The effect of membrane heterogeneity on the predictability of fluxes,with application to the cornea

Many phenomenological treatments of biological membrane transport are based on the assumption that the membrane consists of a single class of passive transport paths; i.e. that the membrane is simple. Simplicity is assumed both in the measurement of the membrane's transport coefficients and in the use of these coefficients to predict membrane fluxes. Such a procedure will in general lead to an error in the prediction of solute flux across parallel arrays. The error depends on the distribution of the reflection coefficients of the parallel paths and upper and lower bounds on it are given in terms of conventionally measured transport coefficients. The frictional representation of electrolyte transport across membranes possessing metabolic pumps is generalized to take this structure effect into account. The flux error resulting from the neglect of membrane heteroreflectivity is essentially the same for nonelectrolytes and electrolytes, irrespective of whether phenomenological or frictional membrane transport properties are used. It is shown that some information about transport structure can be obtained from global measurements made without regard for the organization of pathways across the membrane.The values of the measured transport coefficients of the corneal epithelium and endothelium imply that these cell layers are heteroreflective. Analysis of corneal transport, taking structure effects into account, shows that the corneal thickness may be intrinsically insensitive to tear tonicity, by a mechanism which may be of more general homeostatic significance.     

角膜上皮细胞代谢的研究进展

角膜上皮层位于角膜表面,外邻泪膜,内与角膜前弹力层相连。角膜上皮细胞代谢所需营养及氧分主要通过泪膜、房水和角膜缘毛细血管运送。正常的角膜上皮细胞代谢是维持角膜上皮细胞正常增殖与分化状态的关键。角膜上皮细胞代谢异常可导致上皮损伤或变性,是多种角膜疾病的病理基础。本文就近年来关于角膜上皮细胞代谢相关的组织结构、营养来源、细胞增殖分化以及相关疾病的研究进展进行综述。     

Proteomic analysis of rabbit tear fluid: Defensin levels after an experimental corneal wound are correlated to wound closure

The cornea is the major refracting optical element of the eye and therefore critical for forming a retinal image. The exposed surface of the eye is protected from pathogens by the innate immune system whose components include defensins, naturally occurring peptides with antimicrobial properties, and the physical barrier formed by the outer epithelial layer of the cornea. The proteomic approach has revealed that tear levels of defensins are correlated with the course of healing of an experimental corneal wound. Tears were collected from New Zealand White rabbits prior to (day 0) and daily for 5 days (days 1-5) following a standard unilateral 6 mm diameter corneal epithelial abrasion. Tear protein profiles obtained from wounded and contra-lateral control eyes were compared using SELDI ProteinChip technology. Peptides and proteins of interest were purified by RP-HPLC and characterized by nanoESI-MS/MS. Mass spectra of tears on post-wound day 1, revealed 13 peaks whose level decreased and five that increased. During wound healing the tear protein profile correlated with wound closure. An important finding was that the levels of rabbit defensins (NP-1 and NP-2), which were elevated after wounding returned to normal levels by the time the corneal abrasion healed. Relative quantification of NP-2 in tear fluid prior to (day 0) and after corneal wounding (days 1- 3) was determined using iTRAQ technology. A corneal wound eliminates the barrier function of innate immunity and puts the cornea at risk from microbial attack until the epithelial cells restore the surface barrier. The increased availability of defensins in the tears during healing suggests that these peptides could protect the cornea from microbial attack during a period of increased vulnerability.     

Electrolyte transport across a simple epithelium. Steady-state and transient analysis.

A simple transporting epithelium is represented as a cellular compartment, compliant in all dimensions, and a paracellular channel, of arbitrary shape, between well-stirred mucosal ans serosal baths. The equations for mass balance, Poiseuille flow, and the Nernst-Planck equation are used to describe the continuous behavior of the system along cell and channel, whereas passive transport across membranes is given by the relations of Kedem and Katchalsky. Time-dependent terms are retained to permit study of transient phenomena. Boundary conditions at the baths demand only mass conservation and specify no a priori estimates of the system variables. A numerical model containing Na+,K+,Cl-, and impermeant cellular anions is formulated with membrane parameters taken from the literature on Necturus gallbladder. The differential equations are represented as a finite difference scheme and solved using Newton's method. It appears that apical cellular NaCl cotransport is necessary to obtain a reasonable cell chloride concentration. Investigation of the osmolality of the transepithelial flow shows that at steady state a leaky epithelium cannot separate baths of substantially different tonicity, although this does not guarantee isotonic transport between equiosmolar media. Changes in bath pressure, application of transepithelial electrical potential, and simulation of ion-substitution experiments are performed to understand the role of membrane permeabilities in determining the dynamic behavior of the epithelium.     

Corneal cell proteins and ocular surface pathology

The cornea is a transparent and avascular tissue that functions as the major refractive structure for the eye. A wide variety of growth factors, chemokines, cytokines and their receptors are synthesized by corneal epithelial and stromal cells, and are found in tears. These molecules function in corneal wound healing and in inflammatory responses. Proteoglycans and glycoproteins are essential for normal corneal function, both at the air-epithelial interface and within the extracellular matrix. The ocular MUC mucins may play roles in forming the mucus layer of the tear film, in regulating tear film spread, and in inhibiting the adhesion of pathogens to the ocular surface. Lumican, keratocan and mimecan are the major keratan sulfate proteoglycans of the corneal stroma. They are essential, along with other proteoglycans and interfibrillar proteins, including collagens type VI and XII, for the maintenance of corneal transparency. Corneal epithelial cells interact with a specialized extracellular matrix structure, the basement membrane, composed of a specific subset of collagen type IV and laminin isoforms in addition to ubiquitous extracellular matrix molecules. Matrix metalloprotein-ases have been identified in normal corneal tissue and cells and may play a role in the development of ulcerative corneal diseases. Changes in extracellular matrix molecule localization and synthesis have been noted in other types of corneal diseases as well, including bullous keratopathy and keratoconus.     

