Exp. Eye Res. (1975) 20, 375-381
The Regulation of Cornea1 Hydration to Maintain High Transparency in Fluctuating Ambient Temperatures STUARTHODRON
Unit of Electron Microscopy, Welsh National School of Medicine. Heath Park. Card# CP4 4XW: U.K. (Received6 November1,974,Londorz) Between 25 and 3572, the hydration of the cornea is nearly constant. The cornea1 endothelium which regulates cornea1 hydration shows considerable changes in its metabolism over the same temperature range. The following explanation is proposed: as the outwardly directed active “pump” in the endothelium decreases in lowered temperatures so the inwardly directed passive “leak” across the endothelium correspondingly decreases to maintain a constant cornea1 hydration.
1. Introduction The hydration of the cornea is maintained constant by a dynamic equilibrium. In one direction, cornea1 stroma strives continuously to swell and increase its hydration (Hedbys and Dohlman, 1963; Hedbys, Mishima and Maurice, 1963). In the other direction, cornea1endothelium continuously dehydrates the stroma by an outwardly directed active “pump” (Mishima and Kudo, 1967; Dikstein and Maurice, 1972). The cornea is so placed in vivo that its temperature is probably significantly influenced by tha,t, of its environment and would therefore fluctuate. Temperature fluctuations would alter the metabolic rate of the “dehydrating pump” in the endothelium. It is shown in this paper that even though the metabolic “pump” in the endothelium may halvth itIs rate as its temperature drops from 35 to 25”(‘, cornea1hydration remains nearly constant. An explanation is offered in terms of the model of cornea1 relations described recently (Hodson, 1974). 2. The Model of Cornea1Water Relations The model is illustrated in Fig. 1. It is basedon the modelsof cornea1water relations proposed by Mishima (1968) and Maurice (1972), with modifications which are partially justified in Hodson (1974). There are three major fluxes into or out, of the cornea, all of which flow acrossthe endothelium. (1) Jf, an outward directed salt flux flowing acrossthe endothelium, which is the dehydrating “pump”. It consists either of sodium bicarbonate or the sodiunl salt of a carboxylated molecule synthesized by the endothelial cells. (2) J,, an inward directed salt flux which as it flows across the endothelium generates (according to Hodson, 1974) the spontantlous electrical 1)otential found acrossthe endothelium (Fischbarg, 1972). (3) J,,, a very nearly iso-osmotic water flux acrossthe endothelium which can. in principle. be calculated from the difference of the two (active outward anal passive inward) salt fluxes. When 9, is the same magnitude as J[ there is no bulk flow of water across the clntiothelium (J, =O) although there remains diff’usional exchange of water (Mishima 375
and Trenberth, 1968). This condition of the model represents a normal cornea and gives a further insight into what is meant by the dynamic equilibrium of’ a normal cornea discussed in the introduction to this paper.
FIG. 1. The two-compartment model of the cornea. The cornea1 endothelium separates the cornael stroma from the bathing medium. The cornea1 stroma contains an invariant quantity of fixed negative charge whose concentration varies with stromal thickness. J,” is the outward directed active salt flux. J, is the inward directed passive salt flux. J, is the outward directed passive water flux.
In a swollen cornea, the inward passive flux of salt J, is reduced but the outward active flux of salt Jc remains constant. In this case, J, is greater than zero and the resultant bulk flow of water out of the cornea causesthe swollen cornea to deturgesce, eventually to return to physiological hydration where J, = Jf (in magnitude) and therefore J, =O, which is the simple description of the state of the equilibrated cornea. The full mathematical model (Hodson, 1974) explains the kinetics of the temperature reversal phenomenon extremely well. So that the model may be used quantitatively, it is essentialthat the permeability of the endothelium to salt and water should be measured. The three relevant parameters are its water permeability or its hydraulic conductivity (ri,), its salt permeability (CO),and the reflection coefficient (0). In addition, the activity of the salt “pump”, Jf, must also be measured. Hydraulic conductivity (L,) and the salt reflection coefficient ((T) may be measured by exposing equilibrated corneas to an osmotic shock (Mishima and Hedbys, 1967). The salt “pump” activity (Jf) and the salt permeability (w) may be measured from examination of the temperature reversal phenomenon (Hodson, 1974). The appropriaLe equations are given in the appendix to this paper. 3. Methods Rabbit cornea,s were mounted under the specular method of Dikstein and Maurice (1972). Osmotic shocks corneas by the method of Mishima and Hedbys (1967). shock experiments were performed on de-epithelialized under the specular microscope. Electrical measurements were taken by the method of Hodson (1974).
microscope and perfused by the were administered to equilibrated T W-Odifferences were that osmotic corneas which were mounted across rabbit cornea1 endothelium
4. Results When the temperature of an equilibrated cornea was changed from 35 to 31°C or 25”C, its thickness
varied
only very slightly
(Fig.
