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Anisotropic Swelling Behavior of the Cornea Toyoaki Matsuura,† Hitoe Ikeda,† Naokazu Idota,‡ Ryuhei Motokawa,§ Yoshiaki Hara,† and Masahiko Annaka*,‡ Department of Ophthalmology, Nara Medical UniVersity, Nara 634-8522, Japan, Department of Chemistry, Kyushu UniVersity, Fukuoka 812-8581, Japan, and AdVanced Science Research Center, Japan Atomic Energy Agency, Ibaraki 319-1195, Japan ReceiVed: July 29, 2009; ReVised Manuscript ReceiVed: October 6, 2009
The phase equilibrium property and structural and dynamical properties of pig cornea were studied by macroscopic observation of swelling behavior, dynamic light scattering (DLS), and small-angle X-ray scattering (SAXS) under various conditions. It was found that the corneal gel collapses into a compact state isotropically or anisotropically depending on the external conditions. The corneal gel collapses uniformly into a compact state at a temperature above 55 °C because of the denaturation of collagen, whereas it collapses along an axis parallel to the optic axis with increasing NaCl concentration. Anisotropic deswelling was also observed during desiccation. SAXS measurements revealed that the periodicity of the collagen fiber of the cornea does not change even at higher NaCl concentration, which indicates that hydration and dehydration resulting from changes in salt concentration simply cause swelling and deswelling of the glycosaminoglycan (GAG), which is located between the regular two-dimensional lattices of collagen fibers, which obliges the change in thickness. From observations of the dynamics of light scattered by the corneal gel, intensity autocorrelation functions that revealed two independent diffusion coefficients were obtained. Divergent behavior in the measured total scattered light intensities and diffusion coefficients with varying temperature was observed. That is, a slowing of the dynamic modes accompanied by increased “static” scattered intensities was observed. This is indicative of the occurrence of a phase transition as a function of temperature. Introduction Very often, nature combines different types of macromolecules to form gels. One example is the cornea, which is the outermost protective layer of tissue in the eye that is transparent to visible light.1 Its most voluminous component, corneal stroma, is composed of numerous sheets or layers of highly organized type I collagen fibrils, lamella. Within each layer, a hydrated proteoglycan (PG) and glycosaminoglycan (GAG) matrix that fills the interfibrilar space surrounds the collagen fibrils. Outside this complex gel matrix are cells scattered throughout. Within each lamellar layer, however, the collagen fibrils are unidirectionally aligned in a regular anisotropic order.2 All layers are stacked on each other in parallel with the lateral surface of the cornea; the collagen fibers also lie parallel with respect to the corneal surface. The physical characteristics of the cornea have been well studied, in particular, using electron microscopy3,4 and small-angle static light-scattering methodologies.5-7 The cornea has often been alluded to as a gel network; hence, lightscattering methodologies have been applied to determine its structural properties.5 However, essentially no investigations on the dynamics and phase equilibrium properties of the cornea have been performed to verify indisputably that the cornea is indeed a gel network. Clinically, one index of corneal function or dysfunction is the degree of corneal swelling and the concomitant loss of transparency. To adapt the physical properties of living materials to their biological function, nature has developed macromol* To whom correspondence should be addressed. E-mail: annaka@ chem.kyushu-univ.jp. Fax: +81-92-642-2607. † Nara Medical University. ‡ Kyushu University. § Japan Atomic Energy Agency.
ecules and networks with outstanding physical behaviors. The cornea can maintain its lucidity and moisture content, which requires, however, continuous maintenance by metabolism.8 Metabolic defects lead to turbidity as a result of a change in local structure. We, therefore, focused in this study on the change in the structure and dynamical properties of the cornea induced by hydration and dehydration. Some diseases affect changes in the highly complex structure of the cornea that induce opacification.3,9,10 In addition to diseases, corneal transparency is also impaired when abnormally high pressure is applied.4 Intraocular pressure in acute glaucoma, for example, can induce corneal opacity, which disappears immediately upon alleviation of the pressure.11 The increased usage of contact lenses and their effects on corneal hydration have placed renewed importance on corneal anoxia and swelling. The present research, thus, places an emphasis on investigating the swelling behavior and concomitant change in the physicochemical properties of pig cornea, subjected to changes in the external conditions by dynamic light scattering (DLS) and small-angle X-ray scattering (SAXS). Experimental Section Sample Preparation. Enucleated pig corneas were investigated up to 12 h post mortem. The epithelical and endotherical cells were removed by scraping with a surgical blade, and the cornea was excised from the intact globe. Swelling Experiments. The swelling ratio of the cornea was determined by weighing in a corneal gel in the equilibrium state. The weight w, diameter d, and thickness h of the sample in the equilibrium state were measured. Those values for the sample immediately after preparation, which is at physiological hydra-
10.1021/jp907232h 2009 American Chemical Society Published on Web 12/02/2009
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tion, were w0 ) 1.01 g, d0 ) 14 mm, and h0 ) 1 mm (n ) 10, standard deviation ) 1.1). The swelling ratio was calculated from the ratio w/w0, and at the physiological hydration state, w/w0 ) 1. The increase in mass is also expressed as an index of hydration H, defined as the amount of water per unit dry weight, wdry, of the cornea: H ) (w - wdry)/wdry. In the case of the pig cornea used in this study, H ) 4 at physiological hydration. Solvent attached to the gel was carefully wiped to minimize the error. The time required to attain the equilibrium state was 1 day. Then, the equilibrium swelling ratio was determined. Swelling Kinetics. These excised corneas were placed in distilled deionized water and were allowed to reach their equilibrium shape. The weight, diameter, and thickness of each cornea were recorded using a microscope with an ocular scale, in time, as the cornea became swollen. Time zero was established as the instant the excised cornea was immersed within the distilled deionized water. Dynamic Light Scattering (DLS). DLS experiments were performed on a homemade microscope laser light-scattering spectroscopy (MLLSS) system. A detailed description of the apparatus was given elsewhere.12 The scattering volume within the cornea was approximately (2 µm)3. Data were obtained using a scattering angle ranging from 120° to 140° at a temperature of 25 °C and a focal depth of 1-1.5 mm within the cornea. The temporal fluctuations of the scattered light intensity, I(t), were analyzed in terms of intensity autocorrelation functions13,14
