magnitude, constricted the hepatic vascular space but did not change tracer extraction; norepinephrine secretion remained essentially unchanged, and with this, bulk extraction approached tracer extraction. A theoretical analysis of norepinephrine uptake was developed. Analysis of tracer data with this indicated that the permeability surface products for influx and efflux, expressed per gram liver, did not change. Desipramine did not affect the uptake kinetics, indicating that the uptake process was virtually completely nonneurogenic. Late efflux of tracer normetanephrine product was detected but was small prior to recirculation. The study demonstrates that norepinephrine secretion ordinarily coexists with uptake and provides an approach to quantitating both.

Water extraction fraction and permeability-surface product after intravenous injection in rats.

A quantitative method has been developed to measure the water extraction fraction of rat brain after successive intravenous bolus injections of [15O]water and [11C]butanol based on a mathematical equation developed by the authors. This new method is noninvasive to the brain or craniocervical large vessels and does not require sacrifice of the rats. Arterial concentration curves and total head counts were measured in 8 rats by means of external coincidence detectors. Water extraction fraction in rat brain was 0.67 +/- 0.13 (mean +/- SD) and permeability-surface product was 1.75 ml/g min, where cerebral blood flow and arterial carbon dioxide tension were 1.71 +/- 0.86 ml/g min and 44.8 +/- 14.0 mm Hg, respectively. Water extraction fraction was stable with different measurement times from 20 to 80 seconds.

Decreased basal cardiac interstitial norepinephrine release after neuronal uptake inhibition in dogs.

The effect of neuronal uptake inhibition on basal interstitial release of norepinephrine in the canine heart was examined by use of the multiple tracer dilution-bulk balance technique. A kinetic model incorporating the effects of flow, capillary permeability-surface product for norepinephrine, the interstitial uptake rate constant for neurotransmitter, and plasma norepinephrine input and output values was used to estimate rates of uptake from and release of norepinephrine into the interstitial space. The intravenous injection of the neuronal uptake inhibitor desipramine in anesthetized dogs under basal conditions reduced interstitial uptake of tracer norepinephrine in the heart, without significant changes in plasma concentration of norepinephrine in aorta and coronary sinus. The lack of change in the arteriovenous balance for norepinephrine across the heart, in the face of the lowered uptake for this amine, suggested that the liberation of norepinephrine by cardiac sympathetic fibers was reduced. Analysis of the data with the norepinephrine tracer kinetic-bulk model showed that, after desipramine, the interstitial release of norepinephrine was reduced to the same extent as uptake was diminished. As a result, the concentration of norepinephrine in the extracellular space of the heart did not increase significantly. The findings indicate the presence of a presynaptic neuronal feedback inhibition of release, which serves to fine tune the myocardial interstitial concentration of norepinephrine in the basal state; with this, after desipramine, both norepinephrine uptake and release are correspondingly diminished.

Plasma expansion effect on cardiac capillary and adrenergic exchange in intact dogs

The effect of plasma volume expansion on transcapillary exchange and norepinephrine release in the heart was examined in pentobarbital sodium-anesthetized dogs by use of the multiple indicator-dilution technique. Animals were studied under basal conditions and following infusion of the plasma expander, dextran. Catheters were placed in coronary artery and coronary sinus in a closed-chest preparation. Labeled albumin, sucrose, and norepinephrine were injected into the coronary artery and outflow-dilution curves were secured. Analysis of these provided parameters reflecting coronary flow and permeability-surface product, and a norepinephrine tracer kinetic-bulk model provided simultaneous estimates of the rate of norepinephrine release into the myocardial interstitial space. The infusion of dextran resulted in a large increase in coronary flow without significant changes in myocardial norepinephrine release; at the same time the permeability-surface product values increased, amplifying the capacity of the higher flow to deliver substrates to sarcolemmal cells. The findings indicate that plasma volume expansion increases transcapillary exchange in the heart without activating the cardiac sympathetic system.

