J. Physiol. (1975), 249, pp. 591-600 With 1 text-figure Printed in Great Britain
591
TRANSPORT OF DEUTERIUM OXIDE ACROSS ISOLATED RAT SMALL INTESTINE
By R. J. BYWATER,* R. B. FISHER AND M. L. G. GARDNERt From the Department of Biochemistry, University of Edinburgh Medical School, Teviot Place, Edinburgh, EH8 9A0 and the Department of Veterinary Pharmacology, Royal (Dick) School of Veterinary Studies, University of Edinburgh, Summerhall Square, Edinburgh EH9 1QH
(Received 24 December 1974) SUMMARY
1. Transport of deuterium oxide from a luminal perfusate containing 1% D20 was studied in Fisher & Gardner's (1974) isolated preparation of perfused rat small intestine. 2. The kinetics of appearance of D20 in the intestinal secretion at the serosal surface fitted well to a single exponential function. 3. The steady-state concentration of D20 in this secretion was not significantly different from the concentration in the luminal perfusate. 4. The total tissue water contained D20 at a concentration, on average, 5 % lower than that in the luminal perfusate. 5. There is no evidence to suggest discrimination in transport across the intestinal mucosa between H20 and D20. 6. The kinetics of wash-in of D20 to intestinal secretion show that the ratio of flux out of the lumen to reflux back to the lumen is 1-38: 1. INTRODUCTION
Many authors have used deuterium and tritium oxides as tracers in measurements of the unidirectional flux rates of water across the intestinal mucosa. These studies involve the tacit assumption that there is no isotope effect: i.e. that the tracer and water are absorbed at equal rates by the intestine. * Present address: Beecham Pharmaceuticals, Research Division, Walton Oakes, Tadworth, Surrey. t Correspondence to: Dr M. L. G. Gardner, Department of Biochemistry. The University of Edinburgh Medical School, Teviot Place, Edinburgh, EH8 9AG.
592 R. J. BYWATER, R. B. FISHER AND M. L. G. GARDNER The evidence in the literature concerning the transport rates of deuterated and tritiated water into cells is not clear. Hevesy, Hofer & Krogh (1935) found that water crossed frog skin more rapidly than deuterium oxide did. Parpart (1935) and Brooks (1935) both noted that haemolysis of erythrocytes occurred more slowly in deuterium oxide than in water: observations on the rate of uptake of deuterium oxide into protozoa also suggested that the rate of penetration of deuterium oxide might be less than that of water (Kitching & Padfield, 1960). On the other hand, the rate of penetration of deuterium oxide into sea-urchin eggs (Lucke & Harvey, 1934) and into giant amoeba (Lovtrup & Pigon, 1951) could not be differentiated from that of water. The rates of transport of deuterated and tritiated water have been compared in several preparations, and have either been found to be indistinguishable (Chinard & Enns, 1954; Takashina, Lazzara, Cronvich & Burch, 1962; King, 1969) or the differences seen have been attributed to experimental artifacts (Elford, 1970). This has been taken as indirect evidence for the validity of studies using these isotopic tracers (King, 1969). Barnes (1939) and Lindley, Hoshiko & Leb (1964) observed that exposure of frog skin to saline solutions in deuterated water lowered the potential difference across the skin with respect to controls with aqueous salines. Brooks (1937) suggested that D20 behaved as though it were 'hyperosmotic' with respect to water. Many of these studies involved high concentrations of D20 and shed little light on the behaviour when tracer concentrations (e.g. 1 %) are used. We have used the in vitro intestinal absorption technique of Fisher & Gardner (1974) to test the validity of the crucial assumption that water and D20 are transported at the same rate. In this method, the lumen of an isolated segment of rat small intestine is perfused in a single pass with a segmented flow consisting of slugs of liquid separated by bubbles of oxygen. The water and solutes transported across the mucosa pass into the sub-mucosal tissue fluid, exude from the torn blood vessels and lymphatics, and drip off from the serosal surface of the organ as 'intestinal secretion'. As we show below the kinetic analysis used by Fisher & Gardner to describe the time course of appearance of glucose in this intestinal secretion can be simply extended to describe the time courses for substances, such as deuterium oxide, which can move in two directions across the mucosa. The wash-in of such a solute to the secretion can be predicted to conform to a single-exponential model; the rate constant is a function of the tissue fluid volume and the ratio of two unidirectional flux rates. In practice we find close adherence to this single-exponential model, and we have been able to relate the steady-state concentration of deuterium oxide in the secretion to the concentration in the luminal perfusate. Thus we have
593 TRANSPORT OF DEUTERIUM OXIDE tested whether the tracer is absorbed at the same net rate as water. Further, the estimated rate constant can give an estimate of the ratio of the two unidirectional fluxes across the mucosa. A preliminary account of this work has been reported to the Physiological Society (Bywater, Fisher & Gardner, 1972). THEORY
Theoretical kinetics of the transport of deuterium oxide Consider the time course of transport of tracer from the lumen of the intestine, across the epithelium and the subepithelial space, and on to the serosal surface via the torn lymphatics and blood vessels. Suppose that tracer and water may be differentially absorbed, so that the concentration of deuterium oxide in the fluid entering the mucosa from the lumen may be different from its concentration in the lumen; similarly that the concentration of tracer in the fluid refluxing from the extracellular fluid back into the lumen may not be equal to that in the extracellular fluid. Let P be the concentration of tracer in the lumen, C be the concentration of tracer in the extracellular fluid, and hence in the secretion, i be the rate of unidirectional flux of water out of the lumen, e be the rate of unidirectional flux of water back into the lumen, s be the net rate of water secretion on to the serosal surface, V be the volume (supposed constant) of extracellular fluid with which the secretion mixes, r be the ratio (assumed constant) of mucosal to serosal water flux rate, to the net flux rate, i.e. r = i/s. tracer concentration in fluid leaving lumen tracer concentration in lumen tracer concentration in fluid refluxing into lumen b tracer concentration in extracellular fluid (i.e. a and b are 'isotopic fractionation' factors for efflux and reflux, respectively). Since V remains constant, then i = e+s, but r = i/s, so e = (r-1).s. 22
