- Email: [email protected]
The Ordering of Corneal Collagen Fibrils with Increasing Ionic Strength
doi:10.1016/j.jmb.2003.12.001
J. Mol. Biol. (2004) 336, 179–186
The Ordering of Corneal Collagen Fibrils with Increasing Ionic Strength J.W. Regini1*, G.F. Elliott1 and S.A. Hodson2 1 The Structural Biophysics Group, School of Optometry and Vision Sciences, Cardiff University, Cardiff CF10 3NB UK 2
Nuffield Laboratory of Ophthalmology, University of Oxford, Walton Street, Oxford OX2 6AW, UK *Corresponding author
The fixed stromal charge of bovine corneas, osmotically clamped at physiological hydration, was altered by regulating the amount of chloride ions bound to the matrix. We measured the local fibrillar collagen order using X-ray diffraction methods. As the bound anions increased up to physiological values, the local fibrillar order increased to an optimal value. The coherence distance ðtÞ approximately doubles to a maximum value (409 nm) from 10 mM NaCl to 154 mM NaCl. This then slowly decreased as the bathing solution increased to 1000 mM. In contrast the diameter of the collagen fibrils were minimal at physiological NaCl. q 2003 Elsevier Ltd. All rights reserved.
Keywords: cornea; chloride; fibrillar order
Introduction Corneal stroma is transparent to light and comprises over 90% of the thickness of the mammalian cornea. It consists mainly of aqueous solution and collagen fibrils. Each collagen fibril has a significantly higher refractive index than the aqueous solution and correspondingly scatters a small fraction of light incident upon it. When this scattered light is summated through the whole thickness of the corneal stroma (about 500 mm, fibril diameter 30.8 nm, nearest-neighbour distance 55.3 nm, in humans),1 the cornea would be effectively opaque if the scattering were non-co-operative. Scattered light from neighbouring fibrils must interfere cooperatively and neutralise lateral scattering. It is generally agreed for this co-operative phenomena to exist, the collagen fibrils must all be of an equal diameter, which is smaller than the wavelength of light and oriented approximately orthogonally to the direction of light. However, the need for ordering between nearest neighbours is not generally agreed. Theories have been proposed that range from total ordering (i.e. the collagen fibrils form a regular lattice) to the suggestion that no ordering is required and that any array of equal sized filaments whose diameter is smaller than l/4 will be transparent provided that they are in a pseudoparallel array and that there are no substantial
E-mail address of the corresponding author: [email protected]
voids in the disordered lattice which are comparable in dimension to the wavelength of light. We addressed the nature of the relationship between nearest-neighbour ordering and transparency experimentally, utilising some recent data on the corneal stroma. A striking phenomenon of the corneal stroma is its ability to swell to many times its original weight when it is placed in aqueous solutions. The cause of corneal swelling is well understood and arises from the gel pressure associated with the net fixed negative charge of the corneal stromal matrix (for reviews, see Hodson2 and Elliott & Hodson3). In vivo, the swelling tendency of the corneal stroma does not manifest because of the presence of a balancing outward-directed bicarbonate ion pump located in the corneal endothelium lining the posterior surface of the stroma. If the stroma is allowed to swell it quickly loses its transparency and becomes progressively more opaque. Collagen itself has little net charge at physiological pH, so there are two sources for the corneal stroma’s negative charge, which generate stromal gel pressure. One source comprises the acid groups of the stromal glycosaminoglycans, the keratan sulphate groups and chondroitin/dermatan sulphate groups; the other source is anion binding (usually supplied by the chloride ion in the physiological situation). The net negatively charged glycosaminoglycans radiate from the collagen fibrils into the surrounding interfibrillar fluid. The spatial location of the anion binding ligands is less certain but neutron scattering data favour the suggestion that the anion binding ligands are located within the collagen
0022-2836/$ - see front matter q 2003 Elsevier Ltd. All rights reserved.
180 fibrils.4 Surrounding these negatively charged assemblies are electrical fields, which give rise to double-layer ordering forces.5 – 9 Whereas the acidic groups of the glycosaminoglycans are invariant at physiological pH and generate a constant contribution to the net negative charge of the corneal stroma, stromal anion binding is reversible and so it is possible to alter the stromal net negative charge concentration whilst maintaining the same interfibrillar average distance simply by equilibrating against different salt concentrations in the bathing medium whilst the stroma is osmotically clamped. When this is done it has been shown that the transparency of the corneal stroma increases as the anion binding increases up to physiological concentrations of anion.10 We report here how the interfibrillar structural ordering alters with increasing anion binding.
Ordering of Corneal Collagen Fibrils
Results Hydrations Corneal stromal hydration was specified by the parameter H; where: H¼
wet weight 2 dry weight dry weight
Due to a slight amount of water loss from the tissues during the experiments, all specimens were weighed before and after X-ray exposure. An average weight was then established from the two readings; this allowed us to calculate the tissue hydration at the time of the experiment. The reduction in hydration in individual corneas varied over a range between 1.6% and 2.4%.
Figure 1. The X-ray intensity profiles and first-order interfibrillar reflections from X-ray patterns of corneas in (a) 300 mM NaCl and (b) 30 mM NaCl.