Effect of beta-adrenergic blockade on in vivo norepinephrine release in canine heart.

The beta-adrenergic blockade-induced reduction in myocardial norepinephrine overflow during sympathetic stimulation was examined by use of the multiple indicator-dilution technique. A kinetic model incorporating the effects of flow, capillary permeability surface product for norepinephrine, the interstitial uptake rate constant for neurotransmitter, and plasma norepinephrine input and output values was used to estimate the rate of local release of norepinephrine into the interstitial space. The model was tested by first examining the effects of two drugs that increase myocardial norepinephrine overflow during sympathetic stimulation by differing mechanisms: desmethylimipramine, a norepinephrine uptake inhibitor, and phentolamine, an alpha-adrenergic blocker. The uptake inhibitor was demonstrated to reduce interstitial uptake and the alpha-blocker to increase local neurotransmitter release, without change in blood flow. The beta-adrenergic blocker, in contrast, reduced coronary blood flow and decreased the capillary norepinephrine permeability surface product but did not change the rate of local release. The decreased norepinephrine overflow after beta-blockade was deduced to result from the decrease in transcapillary flux and secondary increase in interstitial uptake.

Changes in cardiac transcapillary exchange with metabolic coronary vasodilation in the intact dog.

The effects of metabolic coronary vasodilation on transcapillary exchange in the heart were examined in anesthetized dogs by use of the multiple indicator dilution technique. Animals were studied under basal conditions and during coronary sinus pacing. To obviate adrenal medullary stimulation, catheters were placed in coronary artery and coronary sinus in a closed chest preparation. Plasma catecholamine concentrations were determined to provide an index of the level of sympathetic tone. Labeled albumin and sucrose were injected into the coronary artery, and outflow dilution curves were secured. Analysis of these, with a model incorporating throughput and returning components, and heterogeneity of capillary transit times, provided parameters reflecting flow, permeability-surface product for sucrose, and capillary heterogeneity. Coronary sinus pacing increased both heart rate and plasma norepinephrine values; in response, myocardial oxygen consumption increased, metabolic vasodilation occurred, and coronary flow increased. The capillary permeability-surface product for sucrose increased with the flow but tended to plateau at higher values, showing a saturation phenomenon. Capillary heterogeneity, present in control animals with low sympathetic tone, was grossly decreased during cardiac metabolic activation. The Crone-Renkin approximation formula for the permeability-surface product yielded values that were too low at low flows and values approaching those from the complete model at high flows. The findings indicate an integrated pattern of circulatory response to cardiac metabolic activation characterized by decreased resistance, increased flow, increased permeability-surface product, and reduced heterogeneity. The last two effects amplify the capacity of increased flow to deliver substrates to heart muscle cells.

Determination of postglomerular permselectivity to neutral dextrans in the dog.

The single-pass multiple-indicator-dilution (MID) technique was used to analyze postglomerular capillary permeability. Anesthetized mongrel dogs (n = 13) during mannitol diuresis received a pulse injection of 125I-albumin (plasma reference), [14C]inulin (glomerular reference), creatinine (interstitial reference), and a homogeneous [3H]dextran molecular weight marker 6,000-12,000 dalton in the left renal artery. Simultaneous left renal venous outflow and right and left urine were rapidly sampled. Left urine recoveries of creatinine, [14C]inulin, and [3H]dextran were identical, indicating no glomerular solute flux limitation. Progressive precession of the [14C]inulin and [3H]dextran renal vein curves relative to creatinine indicated increasing postglomerular limitation to solute flux proportional to molecular size. The postglomerular solute extraction (EPG) (renal vein upslope indicator/125I-albumin) varied inversely with postglomerular renal plasma flow (F), indicating diffusion limitation. Ouabain infusion into the left renal artery significantly reduced Na reabsorption but did not alter the EPG of [14C]inulin or [3H]dextran. Permeability-surface (PS) area products calculated from EPG and F ranged from 4.86 +/- 0.89 to 0.97 +/- 0.25 (SD) cm X s-1 X 100 g-1 for indicators 5,000-12,000 dalton. [14C]Inulin PS products remained constant for F greater than or equal to 2.50 ml X s-1 X 100 g kidney-1. PS[3H]dextran/PS[14C]In (n = 20, F greater than or equal to 2.5 ml X s-1) was used to calculate an effective postglomerular capillary pore radius, r = 55.5 +/- 7.6 (SD) A.