P HYo 249
594 R. J. BYWATER, R. B. FISHER AND M. L. G. GARDNER When infinitesimal changes di, de, and ds occur in i, e, and s respectively, then the corresponding change, dc, in C is given by V.dC = a.P.di-b.C.de-C.ds. So, dC d b.(r-l)+1 ds. (1) a.P.r V
b.(r-1)+1 Integration yields an exponential function of the form C = B+A.e-kv (2) where B. A, and k are constants B- a. P. r (3) b. (r -1) +1 A Co -B where CO is the value of C when v = 0 (4) k b.(r-1)+1 V and v is the cumulated volume of secretion collected. The asymptote, B, is the value of C at the steady state, i.e. when v is infinite. If there were no isotope effect, then a=b=1 and so, B = P, i.e. the steady-state concentration of tracer in the secretion would equal the concentration in the lumen. If, however, there is an isotope effect, then either or both a and b will differ from unity, and consequently, the steady-state concentration in the secretion, B, will not equal the concentration in the lumen, P. A function of the form in eqn. (2) can be fitted to experimental measurements of C and v by procedures such as that of Atkins (1971), and best-fit values obtained for B, A, and k. If the two fractionation factors, a and b, are equal, then eqns. (3) and (4) can be solved. Then, a = b =1-V.k.(1-B/P) (5) and r r pB.(I-b) (6) P.b. (1- BP)(6 If there is no isotope effect a = b = 1 and r = k.V therefore, since i r e
r-1
(7)
595 TRANSPORT OF DEUTERIUM OXIDE the ratio of the two unidirectional flux rates can be estimated from these measurements. An estimate of V is already available from the kinetics of wash-in and wash-out of glucose, protein and total nitrogen into intestinal secretion (Table 4 of Fisher & Gardner, 1974). Eqn. (2) is identical in form to that derived by Fisher & Gardner (1974) to represent the kinetics of, e.g. glucose, in intestinal secretion. The values of B and k (eqns. (3) and (4)) have however been modified by terms in r to take into account the back-flux of fluid into the lumen, and by terms in a and b to allow for possible isotope effects. METHODS A segment, about 80 cm long, of small intestine from a female rat under ether anaesthesia was set up according to the procedure of Fisher & Gardner (1974). The lumen was perfused with the bicarbonate saline medium containing glucose (5 mg/ ml., 28 mM) used by Fisher & Gardner. The 95 °02: 5 % CO2 in the segmented flow and which passed over the serosal surface of the intestinal segment was equilibrated with 1 % deuterium oxide in water vapour (note: this precaution is critical). Five minutes after the intestinal segment had been connected to the perfusion apparatus, the perfusate was replaced by a similar one but which also contained deuterium oxide (1 ml. deuterium oxide supplied by Koch-Light, Ltd. per 100 ml. perfusate). After a 5 min preperiod to allow the luminal conditions to stabilize, serial collections of the secretion which dripped from the serosal surface of the intestine were made over 2 min. periods. The samples of secretion were immediately weighed, diluted with distilled water (0.5 ml.) and covered with Parafilm. They were centrifuged, and their deuterium oxide concentrations estimated by the method of Turner, Neely & Hardy (1960) but without prior distillation. The extinctions at 3 98 /LM were measured on duplicate samples in a Perkin-Elmer Model 257 double beam infra-red spectrophotometer with 'Unipak' 0-1 mm path-length calcium fluoride cells (Ross Scientific Co., Hornchurch, Essex). The reference cell contained distilled water and, to minimize thermal drift, this cell was removed from the spectrophotometer when a measurement was not actually being made. The concentration of deuterium oxide in the luminal perfusate was also estimated as a mean of about six measurements for each experiment. The concentrations in these samples were calculated from the first-order regression of extinction on concentrations for standard solutions containing 0-2, 0.4, 0-6, and 0-8 % w/v deuterium oxide respectively. The digital computer programme of Atkins (1971) was used to fit an exponential function of the following form to the experimental results C = B+A.e-kv, where C is the concentration of tracer in a sample of secretion, v is the cumulated volume of secretion (expressed per unit length of intestine) collected up to the midpoint of the collection, and B, A, and k are constants. As shown in the theoretical section above, the constant term B represents the asymptotic concentration of tracer in the secretion at the steady state. If there were no isotope effect, then this concentration would be indistinguishable from the concentration of deuterium oxide in the lumen perfusate. Atkins' programme was run on the I.B.M. 360150 computer at the Edinburgh Regional Computing Centre. 22-2
596 R. J. BYWATER, R1. B. FISHER AND M. L. G. GARDNER In three experiments the intestinal water was separated by heating the whole intestine, after perfusion, in boiling toluene (40 ml. AnalaR toluene) in a Dean & Stark apparatus in which the mixture of toluene and water vapours is condensed on a reflux condenser in such a way that the water collects in a side-tube (Dean & Stark, 1920). Excellent recovery was achieved of deuterium oxide added to control intestines. RESULTS
Best-fit values for the parameters B, A, and k are given in Table 1 together with respective values of the tracer concentration (P) in the lumen perfusate for ten experiments. Also shown are the ratios, BIP, of the computed steady-state concentration in the secretion, B, to the perfusate concentration, P. T-tests show that (P-B) is not significantly different from zero (t = 0.4), and that B/P is not significantly different from unity (P > 0.7). This indicates that no deuterium isotope effect was detectable. TABLE 1. Kinetics of appearance of deuterium oxide in intestinal secretion. B, A, and k are the best-fit parameters in the function: e = B + A e-" C is the deuterium oxide concentration in secretion (% w/v). v is the cumulated volume of secretion (#L./cm). P is the perfusate concentration of deuterium oxide (% w/v). B is the asymptotic concentration of deuterium oxide,
computed for the steady-state. P 1-038 1-072 1-059 1-068 1-057 1-057 1-063 1-074 1-082 1-082
A B B/P -1-138 1-103 1-0618 1-049 0-9784 -1-371 1-078 1-0181 -1-061 1-028 0-9626 -0-894 0-9711 -0-969 1-026 1-045 0-9889 -1-074 1-053 0-9906 -0-959 0-931 0-8664 -1-089 1-161 1-0736 -1-199 1-104 1-0203 -1-113 Mean 0-9932 s.E. of mean ±0-01834 0-082 *it Each line refers to a separate experiment. *
k 0-0934 0-1772 0-0918 0-1133 0-0979 0-1073 0-1092 0-2033 0-1460 0-1350
t test for difference in B/P from unity.
