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Journal of Physiology (2001), 536.2, pp. 541-553
© Copyright 2001 The Physiological Society
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ABSTRACT |
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10-3 and 1.7 10-3 cm s-1.
10-5 and 1.8 (± 0.3) 10-6 cm s-1, respectively; n = 3 for both, P < 0.01). The permeability of the caecal crypt wall to 10 kDa dextran was higher than that of the descending crypt wall (2.03 (± 0.21) 10-5 cm s-1; n = 3, P < 0.025).
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INTRODUCTION |
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TopAbstractIntroductionMethodsResultsDiscussionAppendixReferences |
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Fluorescence recovery after photobleaching (FRAP) has been used to study the diffusion and convection of macromolecules in complex environments such as extracellular fluid and polymer matrices (Jain et al. 1990; Gribbon & Hardingham, 1998; Periasamy &Verkman, 1998). Confocal scanning laser optical systems have been used both to induce photobleaching of fluorescein isothiocyanate (FITC)-labelled dextran (FITC dextran) and to follow subsequent fluorescence recovery in space and time. We have adapted this technique to determine the rates of fluid uptake into rat colonic crypts in vitro and to determine the permeabilities of different regions of the crypt wall to dextran of two molecular masses (10 and 250 kDa).
The main evidence that crypts absorb fluid is that: (1) they accumulate dextran to a higher concentration in their lumens than is found in the external solution; (2) a hypertonic NaCl solution is observed in the pericryptal space surrounding rat descending crypts; (3) the rat descending colon in vivo generates a large suction tension, which is used to dehydrate faeces (Naftalin & Pedley, 1990; Pedley & Naftalin, 1993; Zammit et al. 1994; Naftalin et al. 1995); and (4) paraffin droplets in the crypt lumen block the accumulation of fluid and FITC dextran, thus preventing the crypts from exerting the suction tension (Naftalin et al. 1999). Amiloride, a blocker of Na+ conductance channels in the distal colon, inhibits Na+ accumulation within the pericryptal sheath, and also inhibits FITC dextran accumulation (Naftalin et al. 1995). In addition, fluid absorption has been observed directly in isolated perfused rat distal colonic crypts (Singh et al. 1995).
Rates of fluid absorption into crypts have been estimated indirectly by examining the extent of steady-state accumulation or concentration polarization of FITC dextran. The accuracy of this estimation is reduced by the variable extent of leakage of FITC dextran across the crypt wall. Therefore it is important to develop a robust method of monitoring crypt absorption. This will be useful in assessing the parameters determining the permeability of the crypt to water and FITC dextran in human colonic biopsy specimens and from other sources. Confocal microscopic methods have been developed in this study which show both qualitatively and quantitatively that the uptake of fluid and FITC dextran by the descending colonic crypts depends on the convective flow of fluid. These methods have been corroborated by simulations of crypt fluid electrolyte and FITC dextran absorption.
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METHODS |
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Chemicals
FITC dextran (molecular mass 10 and 250 kDa) and amiloride were obtained from Sigma Chemicals.
Accumulation of FITC dextran in crypts from isolated mucosa
Wistar rats weighing 200-300 g were killed by cervical dislocation, the descending colon and caecum were removed rapidly and the contents removed by washing with Hanks' balanced salt solution (HBSS (mM): NaCl 137, KCl 5.36, MgSO4 0.4, NaHPO4 0.34, KH2PO4 0.44, MgCl2 0.49, NaHCO3 4.7, CaCl2 1.8 and glucose 5.5). The procedure was performed as described previously by Naftalin et al. (1999). Briefly, the colonic mucosa was stripped of its muscle layer and mounted as a 5 mm2 sheet in a temperature-controlled perfusion chamber at 35 °C. FITC dextrans (20 µM in Earle's solution-Hepes pH 7.35 containing (mM): NaCl 124, KCl 5.4, MgSO4 0.8, NaHPO4 1, NaHCO3 14.3, Hepes 10, CaCl2 1.8 and glucose 5.5) of two different molecular masses (10 and 250 kDa) were introduced into the perfusion chamber and allowed to accumulate within the colonic crypts. Amiloride experiments were performed after incubation with 0.1 mM amiloride for 10-15 min prior to bleaching. Experiments carried out with Na+-free solution were performed as above, followed by washing of the tissue in Na+-free buffer (pH 7.35, containing (mM): N-methyl-glucamine chloride 125, KCl 5.4, MgSO4 0.8, NaHPO4 1, Hepes 20, CaCl2 1.8 and glucose 5.5), then addition of dextran Na+-free solution and photobleaching.
To ascertain whether photobleaching causes sufficient proton release to generate an artifactual 'photobleaching' of FITC dextran, forming protonated non-fluorescent fluorescein, we examined the effects of equal bleaching episodes with different concentrations of Hepes buffer (0, 10 and 20 mM). The extent of photobleaching was similar in all three conditions. This finding eliminates the possibility that light-induced acidification could be a significant factor in the loss of fluorescence.