181
Ordering of Corneal Collagen Fibrils
Low angle X-ray patterns The X-ray patterns of 12 separate corneas ðn ¼ 12Þ were taken at each NaCl concentration. It was found that below physiological NaCl concentration (154 mM) the sharpness of the first order equatorial reflection increased with increasing ionic strength. Figure 1(a) and (b) shows the intensity profiles along the length of the whole X-ray patterns of corneas dialysed against 300 mM NaCl and 30 mM NaCl, respectively. The inserts only show the corresponding low-angle first-order interfibrillar reflections from the X-ray patterns, the central white rectangle is the shadow of the lead backstop. The two profiles and patterns shown are typical of high and low NaCl concentrations (note how diffuse the interfibrilar reflection at 30 mM is when compared with that at 300 mM). As can be clearly seen, at and above 154 mM NaCl the interfibrillar reflections were characterised by welldefined and intense reflections (Figure 1(a)). By comparison, those from 10 mM to 154 mM NaCl were found to show a steady increase in scattered intensity and somewhat broader in relation to the peak height than those at higher concentrations (Figure 1(b)). Moreover, as the concentration was raised from 10 mM to 154 mM NaCl, the intensity of the interfibrillar reflection showed a steady increase. Figure 2 shows the X-ray intensity profiles of 12 averaged corneas at all NaCl concentrations, which demonstrates the effect of increasing intensity and sharpness of the peaks when the ionic strength of the dialysing solution is raised. The slight change in the position of the interfibrillar reflections between all three profiles is due to the slight variation in the hydrations of the corneas studied. After the subtraction of the background scatter, the interfibrillar distance ðdÞ and the angular
width ðbÞ were measured. The interfibrillar distance ðdÞ showed no significant change over the range of NaCl concentrations used, with mean value of 56.5(^ 1.1) nm. Figure 3 shows the interfibrillar peak of the cornea in 154 mM NaCl of Figure 2, before (dotted line) and after (continuous line) a background has been fitted and subtracted. The pattern has been folded around its centre and the x axis is now plotted in inverse space (R). The fibril diameter d was calculated from the first subsidiary maxima of the low-angle X-ray patterns, using the methods described by Meek et al.11 Figure 4 shows the results for six corneas (the standard error for each point was found to be equal to or less than 2% of the mean), and the diameter of the collagen fibrils were minimal at physiological NaCl, although there was no strong trend except at 1 M NaCl. The mean diameter was found to be 38.9 nm (excluding the data at 1 M), which is in good agreement with the value 38.2 nm given by Leonard & Meek12 for bovine corneas. The ordering of the lattice The angular width of a reflection ðbÞ is related to a parameter ðtÞ that gives some measure of the limited size of the lattice, or the disorder in the lattice, by the approximation: b<
2l ðt cos uÞ
ð1Þ
where u is the Bragg angle.13 Stokes13 discusses the possible meanings of the parameter t (section 10 of his article) and gives as one of his possible alternatives “the order of the average distance over which the exact periodicity begins to fail”. This is probably the appropriate meaning in our case. We choose to call this parameter the
Figure 2. The averaged X-ray intensity profiles of corneas at all NaCl concentrations.
182
Ordering of Corneal Collagen Fibrils
Figure 3. The interfibrillar peak of a cornea in 154 mM NaCl before (dotted line) and after (continuous line) a background has been fitted and subtracted. The pattern has been folded around its centre and x axis is now plotted in inverse space ðRÞ:
“coherence distance”. The Bragg equation is: nl ¼ 2d sin u
ð2Þ
where the symbols have their conventional meaning, and we may combine these two equations to give: bt < 2d tan u
ð3Þ
in the first-order of diffraction. At small angles tan u ¼ u; and we obtain: t
2u b
ð4Þ
Note that the numerical constant 2 in equation (2) is replaced by 1, as Stokes13 states that “more exact treatments give a value closer to unity”. The ratio of angles, 2u=b and interfibrillar spacing d we obtained from linear measurements on data sets such as Figure 3 (following convention, b is taken as the angular width of the reflection at half height). Table 1 gives the measured angular width ðbÞ of the reflection and our calculated values of the coherence distance ðtÞ: Figure 5(a) and (b) shows both these parameters plotted as a function of salt concentration (in both cases the standard error was found to be less than or equal to 2.3% of the
Figure 4. The fibril diameter ðdÞ plotted as a function of NaCl concentration. For each point n ¼ 6:
183
Ordering of Corneal Collagen Fibrils
Table 1. The calculated lattice size t and measured angular widths of the interfibrillar peaks at all NaCl concentrations NaCl (mM) 10 30 50 100 154 300 600 1000
t (nm)
b (rad)
235 238 276 329 409 349 397 356
0.000655 0.000648 0.000559 0.000468 0.000376 0.000442 0.000388 0.000428
mean of each value). The data show that at low ionic strength ðtÞ is at about 237 nm, increasing rapidly up to a maximum value of 409 nm at physiological values (Figure 5(a)). At higher salt concentrations the lattice size decreases and remains fairly constant with a mean value about 367 nm. Conversely, the angular width shows an inversely identical trend, with broader peaks at low ionic strength reaching a minimum at 154 nm NaCl (Figure 5(b)). This analysis shows, as a ballpark figure, that the fibrillar order is maintained as an average over about one-half of a lamella
when the ionic strength is high, and only over about half that distance when it is low.
Discussion The data support the concept that corneal transparency and ordering of the fibrillar lattice are related, as we discuss below. We interpret our findings in terms of the anion binding models proposed by Elliott14 and Elliott & Hodson3 who state that as the NaCl concentration is increased, chloride ions increasingly bind to the collagen fibrils. As mentioned earlier, recent neutron scattering data suggest that the location of the chloride binding ligands are located mainly within the collagen fibrils.4 Anion binding ligands are likely to involve the spatial proximity of two or more structural charged groups.15 The result of increased chloride ion binding is that the fibrils become increasingly electro-negative. This increase in negative charge gives rise to an extra repulsive force between the fibrils. It is this repulsive force which we propose is the ordering force of the fibrillar lattice. The measured increments in bound stromal negative charge with increasing chloride
Figure 5. (a) The coherence distance ðtÞ; filled triangles, and (b) the measured angular width ðbÞ; open circles, plotted as a function of salt concentration.