In all cases the exponential model fitted the experimental data well, as shown by an analysis of the residuals at each data point. Over the 11 experiments the mean residuals calculated for each data point did not differ significantly from zero. Fig. 1 shows semilogarithmic plots of loge (C -B)
TRANSPORT OF DEUTERIUM OXIDE
597
0
A'o
-10
.-' s
-2 0
'- -3 0 oo
" 0%
-4-0~~~~~~~~-40 . ". -50 .-. ,
0
I
I
I
*
I3
50 10 20 30 40 60 Cumulated volume of secretion (pi./cm)
Fig. 1. Semilogarithmic plots for the wash-in of deuterium oxide into intestinal secretion in two typical experiments. C is the concentration of D20 in each sample of secretion and B is the computed asymptote for the steady-state concentration of D20 in secretion.
against v for two typical experiments. The straight line, as predicted from the model, is clearly a good fit to the experimental data. In three experiments the entire water in the segment of intesine after at least 30 min of perfusion with the perfusate containing the deuterium oxide was removed in the Dean & Stark apparatus (see Methods section). The concentrations of the tracer in the aqueous phase of each distillate and in each luminal perfusate were determined in triplicate. Their values are shown in Table 2. In each case the over-all concentration of D20 in the water from the tissue was significantly less than the concentration in the perfusate. TABLE 2. Deuterium oxide concentrations in luminal perfusate and Dean & Stark distillates of perfused intestine. Each value is a mean + s.E. of mean of three
determinations
D20 concentrations (% w/v) Experiment 1 2 3
Perfusate P 1-104 + 0-0036
1-107 + 0-0022 1-104 + 0-0010
Tissue water T 1-061 + 0.0 1-071+ 0-0 1-021 + 0-0022
10o P-T P
3-96
3-22 7-52
Mean 4O90
598
R. J. BYWATER, R. B. FISHER AND M. L. G. GARDNER DISCUSSION
The above results show that, under our experimental conditions, the steady-state concentration of deuterium oxide in the tissue fluid does not differ significantly from the concentration of deuterium oxide in the luminal perfusate. But it has been suggested that, despite this, there could be a discrimination in the transport of H20 and D20 across cells which would not be detected by our techniques. Suppose that it were more difficult to transport deuterium oxide than water out of mucosal cells. Then deuterium oxide entering cells freely would accumulate within them. Provided that the transport rate of D20 out of the cells increased with the rise in intracellular concentration, a steady state would be reached sooner or later in which the rate of transport of D20 out of the cells would equal the transport rate into them, and in this state no discrimination between H20 and D20 would be apparent externally. If such a steady state were achieved rapidly then the lag in attainment of it would not be detectable. It was for this reason that the tissue water concentrations of deuterium oxide were measured at the end of some experiments. A concealed discrimination between D20 and H20 should cause the tissue 1D20:H20 ratio to be higher than that in the perfusate. However the observed tissue D20 concentration is lower than the perfusate D20 concentration (Table 2). But the water in the tissue is distributed between mucosal cells, other structures such as nerve and muscle cells and connective tissue, and the extracellular fluid. Interpretation of the results requires consideration of
these compartments. The total water content of the rat small intestine is about 50 jttl./cm (Fisher & Gardner, 1974). An upper limit to the mucosal cell water content can be estimated from the mean mucosal surface area of 6-3cm2 per cm length (Fisher & Parsons, 1950) and from the thickness of the mucosal layer in perfused intestine which can be estimated from P1. 1 of Fisher & Parsons (1949) to be about 0-04 cm. Taking into account the tapering form of mucosal cells this suggests that the total volume of the mucosa may be 20 j/l./cm length and that its intracellular water content would be in the region of 15 /dl./cm. Since Fisher & Gardner (1974) have shown that the volume of readily exchangeable tissue fluid is 30 p1./cm the remainder of the water in the intestinal tissue, in the muscle cells, nerve cells and connective tissue would amount to about 5 /,tl./cm. If 1)20 failed entirely to penetrate into this 5 jul./cm which is improbable, the steady-state tissue concentration of deuterium oxide would be 10 % less than that in the perfusate. In the experiments shown in Table 2 the D20 concentration is on average 95 % of that in the corresponding per-