2). Over the same temperature
range there are great changesin the electrical properties of the endothelium. As the temperature drops, its spontaneous electrical potential decreases(Fig. 3) whilst its
REGULATION
OF
CORNEAL
377
HYDRATIOIL’
electrical resistance increases (Fig. 4). As a rough description, Figs 3 and 4 may be said to show that a falling “pump” rate (reflected but not demonstrated by the trans-endothelial potential) is compensated by a decreasing “leak” rate (reflected in its higher electrical resistance).
I
I
3
FIG. 2. Cornea1 as its temperature
L--.-J
6 Time (hr)
9
thickness as a function of temperature. An equilibrated is changed from 35°C ( n ) to 31°C (A) to 25°C ( 0).
700 ? -?- 600
12
cornea
8..
swells only very
slightly
. l .
t
.
A+Temperature
Fl~‘lc:. 3. The spontaneous electrical is markedly temperature dependent.
% 605 *$
potential
found
I
PC)
across the endothelium
of de-epithelializcd
*. 0
50-
. .. .
l d ‘0
5 40-a, 5 .g 30-
8
15
90
t.
@
.
20-
l* . -e* z .a l *i l *
*
. . .
.
IOI IO
I
20
I
lemperature
FM.
4. The electrical
resistance
of cornea1
I
30
endothelium
40
L.
(“Cl
is markedly
temperature
dependent.
corneas
378
S.
HODSON
The temperature-invariant cornea1 thickness (Fig. 2) is better understood if‘ thri phenomenological coefficients. O, U, and LP together with the “pump” rate Jf ;II’C determined. Typical osmotic shock results calculated after the method of Mishima and Hedbys (1967) are given in Table I. Although the hydraulic conductivity of the endotheliurr~ seems to be only slightly dependent-on temperature, the reflection coefficients of both NaCl and NaHCO, increase with decreasing temperature. I
TABLE
The hydraulic conductivity and rejection coejicients in cornea1 endothelium at various temperatures 35°C Solute KaC! MaHCO, Raff inose
“5-c
31°C’
oLpRT"
CJ
14.1 fO.5 13*s*o*9 23.2*0*s
0.61 0.59 1.0-i
o$,RT" 16.3hO.3 16+3-&0.9 23.6f0.6
CJL@T*
0 0.67 0.68 1*0t
19~0~0~3 19*s*o*i 2143*0~5
CT 0.50 O.Sl 1eot
* Units, mm/min; mosmol 1 -l. i- After Mishima and Heclbys (1967).
When corneas pre-swollen at 4°C are warmed to temperatures of 35, 31 or 25°C they show markedly different properties (Fig. 5). Although they all finally equilibrate at or near physiological thickness, two factors are different. First, the higher the temperature the more rapidly cornea1thickness approaches equilibrium. Second, the
, 4
*4-.~,
8 Time
PUG. 5. The temperature-reversal swollen at 4°C for about 1 day.
12 (hr)
I
I
16
20
phenomenon of cornea at various temperatures. C’orneas wt~ They were then re-warmed to ( n ) 35”C, (A) 31°C. or (a) 25°C’.
pre-
lower the temperature the longer the life-time of the preparation. (The life-time of the preparation is terminated by a rapid and irreversible swelling of the cornea). ,411 the curves in Fig. 5 can be fitted to equation 2 in the appendix by choosing appropriate values for Jf, the salt “pump” activity. The mean values together with their
REGULATION
OF
CORNEA],
HYDRATION
standard errors are given in Fig. 6. Finally using equation 3 in the appendix with the fact that the equilibrated cornea1 thickness is nearly temperature invariant in the range 25-35°C (Fig. 2), the salt permeability may be calculated. The results are given in Pig. 6.