Confocal microscopy and the FRAP protocol
The tissue was viewed using a Nikon Diaphot inverted microscope with a Nikon Fluor 40 lens. The microscope was attached to an MRC 600 confocal scanhead that was equipped with two detection channels and an Ar-Kr mixed-gas laser, which allows excitation at 488 and 568 nm. Movement of the z-axis, with 0.1 µm resolution, was provided by a software-controlled stepper motor, which was attached to the fine focus control.
Pre-bleach images were collected with the laser attenuated at 30 % (neutral density 1). Images were sampled at the mucosal surface and at 10 µm steps in the z-axis up to 40-50 µm into the tissue. During photobleaching the laser was focused 20 µm below the mucosal surface at 100 % intensity (neutral density 0) and a zoom of 4-6, depending on the area required to be bleached. Continuous scanning of the zoomed area for 30 s caused bleaching of the fluorescence. Post-bleaching images were acquired after resetting the confocal laser to neutral density 1 (no zoom) and images were taken as before in 10 µm steps from the surface every 30 s for 2 min, and then at 1 min intervals (see Fig. 1).
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Figure 1 Summary schematic diagram showing fluorescence recovery after photobleaching (FRAP) protocol and dextran distributions during the experiments. | ||
Image analysis
The captured images were analysed using the public domain NIH Image program (written by Wayne Rasband at the US National Institutes of Health, http://rsb.info.nih.gov/nih-image) to quantify the fluorescence. The fluorescence was evaluated by measuring the mean fluorescence intensity of a designated region at each of the depths taken. This procedure was repeated for all time points.
Analysis of FITC dextran uptake into the crypt lumen
Estimates of the rate of fluid inflow into the crypts from the rates of accumulation of FITC dextran. The rate of total accumulative uptake of FITC dextran into the crypt lumen and pericryptal zone was measured after photobleaching. The only route for FITC dextran uptake is via the opening of the crypt lumen. So after photobleaching, FITC dextran first enters the crypt lumen. The only routes by which FITC dextran can leave the crypt are by permeation across the crypt wall via the paracellular pathway into the adjacent pericryptal space, or by back diffusion via the crypt luminal opening. Uptake into the pericryptal sheath occurs only after FITC dextran uptake into the crypt lumen, and hence occurs more slowly.
The fluorescence of FITC dextran in the external solution is unaffected by photobleaching. The amount of FITC dextran transferred into the crypt is estimated as a volume of external solution transferred to the crypt. The total volume of FITC dextran solution taken up per centimetre squared of crypt area per second corresponds to the rate of fluid uptake by the crypt. The steady-state rate of fluid flow is obtained from the initial rate of recovery after photolysis of FITC dextran:
t0 - t 1 - z(FITC dextran(lumen) + FITC dextran(pericrypt)).
This was repeated at intervals during the 5-10 min recovery period following photolysis. FITC dextran(lumen) and FITC dextran(pericrypt) refer to the fluorescence density of FITC dextran at the lumen and pericrypt, respectively, in the particular crypt layer where 1 is the most proximal segment and z the most distal segment examined. The fluorescence was normalized to background values at each successive depth. The cumulative accumulation of dextran is the total amount of dextran accumulated in the crypt at all z planes in the time measured:
t0 - t1 - z(FITC dextran(lumen) + FITC dextran(pericrypt))/FITC dextran(external solution))/dt.
This initial rate of accumulation is estimated from the first derivative of the best polynomial fit of cumulative FITC dextran accumulation in the pericrypt and crypt together against time.
The rate of increase is a measure of the rate of volume uptake from the external solution entering the crypts per centimetre squared of crypt luminal surface area, i.e. the entry velocity of FITC dextran fluid penetrating the crypt lumen. This approach is similar to that adopted by Bassingthwaighte & Goresky (1980) to monitor solute exchange across perfused capillaries.
Measurement of crypt wall permeability to FITC dextran
Any FITC dextran present in the pericryptal sheath and in the lamina propria adjacent to the sheath is also subject to photolysis. Since FITC dextran enters the pericryptal sheath and the lamina propria only after penetrating through the crypt wall from the crypt lumen, it follows that the luminal fluorescence recovers more quickly than the pericryptal fluorescence. The delay in recovery of pericryptal fluorescence can be used to measure crypt wall permeability to FITC dextran:
where JDcrw is FITC dextran flux across the crypt wall, FD(lumen) and FD(pericrypt) are the fluorescence densities in the crypt lumen and pericryptal regions, respectively, in the same segment, and Pcrdex is the permeability of FITC dextran across the crypt wall. This permeability is a combined parameter that includes the permeability of both the crypt wall and the pericryptal sheath. This is obtained by plotting ln(1 - (FD(pericrypt + lamina propria)t/FD(lumen)t)) versus time after FRAP. The slope of the line is the permeability of the crypt wall to FITC dextran. The data points on the line are multiplied by a correction factor that is estimated from the ratio of the permeability of the surface of the crypt luminal perimeter and the extracryptal area in which FITC dextran is observed to accumulate. This scaling factor has an average value of 0.01 cm-1.