TRANSPORT OF DEUTERIUM OXIDE 599 fusate. On the extreme assumption that D20 was excluded from all muscle, nerve and connective tissue this would correspond to a mucosal D20 concentration 15-20 % in excess of the perfusate concentration. But if, as is more reasonable, D20 had penetrated into some part of this 5 1u., then the estimated excess in the mucosal water would fall sharply: a D20 concentration in this 5 1Id. compartment which was half that in the perfusate would correspond to a concentration in the mucosal cells equal to that in the perfusate. There is therefore no substantial backing for any suggestion that the intestinal mucosa transports D20 and H20 at different rates. This is in agreement with the indirect evidence provided by others for other tissues (Takashina et al. 1962; Chinard & Enns, 1964; King, 1969). However the absence of any detectable isotope effect must not be interpreted as evidence against active transport of water. These experiments shed no light on the mechanism of water transport. The kinetic analysis developed above shows that the rate constant for the appearance of tracer on the serosal surface may be used to calculate each unidirectional flux. The ratio of the flux from lumen to tissue fluid to that from tissue fluid to the lumen is 1-38 + 0 040 (10). This value compares favourably with that of P 30 + 0 09 (7) which can be calculated from Berger, Pecikyan & Kanzaki's (1970) data obtained from rat jejunum in vitro. Such a kinetic analysis is however only valid when the unidirectional fluxes remain constant over the duration of the wash-in of tracer into the intestinal secretion. When the sodium salts in the perfusate are replaced by choline salts the concentration of sodium ions in the intestinal secretion falls slowly (Text-fig. 15 of Fisher & Gardner, 1974). The kinetics appear to conform to the single-exponential model, and the apparent ratio of the unidirectional fluxes is (Fisher & Gardner, 1974) Mucosal to serosal flux =1_56. Serosal to mucosal fluxThis value agrees reasonably with other values in the literature (e.g. 1-4 for rat ileum, Curran & Solomon (1957)). We are indebted to the Medical Research Council and to the Moray Fund of the University of Edinburgh for grants. We also thank Miss Elizabeth Middleton for technical help, Dr G. L. Atkins for assistance with curve fitting and Dr C. R. House for valuable advice.
600 R. J. BYWATER, R. B. FISHER AND M. L. G. GARDNER REFERENCES ATKINS, G. L. (1971). A versatile digital computer program for non-linear regression analysis. Biochim. biophys. Acta 252, 405-420. BARNES, T. C. (1939). The influence of heavy water and temperature on the electrical potential of frog skin. J. cell. comp. Physiol. 13, 39-50. BERGER, E. Y., PEcIKYAN, R. & KANZAKI, G. (1970). Water flux across the rat jejunum and ileum. J. apple. Physiol. 29, 130-132. BROOKS, S. C. (1935). The permeability of erythrocytes to deuterium oxide (heavy
water). J. cell. comp. Physiol. 7, 163-171. BROOKS, S. C. (1937). Osmotic effects of deuterium oxide (heavy water) on living cells. Science, N.Y. 86, 497-498. BYWATER, R. J., FIsHER, R. B. & GARDNER, M. L. G. (1972). Deuterium oxide as a water flux tracer in rat small intestine. J. Physiol. 227, 55-56P. CHINARD, F. P. & ENNS, T. (1954). Relative rates of passage of deuterium and tritium oxides across capillary walls in the dog. Am. J. Physiol. 178, 203-205. CURlAN, P. F. & SOLOMON, A. K. (1957). Ion and water fluxes in the ileum of rats. J. gen. Physiol. 41, 143-168. DEAN, E. W. & STARK, D. D. (1920). A convenient method for the determination of water in petroleum and other organic emulsions. J. ind. Engng Chem. 12, 486-490. ELFORD, B. C. (1970). Permeation and distribution of deuterated and tritiated water in smooth and striated muscle. J. Physiol. 211, 73-92. FismER, R. B. & GARDNER, M. L. G. (1974). A kinetic approach to the study of absorption of solutes by isolated perfused small intestine. J. Physiol. 241, 211-234. FISHER, R. B. & PARSONS, D. S. (1949). A preparation of surviving rat small intestine for the study of absorption. J. Physiol. 110, 36-46. FISHER, R. B. & PARsONS, D. S. (1950). The gradient of mucosal surface area in the small intestine of the rat. J. Anat. 84, 272-282. HEvEsY, G. V., HOFER, E. & KROGH, A. (1935). The permeability of the skin of frogs to water as determined by D20 and H20. Skand. Arch. Physiol. 72, 199-214. KING, V. (1969). A study of the mechanism of water transfer across frog skin by a comparison of the permeability of the skin to deuterated and tritiated water. J. Physiol. 200, 529-538. KITCHING, J. A. & PADFIELD, J. E. (1960). The physiology of contractile vacuoles. XI. Effects of heavy water on the water balance of a suctorian. J. exp. Biol. 37, 73-82. LINDLEY, B. D., HosHImo, T. & LEB, D. E. B. (1964). Effects of D20 and osmotic gradients on potential and resistance of the isolated frog skin. J. yen. Physiol. 47, 773-793. LovTRuP, S. & PIG6N, A. (1951). Diffusion and active transport of water in the amoeba Chaos chaos L. C. r. Trav. Lab. Carlsbery (ser. chim.) 28, 1-36. LUCKE', R. & HARvEY, E. N. (1934). The permeability of living cells to heavy water (deuterium oxide). J. cell. comp. Physiol. 5, 473-482. PARPART, A. K. (1 935). The permeability of the mammalian erythrocyte to deuterium oxide (heavy water). J. cell. comp. Physiol. 7, 153-162. TAKASHINA, T., LAzzARA, R., CRONvIcH, J. A. & BURCH, G. E. (1962). Studies of rates of transfer of D20, H3*, Cl36, Na22, and Mg28 across the isolated pericardium of dogs. J. Lab. clin. Med. 60, 662-668. TURNER, M. D., NEELY, W. A. & HARDY, J. D. (1960). Rapid determination of deuterium oxide in biological fluids. J. appl. Physiol. 15, 309-310.