184
concentrations in the bathing medium up to physiological values (charge (mM)/chloride (mM)) are: 3/10, 7/30, 13/50, 18/100, 24/154. These data are consistent with our observations, reported here, of increasing structural order. The relationship between the increase in structurally fixed electrical charge and the resulting force produced has been observed in other biological cylindrical gel systems. For example, Millman & Nickel7 observed similar behaviour in both tobacco mosaic virus and vertebrate striated muscle. In the well documented approximation of the classical theory of corneal light scattering,16 the light scattering cross-section of an individual collagen fibril, besides being a function of the wavelength of the incident light, is related to the fourth power of the fibril diameter and a complex function of the refractive index of the medium surrounding the fibril and the refractive index of the fibril itself. In the experiments reported here, where the fibril diameters change in response to the ionic strength, the changes indicate water removal from the fibril as the salt increases up to physiological strength, followed by a possible charge repulsion effect in the intrafibrillar space which allows water molecules to re-enter. For the purposes of calculating the scattering cross-section of the fibrils exposed to various salt concentrations, we have made the assumption that the diameter changes as the result of the addition or loss of the solvent and its ionic constituents alone, which have a refractive index of 1.335 at 530 nm (with a slight wavelength dependence which is too small to significantly affect the following calculations). In fact, Leonard & Meek12 have shown how it is possible to calculate the refractive index and the surrounding medium and have done so for isotonic solutions, but until these calculations are repeated for non-isotonic media, we shall assume the above model. Using our published values of fibril diameter and the approximations outlined above, we calculate the scattering cross-sections of the fibrils in solutions of differing ionic strengths,
Ordering of Corneal Collagen Fibrils
relative to the fibril in isotonic saline to be: units, % (saline molarity): 101.6 (10); 107.2 (30); 98.2 (50); 96.0 (100); 100 (154); 98.6 (300); 101.6 (600); 104.9 (1000). In general, the simple summation of the light scattering across the whole cornea would give only about 6 –8% transmission of the incident light.16,17 The much higher observed values of transmitted light are ascribed to constructive interference phenomena which is dependent on relative ordering of the fibrillar array which is, of course related to the values of the coherence distance ðtÞ, given here. A simple normalised comparison of light transmission at 400 nm taken from our earlier optical study10 (very slightly corrected for the relative scattering cross-sections of the fibrils) and t is shown in Figure 6. In general, Figure 6 indicates that there is a relationship between light transmission and coherence distance but then the relationship is different for hypotonic values of the bathing solution than it is for hypertonic values. We had previously noticed a similar difference for light transmission: hypo- and isotonic values showed light transmission to follow a l23 law, consistent with classical optical theory, whilst hypertonic values showed a l22 relationship for which we could find no known theory.10 It may be that above a certain level of ion binding, other disorder phenomena could appear and the fibrils themselves begin to lose their structural integrity. For example, hypertonic concentrations of salt are used to extract proteins from biological systems. At present, for want of a theory, it is possible to consider more closely over the whole visible spectrum those corneas exposed only to hypoand isotonic values. Plots of the light transmission corrected for wavelength variation by multiplying by l3 are compared to coherence distance, when the bathing salt is varied between 10 mM and 154 mM and are shown in Figure 7 in order to look for any relationship between these two parameters.
Figure 6. The relative light transmission at 400 nm and the coherence distance plotted as a function of NaCl concentration of the bathing medium of ox corneas at physiological hydration.
185
Ordering of Corneal Collagen Fibrils
Figure 7. A comparison between the coherence distance in the fibrillar lattice and light scattering corrected for wavelength variation in hypo- and isotonic NaCl concentrations.
As the coherence distance diminishes, light scattering increases. It is clear that the coherence distance reaches a minimum value as chloride ion binding tends to zero, and this is certainly because of the presence of repulsive forces between the negatively charged chondroitin sulphate and keratan sulphate in the stromal matrix. Knockout gene technology has established that the presence of keratan sulphate proteoglycans is essential for corneal transparency in the mouse18 and there is, at least the suggestion in our data that at very low chloride ion binding, there may be some compensatory measures taking place that limit the loss of corneal transparency. Possible reasons may be that at very low values of chloride, our assumptions concerning fibrillar and extra-fibrillar refractive index values may be in error. When we examined the relationship between coherence distance and light scattering over the range of bathing media between 50 mM NaCl and 154 mM NaCl, we found there to be a very good linear fit ðR2 ¼ 0:9999Þ: We propose that these two studies indicate that transparency of the cornea is crucially dependant upon the ordering of the collagen fibrils. Clearly, other well-established factors, such as hydration changes and refractive indices of the corneal keratocytes, also influence transparency. But it seems to us that the critical factor in establishing physiological transparency is the ordering of the fibrils and the forces which generate that order.
Materials and Methods Preparations Adult bovine eyes were obtained from a local abattoir immediately after death. The corneal epithelium was removed using a rotating bristle brush, and the cornea together with an approximately 3 mm annulus of sclera was dissected from the eye. The corneal endothelium was removed by wiping the posterior surface of the cornea with tissue paper. Discs of 12 mm in diameter were then cut from the centres of the corneas. The discs were
