Transcellular and Paracellular Flow of Water During Secretion in the Upper Segment of the Malpighian Tubule of Rhodnius Prolixus: Solvent Drag of Molecules of Graded Size

The upper (blind or distal) segment of the Malpighian tubule of Rhodnius is known to secrete a fluid isosmotic to that surrounding it, at rates which may reach 50 ni cm^-2 s^-1, in response to stimulation by varying concentrations of diuretic hormone. The action of the latter can be mimicked by 5-hydroxytryptamine (5-HT) (Maddrell, 1969, 1980a,b). This secretion is currently thought to be transcellular rather than paracellular (O’Donnell, Aldis & Maddrell, 1982; O’Donnell & Maddrell, 1983; O’Donnell, Maddrell & Gardiner, 1984). Transepithelial water osmotic permeability is of the order of 58× 10⁻⁴cm³cm^-2 s^-1 osmol^-1, which it is thought can be explained by transcellular flow, without the need to invoke paracellular routes. In addition, the small relative frontal area of the intercellular spaces, i.e. the area facing the apical epithelial surface, as compared to the whole cell area, is also used as an argument against the possibility of paracellular water flow (O’Donnell et al. 1982). Similar arguments have been used to dismiss the possibility of paracellular water flow in other isosmotic transporting epithelia (which essentially absorb fluid) (Diamond, 1979; Berry, 1983). However, independent experimental evidence indicates that not only the transcellular, but also the paracellular, routes may be used for water flow during the normal function of these epithelia. Thus, in the proximal renal tubule, the transcellular water osmotic permeability is lower than the transepithelial one, suggesting that there is a significant paracellular water osmotic permeability (Whittembury, 1967; Carpi-Medina, Lindemann, González & Whittembury, 1984; González, Carpi-Medina, Linares & Whittembury, 1984; Whittembury et al. 1985). In addition, evidence for the existence of paracellular water flow stems from the observation that water drags some non-electrolytes that are known to be extracellular during absorption in Necturus gall bladder (Hill & Hill, 1978), Necturus proximal tubule (Berry & Boulpaep, 1964), mammalian gall bladder, Necturus and rat proximal tubule (Whittembury, Verde-Martinez, Linares & Paz-Aliaga, 1980; Whittembury et al. 1985), rabbit gall bladder (Steward, 1982a,b) and mammalian salivary glands (Hunter, Case, Steward & Young, 1982). The existence of solvent drag is deduced in these studies from the observation that the passage of extracellular non-electrolytes is accelerated by the absorptive flow to an extent which unstirred layer effects cannot explain. Pathways for water flow bear on the mechanisms of solute-solvent coupling (Hill, 1975; Hill & Hill, 1978; Diamond, 1979; Berry, 1983; Schafer, 1984).

We decided to explore the possibility that truly extracellular molecules may be dragged by solvent in the Malpighian tubules of Rhodnius, which secrete rather than absorb fluid isosmotically. Although it has been dismissed as a possibility (O’Donnell & Maddrell, 1983), the presence of solvent drag of extracellular molecules in this structure would indicate that water could move through the extracellular spaces not only in absorptive epithelia but also in this isosmotically secreting one. In the Malpighian tubules, the permeability of several molecules of graded size has been closely scrutinized (Ramsay, 1958; Maddrell & Gardiner, 1974; O’Donnell et al. 1984). It has been clearly established that mannitol (an extracellular marker in other tissues) enters the Malpighian tubule cells, while sucrose and inulin remain extracellular. However, the relationship between transepithelial flow of these molecules and secretory volume flow has not been systematically studied in this preparation, as it has in vertebrate isosmotic transporting epithelia (see above). An additional feature of the Malpighian tubule is of particular interest for the study of extracellular solvent drag. The morphology of the paracellular route in the Malpighian tubule differs from that of vertebrate epithelia (Lane & Skaer, 1980). In the latter, it is formed by short junctions (<1 μm in depth) which show zonulae occludentes, zonulae adhaerentes and desmosomes (Farquhar & Palade, 1963; Martinez-Palomo & Erlij, 1975), while in the former it is made up of long, smooth septate junctions (Noirot-Timothee, Smith, Cayer & Noirot, 1978; Skaer, Harrison & Lee, 1979). The cells of the Malpighian tubule are about 100fim in diameter. In consequence, the total frontal length of junctions per cm² of epithelium is far smaller than that in mammalian preparations (with cells 10μm in diameter). Thus in the Rhodnius Malpighian tubule the total length of junctions is 230 cm cm^-2 of tubular surface, as compared with 2300 cm cm^-2 in the rabbit proximal tubule (Whittembury, 1967). Finally, the Malpighian tubules can be dissected practically free of connective tissue. Therefore, the evaluation of the space of distribution of the substances used in the solvent drag experiments is free of some problems involved in the estimation of the space of distribution of, for example, the gall bladder, where the connective tissue occupies a space larger than that of the epithelium.