591
TRANSPORT OF DEUTERIUM OXIDE ACROSS ISOLATED RAT SMALL INTESTINE
By R. J. BYWATER,* R. B. FISHER AND M. L. G. GARDNERt From the Department of Biochemistry, University of Edinburgh Medical School, Teviot Place, Edinburgh, EH8 9A0 and the Department of Veterinary Pharmacology, Royal (Dick) School of Veterinary Studies, University of Edinburgh, Summerhall Square, Edinburgh EH9 1QH
(Received 24 December 1974) SUMMARY
1. Transport of deuterium oxide from a luminal perfusate containing 1% D20 was studied in Fisher & Gardner's (1974) isolated preparation of perfused rat small intestine. 2. The kinetics of appearance of D20 in the intestinal secretion at the serosal surface fitted well to a single exponential function. 3. The steady-state concentration of D20 in this secretion was not significantly different from the concentration in the luminal perfusate. 4. The total tissue water contained D20 at a concentration, on average, 5 % lower than that in the luminal perfusate. 5. There is no evidence to suggest discrimination in transport across the intestinal mucosa between H20 and D20. 6. The kinetics of wash-in of D20 to intestinal secretion show that the ratio of flux out of the lumen to reflux back to the lumen is 1-38: 1. INTRODUCTION
Many authors have used deuterium and tritium oxides as tracers in measurements of the unidirectional flux rates of water across the intestinal mucosa. These studies involve the tacit assumption that there is no isotope effect: i.e. that the tracer and water are absorbed at equal rates by the intestine. * Present address: Beecham Pharmaceuticals, Research Division, Walton Oakes, Tadworth, Surrey. t Correspondence to: Dr M. L. G. Gardner, Department of Biochemistry. The University of Edinburgh Medical School, Teviot Place, Edinburgh, EH8 9AG.
592 R. J. BYWATER, R. B. FISHER AND M. L. G. GARDNER The evidence in the literature concerning the transport rates of deuterated and tritiated water into cells is not clear. Hevesy, Hofer & Krogh (1935) found that water crossed frog skin more rapidly than deuterium oxide did. Parpart (1935) and Brooks (1935) both noted that haemolysis of erythrocytes occurred more slowly in deuterium oxide than in water: observations on the rate of uptake of deuterium oxide into protozoa also suggested that the rate of penetration of deuterium oxide might be less than that of water (Kitching & Padfield, 1960). On the other hand, the rate of penetration of deuterium oxide into sea-urchin eggs (Lucke & Harvey, 1934) and into giant amoeba (Lovtrup & Pigon, 1951) could not be differentiated from that of water. The rates of transport of deuterated and tritiated water have been compared in several preparations, and have either been found to be indistinguishable (Chinard & Enns, 1954; Takashina, Lazzara, Cronvich & Burch, 1962; King, 1969) or the differences seen have been attributed to experimental artifacts (Elford, 1970). This has been taken as indirect evidence for the validity of studies using these isotopic tracers (King, 1969). Barnes (1939) and Lindley, Hoshiko & Leb (1964) observed that exposure of frog skin to saline solutions in deuterated water lowered the potential difference across the skin with respect to controls with aqueous salines. Brooks (1937) suggested that D20 behaved as though it were 'hyperosmotic' with respect to water. Many of these studies involved high concentrations of D20 and shed little light on the behaviour when tracer concentrations (e.g. 1 %) are used. We have used the in vitro intestinal absorption technique of Fisher & Gardner (1974) to test the validity of the crucial assumption that water and D20 are transported at the same rate. In this method, the lumen of an isolated segment of rat small intestine is perfused in a single pass with a segmented flow consisting of slugs of liquid separated by bubbles of oxygen. The water and solutes transported across the mucosa pass into the sub-mucosal tissue fluid, exude from the torn blood vessels and lymphatics, and drip off from the serosal surface of the organ as 'intestinal secretion'. As we show below the kinetic analysis used by Fisher & Gardner to describe the time course of appearance of glucose in this intestinal secretion can be simply extended to describe the time courses for substances, such as deuterium oxide, which can move in two directions across the mucosa. The wash-in of such a solute to the secretion can be predicted to conform to a single-exponential model; the rate constant is a function of the tissue fluid volume and the ratio of two unidirectional flux rates. In practice we find close adherence to this single-exponential model, and we have been able to relate the steady-state concentration of deuterium oxide in the secretion to the concentration in the luminal perfusate. Thus we have
593 TRANSPORT OF DEUTERIUM OXIDE tested whether the tracer is absorbed at the same net rate as water. Further, the estimated rate constant can give an estimate of the ratio of the two unidirectional fluxes across the mucosa. A preliminary account of this work has been reported to the Physiological Society (Bywater, Fisher & Gardner, 1972). THEORY
Theoretical kinetics of the transport of deuterium oxide Consider the time course of transport of tracer from the lumen of the intestine, across the epithelium and the subepithelial space, and on to the serosal surface via the torn lymphatics and blood vessels. Suppose that tracer and water may be differentially absorbed, so that the concentration of deuterium oxide in the fluid entering the mucosa from the lumen may be different from its concentration in the lumen; similarly that the concentration of tracer in the fluid refluxing from the extracellular fluid back into the lumen may not be equal to that in the extracellular fluid. Let P be the concentration of tracer in the lumen, C be the concentration of tracer in the extracellular fluid, and hence in the secretion, i be the rate of unidirectional flux of water out of the lumen, e be the rate of unidirectional flux of water back into the lumen, s be the net rate of water secretion on to the serosal surface, V be the volume (supposed constant) of extracellular fluid with which the secretion mixes, r be the ratio (assumed constant) of mucosal to serosal water flux rate, to the net flux rate, i.e. r = i/s. tracer concentration in fluid leaving lumen tracer concentration in lumen tracer concentration in fluid refluxing into lumen b tracer concentration in extracellular fluid (i.e. a and b are 'isotopic fractionation' factors for efflux and reflux, respectively). Since V remains constant, then i = e+s, but r = i/s, so e = (r-1).s. 22