System analysis of vascular membrane water and protein transport: General method and application to canine hindquarters

A system analysis is developed to examine interdependencies of parameters and variables in lymph flux analysis experiments where lymph flux ( L) and lymph/plasma protein concentration ratios ( R = C L C p ) are measured. Homoporosity and right circular cylindrical pores are assumed for simplicity, but complex models are subject to similar methods. Parameters and variables analyzed include reflection coefficient (σ), hydraulic-conductivity surface product ( L p S), permeability surface product ( PS), protein clearance ( LR), permeative protein clearance ( D), convective protein clearance ( B), and fractional permeative protein transport (Fr D). Insights gained are numerous and include: Uncertainties or variations in σ produce magnified and vectorially similar variations in B for loose membranes, but very much smaller and vectorially opposite variations in B in tight membranes. Although errors in R may lead to large errors in some parameters such as PS, these erroneous values may themselves yield very small errors in other computed membrane-solution variables such as Fr D. Hence, Fr D is fairly insensitive to errors in R which may arise when experiments are not precisely at steady-state conditions. Moreover, even an unrealistic 100% error in R transmits virtually no error to computed σ in tight membranes. D rises significantly as L rises, accounting for nearly all the increase in LR for tight membranes. Such an analysis is useful in planning experimental design, and can be used to determine internal consistency of more complex transport models.

Dependency of permeability-surface area product upon solute concentration, and its significance in the interpretation of lymph flux data

The assessment of permeability-surface products ( PS) and reflection coefficients (σ) for macromolecules crossing capillary walls into neighboring lymphatics has until now assumed PS to be independent of solute concentration for homoporous membranes. When serum proteins are used as transport markers, the concentrations are high enough to make PS, and therefore σ, dependent upon protein concentration. Therefore, description of protein flux by the standard homoporous global nonlinear transport equation (GNT) would result in erroneous values for PS and σ. The current study employs a concentration-dependent diffusivity equation (CDDT) to describe the transport by standard irreversible thermodynamics. Results from the literature using the GNT are reinterpreted by the CDDT to show the magnitude of and the qualitative changes in interpretation. PS for albumin is shown to be reduced up to 10% and to be a complex monotonically increasing function across the membrane depending on solute concentration and lymph flow rate. σ is reduced up to 8%, and fractional permeative transport is decreased up to 9%. It is suggested that the CDDT replace the GNT where possible for descriptions of protein transport, especially in situations of low lymph flow and high protein concentration. Although the CDDT is derived for homoporous membranes, it is applicable to several types of heteroporous membranes with acceptable error and in some instances no error. When these equations do not explain transport data, it is an indication either that the experimental design has led to changes in the transport parameters, or that a more complex heteroporous equation is needed.

Effect of vasodilation and flow rate on capillary permeability surface product and interstitial space size in the coronary circulation. A frequency domain technique for modeling multiple dilution data with Laguerre functions.

Effect of vasodilation and flow rate on capillary permeability surface product and interstitial space size in the coronary circulation. A frequency domain technique for modeling multiple dilution data with Laguerre functions.

Permeability of dog lung endothelium to sodium, diols, amides, and water.