Analysis of the pattern of change in FITC dextran concentration along the length of the crypt lumen. The extent of convective flow along the crypt lumen can also be determined by analysis of the changing concentration distribution along the length of the crypt. The initial changes in the concentration profiles should conform to the analytical solution to the second-order diffusion equation, i.e. the evolving pattern of concentration distribution into a film of infinite thickness.
d2c/dx2 - vc,
where Jd is the flux of FITC dextran, D is the diffusion coefficient, c is the dextran concentration and v is the convective velocity. The solution integral to this equation can be modelled simply in terms of the error function complement (erfc) of 
(erfc(); where = x/
(4Dt), x is the distance (in cm), D is the diffusion coefficient of FITC dextran (in cm2 s-1) and t is time (in s; Bird et al. 1960; Beek et al. 1999). Hence:
(4Dt)),
where Ci and Co are the FITC dextran concentrations within the crypt lumen and outside it, respectively. The diffusion coefficients in the saline solutions of FITC dextrans = 
(molecular mass)
, where = 2.7 10-5 and = -0.37 (Gribbon & Hardingham, 1998). Hence, 10 kDa FITC dextran has a diffusion coefficient D = 9 10-7 cm2 s-1, and 250 kDa FITC dextran has a diffusion coefficient D = 2.7 10-7 cm2 s-1.
The concentration profiles of FITC dextran along the crypt length are also fitted empirically to Boltzmann's sigmoidal distribution equation:
where x is the independent variable distance (µm) along the crypt lumen, x0 is the distance (µm) at which the solute concentration is half-way between the concentration maximum (A1) and minimum (A2), and dx is the 'spread' distance along the crypt lumen between A1 and A2. Boltzmann's equation fits concentration profiles that do not fall to zero. The data are fitted to the equations using the Levenberg-Marquardt algorithm, which is built into Kaleidagraph 3.5 by Synergy Software.
Evidence from concentration polarization of FITC dextran within the crypt. FITC dextran is concentrated into crypt lumens as a result of concentration polarization: Ci/Co = exp(-Pe), where Pe is the Peclet number (xv/D; Naftalin et al. 1995). The polarization of FITC dextran concentration in the crypt lumen is reduced as fluid is absorbed through the crypt wall. The extent of this polarization within the crypt lumen is also reduced as FITC dextran permeates through the crypt wall. In a number of mucosal samples, no significant excess accumulation of FITC dextran was observed, since the crypt wall is too permeable. Consequently, the extent of concentration polarization within the crypt lumen is an unreliable means of estimating the velocity of mass flow into the crypt. However, this defect does not apply to the methods described in the above section, although it does detract from the quantitative analysis of the movement of FITC dextran along the crypt length.
Model of crypt function
FITC dextran uptake into crypt lumens, crypt flows and FITC dextran distribution in the crypt lumen and pericryptal space were modelled numerically using the physical dimensions of the crypt and the known parameters of water, Na+ and dextran fluxes. The model crypt is subdivided into segmental layers (see Fig. 8 and the Appendix). Each segment contains a crypt luminal volume element and a pericryptal volume element. Na+ flows from the external solution (colonic lumen) into the first luminal volume element, and then by convective diffusion it passes to the next luminal volume element, or to the adjacent pericryptal volume element across the permeability barrier of the crypt wall. Thereafter it can flow into the submucosal compartment, which is assumed to be unsegmented. Segmentation of the model crypt provides the necessary interactions to generate second-order solutions to the convective diffusion equations for the flux of FITC dextran:
dc/dx - vc.
Using the linear equations for intersegmental flow and diffusion, non-steady-state solutions to the second-order diffusion equation are generated when more than three segments are simulated. Comparison of the solutions for 7-, 10- or 20-segment stacks give qualitatively similar solutions. In general, it is the 10-segment stack that is used. These solutions are compared with semi-analytical solutions generated by the erfc().
Uses of the model
The model was used here to simulate and match the observed crypt uptake of fluid and FITC dextran after FRAP. In addition, the changing distribution of FITC dextran along the length of the crypt lumen was simulated at different rates of Na+ pump activity and compared with the changes observed in isolated mucosa. The model parameters were obtained either from the literature (e.g. diffusion coefficients, etc.) or from direct observations (e.g. crypt dimensions and FITC dextran permeabilities and crypt hydraulic permeabilities (Lp)). The moduli of elasticity were estimates given appropriate to the suction pressures observed in vivo (Naftalin et al. 1999).