A series of molecules of increasing molecular weights and different shapes was chosen, namely urea, erythritol, mannitol, L-glucose, sucrose, polyethyleneglycol (PEG)M_T 800, raffinose, inulin and dextran M_r 15 000–18000 to try to explore the geometry of the pathways they would use to permeate the epithelium. The first four molecules penetrate the cells, while the last five are true extracellular markers. The passage of the first six molecules across the epithelium was accelerated by the rate of fluid secretion much more than expected as a result of unstirred layer effects. Therefore, it may be concluded that these molecules are dragged by water. The passage of the last three was accelerated by the secretory flow in a manner that can be entirely explained by unstirred layer effects and not by solvent drag. Since sucrose and PEG are true extracellular probes, the solvent drag of these molecules must be extracellular. Therefore, water must flow through extracellular pathways in addition to the transcellular routes. Part of this work has been published in a preliminary form (Biondi, Linares, Linares & Whittembury, 1982; Paz-Aliaga, Linares & Whittembury, 1983).

Fifth instar Rhodnius prolixus were used, 1–4 weeks after moulting, from a laboratory culture maintained at 28 °C at a humidity of 95%. Upper Malpighian tubules were isolated into drops of insect Ringer solution (see below) under oxygenated, water-saturated liquid paraffin as described by Ramsay (1958) and Maddrell (1969, 1980a,b). For this purpose, an appropriate chamber was thermostatted at 30°C, the blind end of the tubule was kept immersed near one glass rod, to which an oxygenated Ringer drop with a volume of 0·1–0·5μ1 had been attached under paraffin oil, while the cut end was tied up around another glass rod. These small-sized drops were renewed every 2–5 min. They were chosen in order to achieve appropriate molecular self-stirring of the bathing solution. A sphere of 0·1–0·5 μl has a radius (300–500 μm) critical for self-stirring. The time delay for 90 % equilibration by diffusion can be calculated [using equation 143 (Jacobs, 1935) or equation 6.20 (Crank, 1956)] to be 8 s and 22 s for the 300-and 500-μm-radius drops, respectively. Since our collections were usually performed at intervals of at least 5 min there should have been ample time for mixing. The Ringer solution contained 1 mmol I^-1 of the probing molecule. At time t = 0, secretion was started by addition to the Ringer solution of 5-HT to a concentration which varied from 10⁻⁵ to 10⁻⁷mol I^-1. Periodic collection of the secretion was performed with techniques for handling small volumes (Shipp et al. 1958). Collections lasted for about 2h. Samples were used once the secretory rate stabilized.

The rate of secretion, J_v, was calculated from the volume and duration of collection and the area of tubular surface exposed to the Ringer solution. The area was obtained from camera lucida tracings to measure tubular length. It was assumed that the tubules were well represented by a cylinder. An image splitter was used to evaluate tubule diameters (Carpi-Medina et al. 1984). J_v was expressed in nlcm^-2s^-1. The volume of each collection was directly pipetted into 1ml of distilled water and counted with 3 ml of counting solution in a Packard 3000 liquid scintillation counter. Known volumes of Ringer were similarly counted.

⁠, the rate of secretion per unit bath concentration (C₁), was calculated as J_v×C₂/C₁, where C₂ is the concentration of the radioactive substance in the secreted fluid. has units of nl cm²s^-1.