_” -s I.OOQ L-z -2 I b 25 0
I 30 Cornea1
temperature
6. The variation with temperature of the endothelial pctmeability to NaHC’O, (0, right side ordinate). FIG.
I ) 35
it!-2;
(“C)
salt “pump3”
(a,
left sick ordinate)
anti its
5. Discussion The cornea is well adapted to deal with fluctuations of its temperature. The dynamic “pump versus leak” equilibrium which maintains cornea1 hydration (and therefore transparency) is so arranged that as the “pump” decreases in lowered temperatures, so the “leak” correspondingly decreases. Clearly there is a limiting low temperature when this compensation can no longer apply. For example at 4”C, the cornea does swell, although comparatively slowly. Bito, Roberts and Saraf (1973) have made interesting observations on the cornea of the hibernating woodchuck. which in vivo may be as cold as 9°C. They show that the cornea does not swell becausfl tile pump-leak may still mutually compensate. The in vitro rabbit cornea1 endothelium at telnperatures as low as 9°C demonstrates a pumping activity (Fig. 3). The main point of Bito et al. (1973) is that the cornea does swell in vitro at 9”C, but not in vivo at 9°C. Whether this is a general phenomenon or an adaptation of hibernating animals is difficult to test. Although Bito et al. (1973) show that the 0, consumption at 8°C of co meal endothelium is higher in hibernating than active woodchucks, the nleasurements are made in vitro and do not bear directly on the in vivo: in vitro ctifferences. From Table I and Fig. 6, the following conclusions may be drawn about the properties of cornea1 endothelium in the temperature range 35-25°C. The hydraulic caonductivity decreases only slightly. The energy of activation for water movement across the endothelium is less than 6.0 kcal mol-I. In contrast, the reflection c:oefficients of both NaCl and NaHCO, increase with decreasing temperature. The cornea1 endothelium becomes more like a semi-permeable membrane at lower temperatures. Figure 6 shows the “salt pump” in the endothelium to have a Q10 of 2. The Qlo of’ oxygen . _ consumption by cornea1 endothelium is also 2 (Freeman, 1972). As the endothelial pump is known to be dependent on aerobic metabolism (Riley, personal communication), the equality is probably more than coincidence. According to the present model, the “pump” is the outward directed active salt, flux across the endothelium and the “leak” is the inward directed passive salt flux. The passive flux. J,, is determined by the leakiness of the endothelium. Curiously, it
S.
380
HODSON
is not determined by the salt permeability (4 alone, but by its ratio to reflection coefficient (a)-see equation 3 in the appendix. As Jf decreases order to maintain a constant cornea1 hydration, the ratio 0~:o must decrease by an equal amount. How the cornea works this trick is a mystery. There seems to be no simple way in which these three properties Jf, CO,and CTcould be coupled together to produce the established phenomenon of (limited) temperature invariance of corncal hydration.
Appendix (1) The m,easurement oj’ Lp and a A cornea is equilibrated to constant thickness by bathing in an aqueous medium wnose osmotic pressure is nOe If the cornea is then exposed to a different aqueous med ium whose osmotic pressure is increased by an amount An: the cornea will . shrink to a, new equilibrium thickness. The initial rate of thickness change is given by the equation : dx -= -.aI;$An: d&j where x =corneal thickness, t =time and a and Lp (which we are trying to measure) are respectively the reflection coefficient of the solute which was added to increase the osmotic pressure of the bathing solution and the hydraulic conductivity of the cornea1 endothelium. The equaGon was first given in the definitive paper of Mishima. and Hedbys (1967). They p ointed out, that the initial rate of slvelling is a very difficult quantity to measure accurately and suggested that more accurate values of (Tand L, could be had by investigating the whole time course of the osmotic shrinkage with the equation : In nAn(lc, ---as) aL t + hl +nm ( _ ) ==:(?I +nw (1) (‘rr,+nAv)(x --x8) --T~(cc~-xJ r,(zp -x;,) xp ’ n77,(xp -x8) p *’ ’ ’ with the terminal boundary condition as t--a (xp -Xs>% = km -Xs)(% +nA4 where x = cornea1thickness; xP=thickness of a cornea equilibrated against bathing medium of osmotic pressuren, ; x, = the non-osmotic thickness of the cornea (equal to about 70 ,um) ; 2, =the final thickness of the cornea after it has been exposed to an additional osmotic pressureof AYT; p2=the ratio a:a,; a =the reflection coefficient of the added solute; a, =the reflection coefficient of solute in the original bathing solution LP = hydraulic conductivity of the endothelium; t =time. (2) The measurementof Jf Jf, the salt “pump” activity in the endothelium may be measured from examination of the kinetics of the thickness change of a cornea as it undergoes the temperature reversal phenomenon, from the equation : -(x-x,)
+(xp -x,)coth-1
(z (5 -4
zz 3 +a . . . , c,a
(‘2)
REGULATION
OF
CORNEAL
HYDRATION
3X 1
where c,~=salt concentration in the bathing medium, ccis determined by the boundar! condition at the start of the experiment.