P HYo 249
594 R. J. BYWATER, R. B. FISHER AND M. L. G. GARDNER When infinitesimal changes di, de, and ds occur in i, e, and s respectively, then the corresponding change, dc, in C is given by V.dC = a.P.di-b.C.de-C.ds. So, dC d b.(r-l)+1 ds. (1) a.P.r V
b.(r-1)+1 Integration yields an exponential function of the form C = B+A.e-kv (2) where B. A, and k are constants B- a. P. r (3) b. (r -1) +1 A Co -B where CO is the value of C when v = 0 (4) k b.(r-1)+1 V and v is the cumulated volume of secretion collected. The asymptote, B, is the value of C at the steady state, i.e. when v is infinite. If there were no isotope effect, then a=b=1 and so, B = P, i.e. the steady-state concentration of tracer in the secretion would equal the concentration in the lumen. If, however, there is an isotope effect, then either or both a and b will differ from unity, and consequently, the steady-state concentration in the secretion, B, will not equal the concentration in the lumen, P. A function of the form in eqn. (2) can be fitted to experimental measurements of C and v by procedures such as that of Atkins (1971), and best-fit values obtained for B, A, and k. If the two fractionation factors, a and b, are equal, then eqns. (3) and (4) can be solved. Then, a = b =1-V.k.(1-B/P) (5) and r r pB.(I-b) (6) P.b. (1- BP)(6 If there is no isotope effect a = b = 1 and r = k.V therefore, since i r e
r-1
(7)
595 TRANSPORT OF DEUTERIUM OXIDE the ratio of the two unidirectional flux rates can be estimated from these measurements. An estimate of V is already available from the kinetics of wash-in and wash-out of glucose, protein and total nitrogen into intestinal secretion (Table 4 of Fisher & Gardner, 1974). Eqn. (2) is identical in form to that derived by Fisher & Gardner (1974) to represent the kinetics of, e.g. glucose, in intestinal secretion. The values of B and k (eqns. (3) and (4)) have however been modified by terms in r to take into account the back-flux of fluid into the lumen, and by terms in a and b to allow for possible isotope effects. METHODS A segment, about 80 cm long, of small intestine from a female rat under ether anaesthesia was set up according to the procedure of Fisher & Gardner (1974). The lumen was perfused with the bicarbonate saline medium containing glucose (5 mg/ ml., 28 mM) used by Fisher & Gardner. The 95 °02: 5 % CO2 in the segmented flow and which passed over the serosal surface of the intestinal segment was equilibrated with 1 % deuterium oxide in water vapour (note: this precaution is critical). Five minutes after the intestinal segment had been connected to the perfusion apparatus, the perfusate was replaced by a similar one but which also contained deuterium oxide (1 ml. deuterium oxide supplied by Koch-Light, Ltd. per 100 ml. perfusate). After a 5 min preperiod to allow the luminal conditions to stabilize, serial collections of the secretion which dripped from the serosal surface of the intestine were made over 2 min. periods. The samples of secretion were immediately weighed, diluted with distilled water (0.5 ml.) and covered with Parafilm. They were centrifuged, and their deuterium oxide concentrations estimated by the method of Turner, Neely & Hardy (1960) but without prior distillation. The extinctions at 3 98 /LM were measured on duplicate samples in a Perkin-Elmer Model 257 double beam infra-red spectrophotometer with 'Unipak' 0-1 mm path-length calcium fluoride cells (Ross Scientific Co., Hornchurch, Essex). The reference cell contained distilled water and, to minimize thermal drift, this cell was removed from the spectrophotometer when a measurement was not actually being made. The concentration of deuterium oxide in the luminal perfusate was also estimated as a mean of about six measurements for each experiment. The concentrations in these samples were calculated from the first-order regression of extinction on concentrations for standard solutions containing 0-2, 0.4, 0-6, and 0-8 % w/v deuterium oxide respectively. The digital computer programme of Atkins (1971) was used to fit an exponential function of the following form to the experimental results C = B+A.e-kv, where C is the concentration of tracer in a sample of secretion, v is the cumulated volume of secretion (expressed per unit length of intestine) collected up to the midpoint of the collection, and B, A, and k are constants. As shown in the theoretical section above, the constant term B represents the asymptotic concentration of tracer in the secretion at the steady state. If there were no isotope effect, then this concentration would be indistinguishable from the concentration of deuterium oxide in the lumen perfusate. Atkins' programme was run on the I.B.M. 360150 computer at the Edinburgh Regional Computing Centre. 22-2
596 R. J. BYWATER, R1. B. FISHER AND M. L. G. GARDNER In three experiments the intestinal water was separated by heating the whole intestine, after perfusion, in boiling toluene (40 ml. AnalaR toluene) in a Dean & Stark apparatus in which the mixture of toluene and water vapours is condensed on a reflux condenser in such a way that the water collects in a side-tube (Dean & Stark, 1920). Excellent recovery was achieved of deuterium oxide added to control intestines. RESULTS
Best-fit values for the parameters B, A, and k are given in Table 1 together with respective values of the tracer concentration (P) in the lumen perfusate for ten experiments. Also shown are the ratios, BIP, of the computed steady-state concentration in the secretion, B, to the perfusate concentration, P. T-tests show that (P-B) is not significantly different from zero (t = 0.4), and that B/P is not significantly different from unity (P > 0.7). This indicates that no deuterium isotope effect was detectable. TABLE 1. Kinetics of appearance of deuterium oxide in intestinal secretion. B, A, and k are the best-fit parameters in the function: e = B + A e-" C is the deuterium oxide concentration in secretion (% w/v). v is the cumulated volume of secretion (#L./cm). P is the perfusate concentration of deuterium oxide (% w/v). B is the asymptotic concentration of deuterium oxide,
computed for the steady-state. P 1-038 1-072 1-059 1-068 1-057 1-057 1-063 1-074 1-082 1-082
A B B/P -1-138 1-103 1-0618 1-049 0-9784 -1-371 1-078 1-0181 -1-061 1-028 0-9626 -0-894 0-9711 -0-969 1-026 1-045 0-9889 -1-074 1-053 0-9906 -0-959 0-931 0-8664 -1-089 1-161 1-0736 -1-199 1-104 1-0203 -1-113 Mean 0-9932 s.E. of mean ±0-01834 0-082 *it Each line refers to a separate experiment. *
k 0-0934 0-1772 0-0918 0-1133 0-0979 0-1073 0-1092 0-2033 0-1460 0-1350
t test for difference in B/P from unity.