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RESULTS |
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Illustration of crypt recoveries with FRAP of FITC dextran
The images shown in Fig. 2 illustrate the similar recovery rates obtained after FRAP of 10 and 250 kDa FITC dextran, and the markedly slower recovery of both in the presence of amiloride (0.1 mM). The images of the more permeable and smaller FITC dextran (10 kDa), compared to the larger dextran (250 kDa) also show the slower recovery of the surrounding pericryptal space compared to that of the crypt lumen. It should be noted that the bleaching pulse had little effect on tissue viability since similar recovery rates were obtained from consecutive photobleaching episodes.
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Figure 2. FRAP images of FITC dextrans in rat descending colon Confocal images showing fluorescence recovery after photobleaching with 10 and 250 kDa dextran, and with 10 kDa dextran after treatment with amiloride (0.1 mM), in the descending colonic crypts. Images were taken 30 µm down from the mucosal surface. | ||
Accumulation of 10 and 250 kDa FITC dextran into crypts after photobleaching
FITC dextrans of the different molecular masses, accumulated to a steady state within the descending colonic crypts, were subjected to photobleaching, and the subsequent recovery of fluorescence was followed. The cumulative accumulation of FITC dextran in the descending colon (see Methods) showed that the initial rates of recovery, and therefore fluid inflow, were similar for both the 10 kDa (1.3 10-3 cm s-1) and the 250 kDa (1.7 10-3 cm s-1) FITC dextrans. Figure 3A and B (data points) shows the cumulative recovery for the 10 and 250 kDa FITC dextran, respectively, and the effect of amiloride treatment on these recovery rates. Amiloride (0.1 mM) reduced the rate of 10 kDa FITC dextran uptake by ~70 % (P < 0.001), to 4.3 10-4 cm s-1 (Fig. 3A). Amiloride (0.1 mM) also reduced the rate of 250 kDa FITC dextran uptake by ~90 %, to 1.3 10-4 cm s-1 (P < 0.001; Fig. 3B). In order to confirm that the accumulation of dextran, and therefore fluid uptake, into the crypts is a Na+-dependent process, photobleaching experiments were performed in Na+-free solutions. Figure 4 shows that the rate of recovery of 10 kDa FITC dextran in Na+-free solution was considerably slower (4 10-5 cm s-1, P < 0.001) than in control.
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Figure 3. Comparisons of FRAP of total dextran uptakes into crypts A, cumulative uptake of 10 kDa dextran in rat descending colonic crypts. Data were analysed from a single experiment representative of at least four such experiments and fitted with the best-fit model parameters. Open circles represent the control data, and filled circles represent data obtained in experiments with amiloride (0.1 mM). The continuous line represents the model line fits for the 10 kDa dextran experiment; the dashed line represents the model line fits for the experiment with amiloride (0.1 mM). The only difference between the model line fits for the control and amiloride data is that with amiloride the Na+ pump flux is reduced to zero from 0.3 µmol cm-2 s-1. The following model parameters were used: dextran diffusion coefficient 9.3 | ||
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Figure 4. Cumulative uptake of 10 kDa dextran in descending colon in Na+-free solution Data as in Fig. 3A fitted with a second-order polynomial. Continuous line, 10 kDa dextran in the control condition; dashed line, 10 kDa dextran with Na+-free solution. | ||
A comparative analysis of the caecal crypts and the descending colon (Fig. 3C, data points) shows that the rate of 10 kDa FITC dextran uptake in the caecal crypts was only 37 % of that found in the descending colon (8.0 10-4 cm s-1).
The cumulative accumulations of FITC dextran (10 and 250 kDa) were easily fitted by the crypt model, as this simply involved matching the integral of dextran uptake into the crypt via the crypt opening with the observed data (Fig. 3, fitted lines). Two major factors determine dextran uptake: the Na+ pump flux, which ultimately provides the driving force for mass flow into the crypt, and the hydraulic conductivity of the crypt wall, which is the main determinant of water flow across the crypt wall. The leak permeability of dextran via the crypt wall is determined directly from the recovery data (see below). The decrease in uptake with amiloride is consistent with a decrease in Na+ pump flux from 0.4 µmol cm-2 s-1 in the control condition, to zero after treatment with amiloride or in Na+-free buffer. No other parameters were altered to obtain the modelled fits for the amiloride-inhibited situation.
In Fig. 3C, dextran uptake into the descending colonic and caecal crypts is compared with and fitted by the model. The lower dextran uptake in the caecal crypts was simulated by a reduced capacity of the crypts to generate a hypertonic absorbate. The only differences simulated were the enhanced (by a factor of 15) leakage of Na+ across the crypt and pericryptal sheath. This is due to the absence of a thick pericryptal sheath in the caecum. The overall effect was to reduce fluid absorption via the crypts, as reflected by the observed recovery data.