Themeasuwment
(3)
Salt permeability
of o
~1)may be measured from the equilibrium J:
=---
condition,
mRTQ2 4m, * - - ?
where Q is the ion exchange capacity of the cornea1 stroma (at physiological equal t,o 47 meyuiv./l stromal fluid).
(3) hydration
REFERENCES Bito,
1,. Z., Roberts, J. C. and Saraf, S. (1973). Maintenance of normal cornea1 thickness in t,he cold in vivo (hibernation) as opposed to in vitro. J. Physiol. (London) 231, 71. Dik&ein, S. and Maurice, D. (1972). The metabolic basis to the fluid pump in the cornea. .i, Physiol. (London) 221, 29. Freeman, R. D. (1972). Oxygen consumption by the component layers of the cornea. J. Physiol. (London) 225, 15. Hedbys, B. 0. and Dohlman, C. H. (1963). A new method for the determination of the swelling pressure of the cornea1 stroma in vitro. Exp. Eye Res. 2, 122. Hedbys, B. O., Mishima, S. and Maurice, D. M. (1963). The imbibition pressure of the cornea1 stroma. Exp. Eye Res. 2,99. Hodson, S. (1974). The regulation of cornea1 hydration by a salt pump requiring the presencr ot sodium and bicarbonate ions. J. Physiol. (London) 236, 271. Maurice. D. M. (1957). The structure and transparency of the cornea. J. Physiol. (London) 136, 263.
Jlauricae, D. M. (1972). The location of the fluid pump in the cornea. J. Physiol. (London) 221, 43. Mishima, S. (1968). Cornea1 thickness. Survey Ophthalmol. 13, 57. Mishima, S. and Hedbys, B. 0. (1967). The permeability of the cornea1 epithelium and endothelium to water. Exp. Eye Res. 6, 10. Mishima. S. and Kudo, T. (1967). In vitro incubation of rabbit cornea. Invest. Ophthcxlmol. 6, 329. Mishinla. S. and Trenberth, 8. M. (1968). Permeability of the caorneal endothelium to nonelectroI~tw. Invest. Ophthalmol. 7, 34.
The Regulation of Cornea1 Hydration to Maintain High Transparency in Fluctuating Ambient Temperatures STUARTHODRON
Unit of Electron Microscopy, Welsh National School of Medicine. Heath Park. Card# CP4 4XW: U.K. (Received6 November1,974,Londorz) Between 25 and 3572, the hydration of the cornea is nearly constant. The cornea1 endothelium which regulates cornea1 hydration shows considerable changes in its metabolism over the same temperature range. The following explanation is proposed: as the outwardly directed active “pump” in the endothelium decreases in lowered temperatures so the inwardly directed passive “leak” across the endothelium correspondingly decreases to maintain a constant cornea1 hydration.