Bolus injection of T-1824-albumin, test indicator, and tritiated water into a jugular vein of the anesthetized dog and sequential sampling of blood from a carotid artery yielded multiple-indicator outflow patterns for the lung. Permeability-surface products of the test indicator for the lung endothelial barrier were obtained by comparison of test indicator with T-1824-albumin on the upslope of the test-indicator curve and correction for backdiffusion. The derived endothelial permeability coefficients, based on surface area/wet lung weight-500 cm2/g (mean +/- 2 SE, 10(-5) cm s(-1)), were: sodium ion, 2.9 +/- 0.8; ethylene glycol, 7.3 +/- 1.5; 1, 3-propranediol, 7.9 +/- 3.2; 1, 2-propanediol, 10 +/- 4; 1, 4-butanediol, 14 +/- 8; 1, 5-pentanediol, 21 +/- 6; 1, 6-hexanediol, 41 +/- 11; formamide, 16 +/- 9; acetamide, 13 +/- 4; propionamide, 31 +/- 12; butyramide, 42 +/- 24; valeramide, 79 +/- 12; tritiated water, 150 +/- 50. The backdiffusion correction varies from 8% for sodium to 75% for valeramide. A parallel-pathway model of blood-tissue passive exchange of small nonelectrolyte solutes is compatible with these results, with a lipid pathway through endothelial cells and an aqueous pathway possibly through interendothelial clefts.

Pulmonary capillary permeability in man and a canine model of chemical pulmonary edema

Pulmonary capillary permeability-surface products (PSP) for sucrose and water have been calculated in normal, awake man and in anesthetized dogs using multiple indicator dilution data and a numerical deconvolution technique to estimate maximal extraction. In man and control animals the PSP for sucrose was found to be 9.1 and 7.1 cm 3/sec, respectively, while PSPs for water were found to be 34.0 and 30.9 cm 3/sec. The effects of flow and choice of the reference tracer (red blood cells or albumin) were examined. With the exception of water in man, the PSPs for sucrose and water did not change significantly with an increased cardiac output, regardless of the reference tracer chosen. Pulmonary capillary damage induced by the infusion of 75 mg/kg of alloxan in dogs increased the PSPs for sucrose and water by 35 and 52%, respectively, when red cells formed the reference tracer material. This change was eliminated for sucrose when albumin formed the reference tracer and reduced the magnitude of the change for water from 52 to 34%. The permeability increases in the alloxan damaged dogs occurred in the presence of normal pulmonary artery and wedge pressures. We conclude that the exchange of water is not flow-limited at physiologic or higher rates of perfusion and that albumin is misleading as a reference tracer in multiple indicator dilution studies of pulmonary edema.

Convection and permeation of albumin between plasma and interstitium

Nonequilibrium thermodynamics is combined with compartmental analysis to interpret albumin sieving and tracer experiments in terms of a permeability-surface product PS (permeation) and a solvent drag reflection coefficient σ f (convection) for various blood-tissue barriers. The human whole-body albumin data of Lassen, Parving, and Rossing ( Lassen, Parving, and Rossing, Microvasc. Res. 7, i–iv (1974) ), modified for nonliver tissues by Johnson and Levitt ( Johnson & Levitt, Microvasc. Res. 9, 141 (1975) ) lead to P ∼ 1.8 × 10 −8 cm sec −1 (based on a surface area per unit plasma volume of 700 cm −1) and to σ f ∼ 0.9, which imply, in agreement with Johnson and Levitt, that permeation is the dominant nonliver blood-tissue transport mechanism for albumin in the normal resting human. Similar values are derived from the dog paw muscle data of Garlick and Renkin ( Garlick and Renkin, Amer. J. Physiol. 219, 1595–1605 (1970) ). The Casley-Smith ( Casley-Smith, Microvasc. Res. 9, 43–48 (1975) ) mechanism of uphill albumin transport is verified as possible. It is tentatively inferred that lymph formation in resting tissue does not result from a small difference between a large fluid (volumetric) filtration and an almost equally large fluid reabsorption, either in the same capillary (Starling) or between different capillaries (Zweifach) ( Zweifach, Circ. Res. 34, 858–866 (1974) ). Rather, reabsorption is negligibly small relative to filtration, and lymph flow is comparable to volumetric filtration.