C(τ) ) 〈I(t) · I(t + τ)〉
(1)
where 〈 · · · 〉 represents the time average over t. The rate of fluctuations of the scattered light intensity, which represent the density fluctuations of the vitreous gel, is proportional to the rate of local swelling and shrinking of the gel via molecular Brownian motions. There are also permanent and static inhomogeneities within the vitreous that also contribute to light scattering. The light intensity scattered by these inhomogeneities does not fluctuate with time. The scattered light intensity is, thus, the superposition of contributions from scattering elements that are static and from those that fluctuate dynamically
I(t) ) IS + ID(t)
(2)
In DLS, the time correlation of the intensity of scattered light is recorded. Assuming a Gaussian nature for the scattered light photons, the correlation function of the intensity of scattered light is rewritten in terms of the autocorrelation function, g(τ), of the scattered electric field, E(t), which is related to the scattered light intensity by I(t) ) E(t) · E*(t)
g(τ) ≡
〈E(t) · E*(t + τ)〉 〈E(t) · E*(t)〉
(3)
Then, C(τ) is written as
C(τ) ) (IS + ID)2 + A[ID2g2(τ) + 2ISIDg(τ)]
(4)
where A is the efficiency parameter of the apparatus, which is uniquely determined by the optical configuration of the setup, the value I, and the average intensities scattered by the gel fluctuations and the static inhomogeneities. For the present experiments, A was determined to be 0.8. The electric field autocorrelation function, g(τ), can be easily extracted from the intensity autocorrelation function, C(τ), from knowledge of the initial value C(0), the baseline value C(∞), and the coefficient A, using the above relations. As we shall see later and as shown in Figure 5 below, the autocorrelation functions can have a distinct double-exponential feature. This indicates the presence
of two different modes within the gel. Therefore, the correlation functions g(τ) are analyzed using the relationship
g(τ) )
Afast Aslow exp(-Γfastτ) + × Afast + Aslow Afast + Aslow exp(-Γslowτ) (5)
where Afast and Aslow are the amplitudes and Γfast and Γslow are the relaxation rates of the fast and slow components, respectively, in the bimodal distribution. The wavevector q is defined as q ) (4nπ/λ) sin(θ/2), where n is the refractive index of the solution, λ is the wavelength of the incident beam (λ ) 632.8 nm), and θ is the scattering angle. Small-Angle X-ray Scattering. Small-angle X-ray scattering (SAXS) experiments were carried out with a two-dimensional SAXS spectrometer (BL45XU) installed at Japan Synchrotron Radiation Research Institute (JASRI, SPring 8). An incident X-ray beam from the synchrotron orbital radiation was monochromatized to 1.49 Å. The scattered X-rays were detected by a two-dimensional CCD camera positioned at 1 m from the sample; the magnitude of the observed scattering vector ranged from 0.008 to 0.15 Å-1. The samples were sealed in a cell whose temperature was controlled to within 0.1 °C of the desired temperature. The intensities were accumulated for 0.1 s in order to ensure sufficient statistical accuracy without degrading the gel samples by X-ray irradiation. The scattered intensities were corrected for the cell scattering and absorption and then normalized by the thickness of the sample and the irradiation time. Results and Discussion Swelling Behavior. The corneal stroma is a typical biological gel composed of collagen type I fibrils embedded in a hydrated proteoglycan (PG) and glycosaminoglycan (GAG) matrix. These components form a complex in the cornea and build up the three-dimensional polymer networks of the gel. Approximately 60% of the corneal GAGs of man, cattle, and most other species that have been investigated is keratan sulfate, and the remaining 40% is chondroitin 4-sulfate. GAGs carry high, negatively charged sulfate groups, and therefore, the cornea is a multicomponent polyelectrolyte gel.15 Salt Concentration Dependence. The corneal stroma was placed in distilled and deionized water and was allowed to swell. Above physiological hydration, the cornea becomes opaque, and a fully hydrated corneal gel appears to be a cylinder with a diameter of dS ) 14 mm (parallel to the corneal surface) and a thickness of hS ) 7.7 mm (perpendicular to the corneal surface). The weight of the fully hydrated cornea was wS ) 1.01 g, which is approximately 3.5 times its weight at physiological hydration. Figure 1 shows the swelling ratios in weight (w/wS), thickness (h/hS), and diameter (d/dS) of a cornea as a function of NaCl concentration. The weight of the corneal gel gradually decreased with NaCl concentration to 55% of the value fully hydrated in water. It is worth mentioning that the hydration degree of the corneal gel in 1 M NaCl was above that for the physiological state and the corneal gel was still opaque. The decrease in the thickness was similar to the decrease in the weight of the corneal gel. No change, however, was observed in the diameter within the concentration range studied here. Interestingly, we found that the corneal gel collapsed nonuniformly, as shown in Figure 1. The corneal gel collapsed along an axis parallel to the optic axis. This phenomenon suggests that there are structures that lead to shrinkage along the orbital axis. Because of the hydrophobic nature of the collagen fibers of the stroma, water
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Figure 2. Swelling ratios in terms of weight (w/wS), thickness (h/hS), diameter (d/dS), and hydration degree (H) of a cornea as a function of temperature. Figure 1. Swelling ratios (a) in thickness, h/hS, and diameter, d/dS, and (b) in weight, w/wS, and hydration degree, H, of a cornea as a function of NaCl concentration. Here, wS, dS, and hS are the weight, diameter, and thickness, respectively, of the corneal gel in the fully hydrated state. The normalized corneal gel thickness, h/hS, follows the asymptotic behavior h/hS ∼ n-3/5.