kept close to physiological hydration ðH ¼ 3:2Þ and their NaCl concentrations adjusted by dialysing them across Visking membranes against solutions containing polyethylene glycol (PEG) (nominal Mr ¼ 20 kDa)11 and: 10, 30, 50, 100, 154, 300, 600 or 1000 mM NaCl. All samples were dialysed and stirred for a period for 24 hours at 4 8C before use. All solutions were buffered with 5 mM Hepes adjusted with KOH to pH 7.4. The percentage of PEG used for each corresponding solution was: 3.9, 3.5, 3.2, 3, 4, 3.4, 2.7 and 2.4. In all potentially hypotonic salt solutions, the osmotic pressure was maintained isotonic to 154 mM NaCl by supplementing with appropriate concentrations of sorbitol. X-ray diffraction The X-ray diffraction experiments were conducted at the synchrotron radiation source (SRS) of the Council for the Laboratory of the Research Councils at Daresbury, UK. Corneal stromas were held in airtight Perspex chambers between two Mylar windows. The specimens were placed in a monochromatic X-ray beam on SRS low angle station 2.1. The dimensions of the beam were ˚ . The 1.5 mm £ 1 mm and its wavelength was 1.54 A path of the beam was always coaxial with the optical axis of the cornea. For the low angle studies, the exposure time was five minutes, with the X-ray diffraction pattern being recorded using a gas-filled multiwire, area detector with 512 £ 512 pixels and wire-to-wire resolution of 1 mm. An evacuated tube between the specimen and the detector gave a total camera length of 8.25 m. To avoid damage, a lead back stop was placed next to the detector directly in the path of the main beam. The detector was calibrated using wet rat-tail tendon, which gave meridional reflections corresponding to the 67 nm D-periodicity of collagen. The X-ray patterns were recorded and analysed using BSL (Daresbury Laboratory, UK) and Statistica (Statsoft, Tusla, USA) software packages. A detailed description of the methods used to analyse the patterns is given by Quantock et al.18 For each specimen, a vertical scan was taken through the centre of the pattern. This gave a profile of X-ray intensity ðIÞ versus radial position ðRÞ: It was from this intensity profile that all measurements of the diffracted X-ray reflections were made, after a background had been fitted and subtracted. The low X-ray diffraction pattern from corneal stroma
186
Ordering of Corneal Collagen Fibrils
gives two sets of reflections, meridional and equatorial. The meridional reflections (as in rat tail tendon) are attributed to the D-periodicity along the length of the collagen fibres. The equatorial reflection is that portion of the X-ray pattern that will be studied for the purposes of these experiments. These reflections were first interpreted by Goodfellow et al.19 and are discussed by Meek et al.11 A detailed account of the theoretical considerations is given by Meek & Quantock.20 The equatorial reflection is given by: IðKÞ ¼ F2 GðKÞ
ð5Þ
where IðKÞ is the distribution of the scattered intensity in the X-ray pattern, F2 is the product of the square of the scattered intensity of a single cylinder (in this case a single collagen fibril) often referred to as the cylinder transform and GðKÞ is the interference function. GðKÞ is dependent on the scattering vector K and the relative positions of the cylinders. The first-order equatorial reflection is often referred to as the interfibrillar reflection (that is the first maxima of the interference function) as its position gives a value of the average centre-tocentre collagen fibrillar Bragg spacing. Note that in the raw data taken from the X-ray pattern the interference function still contains scattered intensity from the cylinder transform. To obtain the true value of the interfibrillar spacing, the fibrillar Bragg spacing has to be multiplied by a factor of 1.12, in order to take into account the liquid-like packing of the fibrils.21 The intensity and width of the interfibrillar reflection also gives a strong qualitative indication of the degree of local order of the collagen fibrils within the stroma. A stroma with a narrow range of nearest-neighbour spacings between the fibrils will produce a reflection with a narrow width in relation to the peak height, as compared with a stroma with a wide range of spacings. Thus, the reflection in this case is said to be “sharper” than in a stroma with a wide range of interfibrillar spacing. The intensity of the reflection will also be greater with a narrow range, as there will be more collagen fibrils sampled by the cross-sectional area of the X-ray beam.
Acknowledgements This work was supported by EPSRC grant GR/ M43067, and MRC program grant G0001033. We thank Professor Keith Meek for useful discussions.
References 1. Meek, K. M. & Leonard, D. W. (1993). Ultrastructure of the corneal stroma: a comparative study. Biophys. J. 64, 273–280. 2. Hodson, S. A. (1997). Corneal stromal swelling. Prog. Retin. Eye Res. 16, 99 –116. 3. Elliott, G. F. & Hodson, S. A. (1998). Cornea, and the swelling of polyelectrolyte gels of biological interest. Rep. Prog. Phys. 61, 1325– 1365.
4. Regini, J. W., Timmins, P. A., Elliott, G. F. & Hodson, S. A. (2003). Neutron and X-ray scattering by ox corneal stroma differentially loaded with bound anions. Biochim. Biophys. Acta, 1620, 54 – 58. 5. Alexandrowitz, Z. & Katchalsky, A. (1963). Colligative properties of polyelectrolyte solutions in excess of salt. J. Polym. Sci. part A, 1, 3231– 3260. 6. Elliott, G. F. (1968). Force-balances and stability in hexagonally-packed polyelectrolyte systems. J. Theor. Biol. 21, 71 – 87. 7. Millman, B. M. & Nickel, B. G. (1980). Electrostatic forces in muscle and cylindrical gel systems. Biophys. J. 32, 49– 63. 8. Elliott, G. F. & Bartels, E. M. (1982). Donnan potential measurements in extended hexagonal polyelectrolyte gels such as muscle. Biophys. J. 38, 195– 199. 9. Naylor, G. R. S. (1982). On the average electrostatic potential between the filaments in striated muscle and its relation to a simple Donnan potential. Biophys. J. 38, 201– 204. 10. Kostyuk, O., Nalovina, O., Mubard, T. M., Regini, J. W., Meek, K. M., Quantock, A. J. et al. (2002). Transparency of the bovine corneal stroma at physiological hydration and its dependence on concentration of the ambient anion. J. Physiol. 543, 633– 642. 11. Meek, K. M., Fullwood, N. J., Cooke, P. H., Elliott, G. F., Maurice, D. M., Quantock, A. J. et al. (1991). Synchrotron x-ray diffraction studies of the cornea, with implications for stromal hydration. Biophys. J. 60, 467–474. 12. Leonard, D. W. & Meek, K. M. (1997). Refractive indices of the collagen fibrils and extrafibrillar material of the corneal stroma. Biophys. J. 72, 1382– 1387. 13. Stokes, A. R. (1955). The theory of X-ray fibre diagrams. Prog. Biophys. 5, 5– 167. 14. Elliott, G. F. (1980). Measurements of the electric charge and ion-binding of the protein filaments in intact muscle and cornea, with implications for filament assembly. Biophys. J. 32, 95 – 97. 15. Saroff, H. A. (1965). The structure of ribonuclease derived from the clustering of its ionisable groups. J. Theor. Biol. 9, 229– 238. 16. Hart, R. W. & Farrell, R. A. (1969). Light scattering in the cornea. J. Opt. Soc. Am. 59, 766– 774. 17. Maurice, D. M. (1957). The structure and transparency of the corneal stroma. J. Physiol. 136, 263– 286. 18. Quantock, A. J., Meek, K. M. & Chakravarti, S. (2001). An X-ray diffraction investigation of corneal structure in lumican-deficient mice. Invest. Ophthalmol. Vis. Sci. 42, 1750– 1756. 19. Goodfellow, J. M., Elliott, G. F. & Woolgar, A. E. (1978). X-ray diffraction studies of the corneal stroma. J. Mol. Biol. 119, 237– 252. 20. Meek, K. M. & Quantock, A. J. (2001). The use of X-ray scattering techniques to determine corneal ultrastructure. Prog. Retin. Eye Res. 20, 95 – 137. 21. Worthington, C. R. & Inouye, H. (1985). X-ray diffraction study of the cornea. Int. J. Biol. Marcomol. 7, 2 – 8.