1. Introduction The hydration of the cornea is maintained constant by a dynamic equilibrium. In one direction, cornea1 stroma strives continuously to swell and increase its hydration (Hedbys and Dohlman, 1963; Hedbys, Mishima and Maurice, 1963). In the other direction, cornea1endothelium continuously dehydrates the stroma by an outwardly directed active “pump” (Mishima and Kudo, 1967; Dikstein and Maurice, 1972). The cornea is so placed in vivo that its temperature is probably significantly influenced by tha,t, of its environment and would therefore fluctuate. Temperature fluctuations would alter the metabolic rate of the “dehydrating pump” in the endothelium. It is shown in this paper that even though the metabolic “pump” in the endothelium may halvth itIs rate as its temperature drops from 35 to 25”(‘, cornea1hydration remains nearly constant. An explanation is offered in terms of the model of cornea1 relations described recently (Hodson, 1974). 2. The Model of Cornea1Water Relations The model is illustrated in Fig. 1. It is basedon the modelsof cornea1water relations proposed by Mishima (1968) and Maurice (1972), with modifications which are partially justified in Hodson (1974). There are three major fluxes into or out, of the cornea, all of which flow acrossthe endothelium. (1) Jf, an outward directed salt flux flowing acrossthe endothelium, which is the dehydrating “pump”. It consists either of sodium bicarbonate or the sodiunl salt of a carboxylated molecule synthesized by the endothelial cells. (2) J,, an inward directed salt flux which as it flows across the endothelium generates (according to Hodson, 1974) the spontantlous electrical 1)otential found acrossthe endothelium (Fischbarg, 1972). (3) J,,, a very nearly iso-osmotic water flux acrossthe endothelium which can. in principle. be calculated from the difference of the two (active outward anal passive inward) salt fluxes. When 9, is the same magnitude as J[ there is no bulk flow of water across the clntiothelium (J, =O) although there remains diff’usional exchange of water (Mishima 375
and Trenberth, 1968). This condition of the model represents a normal cornea and gives a further insight into what is meant by the dynamic equilibrium of’ a normal cornea discussed in the introduction to this paper.
FIG. 1. The two-compartment model of the cornea. The cornea1 endothelium separates the cornael stroma from the bathing medium. The cornea1 stroma contains an invariant quantity of fixed negative charge whose concentration varies with stromal thickness. J,” is the outward directed active salt flux. J, is the inward directed passive salt flux. J, is the outward directed passive water flux.
In a swollen cornea, the inward passive flux of salt J, is reduced but the outward active flux of salt Jc remains constant. In this case, J, is greater than zero and the resultant bulk flow of water out of the cornea causesthe swollen cornea to deturgesce, eventually to return to physiological hydration where J, = Jf (in magnitude) and therefore J, =O, which is the simple description of the state of the equilibrated cornea. The full mathematical model (Hodson, 1974) explains the kinetics of the temperature reversal phenomenon extremely well. So that the model may be used quantitatively, it is essentialthat the permeability of the endothelium to salt and water should be measured. The three relevant parameters are its water permeability or its hydraulic conductivity (ri,), its salt permeability (CO),and the reflection coefficient (0). In addition, the activity of the salt “pump”, Jf, must also be measured. Hydraulic conductivity (L,) and the salt reflection coefficient ((T) may be measured by exposing equilibrated corneas to an osmotic shock (Mishima and Hedbys, 1967). The salt “pump” activity (Jf) and the salt permeability (w) may be measured from examination of the temperature reversal phenomenon (Hodson, 1974). The appropriaLe equations are given in the appendix to this paper. 3. Methods Rabbit cornea,s were mounted under the specular method of Dikstein and Maurice (1972). Osmotic shocks corneas by the method of Mishima and Hedbys (1967). shock experiments were performed on de-epithelialized under the specular microscope. Electrical measurements were taken by the method of Hodson (1974).
microscope and perfused by the were administered to equilibrated T W-Odifferences were that osmotic corneas which were mounted across rabbit cornea1 endothelium
4. Results When the temperature of an equilibrated cornea was changed from 35 to 31°C or 25”C, its thickness
varied
only very slightly
(Fig.
2). Over the same temperature
range there are great changesin the electrical properties of the endothelium. As the temperature drops, its spontaneous electrical potential decreases(Fig. 3) whilst its
REGULATION
OF
CORNEAL
377
HYDRATIOIL’
electrical resistance increases (Fig. 4). As a rough description, Figs 3 and 4 may be said to show that a falling “pump” rate (reflected but not demonstrated by the trans-endothelial potential) is compensated by a decreasing “leak” rate (reflected in its higher electrical resistance).
I
I
3
FIG. 2. Cornea1 as its temperature
L--.-J
6 Time (hr)
9
thickness as a function of temperature. An equilibrated is changed from 35°C ( n ) to 31°C (A) to 25°C ( 0).