Measurement of the permeability of the crypt wall and pericryptal sheath to FITC dextran with FRAP in the descending colonic and caecal crypts
Recovery after photolysis in the pericryptal region is slower than in the crypt lumen. This is consistent with the sequential entry of FITC dextran into the pericryptal region by first entering into the crypt lumen and then across the crypt wall. The permeability of the crypt wall to 10 kDa FITC dextran (Fig. 5) was estimated to be 1.05 (± 0.18) 10-5 cm s-1 (n = 3). With the 250 kDa FITC dextran, the crypt wall permeability was 2.3 (± 0.2) 10-6 cm s-1 (n = 3). The (75 %) reduction in crypt wall permeability (P = 0.01) matches the lower diffusion coefficient of 250 kDa FITC dextran (70 %) compared to 10 kDa FITC dextran (Gribbon & Hardingham, 1998). This is consistent with the view that FITC dextran permeates via a few very large pores across the crypt wall. Caecal crypts are more permeable to 10 kDa FITC dextran than are the descending colonic crypts (2.03 (± 0.21) 10-5 cm s-1; P < 0.02). This is consistent with previous findings that the caecal pericryptal sheath is much sparser than that surrounding descending colonic crypts (Naftalin & Pedley, 1999).
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Figure 5. Permeability of 10 and 250 kDa dextran from the crypt into the pericrypt Data were analysed from descending colon and caecal crypts after photobleaching, and scaled (see Results). Average permeability calculated from the linear fit for 10 kDa dextran in the descending colon (circles) = 1.05 (± 0.18) | ||
Changes in the rates of FITC dextran accumulation along the length of the crypts
Control. Figure 6A and B shows the changing profiles of 10 kDa FITC dextran entry down the crypt at fixed times and at fixed distances along the lumen, respectively. The data points presented in Fig. 6A indicate the concentration of dextran at fixed depths along the crypt length. This increases with time as the dextran moves down the lumen and accumulates. Similarly, Fig. 6B shows the depth-dependent increase in dextran concentration with time. The modelled fits (fitted lines) were obtained by matching the increases in dextran concentrations with time at the assigned distances along the model crypt. The increased delay in fluorescence recovery with increasing depth is a complex function of mass flow along the length of the crypt, which is diminished by increases in the flow of both water and dextran across the crypt wall. This is therefore dependent primarily on both the total fluid entry into the crypt and the differential rate of fluid loss across the crypt wall. The faster fluid is withdrawn, the longer the delays between successive segments at increasing depth. This is determined mainly by two factors, the Na+ pump rate and the crypt wall hydraulic permeability (Lp(crypt wall)). In addition, recovery is slowed along the crypt lumen by a more rapid loss of dextran across the crypt wall. This is controlled by the crypt wall permeability to dextran (Pcrdex)). The advance in the concentration profile along the crypt with time can be measured simply by monitoring the position of the median concentration at different times. The rate of increase in the median concentration position therefore provides an indication of the rate of dextran advance down the crypt (Fig. 7).
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Figure 6. Changes in FITC distributions along crypt lumen after FRAP A, distribution of 10 kDa dextran along the crypt length with time. Observed data (symbols) analysed from a single experiment representative of at least four, and fitted (lines) using model at variable times (in s) for constant depths down the crypt lumen. B, distribution of 10 kDa dextran along the crypt length at constant times. Observed data (symbols) analysed from a single experiment representative of at least four. The parameters are the same as in Fig. 3A except that the Na+ pump flux, JNa pump = 0.25 µmol cm-2. C, distribution of 10 kDa dextran as in A except with amiloride (0.1 mM). JNa pump = 0. D, distribution of 10 kDa dextran as in B except with amiloride (0.1 mM). JNa pump = 0. | ||
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Figure 7. Change in median distribution with time for 250 kDa dextran Data taken from the centre point ( | ||
Amiloride (0.1 mM). The addition of amiloride (0.1 mM) resulted in a reduction in the rate of advance of the concentration profile by approximately 10-fold (to 1.53 10-6 cm s-1; Fig. 6C and Fig. 7). The decreased progression of dextran was simulated and matched to the observed data only by reducing the active Na+ pump flux to zero and holding all the other parameters constant. The very small changes in dextran movement are due to the absence of mass flow. With amiloride present, the only factor generating dextran entry into the crypt is the diffusion coefficient of dextran along the crypt lumen.