The Ringer solution has the following composition (Maddrell, 1969, 1980a,b) in mmoll^-1: NaCl, 129; KC1, 8·6; NaH₂PO₄, 4·3; NaHCO₃, 10·2; CaCl₂, 2·0; glucose, 34; alanine, 3. The pH was 7·35–7·45 and the osmolality 340mosmolkg^-1, as measured by the freezing point method. The chemicals were from E. Merck, Darmstadt, except dextran (Sigma Chemical Co.). The following radioactive substances (New England Nuclear Corp.) were used: [¹⁴C]urea, [¹⁴C]mannitol, [³H]L-glucose, [¹⁴C]sucrose, [³H] raffinose, [³H] polyethyleneglycol 800, [¹⁴C]-inulin, [¹⁴C]dextran. Enough counts of these substances in 1 mmoll^-1 carrier were added to the Ringer solution drop that bathed the tubule. Chromatographic runs indicated that these substances had not hydrolysed.

The tubules were treated as described above. Samples were obtained to measure the secretion concentration (C₂) and the bath concentration (C₁) of the probing molecules. The tubules were then taken out of the bath with a glass hook. They were then quickly immersed for 1 s in each of three Ringer baths (10μl each). This removed at least 95 % of the radioactive counts outside the tubule. The tubules were then dipped in 1 ml of water in a counting vial. Aliquots of the secreted and bathing solutions were also counted. From the lumen volume (V^L) and concentration of the probing molecule (C₂), the probing molecule tubular lumen content (C^L) was calculated. The tissue content (C^T) (as determined from the radioactive counts in the tissue) minus the lumen content gave the cell content C^c which, divided by the cell volume, V^c, gave the concentration, C₃. The space of distribution S = C₃/C₁. S is the fraction of V^e occupied by the probe under the assumption that the latter is not concentrated by some subcellular fraction. The probe distributes in the whole tubular cell structure if S = 1·00 and it does not enter the cell interior if S = 0·00. V^L was calculated from the average lumen diameter (35 μm) and V^c from the average external tubule diameter (55 μm), assuming that the tubules are well represented as cylinders. Thus V^L — 9·6 and V^c = 14·1 nl cm^-1 tubule length (Table 1).

After dissection, the upper tubules were used immediately. They were stimulated to secrete with 5-HT as indicated above. After 30 min, the bathing fluid was changed to a glutaraldehyde fixative (100 ml of the basic fixative contained 1 g of glutaraldehyde plus 10ml of insect Ringer buffered with phosphate buffer to pH 7·3–7·4). The osmolality of the fixative was adjusted to 340mosmolkg^-1. After 15–20 min, 1-mm long pieces of tubule were immersed in the same fixative and left overnight at 4°C. After being washed in buffer they were post-fixed in Na-cacodylate-buffered 2% OsO₄ solution (10 mg ml^-1), dehydrated in acetone, washed in propylene oxide and embedded in Epon 812 (Whittembury & Rawlins, 1971; Whittembury & Hill, 1982). Pale gold to silver sections were stained with uranyl acetate and lead citrate, and examined in a Siemens Elmiskop 1A electron microscope.

Urea, erythritol, mannitol and L-glucose distribute themselves in most of the intracellular space, while sucrose, raffinose, PEG, inulin and dextran occupy about 5 % of the tissue space. The peritubular extracellular matrix is 0·5 μm thick (Figs 6, 7), which is about 6% of the cell space, which is 14nlcm^-1 length (lumen excluded, see footnote to Table 1). Assuming that the intercellular spaces are 0·1 μm wide, it can be calculated that the tissue intercellular space would be 0·23 % of the tissue volume. These observations warrant the use of sucrose, raffinose, PEG, inulin and dextran as extracellular substances in the Malpighian tubule upper segment. Urea, erythritol, L-glucose and mannitol must certainly cross the cell in addition to distributing themselves in the extracellular space.