700 ? -?- 600
12
cornea
8..
swells only very
slightly
. l .
t
.
A+Temperature
Fl~‘lc:. 3. The spontaneous electrical is markedly temperature dependent.
% 605 *$
potential
found
I
PC)
across the endothelium
of de-epithelializcd
*. 0
50-
. .. .
l d ‘0
5 40-a, 5 .g 30-
8
15
90
t.
@
.
20-
l* . -e* z .a l *i l *
*
. . .
.
IOI IO
I
20
I
lemperature
FM.
4. The electrical
resistance
of cornea1
I
30
endothelium
40
L.
(“Cl
is markedly
temperature
dependent.
corneas
378
S.
HODSON
The temperature-invariant cornea1 thickness (Fig. 2) is better understood if‘ thri phenomenological coefficients. O, U, and LP together with the “pump” rate Jf ;II’C determined. Typical osmotic shock results calculated after the method of Mishima and Hedbys (1967) are given in Table I. Although the hydraulic conductivity of the endotheliurr~ seems to be only slightly dependent-on temperature, the reflection coefficients of both NaCl and NaHCO, increase with decreasing temperature. I
TABLE
The hydraulic conductivity and rejection coejicients in cornea1 endothelium at various temperatures 35°C Solute KaC! MaHCO, Raff inose
“5-c
31°C’
oLpRT"
CJ
14.1 fO.5 13*s*o*9 23.2*0*s
0.61 0.59 1.0-i
o$,RT" 16.3hO.3 16+3-&0.9 23.6f0.6
CJL@T*
0 0.67 0.68 1*0t
19~0~0~3 19*s*o*i 2143*0~5
CT 0.50 O.Sl 1eot
* Units, mm/min; mosmol 1 -l. i- After Mishima and Heclbys (1967).
When corneas pre-swollen at 4°C are warmed to temperatures of 35, 31 or 25°C they show markedly different properties (Fig. 5). Although they all finally equilibrate at or near physiological thickness, two factors are different. First, the higher the temperature the more rapidly cornea1thickness approaches equilibrium. Second, the
, 4
*4-.~,
8 Time
PUG. 5. The temperature-reversal swollen at 4°C for about 1 day.
12 (hr)
I
I
16
20
phenomenon of cornea at various temperatures. C’orneas wt~ They were then re-warmed to ( n ) 35”C, (A) 31°C. or (a) 25°C’.
pre-
lower the temperature the longer the life-time of the preparation. (The life-time of the preparation is terminated by a rapid and irreversible swelling of the cornea). ,411 the curves in Fig. 5 can be fitted to equation 2 in the appendix by choosing appropriate values for Jf, the salt “pump” activity. The mean values together with their
REGULATION
OF
CORNEA],
HYDRATION
standard errors are given in Fig. 6. Finally using equation 3 in the appendix with the fact that the equilibrated cornea1 thickness is nearly temperature invariant in the range 25-35°C (Fig. 2), the salt permeability may be calculated. The results are given in Pig. 6.