pressure arises from the effect of ions. Because of the unequal distribution of ions inside and outside of the gel, an osmotic pressure is given by
Πion ) NAkBT is held by the GAGs, which are located between the regular two-dimensional lattice of collagen fibers. Therefore, hydration and dehydration are simply considered to be caused swelling and deswelling, respectively, of the GAGs, which obliged the change in thickness of the corneal gel. The swelling behavior of an ionic gel is determined by the osmotic pressure of the gel. The osmotic pressure of the gel consists of four contributions: the rubber elasticity of the polymer network, the effects of the counterion of the ionic group on the polymer network, the interaction free energy between the polymer and the solvent, and the mixing entropy. The balance of these four factors determines the equilibrium swelling ratio of the gel. The osmotic pressure, Π, of a charged gel is given by16,17
Π ) Πmix + Πelastic + Πion
(6)
where Πmix, Πelastic, and Πion are the contributions to the osmotic pressure due to polymer-solvent mixing, polymer chain elasticity, and the Donnan potential, respectively. In the context of the conventional theory of swelling,17 Πmix and Πelastic are functions of the polymer volume fraction, φ, and are given by
Πmix ) -
NAkBT [φ + ln(1 - φ) + χφ2] V
(7)
and
Πelastic )
[( ) ( ) ]
NCkBT 1 φ φ V0 2 φ0 φ0
1/3
(8)
where NA is Avogadro’s number, kB is the Boltzmann constant, T is the absolute temperature, V is the molar volume of the solvent, χ is the Flory-Huggins interaction parameter, and NC is the number of effective chains contributing to the elasticity. φ0 and V0 are the polymer volume fraction and the gel volume at the reference state, respectively. In the case of ionic gels, an additional term due to the repulsion between chains has to be taken into account. In particular, one has to consider (i) the effect of the polymer network charges, which exert marked mutual Coulomb repulsions, and (ii) the effect of the ions, which give rise to an additional contribution to the system osmotic pressure through the Donnan effect. Within the weak screening limit (κR < 1, where R is the size of a polymer chain and κ is the inverse of the Debye length), the first of the two effects is much less than the other, and thus the ionic contribution to the total osmotic
∑ (ni - n*)i
(9)
i
where ni and n*i refer to the concentrations of the ith ionic species inside and outside the gel, respectively. Equation 9 is the general expression accounting for the ionic contribution to the total osmotic pressure. If the bath salt concentration, n, is smaller than the counterion concentration inside the gel, then eq 9 reduces to18,19
Πion )
k BT φ f V0 φ0
(10)
where f is the total number of mobile counterions inside the gel. In this limit, the difference in salt concentration is small, and the osmotic pressure is that of the ideal gas of the counterions and is independent of the salt concentration. In the limit where the salt concentration in the bath is larger than the counterion concentration, the osmotic pressure is given by18
Πion )
kBTφ2f 2 1 4V 2φ 2 n 0
(11)
0
where Πion decays as n-1 for high ionic strengths. For sufficiently high salt concentrations, one enters into the strong screening limit, where ionic effects become negligible in relation to direct electrostatic interactions. The mixing term is not the significant term contributing to the swelling pressure of the corneal gel, and therefore, the gel size is controlled by the competition between the elastic and ionic terms. For isotropic swelling, the gel size R follows the asymptotic behavior R ∼ n-1/5, irrespective of the gel charge by balancing eqs 8 and 11.18 In the case of the corneal gel, because of the anisotropic swelling along the optic axis as shown in Figure 1, the gel thickness h is considered to follow the asymptotic behavior h ∼ n-3/5. Sulfate groups of GAGs are considered to be ionized completely throughout the entire range of salt concentrations, so the volume of the corneal gel should be constant until the salt concentration becomes comparable to the counterion concentration inside the gel, which is equal to the network charge in this region. This prediction agrees with the experimental result. The gel thickness is constant for salt concentrations below 0.05 M. Once this limit is surpassed, the theoretically predicted asymptotic behavior relating the gel thickness to the bath salt concentration is observed. Temperature Dependence. Figure 2 shows the swelling ratios in terms of weight (w/wS), diameter (d/dS), and thickness (h/hS)
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Figure 3. Two-dimensional and one-dimensional (azimuthally averaged) SAXS intensity profiles for corneal gel: (a) immediately after preparation at physiological hydration (H ) 4), (b) hydrated in 1 M NaCl aqueous solution (H ) 8.6), and (c) in the fully hydrated state (H ) 16). (d) Schematic illustration of a five-stranded microfibril for type I collagen with periodicity D.