Figs 1–4 and Table 2 summarize the relationship between the net secretory flux of the probing molecules (per unit bath concentration), ⁠, and J_v, the secretory flow rate. Although more complex functions may also fit the data, the straight line is the simplest fit, with a very high correlation coefficient for urea, erythritol, mannitol, L-glucose, sucrose and PEG. Fig. 5 gives the ratio C₂/C₁ as a function of the relative molecular mass of the probing molecules for three rates of J_v.

For urea, erythritol, L-glucose, mannitol, sucrose and PEG, the dashed (diffusion) line is statistically different from the line representing the experimental values (Figs 1–3; Table 2).

Since the relationship between and J_v for raffinose and dextran is not statistically significant, no regression line has been drawn (Fig. 4). Inulin shows a regression line with a slope significantly different from zero (Fig. 4). However, the distribution of none of these three substances is different from the distribution expected from diffusion due to unstirred layer effects because the dashed line and the experimental values coincide (Table 2). Fig. 5 shows the relationship between C₂/C₁ and M_r of the probing molecules. C₂/ C₁ decreases progressively as Af_r increases, as Ramsay (1958) and Maddrell & Gardiner (1974) observed. Fig. 5 also illustrates that C₂/ C₁ ratios decrease as J_v increases.

Thin section electron micrographs (Figs 6, 7) show normal tubular appearance (Wigglesworth & Salpeter, 1962). In addition, structures may be observed that extend from basolateral infoldings to the apex of the cell in the form of parallel lines. These structures, previously described by Wessing (1965), seem to be open at both cell ends. These observations agree with recent observations using thick sections and high voltage electron microscopy (Bergeron et al. 1985).

The first task of the present work was to study the space of distribution of probing molecules of increasing molecular weight to differentiate truly extracellular probes from those that penetrate the cell membrane. The Malpighian tubule upper segment is particularly suited for this purpose since it is surrounded by only about 6% of extracellular material (Figs 6, 7). Urea, erythritol, mannitol and L-glucose do penetrate the cell membrane (Table 1) in agreement with observations indicating that methyl glucose, mannitol and erythritol enter the intracellular space (O’Donnell et al. 1984). In contrast, sucrose, PEG, raffinose, inulin and dextran occupy only some 5 % of the tubular volume (lumen subtracted). Therefore, these substances must be true extracellular markers, in agreement, again, with observations of O’Donnell et al. (1984) for inulin and sucrose. The C₂/ C₁ ratio shows an inverse relationship with the M_r of the probing molecules (Fig. 5), in agreement with observations of Ramsay (1958), Maddrell & Gardiner (1974) and O’Donnell et al. (1984). In addition, the ratio C₂/ C₁ varies inversely with J_v, C₂/ C₁ ratios being higher at low J_v values and lower at high J_v values (Fig. 5).

A second observation of the present work is the relationship between the net secretory flux per unit bath concentration, ⁠, of several of the probing molecules and J_v. Recalculation of the work of Ramsay (1958) on the stick insect and of O’Donnell et al. (1984) on Rhodnius Malpighian tubules shows that this relationship was also present in their experiments. Thus Ramsay studied the excretion of urea and sucrose, among other probes. The rate of urine flow (7?) (similar to J_v) and the probing molecule concentration in the secreted fluid (C₂) and in the bathing fluid (C₁) may be used to construct a plot of (C₂.R/C₁) vs R which shows a highly significant correlation, with experimental points falling around the identity line for urea, as in Fig. 1 of the present work. A similar plot for sucrose using the data from tables 4, 7 and 8 of Ramsay (1958) also shows a statistically significant positive slope relating C₂-R/ C₁ as a function of R.

It may be seen (Fig. 5) that C₂/ C₁ ratios vary as a function of J_v. Therefore, o would apparently vary as a function of J_v. Asa matter of fact, useful o values can only be obtained as the highest values of J_v are approached, from σ= 1–2m/(l + C₂/ C₁). These values are given in Table 2 (σ values calculated at low J_v figures can be artefactual; Renkin, 1985).