Influence of maximal vasodilatation on glucose and sodium blood-tissue transport in canine heart

Vascular conductance ( G = flow pressure ) and permeability-surface products ( PS) of sodium and glucose were measured in the control state and during continuous infusion of vasodilating drugs in the isolated spontaneously beating canine heart perfused with blood at constant flow. PS was determined by means of the first-circulation multiple tracers dilution method. Mean control G was 0.77 ml × min −1 × mm Hg −1 × 100 g. The extent of vasodilatation was assessed by the ratio G- drug G- control :papaverine, mean ratio 3.70 (2.59–4.73); dipyridamole, 3.50 (1.67–5.88); norepinephrine, 2.65 (1.18–4.23); nitroglycerin, 2.27 (1.66–3.25). The ratio for maximal vasodilatation was estimated to be 4–5. PS-Na and PS-glucose increased in a graded fashion with vasodilatation. With maximal vasodilatation the greatest increase observed in PS-Na was twofold, in PS-glucose 2.4-fold. The increase in PS most likely results from a change in capillary surface area. These data demonstrate a large reserve of capillary transport capacity and a wide range of possible control of transcapillary diffusion in the coronary microcirculation.

Transcapillary exchange in the working left ventricle of the dog.

Sets of multiple indicator dilution curves were obtained from working hearts of dogs with closed chests. A multiple capillary adaptation of a permeability-limited capillary model which assumes that exchanging material returns to the capillary at its site of escape was tested on these curves. The model has only two lumped parameters: a permeability surface product per accessible extravascular volume, and flow per extravascular volume. Labeled red cells and albumin were used as vascular indicators. The model provided close fits for the curves of diffusion-limited indicators (sucrose, inulin, sulfate, sodium, chloride, and urea), and unique values were obtained for both parameters. The accessible extravascular volume obtained by this method was independent of flow whereas the permeability surface product per accessible extravascular volume (a relatively low value for these indicators) increased with flow. In this first group the outflow patterns varied with the size of the test molecule. For a second group of substances (water, ethanol and antipyrine), the outflow patterns were virtually identical and independent of molecular size (i.e., flow-limited). The modeling did not provide an appropriate description of these curves, and analysis indicated that the exchanging indicator may intercommunicate between capillaries in a random fashion, i.e., that the indicator may not return to each capillary at the same site at which it escaped.

Kinetics of rubidium uptake in the working dog heart.

More than 50% of tracer rubidium entering the coronary circulation is actively taken up by the heart muscle cells during a single passage. Rubidium ions must traverse the capillary wall, the interstitial space, and the muscle cell membrane to enter the very large potential rubidium pool within the cells. The aim of this investigation was to determine which, if any, of these steps are rate limiting. The anterior descending branch of the left common coronary artery was perfused at its origin. Pulse injections containing 86 Rb + , 22 Na + or 14 C-sucrose, and 125 I-albumin were made into the perfusion line and timed serial samples of coronary sinus blood were collected and analyzed. A model was designed which incorporates rate constants describing both the exchange of 80 Rb + at the capillary wall and its entry at the muscle cell membrane. Labeled sucrose or 22 Na + was used to determine flow per interstitial fluid volume, a parameter necessary for the application of the model. It was assumed that the interstitial fluid volume available for labeled sucrose or 22 Na + was identical to that available for 86 Rb + . The rate constant describing exchange at the capillary wall (the permeability surface product per unit accessible interstitial fluid volume) increased with perfusion, whereas that for uptake by the myocardial cells was relatively constant and independent of flow.

The influence of elevated venous pressure on blood-tissue exchange of 22Na in perfused hindlimbs of dogs.