Edited by M. F. Moody (Received 14 May 2003; received in revised form 23 October 2003; accepted 2 December 2003)
J. Mol. Biol. (2004) 336, 179–186
The Ordering of Corneal Collagen Fibrils with Increasing Ionic Strength J.W. Regini1*, G.F. Elliott1 and S.A. Hodson2 1 The Structural Biophysics Group, School of Optometry and Vision Sciences, Cardiff University, Cardiff CF10 3NB UK 2
Nuffield Laboratory of Ophthalmology, University of Oxford, Walton Street, Oxford OX2 6AW, UK *Corresponding author
The fixed stromal charge of bovine corneas, osmotically clamped at physiological hydration, was altered by regulating the amount of chloride ions bound to the matrix. We measured the local fibrillar collagen order using X-ray diffraction methods. As the bound anions increased up to physiological values, the local fibrillar order increased to an optimal value. The coherence distance ðtÞ approximately doubles to a maximum value (409 nm) from 10 mM NaCl to 154 mM NaCl. This then slowly decreased as the bathing solution increased to 1000 mM. In contrast the diameter of the collagen fibrils were minimal at physiological NaCl. q 2003 Elsevier Ltd. All rights reserved.
Keywords: cornea; chloride; fibrillar order
Introduction Corneal stroma is transparent to light and comprises over 90% of the thickness of the mammalian cornea. It consists mainly of aqueous solution and collagen fibrils. Each collagen fibril has a significantly higher refractive index than the aqueous solution and correspondingly scatters a small fraction of light incident upon it. When this scattered light is summated through the whole thickness of the corneal stroma (about 500 mm, fibril diameter 30.8 nm, nearest-neighbour distance 55.3 nm, in humans),1 the cornea would be effectively opaque if the scattering were non-co-operative. Scattered light from neighbouring fibrils must interfere cooperatively and neutralise lateral scattering. It is generally agreed for this co-operative phenomena to exist, the collagen fibrils must all be of an equal diameter, which is smaller than the wavelength of light and oriented approximately orthogonally to the direction of light. However, the need for ordering between nearest neighbours is not generally agreed. Theories have been proposed that range from total ordering (i.e. the collagen fibrils form a regular lattice) to the suggestion that no ordering is required and that any array of equal sized filaments whose diameter is smaller than l/4 will be transparent provided that they are in a pseudoparallel array and that there are no substantial
E-mail address of the corresponding author: [email protected]
voids in the disordered lattice which are comparable in dimension to the wavelength of light. We addressed the nature of the relationship between nearest-neighbour ordering and transparency experimentally, utilising some recent data on the corneal stroma. A striking phenomenon of the corneal stroma is its ability to swell to many times its original weight when it is placed in aqueous solutions. The cause of corneal swelling is well understood and arises from the gel pressure associated with the net fixed negative charge of the corneal stromal matrix (for reviews, see Hodson2 and Elliott & Hodson3). In vivo, the swelling tendency of the corneal stroma does not manifest because of the presence of a balancing outward-directed bicarbonate ion pump located in the corneal endothelium lining the posterior surface of the stroma. If the stroma is allowed to swell it quickly loses its transparency and becomes progressively more opaque. Collagen itself has little net charge at physiological pH, so there are two sources for the corneal stroma’s negative charge, which generate stromal gel pressure. One source comprises the acid groups of the stromal glycosaminoglycans, the keratan sulphate groups and chondroitin/dermatan sulphate groups; the other source is anion binding (usually supplied by the chloride ion in the physiological situation). The net negatively charged glycosaminoglycans radiate from the collagen fibrils into the surrounding interfibrillar fluid. The spatial location of the anion binding ligands is less certain but neutron scattering data favour the suggestion that the anion binding ligands are located within the collagen
0022-2836/$ - see front matter q 2003 Elsevier Ltd. All rights reserved.
180 fibrils.4 Surrounding these negatively charged assemblies are electrical fields, which give rise to double-layer ordering forces.5 – 9 Whereas the acidic groups of the glycosaminoglycans are invariant at physiological pH and generate a constant contribution to the net negative charge of the corneal stroma, stromal anion binding is reversible and so it is possible to alter the stromal net negative charge concentration whilst maintaining the same interfibrillar average distance simply by equilibrating against different salt concentrations in the bathing medium whilst the stroma is osmotically clamped. When this is done it has been shown that the transparency of the corneal stroma increases as the anion binding increases up to physiological concentrations of anion.10 We report here how the interfibrillar structural ordering alters with increasing anion binding.
Ordering of Corneal Collagen Fibrils
Results Hydrations Corneal stromal hydration was specified by the parameter H; where: H¼
wet weight 2 dry weight dry weight
Due to a slight amount of water loss from the tissues during the experiments, all specimens were weighed before and after X-ray exposure. An average weight was then established from the two readings; this allowed us to calculate the tissue hydration at the time of the experiment. The reduction in hydration in individual corneas varied over a range between 1.6% and 2.4%.
Figure 1. The X-ray intensity profiles and first-order interfibrillar reflections from X-ray patterns of corneas in (a) 300 mM NaCl and (b) 30 mM NaCl.