of an excised cornea as a function of temperature. The corneal gel uniformly collapsed into a compact state at temperatures above 55 °C and did not regain the original volume and shape when reswollen in water. The observed irreversible transition is considered to be due to the denaturation of collagen fibrils.20,21 Regarding fibril denaturation, the denaturation temperature is known to vary depending on the conditions. For example, when the collagen fibrils were suspended in distilled water, the denaturation endotherm for the tendon was observed near 60 °C, whereas when the collagen fibrils were swollen by addition of 0.5 M acetic acid, the position of the endotherm was seen to be more than 20 °C lower. When the fibrils are swollen, the collagen molecules act essentially independently. In our case, when the collagen fibrils of the corneal stroma were in water, the collagen molecules were more tightly packed together in fibrils and were more stabilized in the fibers. Therefore, the denauration temperature was close to 60 °C, which is consistent with the observations. Small-Angle X-ray Scattering (SAXS). In the previous section, the phase behavior in the corneal gel was studied in terms of simple swelling-ratio measurements as a function of salt concentration and temperature. Although these studies demonstrated the essential roles of the fundamental interactions for phase behavior in gels, these measurements did not provide any microscopic view of the structure of corneal gels. Therefore, we investigated the microscopic structure of corneal gels by means of SAXS to elucidate the swelling mechanism of corneal gels. Figure 3 shows two-dimensional SAXS patterns and their onedimensional SAXS profiles of (a) the cornea immediately after preparation, (b) the hydrated cornea in 1 M NaCl aqueous solution, and (c) the fully hydrated cornea. The excised cornea shows three isotopic peaks, peak A at (1.14 ( 0.01) × 10-2 Å-1, peak B at (2.86 ( 0.01) × 10-2 Å-1, and peak C at (4.70 ( 0.02) × 10-2 Å-1. Peak A disappears when the cornea is hydrated in NaCl aqueous solution or in water. Therefore, peak A corresponds to the spacing between the collagen fibrils, 570 Å. In addition, the fact that peak A is intensive and isotropic is in agreement with the well-known corneal structure: the cornea
Figure 4. One-dimensional SAXS profiles of the corneal gel as a function of temperature in the range between 20 and 80 °C.
consists of hundreds of sheets where collagen fibers with precisely the same spacing run in one direction and the directions of the collagen fibril between the sheets are randomly distributed. Peaks B and C result in a periodic structure within the collagen fibril because they are also observed in the cornea hydrated in water. Peaks B and C are considered to correspond to the third- and fifth-order reflections, respectively, of the periodic structure of the collagen fibril.22,23 In this case, the periodicity D was found to be 668 ( 3 Å. Figure 4 shows the one-dimensional SAXS profiles of the excised cornea as a function of temperature in the range between 20 and 80 °C. At 60 °C, the first-order equatorial reflection started to decrease, and the third- and fifth-order meridional reflections became diffusive. Above 65 °C, the X-ray reflections from the cornea disappeared, and the scattered intensities decreased monotonically with the scattering vector q, which clearly indicates the denaturaton of collagen. Anisotropic deswelling was also observed during desiccation. Changes in the properties of cornea due to the desiccation are also important in interpreting some clinical appearances. They are typically observed during surgical operations such as in excimer-laser-assisted in situ keratomileusis10 or laser thermal keratoplasty.11 The thickness of the cornea decreased along the
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Figure 5. (a) Photos of a cornea at physiological hydration and dry. (b,c) SAXS intensity profiles of a dry cornea: (b) two-dimensional SAXS pattern and (a) its one-dimensional profile (azimuthally averaged). The numbers in the panels b and c indicate the order of reflections. The table in panel c lists the order and q values of the peaks.