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DISCUSSION |
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The most salient feature of the results presented here is that recovery after photobleaching of FITC dextran in rat descending colonic crypts is readily measurable using confocal fluorescence microscopy, and that this provides useful information about the fluid absorptive capacity of the crypts. The accumulation of FITC dextran within the crypt lumen reflects the rate of fluid inflow into the crypt and has been measured to be between 1 10-3 and 2 10-3 cm s-1. The rate of fluid uptake was measured accurately using the normalized rates of total FITC dextran uptake into the crypt lumen and pericryptal sheath. This method is simple, reproducible and is unaffected by the rate of FITC leakage across the crypt lumen. The rates of fluid uptake estimated using 10 and 250 kDa FITC dextran were similar, consistent with entry as determined by mass flow, which does not discriminate on the basis of solute size. Although the computer model may be used to simulate the rates of fluid and dextran uptake, the rates themselves were estimated independently from the first differential of the time course of normalized dextran uptake into the crypts.
Amiloride (0.1 mM) inhibits crypt Na+ conductance channels specifically in the descending colon (Bridges et al. 1989). The slowing of the rate of FITC dextran uptake into the crypts is consistent with the inhibition of fluid absorption by amiloride, which occurs as a direct consequence of inhibition of Na+ absorption. The 70-90 % decrease in the net FITC dextran uptake indicates that convection by fluid uptake into the crypt lumen accelerates FITC dextran uptake by at least 5- to 10-fold.
The rates of flow along the crypt lumen of FITC dextran were also measured using the z-axis scanning facility of the confocal microscope. This showed that the median concentration of FITC dextran spread more rapidly along the crypt length in control conditions than with amiloride present, when the concentration distribution was virtually static. This is a direct demonstration that dextran movement along the crypt is a function of convective flow. The system can be simulated using a model of crypt transport in which the water and dextran flows are coupled to the flow of Na+ via osmotic pressure-induced mass flows across the crypt wall and down the length of the crypt lumen. This permits both corroboration of the observed data and a more advanced analysis of the processes involved in crypt flow.
The other major new result was the direct measurement of FITC dextran permeability across the crypt wall. The significantly slower rate of permeation of 250 kDa FITC dextran than 10 kDa FITC dextran is consistent with permeation through large channels that do not show any significant size discrimination between the two macromolecules. The higher permeability of the caecal crypts to 10 kDa FITC dextran is consistent both with the lower dextran accumulation in these crypt lumens and their lower capacity to dehydrate faeces.
Na+, water and FITC dextran fluxes in the descending colonic crypts.
The singular property of crypts is that they create sufficient suction tension to dehydrate faeces. This implies that a sufficiently hypertonic absorbate must be present in the pericryptal space to generate the osmotic pressure across the crypt wall required to absorb fluid against the large resistance imposed by very high faecal viscosity (McKie et al. 1990). The crypt wall must therefore withstand the large luminal suction tension without collapsing.
The high rate of amiloride-sensitive dextran inflow into the narrow crypt lumens, as demonstrated here, indicates that mass inflow is dependent upon Na+ pump flux. The extent of this inflow and its attenuation along the crypt length can be used to estimate the hydraulic conductivity and dextran permeability of the crypt wall. Estimation of the hydraulic conductivity of the crypt wall depends primarily upon both the rate of fluid flow and the osmotic pressure difference across the crypt wall. The accumulation of dextran in the pericryptal space is also used to estimate the barrier function of the pericryptal sheath.
The comparison of dextran uptake into descending colonic crypts, which have a thick pericryptal sheath, and caecal crypts, which do not (Naftalin & Pedley, 1999), is useful as it gives an indication of the extent to which the pericryptal sheath, or its absence, affects crypt fluid inflow. The rate of fluid uptake is lower in the caecal crypts, and permeability across the caecal crypt wall is greater than in the descending colon. These findings are consistent with the absence of a pericryptal sheath in the caecum, but may also be consistent with raised paracellular permeability in the caecum (Naftalin et al. 1999). However, aquaporin 4 (AQP4)-knockout mice have a much lower caecal hydraulic permeability than wild-type mice (Wang et al. 2000). Since AQP4 is normally present in the basolateral membranes of caecal colonocytes, the reduced hydraulic conductivity of the knockout mutants suggests that paracellular permeability to water may be less important than has previously been thought.
Sodium Green accumulation in the rat descending colonic pericryptal space indicates that Na+ accumulates there to a concentration of 200-300 mM (Pedley & Naftalin, 1993). Na+ accumulates to a much lesser extent around the caecal crypts. More recently, we have used a new, low-affinity Na+ fluorescence indicator dye, Sodium Red (Molecular Probes), to show that the pericryptal sheath of murine descending colonic crypts in vivo has a high Na+ concentration (~500 mM; Jayaraman et al. 2001; Thiagarajah et al. 2001). The flow rate into the descending colonic crypts is 1-2 10-3 cm s-1. There are approximately 15 000 crypts cm-2, and the working length of the crypts is ~170 µm. The radius of the crypt lumen is 6 µm; hence the absorptive surface = 2
r n length 1 cm2 cm-2. Fluid absorption via the crypt lumen is around 25 µl cm-2 h-1 (Naftalin et al. 1995, 1999), hence the Lp of crypt walls is 1-5 10-9 cm s-1 cmH2O-1. The Lp is the combined series conductance of the crypt lumen, crypt wall and the pericryptal sheath. This low crypt luminal Lp is necessary to retard fluid absorption and thereby prevent the dilution of the crypt absorbate. This tight pericryptal sheath makes the crypt wall much less permeable to both water and ions than is the surface mucosa (Gitter et al. 2000).