In order to study the effect of the increase in venous pressure on the exchange of Na ion between the blood and tissue, the hindlimb of dog was perfused under the condition of constant venous outflow to measure the diffusion capacity (PS, the permeability-surface product) for 22Na, using 'indicator diffusion' method (with RISA or Evans blue as indicators and 22NaCl as test substance). As the results, the following findings were obtained; 1) The values of PS, resistance to blood flow, the recovery of indicator sub-stance and outflow-inflow ratio were found reproducible, with coefficient of variation of ±13%, ±16%, ±10%, and ±5%, respectively, in 3 determinations repeated in one and the same dog with normal venous pressure. 2) PS was reduced when the venous pressure was elevated to 200mmH2O. PS was decreased by about 40% in those hindlimbs where venous congestion was produced with relatively fixed outflow-inflow ratio and indicator recovery fixed at normal levels, namely, a circumstance where the same capillary bed is thought to be subjected to isotope studies in the control state as well as during venous congestion. A comparable decrease in PS occurred even in case of venous congestion associated with a decrease in indicator recovery. 3) Resistance to blood flow was not influenced by venous congestion. 4) In view of these results, it is nearly certain that PS is reduced during venous congestion. It is suggested that the venous congestion leads to a closure of precapillary sphincters, with associated re-distribution of blood flow, in the areas of circulation subjected to a high venous pressure. It is probable that, while the blood flows mainly through nutrient capillaries with higher PS in the control state, the blood flow is re-distributed in favor of vessels with lower PS, such as throughfare channels, during venous congestion.

Fractional extraction and transcapillary exchange during continuous and instantaneous tracer administration.

The relation between extraction fraction, E, measured by the multiple-tracer, instantaneous intra-arterial injection method and by single-tracer, continuous injection was studied by experiments on gastric wall, liver, and skeletal muscle of anesthetized dogs. E was calculated from ratios of diffusible to nondiffusible tracer concentrations in successive samples of venous blood. Initial extraction, E(0), was the same by instantaneous or continuous injection. E diminished with time due to back-diffusion. In liver, E(0) for water- 3 H, mannitol- 3 H, and glucose- 3 H remained close to unity, indicating that transcapillary transport was flow-limited. E(0) for 22 Na, 36 Cl, and mannitol- 3 H in gastric wall, and for 22 Na and 86 Rb in skeletal muscle were less than unity and decreased with increasing blood flow, indicating diffusion limitation. E for 86 Rb in skeletal muscle eventually reached a plateau level, due to the large "sink" for 86 Rb in cell K. Both E(0) and plateau E for 86 Rb in muscle increased during exercise. Permeability surface products PS were calculated from measured E's and blood flows, Q, by the relation PS = -Q ln (1 - E). Their values suggest that E(0) reflects relative capillary permeabilities to different tracers, but only for capillaries of fastest arteriovenous transit. Plateau E's, such as for 86 Rb in skeletal muscle, represent all the capillaries, but are influenced also by extracapillary barriers.

POTASSIUM, SODIUM, AND IODIDE TRANSCAPILLARY EXCHANGE IN THE DOG HEART.

Simultaneous first-passage dilution curves of the electrolytes were performed in the blood-perfused isolated dog heart. Quantification of transcapillary exchange was accomplished by means of the parameters "fractional extraction" from the blood, E, and "fractional turnover rate of exchange" of the interstitial compartment with the blood, k. The results show that E for Rb86+ and K42+ is 0.69 ± 0.08, for Na22+ 0.74 ± 0.12, and for I131– 0.54 ± 0.03. The values of k for Na22+ ranged between 0.11 and 3.00 min–1 and for I131 between 0.76 and 3.54. The k's varied with the blood flow but apparently the E's did not. There was a high linear correlation between the plasma clearance of the ions and the flow. From the data the heart interstitial fluid volume was calculated as 0.15 ± 0.04 ml/g. In some experiments various ions were studied simultaneously and the E's used to compute permeability-surface products, PS. The PS ratios for sodium and potassium were not significantly different from the ratio of free diffusion in water constants.