We have used this equation to calculate as a function of J_v for the probes as shown by the dashed lines of Figs 1–4 with (a) values for d′ and d″ of 2×500 μm and 2×17·5 μm (i.e. values twice the unstirred layer thicknesses of the bath and secretory side, respectively, to be on the safe side), (b) values as given in Table 2, (c) J_v values of 0, 5, 10, 15, 20, 15 and 30nlcm^-2 s^-1 and the corresponding experimental C₂/ C₁ ratios. The dashed line interpolates the values obtained at 5nlcm^-2s^-1 intervals of J_v.

In Figs 1–4 the solid lines represent the total observed flow, (with slope values shown in Table 2). The differences between the slopes of the solid and the dashed lines give the convective flows ⁠. The probability that this difference is statistically significant is shown as P* in Table 2. If the continuous and the dashed lines are not statistically different, any relationship between and J_v is due to the contribution of ⁠, i.e. to unstirred layer effects. P* in Table 2 is non-significant for raffinose, inulin and dextran. This indicates that the increase in secretory flow of raffinose, inulin and dextran as a function of J_v can be entirely explained by unstirred layer effects (Fig. 4). Inspection of equations 1 and 2 helps to clarify the relative changes in the weight of and as a function of M_r, the probe relative molecular mass. It is known that the diffusion coefficient, D_a, of the probing molecule is inversely related to M_r. For example D₈ for sucrose, raffinose, PEG, inulin and dextran are, respectively, 6, 4·3, 2·6, 1·8 and 0·9× 10⁻⁶cm²s^-1. Inconsequence, the unstirred layer effects (which are inversely proportional to D_s) and the relative importance of will be larger with the larger probes than with the smaller ones, provided ⁠. On the other hand, the weight of decreases the larger the probe, because the value of a approaches 1, and 1 —σ approaches 0.

Figs 1–3 show that for urea, erythritol, L-glucose, mannitol, sucrose and PEG the convective component (i.e. highly significant, Table 2). Obviously, for the molecules entrained by water at J_v — 0, ⁠. As J_v increases, the convective component becomes progressively more important until at J_v> 15nlcm^-2s^-1, ⁠.

By contrast, it is illustrative to calculate the concentration difference that would be required to explain exclusively by diffusion the net solute flows observed in Figs 1–3 at high J_v values. In the case of urea, erythritol, mannitol, L-glucose, sucrose and PEG, the values for at Jv = 20–30cm^-2 s^-1 are 5–10 times higher than at low J_v values. Therefore, a concentration difference of 5-10 mmol I^-1 would be required to explain the observed net solute fluxes at high J_v values (instead of the concentration difference of 1 mmol I^-1, originally set up). These concentration differences cannot be maintained in the small bathing fluid drops used in the present work because selfstirring should counterbalance within a few seconds any tendency to solute accumulation (see Materials and Methods). In other words, 5–10 mm diameter drops would be required to explain by unstirred-layer effects the experimental results shown in Figs 1–3.

Examination of equation lb indicates that changes in as a function of J_v could also result in an increase in as a function of J_v. It is possible that faster fluid secretion leads to a higher intraluminal hydrostatic pressure which in turn might lead to changes in ⁠. O’Donnell et al. (1984) showed that increasing fluid perfusion rates along the lumen of cannulated tubules produced increased rates of sucrose penetration very similar to those produced by similar changes in the rate of fluid secretion across the epithelial wall. Although we do not know the exact explanation for these, we believe that the possibility that has increased in our experiments is remote for the following reasons. (1) By definition, ⁠, where A/A_o is the pathway area per cm² of epithelium, Δx is the pathway length and D_s the solute diffusion coefficient. Therefore, an increase in is expected if the geometry of the pathways changes. At high J_v values, for sucrose is 5–10 times the value obtained at low J_v (Fig. 3). To explain that a five-to tenfold increase in for sucrose (with a molecular radius of 0·45 nm) is due to geometrical changes, one requires either a five-to tenfold decrease in Ax (which is remote) or a five-to tenfold increase in A/A₀. The latter would require that the frontal area of the intercellular clefts increases five-to tenfold (either in length or in width). Just a twofold increase in width means a change in width from a slit with a half-width of 0·6 nm (Fig. 8) to one of 1·2 nm. Such a pathway would easily let through raffinose, with a molecular radius of 0·59 nm, which is not the case, since raffinose is retained by the epithelium (Fig. 4). (2) σ may be defined as 1 – i.e. σ is equal to the amount of solute that does not sift through the membrane per unit time divided by the amount arriving at the membrane during that time (Whittembury et al. 1980; Renkin, 1985). For sucrose, σ— 0·90 at high J_v values and 0·89 at J_v = 5 nlcm^-2s^-1 and for PEG, 1σ — 0·91 and 0·89, respectively. If the changes in were due to increases in ⁠, and therefore to increases in the pathway area, σ should decrease at high J_v values, since σ also depends on the geometry of the pathways (see 3, below). The observation that σ does not significantly change with J_v argues against possible changes in the geometry of the pathways used by the solute to cross the preparation. (3) Alternatively, one can calculate the magnitude of the change in A/A₀ of the pathway that would allow solvent drag of raffinose, so that σfor raffinose would be 0·90 (instead of the experimental finding of 1·00), i.e. similar to the values observed for sucrose and PEG (which have σ= 0·9). This calculation can be undertaken using the following equation (equations Alla and A15 of Renkin & Curry, 1979) for slits:

One must therefore conclude that urea, erythritol, L-glucose, mannitol, sucrose and PEG are entrained by water. Sucrose and PEG must be dragged by water exclusively, following extracellular pathways, while urea, erythritol, L-glucose and mannitol must be dragged by water following extracellular pathways; they may also be dragged through the cells, although their transcellular movement could mainly be diffusive.

The results shown in Figs 1–4 seem related to the M_r of the probe; raffinose (M_r594), inulin (M_r5000) and dextran (M_r15000–18000) are not entrained, whereas the smaller molecules are dragged by water. However, this argument does not apply to PEG (M_r800), since this is dragged while raffinose, for example, is not. Do steric factors play a role in this discrimination of the epithelium against the probing molecules? Urea, erythritol, mannitol, L-glucose, sucrose and raffinose are quasi- spherical, while PEG, inulin and dextran are long, rod-like molecules with major-to-minor axis ratios of about 5, 15–18 and 21, respectively. Rod-like solute particles in solution flow are oriented by the hydrodynamic forces such that their major axis will tend to be parallel to the direction of the stream lines, due to the fact that the velocity of the solvent in relation to the particle surface is higher at the middle of the molecule than at its ends and is exerted in a direction parallel to the molecule long axis (Schlichting, 1979). When entering a pore-like structure, they will be inserted endon into it (Cerf & Scheraga, 1942; Nozaki, Schechter, Reynolds & Tanford, 1976). If this criterion is applied, the discrepancy between the experimental results with PEG and raffinose disappears since the end dimensions of PEG are smaller than the diameter of raffinose (Table 2). Therefore, PEG can sieve through any pore or slit with more ease than raffinose (Fig. 8).

Toa first approximation, the upper limit in the dimensions of the structure where solutes are entrained by water must be about 0-6 nm, since molecules with a radius r_m near or larger than 0·6 nm are not dragged and those with r_m near or less than 0·55 nm are entrained. The lower limit for this structure must discriminate between markers that penetrate the cell (urea, erythritol, L-glucose and mannitol) and those that remain outside it (PEG and sucrose) (Table 1).

Therefore the cell membrane excludes molecules with an r_m near or larger than 0·4nm. The pathway where sucrose and PEG are entrained by water must therefore be twice 0·4–0·6nm wide. This is illustrated in Fig. 8, which compares the dimensions of a 1·2nm wide slit with those of the probes. It should be kept in mind that molecules excluded by the slit can still permeate the epithelium, in which case because of the existence of alternative diffusive, but not convective, pathways.