The main questions regarding colonic crypt absorptive function that remain to be answered concern the extent to which the osmotic pressure gradient across the crypt wall can be transduced to produce a suction tension within the crypt lumen. Assuming that Poiseuille's law describes flow along the cylindrical crypt lumen, then the pressure (g cm-2) required to induce a water flow rate Jv = 2 10-3 cm s-1 through the mucus solution in the crypt lumen (viscosity, 
= 0.02-0.05 P), which has variable radius r = 0.5-5 µm and working length l = 100 µm, is:
Pressure =
2 10-3 r2 8l/(r4) 
1 10-5/r2.
For a tube of radius 1 µm, the pressure required to drive the fluid at a rate of 2 10-3 cm s-1 1 atm (where 1 atm = 101.3 kPa). In addition pressure is required to overcome the external resistance generated by the very high viscosity in faeces (McKie et al. 1990).
In conclusion, we have shown the feasibility of using FRAP to measure fluid inflow into the crypts, and that this inflow is amiloride sensitive. An important outcome of this is new methodology is that crypt wall permeability can be determined accurately, independent of the surface mucosal permeability. This may be a useful quantitative measure of the loss of crypt integrity in pathological conditions involving colonic dysfunction, e.g. following ionizing radiation (Thiagarajah et al. 2000).
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APPENDIX |
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For a description of model equations see Fig. 8.
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Figure 8. Diagram of crypt model parameters J, flux; Lp, hydraulic permeability; P, permeability to Na+; dex, dextran. | ||
Description of model Na+ flows
Three factors govern Na+ movement into crypts, namely diffusion, convection and active transport.
Equation describing Na+ flow into the model crypt lumen. Na+ flow, JcrNa, from crypt luminal element 1 to element 2 is:
| (A1) |
where NaDiffc is the Na+ diffusion coefficient within the crypt lumen corrected for the length of the crypt element DiffNa = 5 10-6 cm2 s-1. The [Na+] in each crypt luminal segment z is CrNa(z). The simulated functional total crypt length is 100 µm; hence for a 10-element crypt, each element length is 10 µm, and for a 20-element crypt each element is 5 µm long. Water flow, Jcw1 is the mass flow between crypt luminal elements 1 and 2. This mass flow generates the convective movements of FITC dextran and also of Na+ along the length of the crypt lumen.
Equation describing Na+ flow across the model crypt wall mucosa. Na+ is actively pumped across the crypt luminal wall. The Km of the Na+ pump is 15 mM Na+ in the crypt lumen. Na+ also moves across the crypt wall by passive permeation, thus the equation describing Na+ flux across the crypt wall, JcNae, is:
| (A2) |
where PNacr (cm s-1) is the Na+ permeability coefficient across the crypt wall and pcryptNa(z) is the [Na+] in the pericryptal segment z.
Equation describing Na+ flow across the model pericryptal barrier. Na+ flows passively between the pericryptal space and the submucosal solution by permeation, and in the convective stream of water flow across the pericryptal sheath:
| (A3) |
where Naex is the external [Na+] and Jwpcs is the water flow across the pericryptal sheath. Since the only way for Na+ to enter the crypt is via the crypt lumen, as it passes along the length of the crypt, both the crypt luminal and pericryptal [Na+] decrease.
Description of water flows
Equation for water flow across the model crypt mucosal wall. Water flux across the crypt wall, Jwt, is determined by the osmotic and hydrostatic pressure gradients existing between the crypt lumen and the adjacent pericryptal sheath. Flow is also determined by the crypt wall hydraulic conductance, Lp(crypt wall). The osmotic and pressure gradients are generated by Na+ flows and by the physical properties of the crypt lumen and pericryptal sheath, which constrain the movement of both water and Na+:
where the osmotic pressure exerted by 1 mM NaCl is 56 cmH2O and crypt luminal pressure, CrP(z), and pericryptal hydrostatic pressure, pcpP(z), are expressed as cmH2O in each segment.