orbital axis, and no change was observed in the diameter as shown in Figure 5a. Figure 5b,c shows a two-dimensional SAXS pattern and its one-dimensional profile, respectively, of the dehydrated cornea. In the relatively higher-q region (q > 0.05 Å-1), the dehydrated cornea shows definite peaks with the same spacing [∆q ) (9.45 ( 0.03) × 10-3 Å-1], corresponding to the periodicity D of 665 ( 2 Å. Peaks less than fifth-order are not clearly observed, although they are generally observed in collagen fibers as definite scattering. We deduced that those scatterings would be hidden by the intense scattering from a domain where mucopolysaccharide was condensed upon dehydration. From Guinier’s approximation, the size of the domain was found to be ∼200 Å. On the other hand, as shown in Figure 5b, definite and isotropic reflections were observed from sixthto 11th-order reflections. This means that the collagen fibrils of the dehydrated cornea maintained a fine structure in each sheet. SAXS experiments indicate that the desiccation also simply caused deswelling of the GAGs, which obliged the change in thickness, as observed in the collapse of the corneal gel in aqueous solution of NaCl. Although the collagen fibers were pushed apart during dehydration, they retained their ordered structure in all directions. It is worth noting that the third- and fifth-order reflections were observed in the swollen cornea, whereas the sixth-, ninth-, and 11th-order reflections showed relatively strong intensity in the dehydrated cornea. The scattering features of dry corneas have been well explained by the inner structure of the collagen fibril consisting of microfibrils of tropocollagen, as proposed by Miller et al.41 The five tropocollagens form a periodic unit with a length of 670 Å along the collagen fibril axis, and there is a gap of about 400 Å along one of the five tropocollagens in the structural unit. Therefore, the collagen fibril forms a periodic single-square well, such as a Kronig-Penny potential, with a well length of 0.6D. However, the scattering from the swollen cornea does not agree with Miller et al.’s model. One possible explanation is that the packing of the tropocollagen could be shifted and the length of the well could change to be 0.5D in the swollen cornea fibril. This difference is, however, still substantial and the subject of future investigations. From these observations, it is confirmed that the collagen fibrils of the swollen state and dry state maintain the same fine
structures as those of the intact cornea in each sheet. The SAXS results and the swelling behavior observed in the corneal gel, therefore, indicate the following feature of the observed swelling behavior of cornea. Because of the hydrophobic nature of the collagen fibers of the stroma, water is held by the GAGs, which are located between the regular two-dimensional lattices of collagen fibers. Therefore, the hydration and dehydration caused by changing the concentration of salt simply cause swelling and deswelling, respectively, of the GAG base material, which obliges the change in thickness. On the other hand, the collagen fibers of the corneal gel are denatured with increasing temperature, which is followed by subsequent intermolecular aggregation of the collagen. Dynamics of the Corneal Gel. A critical juncture in the advancement of gel research was the realization that fluctuations in scattered light intensity, arising from concentration or density fluctuations within gels, represent thermally excited acoustic or elastic vibrations of the gel matrix (phonons) that are rapidly dampened by frictional forces. Subsequent light-scattering experiments were able to verify that (1) the magnitude of scattered light intensity fluctuations is dependent on the compressibility of the gel network; (2) the ratio of the elastic modulus to the frictional coefficient of the network in its fluid medium, or the effective mesh size of the network, can be determined by the gel diffusion coefficients; and (3) as the gel approaches the critical point, critical phenomena can be evidenced in the form of divergent behavior in the observed scattered light intensities and the gel diffusion coefficients.24 Specifically, the gel simultaneously becomes infinitely compressible as the pore size becomes infinitely large. Thus, the observed scattered light intensities should markedly increase as the diffusion coefficients diminish toward zero. Essentially no investigations on the dynamics, however, have been performed to verify that the cornea is indeed a gel-like tissue. The reversible property of corneal gel opacities perceptibly demonstrates that the cornea can behave typically like a gel network, as its chemical makeup would indicate. If indeed the cornea were a gel network, well-established theories would predict that the cornea should exhibit phase-transition and critical phenomena in response to varied external conditions.
Anisotropic Swelling Behavior of the Cornea
Figure 6. (a) Correlation function obtained from the anterior surface of the corneal gel at an approximate depth of 0.1 mm at a scattering angle 135° and at 25 °C. (b) q2 dependence of Γq-2 for the corneal gel.
Dynamic Light Scattering (DLS). Figure 6a shows a correlation function obtained from the anterior surface of the corneal gel at an approximate depth of 0.1 mm at a scattering angle 135° and at 25 °C. From a nonlinear least-squares fit to the data using eqs 4 and 5 (the solid line in Figure 6a), the essential parameters for the diffusion constants that represent the two apparent, collective diffusion motions of the corneal gel, designated as fast and slow motions, respectively, were derived as Dfast ) 2.1 × 10-7 cm2/s and Dslow ) 9.6 × 10-9 cm2/s. Other significant parameters of the computer-generated fit include the relative contributions of the fast and slow components to the overall dynamic scattered light intensity ID, designated as %Afast and %Aslow, respectively, where %Afast ) 100 × Afast/(Afast + Aslow) and similarly for %Aslow. Also determined were the static (%IS) and dynamic (%ID) components of the scattered light intensities, where %ID ) 100 × ID/(ID + IS) and similarly for %IS, to the total scattered light intensity, Itotal, observed at a particular wave vector. For the data shown in Figure 6, %Afast ≈ 40 and %ID ≈ 30. For a diffusive mode, one expects Γ to be proportional to q2, with Γ ) Dq2, where D is the diffusion coefficient. For all scattering angles, the values of Γq-2 for both fast and slow modes are almost independent of q within experimental error, as shown in Figure 6b. This indicates that the observed two modes are diffusive. It should be mentioned that the apparent q2 dependence of Γq-2 is within experimental error. It is also worth mentioning that neither Dfast nor Dslow exhibits statistically significant differences with respect to either the position on the anterior surface of the cornea or the depth at which scattered light was sampled (see Supporting Information). Figure 7a displays the averaged fast and slow diffusion coefficients, Dfast and Dslow, obtained from three different corneas in the temperature range between 5 and 65 °C. As shown, both Dfast and Dslow increased with temperature up to 35 °C and then began to decrease at about 55-65 °C. The initial rise, up to 35 °C, in the values of both Dfast and Dslow reflects a decrease in the frictional coefficients f due to changes in the viscosity of water with respect to temperature. The observed decreases in Dfast and Dslow with respect to increasing temperatures were also accompanied by a divergent behavior in the measured scattering intensity. Figure 7b shows the total intensity of light, Itotal, scattered by the cornea at a scattering angle of 135° with respect to temperature. In the temperature range of 5-35 °C, Itotal is essentially constant. As the temperature exceeds 35 °C, Itotal increases dramatically, and the cornea exhibits “cloudiness”. In instances where the temperature was reversed upon reaching 50 °C, the divergent
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Figure 7. (a) Average fast and slow diffusion coefficients, Dfast (b) and Dslow (9), obtained from three different corneas in the temperature range between 5 and 65 °C. The open circles and squares represent the measured values of Dfast and Dslow, respectively, as the temperature was reversed from 55 °C. (b) Total intensity of light, Itotal (b), scattered by the cornea at a scattering angle of 135° with respect to increasing temperatures. The intensity (O) diminishes to its original value as the temperature is reversed upon reaching 55 °C.