181
Ordering of Corneal Collagen Fibrils
Low angle X-ray patterns The X-ray patterns of 12 separate corneas ðn ¼ 12Þ were taken at each NaCl concentration. It was found that below physiological NaCl concentration (154 mM) the sharpness of the first order equatorial reflection increased with increasing ionic strength. Figure 1(a) and (b) shows the intensity profiles along the length of the whole X-ray patterns of corneas dialysed against 300 mM NaCl and 30 mM NaCl, respectively. The inserts only show the corresponding low-angle first-order interfibrillar reflections from the X-ray patterns, the central white rectangle is the shadow of the lead backstop. The two profiles and patterns shown are typical of high and low NaCl concentrations (note how diffuse the interfibrilar reflection at 30 mM is when compared with that at 300 mM). As can be clearly seen, at and above 154 mM NaCl the interfibrillar reflections were characterised by welldefined and intense reflections (Figure 1(a)). By comparison, those from 10 mM to 154 mM NaCl were found to show a steady increase in scattered intensity and somewhat broader in relation to the peak height than those at higher concentrations (Figure 1(b)). Moreover, as the concentration was raised from 10 mM to 154 mM NaCl, the intensity of the interfibrillar reflection showed a steady increase. Figure 2 shows the X-ray intensity profiles of 12 averaged corneas at all NaCl concentrations, which demonstrates the effect of increasing intensity and sharpness of the peaks when the ionic strength of the dialysing solution is raised. The slight change in the position of the interfibrillar reflections between all three profiles is due to the slight variation in the hydrations of the corneas studied. After the subtraction of the background scatter, the interfibrillar distance ðdÞ and the angular
width ðbÞ were measured. The interfibrillar distance ðdÞ showed no significant change over the range of NaCl concentrations used, with mean value of 56.5(^ 1.1) nm. Figure 3 shows the interfibrillar peak of the cornea in 154 mM NaCl of Figure 2, before (dotted line) and after (continuous line) a background has been fitted and subtracted. The pattern has been folded around its centre and the x axis is now plotted in inverse space (R). The fibril diameter d was calculated from the first subsidiary maxima of the low-angle X-ray patterns, using the methods described by Meek et al.11 Figure 4 shows the results for six corneas (the standard error for each point was found to be equal to or less than 2% of the mean), and the diameter of the collagen fibrils were minimal at physiological NaCl, although there was no strong trend except at 1 M NaCl. The mean diameter was found to be 38.9 nm (excluding the data at 1 M), which is in good agreement with the value 38.2 nm given by Leonard & Meek12 for bovine corneas. The ordering of the lattice The angular width of a reflection ðbÞ is related to a parameter ðtÞ that gives some measure of the limited size of the lattice, or the disorder in the lattice, by the approximation: b<
2l ðt cos uÞ
ð1Þ
where u is the Bragg angle.13 Stokes13 discusses the possible meanings of the parameter t (section 10 of his article) and gives as one of his possible alternatives “the order of the average distance over which the exact periodicity begins to fail”. This is probably the appropriate meaning in our case. We choose to call this parameter the
Figure 2. The averaged X-ray intensity profiles of corneas at all NaCl concentrations.
182
Ordering of Corneal Collagen Fibrils
Figure 3. The interfibrillar peak of a cornea in 154 mM NaCl before (dotted line) and after (continuous line) a background has been fitted and subtracted. The pattern has been folded around its centre and x axis is now plotted in inverse space ðRÞ:
“coherence distance”. The Bragg equation is: nl ¼ 2d sin u
ð2Þ
where the symbols have their conventional meaning, and we may combine these two equations to give: bt < 2d tan u
ð3Þ
in the first-order of diffraction. At small angles tan u ¼ u; and we obtain: t
2u b
ð4Þ
Note that the numerical constant 2 in equation (2) is replaced by 1, as Stokes13 states that “more exact treatments give a value closer to unity”. The ratio of angles, 2u=b and interfibrillar spacing d we obtained from linear measurements on data sets such as Figure 3 (following convention, b is taken as the angular width of the reflection at half height). Table 1 gives the measured angular width ðbÞ of the reflection and our calculated values of the coherence distance ðtÞ: Figure 5(a) and (b) shows both these parameters plotted as a function of salt concentration (in both cases the standard error was found to be less than or equal to 2.3% of the
Figure 4. The fibril diameter ðdÞ plotted as a function of NaCl concentration. For each point n ¼ 6:
183
Ordering of Corneal Collagen Fibrils
Table 1. The calculated lattice size t and measured angular widths of the interfibrillar peaks at all NaCl concentrations NaCl (mM) 10 30 50 100 154 300 600 1000
t (nm)
b (rad)
235 238 276 329 409 349 397 356
0.000655 0.000648 0.000559 0.000468 0.000376 0.000442 0.000388 0.000428
mean of each value). The data show that at low ionic strength ðtÞ is at about 237 nm, increasing rapidly up to a maximum value of 409 nm at physiological values (Figure 5(a)). At higher salt concentrations the lattice size decreases and remains fairly constant with a mean value about 367 nm. Conversely, the angular width shows an inversely identical trend, with broader peaks at low ionic strength reaching a minimum at 154 nm NaCl (Figure 5(b)). This analysis shows, as a ballpark figure, that the fibrillar order is maintained as an average over about one-half of a lamella
when the ionic strength is high, and only over about half that distance when it is low.
Discussion The data support the concept that corneal transparency and ordering of the fibrillar lattice are related, as we discuss below. We interpret our findings in terms of the anion binding models proposed by Elliott14 and Elliott & Hodson3 who state that as the NaCl concentration is increased, chloride ions increasingly bind to the collagen fibrils. As mentioned earlier, recent neutron scattering data suggest that the location of the chloride binding ligands are located mainly within the collagen fibrils.4 Anion binding ligands are likely to involve the spatial proximity of two or more structural charged groups.15 The result of increased chloride ion binding is that the fibrils become increasingly electro-negative. This increase in negative charge gives rise to an extra repulsive force between the fibrils. It is this repulsive force which we propose is the ordering force of the fibrillar lattice. The measured increments in bound stromal negative charge with increasing chloride
Figure 5. (a) The coherence distance ðtÞ; filled triangles, and (b) the measured angular width ðbÞ; open circles, plotted as a function of salt concentration.