Equation for water flow into the model crypt lumen. Water flux along the length of the crypt lumen, Jcw, is related to the hydrostatic pressure gradient between neighbouring crypt luminal segments. The Lp of the crypt lumen, Lp(crlum), which includes the combined effects of variation of crypt luminal radius and the fluid viscosity within the crypt, determines the rate of water flow along the crypt lumen per cmH2O pressure:
| Jcw1 = Lp(crlum)(CrP1 - CrP2). | (A5) |
Equation for water flow across the model pericryptal sheath. Water flow across any segment z of the pericryptal sheath, Jwpcs(z), is determined by the hydraulic resistance, Lppcp, of the pericryptal sheath and the pressure within the pericryptal sheath segment z, pcpP(z):
|
Jwpcs1 = Lppcp pcpP1.
| (A6) |
Water flow is maximal at the crypt luminal opening and decreases along the length of the crypt as fluid progressively crosses the crypt wall.
Equations determining pressure in the crypt lumen and the pressure change in the model pericryptal sheath
Fluid loss from the crypt generates a large negative pressure within the crypt lumen as the lumen decreases in volume, thereby creating tension in the crypt wall and lumen. As the segmental length is assumed to be constant, the tension within the crypt lumen is assumed to relate to the square root of the crypt segmental volume, Crw(z). Thus:
CrP1 = -Constant +  cr(Crw1),
| (A7) |
where cr is Young's modulus of elasticity of the crypt cells. This is estimated as follows. For each volume element, the cross-sectional area, Crw = r2l. Assuming length is constant, then Crw 
r. By Laplace's law the wall tension, 
, in a cylinder wall is Pr; where P is the pressure in the lumen and r is the lumen radius; hence P Crw. The constant is assigned to give zero pressure at the initial starting volume of Crw(z).
The pressure within the pericryptal sheath pcpP is related to:
|
pcpP1 = -Constant + (pcrptw1) pcc,
| (A8) |
where pcc is Young's modulus of elasticity of the pericryptal sheath. The constant is assigned to give a zero value for pressure at the initial value of the pericryptal volume element pcrptw(z).
Description of FITC dextran flows
Equation for FITC dextran flow along the crypt lumen. FITC dextran flux, Jd(z), along the length of the crypt lumen is, like Na+ flux, related to the concentration gradient 
CrDc(1-2) between neighbouring crypt luminal compartments and the diffusion coefficient of FITC dextran within the crypt lumen. FITC dextran flow is also related to the mass flow along the crypt lumen, Jcw, and the average concentration between each neighbouring segment: (CrDc1 + CrDc2)/2. Hence:
| (A9) |
where dexdiffc is the FITC dextran diffusion coefficient corrected for the length of each luminal segment (10 µm).
Equation for FITC dextran flow across the crypt wall mucosa. FITC dextran flux across any segment z of the crypt wall, JDcrl(z) is determined by its permeation. This is related to the crypt wall permeability to FITC dextran, PcpD, and to the concentration difference of FITC dextran between the crypt lumen and the pericryptal space in the same segment (z), e.g. CrDc1 - pCrpDc1. Hence:
| (A10) |
Equation for FITC dextran flow across the pericryptal sheath. FITC dextran flux across the pericryptal sheath JDpcp(z) in any segment z is determined by the permeability of the sheath to FITC dextran, PDs, and the water flow across the sheath, Jwpcs. It is assumed the submucosal FITC dextran concentration is zero:
| (A11) |
Simulation of FRAP of FITC dextran
Light-induced loss of FITC dextran fluorescence was simulated in all of the compartments where FITC dextran accumulated by an exponential decrease in the amount of FITC dextran in the crypt luminal compartment, D(1-10) or pericryptal JDF compartment, pcD(1-10). Thus photobleaching is simulated as follows:
kp
or
kp2,
where kp and kp2 are the rate constants for loss of FITC dextran in the crypt lumen and pericryptal sheath. Here, FRAP is simulated by simultaneous photolytic loss of FITC dextran fluorescence in all of the crypt luminal and pericryptal segments.
The system of simultaneous differential equations was generated and processed using an extremely fast simulation package, Berkeley Madonna version 8.01 (http://www.berkeleymadonna.com). They were solved using the Rosenbrock method for stiff equations, which uses variable time intervals and is a very efficient method of obtaining solutions. The variables shown here are at steady state and are all plotted against distance along the crypt. A copy of the program may be obtained on application by email to R.J.N.
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REFERENCES |
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Acknowledgements
We wish to thank Professor Alan Verkman University of California San Francisco for advice. The authors are grateful to the Wellcome Trust and the Institute for Nuclear Protection and Security, Fontanay aux Roses, France for financial support.
Corresponding author
R. J. Naftalin: King's College London, Guy's Campus, New Hunts House, Room 2-32, London Bridge, London SE1 1UL, UK.
Email: richard.naftalin{at}kcl.ac.uk
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), as calculated from the sigmoidal distribution of dextran along the crypt length (see Results). Continuous line, 250 kDa dextran; dashed line, 250 kDa dextran with amiloride (0.1 mM).