Figure 8. Static, IS (O), and dynamic, ID (b), component contributions to the total scattered light intensity, Itotal, obtained from fits to correlation functions using eqs 3 and 4 as a function of increasing temperature. The corresponding contribution of the slow scatterer, %As (0), to the overall increase in ID is also shown. The dramatic increase in ID is indicative of the increasing amplitude of local density fluctuations that usually accompany a phase transition.
behavior observed between the measured diffusion coefficients and static scattered light intensities was reversible (see Figure 7b). That is, both the observed diffusion coefficients and the scattered light intensities recovered to their original values when the temperature was reversed upon reaching 50 °C. Recovery of diffusion coefficients and scattered light intensities was, however, not observed with the reversal of temperature upon reaching 65 °C (data not shown). This is due to the denaturaton of collagen and consistent with the results observed in swelling experiments and SAXS measurements. Under conditions of increased temperatures, as a result of large-scale temporal fluctuations in the local densities of the collagen gel, regions of high and low collagen densities formed. Thus, as the phase transition was approached, the magnitude of the intensity fluctuations increased, and the fluctuations became slower. A divergent behavior in the observed scattered light intensities (Itotal) and diffusion coefficients (Dfast and Dslow) readily evidenced this behavior. Moreover, the dramatic increase in the observed scattered light intensities, Itotal, was associated directly with an increase in the dynamic component of the scattered light ID rather than the static component IS, as shown in Figure 8. The primary contributor to the increase in ID is the slow mode, where an increase in %As was also observed as the temperature was increased. This behavior is indicative of a gel undergoing a phase transition. The cornea is a very dense matrix of collagen fibrils whose transparency, as first demonstrated theoretically by Benedek,1
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is maintained not because of regular long-range ordering, but because spatial fluctuations in the number density of fibrils are small compared to 1. Simply put, the distance between collagen fibrils within the lamellar layers need only be shorter than the typical wavelength of light for the cornea to be transparent. Light can, however, be scattered by the collagen fibrils when their positions are randomly displaced, in time, as a result of thermal motions.25 Light can also be scattered by large “superstructures” or cells that are present throughout that stroma, which have an approximate size in the range of 1-20 µm.4,6,26 Stromal cells, primarily keratocytes, have dimensions of ∼20 µm.6 The possibility that the superstructures are “wavy” lamellae that form in the absence of “normal” intraocular pressure (IOP) has also been proposed.8 On the time scale τ used to calculate the intensity correlation functions C(τ) from observations of light scattered from within the cornea, neither the motions of keratocytes nor the wavy lamellae of the approximate size ranging from 1000 to 20000 nm would be correlated. Hence, light scattered by either the stromal cells or the wavy lamellae would contribute to the static component (IS) of the overall scattered light (Itotal) and not its dynamic component (ID), as defined by eq 2. It is worth mentioning that the origin of the observed two diffusive modes is still unknown. Recently, Sasaki and Schipper27 investigated the coupled diffusion of segments and counterions in polyelectrolyte gels and solutions. Based on DLS measurements for the cooperative diffusion on polyelectrolytes in the semidilute regime and pulsed field gradient NMR measurements to determine the diffusion constant of counterions, they concluded that the dynamical properties of chain segments and counterions in the polyelectrolyte solutions and gels are alike and that the coupling of chain-segment and counterion dynamics creates the fast mode observed in the DLS measurements. The corneal stroma is a complex heterogeneous system in which a matrix of collagen fibrils is embedded in a GAG ground substance. Even though the swelling of the corneal gel is mainly due to the hydration of the GAG, it is natural to consider the motion of the GAG to be coupled to the dynamics of the collagen motion. Therefore, we cannot assume that the dynamic component of the scattered light consists of two independent and uncorrelated diffusion processes characterizing local density fluctuations within the cornea. Kinetics of Corneal Swelling. Based on the cooperative diffusion of polymer network in a medium, Tanaka and Fillmore (TF) demonstrated that the characteristic time of gel swelling, τ, is described as τ ≈ R2/D, where R and D are the size of the gel and the cooperative diffusion coefficient of the gel network, respectively.28 TF theory indicates that macroscopic gel swelling is related to microscopic concentration fluctuations through the diffusion coefficient of the network, D, which is determined by DLS. An excised cornea was placed in distilled and deionized water and allowed to swell. In this particular case, the initial equilibrium state of the cornea, where the condition of zero osmotic pressure applies, was abruptly altered by immersion into distilled deionized water at 25 °C. If this perturbation were sufficiently small, the kinetics of the subsequent relaxation process (volume change) as the cornea tended toward a new equilibrium state would simply be exponential in form. Figure 9a shows the change in time in the thickness, h, of an excised cornea from its initial thickness, h(0) ) 0.1 cm, as it proceeds toward the new equilibrium state, h(∞) ) 0.8 cm. To determine the characteristic relaxation time τ for the change in h, the relative swelling ∆h/∆h0 defined by
Matsuura et al.