In all cases the exponential model fitted the experimental data well, as shown by an analysis of the residuals at each data point. Over the 11 experiments the mean residuals calculated for each data point did not differ significantly from zero. Fig. 1 shows semilogarithmic plots of loge (C -B)
TRANSPORT OF DEUTERIUM OXIDE
597
0
A'o
-10
.-' s
-2 0
'- -3 0 oo
" 0%
-4-0~~~~~~~~-40 . ". -50 .-. ,
0
I
I
I
*
I3
50 10 20 30 40 60 Cumulated volume of secretion (pi./cm)
Fig. 1. Semilogarithmic plots for the wash-in of deuterium oxide into intestinal secretion in two typical experiments. C is the concentration of D20 in each sample of secretion and B is the computed asymptote for the steady-state concentration of D20 in secretion.
against v for two typical experiments. The straight line, as predicted from the model, is clearly a good fit to the experimental data. In three experiments the entire water in the segment of intesine after at least 30 min of perfusion with the perfusate containing the deuterium oxide was removed in the Dean & Stark apparatus (see Methods section). The concentrations of the tracer in the aqueous phase of each distillate and in each luminal perfusate were determined in triplicate. Their values are shown in Table 2. In each case the over-all concentration of D20 in the water from the tissue was significantly less than the concentration in the perfusate. TABLE 2. Deuterium oxide concentrations in luminal perfusate and Dean & Stark distillates of perfused intestine. Each value is a mean + s.E. of mean of three
determinations
D20 concentrations (% w/v) Experiment 1 2 3
Perfusate P 1-104 + 0-0036
1-107 + 0-0022 1-104 + 0-0010
Tissue water T 1-061 + 0.0 1-071+ 0-0 1-021 + 0-0022
10o P-T P
3-96
3-22 7-52
Mean 4O90
598
R. J. BYWATER, R. B. FISHER AND M. L. G. GARDNER DISCUSSION
The above results show that, under our experimental conditions, the steady-state concentration of deuterium oxide in the tissue fluid does not differ significantly from the concentration of deuterium oxide in the luminal perfusate. But it has been suggested that, despite this, there could be a discrimination in the transport of H20 and D20 across cells which would not be detected by our techniques. Suppose that it were more difficult to transport deuterium oxide than water out of mucosal cells. Then deuterium oxide entering cells freely would accumulate within them. Provided that the transport rate of D20 out of the cells increased with the rise in intracellular concentration, a steady state would be reached sooner or later in which the rate of transport of D20 out of the cells would equal the transport rate into them, and in this state no discrimination between H20 and D20 would be apparent externally. If such a steady state were achieved rapidly then the lag in attainment of it would not be detectable. It was for this reason that the tissue water concentrations of deuterium oxide were measured at the end of some experiments. A concealed discrimination between D20 and H20 should cause the tissue 1D20:H20 ratio to be higher than that in the perfusate. However the observed tissue D20 concentration is lower than the perfusate D20 concentration (Table 2). But the water in the tissue is distributed between mucosal cells, other structures such as nerve and muscle cells and connective tissue, and the extracellular fluid. Interpretation of the results requires consideration of
these compartments. The total water content of the rat small intestine is about 50 jttl./cm (Fisher & Gardner, 1974). An upper limit to the mucosal cell water content can be estimated from the mean mucosal surface area of 6-3cm2 per cm length (Fisher & Parsons, 1950) and from the thickness of the mucosal layer in perfused intestine which can be estimated from P1. 1 of Fisher & Parsons (1949) to be about 0-04 cm. Taking into account the tapering form of mucosal cells this suggests that the total volume of the mucosa may be 20 j/l./cm length and that its intracellular water content would be in the region of 15 /dl./cm. Since Fisher & Gardner (1974) have shown that the volume of readily exchangeable tissue fluid is 30 p1./cm the remainder of the water in the intestinal tissue, in the muscle cells, nerve cells and connective tissue would amount to about 5 /,tl./cm. If 1)20 failed entirely to penetrate into this 5 jul./cm which is improbable, the steady-state tissue concentration of deuterium oxide would be 10 % less than that in the perfusate. In the experiments shown in Table 2 the D20 concentration is on average 95 % of that in the corresponding per-