_” -s I.OOQ L-z -2 I b 25 0
I 30 Cornea1
temperature
6. The variation with temperature of the endothelial pctmeability to NaHC’O, (0, right side ordinate). FIG.
I ) 35
it!-2;
(“C)
salt “pump3”
(a,
left sick ordinate)
anti its
5. Discussion The cornea is well adapted to deal with fluctuations of its temperature. The dynamic “pump versus leak” equilibrium which maintains cornea1 hydration (and therefore transparency) is so arranged that as the “pump” decreases in lowered temperatures, so the “leak” correspondingly decreases. Clearly there is a limiting low temperature when this compensation can no longer apply. For example at 4”C, the cornea does swell, although comparatively slowly. Bito, Roberts and Saraf (1973) have made interesting observations on the cornea of the hibernating woodchuck. which in vivo may be as cold as 9°C. They show that the cornea does not swell becausfl tile pump-leak may still mutually compensate. The in vitro rabbit cornea1 endothelium at telnperatures as low as 9°C demonstrates a pumping activity (Fig. 3). The main point of Bito et al. (1973) is that the cornea does swell in vitro at 9”C, but not in vivo at 9°C. Whether this is a general phenomenon or an adaptation of hibernating animals is difficult to test. Although Bito et al. (1973) show that the 0, consumption at 8°C of co meal endothelium is higher in hibernating than active woodchucks, the nleasurements are made in vitro and do not bear directly on the in vivo: in vitro ctifferences. From Table I and Fig. 6, the following conclusions may be drawn about the properties of cornea1 endothelium in the temperature range 35-25°C. The hydraulic caonductivity decreases only slightly. The energy of activation for water movement across the endothelium is less than 6.0 kcal mol-I. In contrast, the reflection c:oefficients of both NaCl and NaHCO, increase with decreasing temperature. The cornea1 endothelium becomes more like a semi-permeable membrane at lower temperatures. Figure 6 shows the “salt pump” in the endothelium to have a Q10 of 2. The Qlo of’ oxygen . _ consumption by cornea1 endothelium is also 2 (Freeman, 1972). As the endothelial pump is known to be dependent on aerobic metabolism (Riley, personal communication), the equality is probably more than coincidence. According to the present model, the “pump” is the outward directed active salt, flux across the endothelium and the “leak” is the inward directed passive salt flux. The passive flux. J,, is determined by the leakiness of the endothelium. Curiously, it
S.
380
HODSON
is not determined by the salt permeability (4 alone, but by its ratio to reflection coefficient (a)-see equation 3 in the appendix. As Jf decreases order to maintain a constant cornea1 hydration, the ratio 0~:o must decrease by an equal amount. How the cornea works this trick is a mystery. There seems to be no simple way in which these three properties Jf, CO,and CTcould be coupled together to produce the established phenomenon of (limited) temperature invariance of corncal hydration.
Appendix (1) The m,easurement oj’ Lp and a A cornea is equilibrated to constant thickness by bathing in an aqueous medium wnose osmotic pressure is nOe If the cornea is then exposed to a different aqueous med ium whose osmotic pressure is increased by an amount An: the cornea will . shrink to a, new equilibrium thickness. The initial rate of thickness change is given by the equation : dx -= -.aI;$An: d&j where x =corneal thickness, t =time and a and Lp (which we are trying to measure) are respectively the reflection coefficient of the solute which was added to increase the osmotic pressure of the bathing solution and the hydraulic conductivity of the cornea1 endothelium. The equaGon was first given in the definitive paper of Mishima. and Hedbys (1967). They p ointed out, that the initial rate of slvelling is a very difficult quantity to measure accurately and suggested that more accurate values of (Tand L, could be had by investigating the whole time course of the osmotic shrinkage with the equation : In nAn(lc, ---as) aL t + hl +nm ( _ ) ==:(?I +nw (1) (‘rr,+nAv)(x --x8) --T~(cc~-xJ r,(zp -x;,) xp ’ n77,(xp -x8) p *’ ’ ’ with the terminal boundary condition as t--a (xp -Xs>% = km -Xs)(% +nA4 where x = cornea1thickness; xP=thickness of a cornea equilibrated against bathing medium of osmotic pressuren, ; x, = the non-osmotic thickness of the cornea (equal to about 70 ,um) ; 2, =the final thickness of the cornea after it has been exposed to an additional osmotic pressureof AYT; p2=the ratio a:a,; a =the reflection coefficient of the added solute; a, =the reflection coefficient of solute in the original bathing solution LP = hydraulic conductivity of the endothelium; t =time. (2) The measurementof Jf Jf, the salt “pump” activity in the endothelium may be measured from examination of the kinetics of the thickness change of a cornea as it undergoes the temperature reversal phenomenon, from the equation : -(x-x,)
+(xp -x,)coth-1
(z (5 -4
zz 3 +a . . . , c,a
(‘2)
REGULATION
OF
CORNEAL
HYDRATION
3X 1
where c,~=salt concentration in the bathing medium, ccis determined by the boundar! condition at the start of the experiment.
Themeasuwment
(3)
Salt permeability
of o
~1)may be measured from the equilibrium J:
=---
condition,
mRTQ2 4m, * - - ?
where Q is the ion exchange capacity of the cornea1 stroma (at physiological equal t,o 47 meyuiv./l stromal fluid).
(3) hydration
REFERENCES Bito,
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