∆h h(t) - h(0) t ) ≈ exp ∆h0 h(∞) - h(0) τ
( )
(12)
where h(t) is the corneal gel thickness at time t, was plotted against time t, as shown in Figure 9b. The data in Figure 9b correspond to those in Figure 9a. The slope of the line gives the characteristic relaxation time as τ ) 2.65 × 103 s. In TF theory, TF assumed the shear modulus µ of the gel to be negligible compared to the osmotic bulk modulus. Peters and Candau29,30 and Li and Tanaka31 extended TF theory to the case of gels with non-negligible shear moduli (µ * 0) and investigated the swelling kinetics for long cylindrical gels and large disk gels. The effect of nonzero shear modulus is to reduce the speed of diffusion process. The diffusion occurs in all three dimensions for a sphere, two dimensions (radial) for a cylinder, and only one dimension for a disk (axial). According to Li and Tanaka, the reduction factor of the diffusion coefficient can be obtained qualitatively by a simple dimension-counting argument and is directly related to the ratio of the number of diffusion dimensions to the total number of dimensions, 3. The reduction factors, therefore, are 3/3, 2/3, and 1/3, for spheres, cylinders, and disks, respectively. The diffusion of the corneal gel occurs in one dimension; therefore, the effective diffusion coefficient for the corneal gel De can be expressed as
1 1 h2 De ) D0 ) 3 3τ
(13)
where D0 is the diffusion coefficient of the spherical gel whose diameter is equal to the thickness of the disk gel. Substituting h(∞) ) 0.8 cm and τ ) 2.65 × 103 s into eq 13 yields D ) 8.05 × 10-5 cm2/s, which is approximately 2-4 orders of magnitude greater than the values obtained from DLS measurements of the same sample. From the outset, calculations of the collective diffusion coefficients from swelling kinetics assume that the characteristic time of swelling corresponds to the temporal change in thickness of the whole cornea, whose initial thickness h(0) was 0.1 cm. The overestimation of D suggests that the observed kinetics of corneal swelling occurred too rapidly for a cornea of this thickness and known collective diffusion coefficient. Because the measurements of both τ Rand D are relatively unambiguous, it is then possible to hypothesize that the inherent layered structure of the corneal stroma gives rise to the overestimation of D. It is plausible to explain that each lamellar sheet within the corneal stroma behaves as an individual disk gel. Elliott and Hodson32 reported that, at high hydrations, some of the water imbibed by the total tissue does not go into the
Figure 9. (a) Change in time of the thickness, h, of an excised cornea from its initial thickness h(0) toward the new equilibrium state h(∞). (b) Normalized thickness change, ∆h/∆h0, plotted semilogarithmically against t.
Anisotropic Swelling Behavior of the Cornea
Figure 10. Schematic representation of the swelling of stroma. (a) Schematics of the cross section of corneal stroma. (b) Rigid collagen type I fibrils and smaller strands of proteoglycans composing the lamellae of the corneal stroma. (c) Anisotropic swelling behavior simply causes swelling and deswelling of proteoglycan, located between the regular two-dimensional lattices of collagen fibers, which oblige the change in thickness.