TRANSPORT OF DEUTERIUM OXIDE 599 fusate. On the extreme assumption that D20 was excluded from all muscle, nerve and connective tissue this would correspond to a mucosal D20 concentration 15-20 % in excess of the perfusate concentration. But if, as is more reasonable, D20 had penetrated into some part of this 5 1u., then the estimated excess in the mucosal water would fall sharply: a D20 concentration in this 5 1Id. compartment which was half that in the perfusate would correspond to a concentration in the mucosal cells equal to that in the perfusate. There is therefore no substantial backing for any suggestion that the intestinal mucosa transports D20 and H20 at different rates. This is in agreement with the indirect evidence provided by others for other tissues (Takashina et al. 1962; Chinard & Enns, 1964; King, 1969). However the absence of any detectable isotope effect must not be interpreted as evidence against active transport of water. These experiments shed no light on the mechanism of water transport. The kinetic analysis developed above shows that the rate constant for the appearance of tracer on the serosal surface may be used to calculate each unidirectional flux. The ratio of the flux from lumen to tissue fluid to that from tissue fluid to the lumen is 1-38 + 0 040 (10). This value compares favourably with that of P 30 + 0 09 (7) which can be calculated from Berger, Pecikyan & Kanzaki's (1970) data obtained from rat jejunum in vitro. Such a kinetic analysis is however only valid when the unidirectional fluxes remain constant over the duration of the wash-in of tracer into the intestinal secretion. When the sodium salts in the perfusate are replaced by choline salts the concentration of sodium ions in the intestinal secretion falls slowly (Text-fig. 15 of Fisher & Gardner, 1974). The kinetics appear to conform to the single-exponential model, and the apparent ratio of the unidirectional fluxes is (Fisher & Gardner, 1974) Mucosal to serosal flux =1_56. Serosal to mucosal fluxThis value agrees reasonably with other values in the literature (e.g. 1-4 for rat ileum, Curran & Solomon (1957)). We are indebted to the Medical Research Council and to the Moray Fund of the University of Edinburgh for grants. We also thank Miss Elizabeth Middleton for technical help, Dr G. L. Atkins for assistance with curve fitting and Dr C. R. House for valuable advice.
600 R. J. BYWATER, R. B. FISHER AND M. L. G. GARDNER REFERENCES ATKINS, G. L. (1971). A versatile digital computer program for non-linear regression analysis. Biochim. biophys. Acta 252, 405-420. BARNES, T. C. (1939). The influence of heavy water and temperature on the electrical potential of frog skin. J. cell. comp. Physiol. 13, 39-50. BERGER, E. Y., PEcIKYAN, R. & KANZAKI, G. (1970). Water flux across the rat jejunum and ileum. J. apple. Physiol. 29, 130-132. BROOKS, S. C. (1935). The permeability of erythrocytes to deuterium oxide (heavy
water). J. cell. comp. Physiol. 7, 163-171. BROOKS, S. C. (1937). Osmotic effects of deuterium oxide (heavy water) on living cells. Science, N.Y. 86, 497-498. BYWATER, R. J., FIsHER, R. B. & GARDNER, M. L. G. (1972). Deuterium oxide as a water flux tracer in rat small intestine. J. Physiol. 227, 55-56P. CHINARD, F. P. & ENNS, T. (1954). Relative rates of passage of deuterium and tritium oxides across capillary walls in the dog. Am. J. Physiol. 178, 203-205. CURlAN, P. F. & SOLOMON, A. K. (1957). Ion and water fluxes in the ileum of rats. J. gen. Physiol. 41, 143-168. DEAN, E. W. & STARK, D. D. (1920). A convenient method for the determination of water in petroleum and other organic emulsions. J. ind. Engng Chem. 12, 486-490. ELFORD, B. C. (1970). Permeation and distribution of deuterated and tritiated water in smooth and striated muscle. J. Physiol. 211, 73-92. FismER, R. B. & GARDNER, M. L. G. (1974). A kinetic approach to the study of absorption of solutes by isolated perfused small intestine. J. Physiol. 241, 211-234. FISHER, R. B. & PARSONS, D. S. (1949). A preparation of surviving rat small intestine for the study of absorption. J. Physiol. 110, 36-46. FISHER, R. B. & PARsONS, D. S. (1950). The gradient of mucosal surface area in the small intestine of the rat. J. Anat. 84, 272-282. HEvEsY, G. V., HOFER, E. & KROGH, A. (1935). The permeability of the skin of frogs to water as determined by D20 and H20. Skand. Arch. Physiol. 72, 199-214. KING, V. (1969). A study of the mechanism of water transfer across frog skin by a comparison of the permeability of the skin to deuterated and tritiated water. J. Physiol. 200, 529-538. KITCHING, J. A. & PADFIELD, J. E. (1960). The physiology of contractile vacuoles. XI. Effects of heavy water on the water balance of a suctorian. J. exp. Biol. 37, 73-82. LINDLEY, B. D., HosHImo, T. & LEB, D. E. B. (1964). Effects of D20 and osmotic gradients on potential and resistance of the isolated frog skin. J. yen. Physiol. 47, 773-793. LovTRuP, S. & PIG6N, A. (1951). Diffusion and active transport of water in the amoeba Chaos chaos L. C. r. Trav. Lab. Carlsbery (ser. chim.) 28, 1-36. LUCKE', R. & HARvEY, E. N. (1934). The permeability of living cells to heavy water (deuterium oxide). J. cell. comp. Physiol. 5, 473-482. PARPART, A. K. (1 935). The permeability of the mammalian erythrocyte to deuterium oxide (heavy water). J. cell. comp. Physiol. 7, 153-162. TAKASHINA, T., LAzzARA, R., CRONvIcH, J. A. & BURCH, G. E. (1962). Studies of rates of transfer of D20, H3*, Cl36, Na22, and Mg28 across the isolated pericardium of dogs. J. Lab. clin. Med. 60, 662-668. TURNER, M. D., NEELY, W. A. & HARDY, J. D. (1960). Rapid determination of deuterium oxide in biological fluids. J. appl. Physiol. 15, 309-310.