184
concentrations in the bathing medium up to physiological values (charge (mM)/chloride (mM)) are: 3/10, 7/30, 13/50, 18/100, 24/154. These data are consistent with our observations, reported here, of increasing structural order. The relationship between the increase in structurally fixed electrical charge and the resulting force produced has been observed in other biological cylindrical gel systems. For example, Millman & Nickel7 observed similar behaviour in both tobacco mosaic virus and vertebrate striated muscle. In the well documented approximation of the classical theory of corneal light scattering,16 the light scattering cross-section of an individual collagen fibril, besides being a function of the wavelength of the incident light, is related to the fourth power of the fibril diameter and a complex function of the refractive index of the medium surrounding the fibril and the refractive index of the fibril itself. In the experiments reported here, where the fibril diameters change in response to the ionic strength, the changes indicate water removal from the fibril as the salt increases up to physiological strength, followed by a possible charge repulsion effect in the intrafibrillar space which allows water molecules to re-enter. For the purposes of calculating the scattering cross-section of the fibrils exposed to various salt concentrations, we have made the assumption that the diameter changes as the result of the addition or loss of the solvent and its ionic constituents alone, which have a refractive index of 1.335 at 530 nm (with a slight wavelength dependence which is too small to significantly affect the following calculations). In fact, Leonard & Meek12 have shown how it is possible to calculate the refractive index and the surrounding medium and have done so for isotonic solutions, but until these calculations are repeated for non-isotonic media, we shall assume the above model. Using our published values of fibril diameter and the approximations outlined above, we calculate the scattering cross-sections of the fibrils in solutions of differing ionic strengths,
Ordering of Corneal Collagen Fibrils
relative to the fibril in isotonic saline to be: units, % (saline molarity): 101.6 (10); 107.2 (30); 98.2 (50); 96.0 (100); 100 (154); 98.6 (300); 101.6 (600); 104.9 (1000). In general, the simple summation of the light scattering across the whole cornea would give only about 6 –8% transmission of the incident light.16,17 The much higher observed values of transmitted light are ascribed to constructive interference phenomena which is dependent on relative ordering of the fibrillar array which is, of course related to the values of the coherence distance ðtÞ, given here. A simple normalised comparison of light transmission at 400 nm taken from our earlier optical study10 (very slightly corrected for the relative scattering cross-sections of the fibrils) and t is shown in Figure 6. In general, Figure 6 indicates that there is a relationship between light transmission and coherence distance but then the relationship is different for hypotonic values of the bathing solution than it is for hypertonic values. We had previously noticed a similar difference for light transmission: hypo- and isotonic values showed light transmission to follow a l23 law, consistent with classical optical theory, whilst hypertonic values showed a l22 relationship for which we could find no known theory.10 It may be that above a certain level of ion binding, other disorder phenomena could appear and the fibrils themselves begin to lose their structural integrity. For example, hypertonic concentrations of salt are used to extract proteins from biological systems. At present, for want of a theory, it is possible to consider more closely over the whole visible spectrum those corneas exposed only to hypoand isotonic values. Plots of the light transmission corrected for wavelength variation by multiplying by l3 are compared to coherence distance, when the bathing salt is varied between 10 mM and 154 mM and are shown in Figure 7 in order to look for any relationship between these two parameters.
Figure 6. The relative light transmission at 400 nm and the coherence distance plotted as a function of NaCl concentration of the bathing medium of ox corneas at physiological hydration.
185
Ordering of Corneal Collagen Fibrils
Figure 7. A comparison between the coherence distance in the fibrillar lattice and light scattering corrected for wavelength variation in hypo- and isotonic NaCl concentrations.
As the coherence distance diminishes, light scattering increases. It is clear that the coherence distance reaches a minimum value as chloride ion binding tends to zero, and this is certainly because of the presence of repulsive forces between the negatively charged chondroitin sulphate and keratan sulphate in the stromal matrix. Knockout gene technology has established that the presence of keratan sulphate proteoglycans is essential for corneal transparency in the mouse18 and there is, at least the suggestion in our data that at very low chloride ion binding, there may be some compensatory measures taking place that limit the loss of corneal transparency. Possible reasons may be that at very low values of chloride, our assumptions concerning fibrillar and extra-fibrillar refractive index values may be in error. When we examined the relationship between coherence distance and light scattering over the range of bathing media between 50 mM NaCl and 154 mM NaCl, we found there to be a very good linear fit ðR2 ¼ 0:9999Þ: We propose that these two studies indicate that transparency of the cornea is crucially dependant upon the ordering of the collagen fibrils. Clearly, other well-established factors, such as hydration changes and refractive indices of the corneal keratocytes, also influence transparency. But it seems to us that the critical factor in establishing physiological transparency is the ordering of the fibrils and the forces which generate that order.
Materials and Methods Preparations Adult bovine eyes were obtained from a local abattoir immediately after death. The corneal epithelium was removed using a rotating bristle brush, and the cornea together with an approximately 3 mm annulus of sclera was dissected from the eye. The corneal endothelium was removed by wiping the posterior surface of the cornea with tissue paper. Discs of 12 mm in diameter were then cut from the centres of the corneas. The discs were