fibril lattice but is held somewhere else in the structure. This nonlattice water is not a large feature of the system at hydrations up to physiological hydration, but it becomes increasingly important beyond physiological hydration of the corneal gel. This water, called “lake water” has been implicated as a cause of the loss of transparency at these high hydrations. Therefore, the formations of fibril “lakes” within the lamellar layers might well account for the rapid swelling of the corneal gel. The discrepancy of the dynamics of the corneal gel observed between by DLS and by swelling kinetics can be explained when better procedures to determine the swelling kinetics of individual lamellar layers are followed, a subject of future investigations.32 Concluding Remarks In this study, the phase equilibrium and structural and dynamical properties of pig cornea were studied by macroscopic observations of swelling behavior, dynamic light scattering (DLS), and small-angle X-ray scattering (SAXS) under various conditions. It was found that the corneal gel collapses into a compact state isotropically or anisotropically depending on the external conditions. The corneal gel uniformly collapses into a compact state at temperatures above 55 °C as a result of the denaturation of collagen, whereas it collapses along an axis parallel to the optic axis with increasing NaCl concentration. Anisotropic deswelling was also observed during desiccation. SAXS measurements revealed that the periodicity of the collagen fibers in the cornea does not change and that the hydration and dehydration accompanying changes in the salt concentration or desiccation simply cause swelling and deswelling of the GAG, which is located between the regular two-dimensional lattices of collagen fibers and obliges the change in thickness (Figure 10). From observations of the dynamics of light scattered by the corneal gel, intensity autocorrelation functions that revealed two independent diffusion coefficients were obtained. The collective diffusion coefficients from the intensity correlation function decreased with temperature, beginning at 55 °C. Parallel to the decrease of the diffusion coefficients, the measured intensity increased and appeared to diverge as the temperature approached 55 °C. The
J. Phys. Chem. B, Vol. 113, No. 51, 2009 16321 divergent behavior of the observed diffusion coefficients and total scattered light intensities is indicative of the occurrence of a phase transition with increasing calcium ion concentration. To adapt the physical properties of living materials to their biological function, nature has developed macromolecules and networks with outstanding physical behavior. The cornea can maintain its lucidity and moisture content, which requires, however, a continuous maintenance by metabolism. Metabolic defects or diseases lead to turbidity as a result of changes in local structure. This is one example of the close correlation between diseases and local structure. More extensive study is needed, however, to manipulate the structure and dynamics of macromolecules and networks consisting of cornea, which leads to a bridge in the gap between the physiological function and physicochemical properties of corneas at the molecular level. Acknowledgment. The work was partly supported by a Grant-in-Aid for Scientific Research on Priority Areas “Soft Matter Physics” and by a Grant-in-Aid for the Global COE Program, “Science for Future Molecular Systems”, from the Ministry of Education, Culture, Science, Sports, and Technology of Japan. SAXS experiments were performed with the approval of the Spring-8 (Proposal 2001A0265-NL-np). Supporting Information Available: Dicussion of the dependence of values of Dfast and Dslow on the location and depth of measurement from the anterior surface. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Benedek, G. E. Appl. Opt. 1971, 10, 459. (2) Fatt, I. Physiology of the Eye; Butterworth: Boston, 1971; p 92. (3) Farrel, R. A.; McCally, R. L. J. Opt. Soc. Am. 1976, 66, 342. Maurice, D. M. The Cornea and Sclera. In The Eye; Davison, H., Ed.; Academic Press: New York, 1984; p 1. (4) Gisselberg, M.; Clark, J. I.; Vaezy, S.; Osgood, T. B. Am. J. Anat. 1991, 191, 408. (5) Bettelheim, F. A.; Vinciguerra, M. J. Biochim. Biophys. Acta 1969, 177, 259. (6) Cejtlin, J.; Vinciguerra, M. J.; Bettelheim, F. A. Biochim. Biophys. Acta 1971, 237, 530. (7) McCally, R. L.; Farrel, R. A. Polymer 1977, 18, 444. (8) Nishida, T. Cornea: Anatomy and Physiology. In Cornea, 2nd ed.; Krachmer, J. H., Mannis, M. J., Holland, E. J., Eds.; Elsevier: New York, 2005; pp 3-27. (9) Joo, D. K.; Kim, T. G. J. Cataract RefractiVe Surg. 1999, 25, 1165. (10) Feltham, M. H.; Stapleton, F. Clin. Exp. Ophthalmol. 2000, 28, 185. (11) Waltman, S. R.; Hart, W. M. The Cornea. In Adler’s Physiology of the Eye, Clinical Application; Moses, R. A., Ed.; Mosby: St. Louis, MO, 1970; p 36. (12) Matsuura, T.; Hara, Y.; Maruoka, S.; Kawasaki, S.; Sasaki, S.; Annaka, M. Macromolecules 2004, 37, 7784. (13) Munch, J. P.; Candau, S.; Herz, J.; Hild, G. J. Phys. (Paris) 1977, 38, 971. (14) Munch, J. P.; Lemarechal, P.; Candau, S. J. Phys. (Paris) 1977, 38, 1499. (15) GAG. (16) Tanaka, T.; Fillmore, D.; Nishio, I.; Sun, S.-T.; Shah, A.; Swislow, G. Phys. ReV. Lett. 1980, 45, 1636. (17) Flory, P. J. In Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953; pp 541-593. (18) Barret, J. L.; Joanny, J. F.; Pincus, P. J. Phys. II (France) 1992, 2, 1531. (19) Fernandez-Nieves, A.; Fernandez-Bardero, A.; de la Nieves, F. J. J. Chem. Phys. 2001, 16, 7644. (20) Tiktopulo, E. I.; Kajava, A. V. Biochemistry 1998, 37, 8147. (21) Miles, C. A.; Burjanadze, T. V.; Bailey, A. J. J. Mol. Biol. 1995, 245, 437. (22) Meek, K. M.; Fullwood, N. J.; Cooke, P. H.; Elliott, G. F.; Maurice, D. M.; Quantock, A. J.; Wall, R. S.; Worthington, C. R. Biophys. J. 1991, 60, 467.
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(23) Fratzl, P.; Daxer, A. Biophys. J. 1993, 64, 1210. (24) Tanaka, T.; Hocker, L. O.; Benedek, G. B. J. Chem. Phys. 1973, 59, 5151. (25) Fuek, T. IEEE Trans. Biomed. Eng. 1970, 17, 186. (26) Kikkawa, Y. J. Physiol. Soc. Jpn. 1960, 10, 292. (27) Sasaki, S.; Schipper, F. J. M. J. Chem. Phys. 2001, 105, 4349. (28) Tanaka, T.; Fillmore, D. J. J. Chem. Phys. 1979, 70, 1214.
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