Further quantification should follow steric hindrance theories (cf. Renkin & Curry, 1979): σ= [1 — (A_sf/A_wf)] may be used. A_sf and A_wf are, respectively, the areas available for passage of solute and water during filtration. A_sf may be written as a function of (r_m/r_p), the ratio of the dimensions of the probe to those of the pore or slit, and A_wf as a function of (r_w/r_p), the ratio of the dimensions of water to those of the pore or slit. Such a treatment using the values of σ (Table 2) indicates that a cylindrical pore of about 0·57 nm in radius and a slit with a half-width of 0·5 nm best fit the data. More precision is not possible at present because we have neither independent determinations of σ, nor a quantitative treatment for the sieving properties of rod-like molecules, nor enough information to be able to use equations for membranes in series and in parallel (cell membrane and intercellular space being in parallel and the septate and non-septate part of the intercellular spaces in series).

Fig. 9 depicts possible pathways for transepithelial water flow. In pathway 1, after crossing the cell membrane (possibly via aqueous pores, see Whittembury, Carpi, González & Linares, 1984) water would dissolve in the cytosol and would cross to the other end of the cell. Through this pathway water could, to some extent, drag small molecules that can cross the cell such as urea, erythritol, mannitol and L-glucose.

Pathway 2 is formed by the 15–20 μm long intercellular spaces which, in the Malpighian tubule, are formed by some 7 μm long smooth septate junctions in series with the rest of the intercellular space proper (Figs 6, 7). These junctions are known to let through La³⁺ (Lane & Skaer, 1980), which is as big as Na⁺ (Whittembury & Rawlins, 1971). Therefore, it is conceivable that water can also leak through. Through these pathways, water could drag only extracellular solutes like PEG and sucrose (and also the smaller probes mentioned above). A high degree of coupling between probes and solvent should not be surprising since, given the small relative frontal area of pathway 2, the speed of flow through these pathways should be very large.

Pathway 2a illustrates the structures described by Wessing (1965) and Bergeron et al. (1985) that extend from basolateral infoldings to cell apex. These structures appear in thin section electron micrographs as sets of parallel lines for such a length that they must represent sections of two parallel membranes forming slits (Figs 6, 7). They also appear as chains of vesicles or tubules (Bergeron et al. 1985). Since these structures are believed to open at both cell ends (Wessing, 1965), it is crucial at present to know whether these structures function as continuous pathways crossing the epithelium from base to apex. If that were the case, they could constitute a new pathway, effectively bypassing the cytosol where solvent drag could take place as in the intercellular pathway. An analogous possibility has been suggested as a pathway in some mammalian epithelia (Møllgård & Rostgaard, 1981). Pathways 2 and 2a would complement each other. However, pathway 2a must remain only hypothetical until further experiments prove or disprove it as an effective pathway.

In pathway 3, water could cross in vesicles or vacuoles. This pathway would explain neither the discrimination of the vesicles for the different probes (because it would imply that some vesicles would have different contents of solutes), nor that inulin, dextran and raffinose are not dragged by water (unless the vesicles are connected with each other by narrow structures with characteristics similar to those already outlined for the pathway where solvent drag has been shown to occur). Calculations illustrate that the pathways for transepithelial water flow occupy only a small fraction of the epithelial area. This holds both for the possibility that all water flow is transcellular and for the extreme that it is all paracellular. The relative frontal area of the transcellular pathway, considering pores of about 0·4 nm in radius, would cover 0·6% of the epithelial area; the paracellular pathway constitutes 0·08% of the epithelial area (Whittembury et al. 1984, 1985).

It is a pleasure to thank Professor Josué Nuñez who developed the culture of Rhodnius and introduced us to the Malpighian tubule preparation. Mr José Mora, Mrs D. Otero, Mr A. Cazorla, Mr Mardonio Diaz and Mr J. Bigorra helped in different stages of this research. Thanks are due to Mrs Rebeca Godoy and Elena Suárez for typing the manuscript. Miss A. Biondi’s trip to Venezuela and her stay at IVIC were covered by Grants from Universidad de Tucumán and IVIC. This work constituted part of the Ph.Sc. thesis of A. Paz-Aliaga at the Centro de Estudios Avanzados, IVIC, Caracas. GW is also a member of Centro Internacional de Estudios Avanzados, IDEA, Caracas. Drs T. J. Pedley and G. K. Aldis kindly helped GW understand several of the unstirred layer problems involved.