kept close to physiological hydration ðH ¼ 3:2Þ and their NaCl concentrations adjusted by dialysing them across Visking membranes against solutions containing polyethylene glycol (PEG) (nominal Mr ¼ 20 kDa)11 and: 10, 30, 50, 100, 154, 300, 600 or 1000 mM NaCl. All samples were dialysed and stirred for a period for 24 hours at 4 8C before use. All solutions were buffered with 5 mM Hepes adjusted with KOH to pH 7.4. The percentage of PEG used for each corresponding solution was: 3.9, 3.5, 3.2, 3, 4, 3.4, 2.7 and 2.4. In all potentially hypotonic salt solutions, the osmotic pressure was maintained isotonic to 154 mM NaCl by supplementing with appropriate concentrations of sorbitol. X-ray diffraction The X-ray diffraction experiments were conducted at the synchrotron radiation source (SRS) of the Council for the Laboratory of the Research Councils at Daresbury, UK. Corneal stromas were held in airtight Perspex chambers between two Mylar windows. The specimens were placed in a monochromatic X-ray beam on SRS low angle station 2.1. The dimensions of the beam were ˚ . The 1.5 mm £ 1 mm and its wavelength was 1.54 A path of the beam was always coaxial with the optical axis of the cornea. For the low angle studies, the exposure time was five minutes, with the X-ray diffraction pattern being recorded using a gas-filled multiwire, area detector with 512 £ 512 pixels and wire-to-wire resolution of 1 mm. An evacuated tube between the specimen and the detector gave a total camera length of 8.25 m. To avoid damage, a lead back stop was placed next to the detector directly in the path of the main beam. The detector was calibrated using wet rat-tail tendon, which gave meridional reflections corresponding to the 67 nm D-periodicity of collagen. The X-ray patterns were recorded and analysed using BSL (Daresbury Laboratory, UK) and Statistica (Statsoft, Tusla, USA) software packages. A detailed description of the methods used to analyse the patterns is given by Quantock et al.18 For each specimen, a vertical scan was taken through the centre of the pattern. This gave a profile of X-ray intensity ðIÞ versus radial position ðRÞ: It was from this intensity profile that all measurements of the diffracted X-ray reflections were made, after a background had been fitted and subtracted. The low X-ray diffraction pattern from corneal stroma
186
Ordering of Corneal Collagen Fibrils
gives two sets of reflections, meridional and equatorial. The meridional reflections (as in rat tail tendon) are attributed to the D-periodicity along the length of the collagen fibres. The equatorial reflection is that portion of the X-ray pattern that will be studied for the purposes of these experiments. These reflections were first interpreted by Goodfellow et al.19 and are discussed by Meek et al.11 A detailed account of the theoretical considerations is given by Meek & Quantock.20 The equatorial reflection is given by: IðKÞ ¼ F2 GðKÞ
ð5Þ
where IðKÞ is the distribution of the scattered intensity in the X-ray pattern, F2 is the product of the square of the scattered intensity of a single cylinder (in this case a single collagen fibril) often referred to as the cylinder transform and GðKÞ is the interference function. GðKÞ is dependent on the scattering vector K and the relative positions of the cylinders. The first-order equatorial reflection is often referred to as the interfibrillar reflection (that is the first maxima of the interference function) as its position gives a value of the average centre-tocentre collagen fibrillar Bragg spacing. Note that in the raw data taken from the X-ray pattern the interference function still contains scattered intensity from the cylinder transform. To obtain the true value of the interfibrillar spacing, the fibrillar Bragg spacing has to be multiplied by a factor of 1.12, in order to take into account the liquid-like packing of the fibrils.21 The intensity and width of the interfibrillar reflection also gives a strong qualitative indication of the degree of local order of the collagen fibrils within the stroma. A stroma with a narrow range of nearest-neighbour spacings between the fibrils will produce a reflection with a narrow width in relation to the peak height, as compared with a stroma with a wide range of spacings. Thus, the reflection in this case is said to be “sharper” than in a stroma with a wide range of interfibrillar spacing. The intensity of the reflection will also be greater with a narrow range, as there will be more collagen fibrils sampled by the cross-sectional area of the X-ray beam.
Acknowledgements This work was supported by EPSRC grant GR/ M43067, and MRC program grant G0001033. We thank Professor Keith Meek for useful discussions.
References 1. Meek, K. M. & Leonard, D. W. (1993). Ultrastructure of the corneal stroma: a comparative study. Biophys. J. 64, 273–280. 2. Hodson, S. A. (1997). Corneal stromal swelling. Prog. Retin. Eye Res. 16, 99 –116. 3. Elliott, G. F. & Hodson, S. A. (1998). Cornea, and the swelling of polyelectrolyte gels of biological interest. Rep. Prog. Phys. 61, 1325– 1365.
4. Regini, J. W., Timmins, P. A., Elliott, G. F. & Hodson, S. A. (2003). Neutron and X-ray scattering by ox corneal stroma differentially loaded with bound anions. Biochim. Biophys. Acta, 1620, 54 – 58. 5. Alexandrowitz, Z. & Katchalsky, A. (1963). Colligative properties of polyelectrolyte solutions in excess of salt. J. Polym. Sci. part A, 1, 3231– 3260. 6. Elliott, G. F. (1968). Force-balances and stability in hexagonally-packed polyelectrolyte systems. J. Theor. Biol. 21, 71 – 87. 7. Millman, B. M. & Nickel, B. G. (1980). Electrostatic forces in muscle and cylindrical gel systems. Biophys. J. 32, 49– 63. 8. Elliott, G. F. & Bartels, E. M. (1982). Donnan potential measurements in extended hexagonal polyelectrolyte gels such as muscle. Biophys. J. 38, 195– 199. 9. Naylor, G. R. S. (1982). On the average electrostatic potential between the filaments in striated muscle and its relation to a simple Donnan potential. Biophys. J. 38, 201– 204. 10. Kostyuk, O., Nalovina, O., Mubard, T. M., Regini, J. W., Meek, K. M., Quantock, A. J. et al. (2002). Transparency of the bovine corneal stroma at physiological hydration and its dependence on concentration of the ambient anion. J. Physiol. 543, 633– 642. 11. Meek, K. M., Fullwood, N. J., Cooke, P. H., Elliott, G. F., Maurice, D. M., Quantock, A. J. et al. (1991). Synchrotron x-ray diffraction studies of the cornea, with implications for stromal hydration. Biophys. J. 60, 467–474. 12. Leonard, D. W. & Meek, K. M. (1997). Refractive indices of the collagen fibrils and extrafibrillar material of the corneal stroma. Biophys. J. 72, 1382– 1387. 13. Stokes, A. R. (1955). The theory of X-ray fibre diagrams. Prog. Biophys. 5, 5– 167. 14. Elliott, G. F. (1980). Measurements of the electric charge and ion-binding of the protein filaments in intact muscle and cornea, with implications for filament assembly. Biophys. J. 32, 95 – 97. 15. Saroff, H. A. (1965). The structure of ribonuclease derived from the clustering of its ionisable groups. J. Theor. Biol. 9, 229– 238. 16. Hart, R. W. & Farrell, R. A. (1969). Light scattering in the cornea. J. Opt. Soc. Am. 59, 766– 774. 17. Maurice, D. M. (1957). The structure and transparency of the corneal stroma. J. Physiol. 136, 263– 286. 18. Quantock, A. J., Meek, K. M. & Chakravarti, S. (2001). An X-ray diffraction investigation of corneal structure in lumican-deficient mice. Invest. Ophthalmol. Vis. Sci. 42, 1750– 1756. 19. Goodfellow, J. M., Elliott, G. F. & Woolgar, A. E. (1978). X-ray diffraction studies of the corneal stroma. J. Mol. Biol. 119, 237– 252. 20. Meek, K. M. & Quantock, A. J. (2001). The use of X-ray scattering techniques to determine corneal ultrastructure. Prog. Retin. Eye Res. 20, 95 – 137. 21. Worthington, C. R. & Inouye, H. (1985). X-ray diffraction study of the cornea. Int. J. Biol. Marcomol. 7, 2 – 8.
Edited by M. F. Moody (Received 14 May 2003; received in revised form 23 October 2003; accepted 2 December 2003)