The corneal surface of aquatic vertebrates: microstructures with optical and nutritional function?

The anterior surface of the mammalian cornea plays an important role in maintaining a smooth optical interface and consequently a sharp retinal image. The smooth surface is produced by a tear film, which adheres to a variety of microprojections, which increase the cell surface area, improve the absorbance of oxygen and nutrients and aid in the movement of metabolic products across the outer cell membrane. However, little is known of the structural adaptations and tear film support provided in other vertebrates from different environments. Using field emission scanning electron microscopy; this study examines the density and surface structure of corneal epithelial cells in representative species of the classes Cephalaspidomorphi, Chondrichthyes, Osteichthyes, Amphibia, Reptilia, Aves and Mammalia, including some Marsupialia. Variations in cell density and the structure and occurrence of microholes, microridges, microplicae and microvilli are described with respect to the demands placed upon the cornea in different aquatic environments such as marine and freshwater. A progressive decrease in epithelial cell density occurs from marine (e.g. 29348 cells mm(-2) in the Dover sole Microstomius pacficus) to estuarine or freshwater (e.g. 5999 cells mm(-2) in the black bream Acanthopagrus butcheri) to terrestrial (e.g. 2126 cells mm(-2) in the Australian koala Phascolarctos cinereus) vertebrates, indicating the reduction in osmotic stress across the corneal surface. The microholes found in the Southern Hemisphere lampreys, namely the pouched lamprey (Geotria australis) and the shorthead lamprey (Mordacia mordax) represent openings for the release of mucus, which may protect the cornea from abrasion during their burrowing phase. Characteristic of marine teleosts, fingerprint-like patterns of corneal microridges are a ubiquitous feature, covering many types of sensory epithelia (including the olfactory epithelium and the oral mucosa). Like microplicae and microvilli, microridges stabilize the tear film to maintain a smooth optical surface and increase the surface area of the epithelium, assisting in diffusion and active transport. The clear interspecific differences in corneal surface structure suggest an adaptive plasticity in the composition and stabilization of the corneal tear film in various aquatic environments.     

Mathematical modelling of corneal swelling

This paper presents a differential model of the corneal transport system capable of modelling thickness changes in response to osmotic perturbations applied to either limiting membrane. The work is directed towards understanding corneal behaviour in vivo. The model considers the coupled viscous flows within the corneal stroma and across the epithelial and endothelial membranes. The flows within the stroma are established based on transport theory in porous media, while the flows across the membranes are described using the phenomenological equations of irreversible thermodynamics. The ability of the numerical model to reproduce corneal thickness changes in response to endothelial perturbations was tested against available experimental data. The sensitivity of the model to changes in stromal and membrane transport coefficients was examined.     

A model of epithelial water transport. The corneal endothelium.

To try to understand how an epithelial tissue can transport water between bathing solutions of equal tonicity and how intracellular solute and protein concentration are related to the structural specialization of the cell membrane at its apical, basal, and lateral margins, we have formulated and solved, using approximate analytical techniques, a new model which combines the detailed transport of local osmotic flow in extracellular channel with the multicompartment approach of thermodynamic models requiring the overall conservation of water and solute for the entire cell layer. Thus, unlike most previous models, which dealt exclusively with either the average properties of the cell layer or the local transport in the extracellular channel, we are able to solve simultaneously for the interaction of the cell with its environments across its apical, basal, and lateral cell membranes as well as the detailed transport in the extracellular channel. The model is then applied to corneal endothelium to obtain new insight into the water flow movement in this tissue under in vitro and in vivo conditions. Then in vitro solution shows that the cell at 297 mosmol/liter is slightly hypotonic to the 300-mosmol/liter external bathing solutions which drive water equally out both the aqueous (apical) and stromal (basal) cell faces. This water is replaced from the extracellular channel. There is a net flow of water because more water enters the channel through its open stromal end than through the higher resistance tight junction. In vivo, the solution predicts that the stromal swelling pressure forces water through the tight junctions towards the stroma so that there is no net flow. The interesting new features of our solution are the water recirculation pattern and the role of the osmotically active proteins in making the cell hypertonic relative to the channel.     

Crowding Effects in Vehicular Traffic

While the impact of crowding on the diffusive transport of molecules within a cell is widely studied in biology, it has thus far been neglected in traffic systems where bulk behavior is the main concern. Here, we study the effects of crowding due to car density and driving fluctuations on the transport of vehicles. Using a microscopic model for traffic, we found that crowding can push car movement from a superballistic down to a subdiffusive state. The transition is also associated with a change in the shape of the probability distribution of positions from a negatively-skewed normal to an exponential distribution. Moreover, crowding broadens the distribution of cars’ trap times and cluster sizes. At steady state, the subdiffusive state persists only when there is a large variability in car speeds. We further relate our work to prior findings from random walk models of transport in cellular systems.     

A New Approach to Epithelial Isotonic Fluid Transport: An Osmosensor Feedback Model

A model for control of the transport rate and osmolarity of epithelial fluid (isotonic transport) is presented by using an analogy with the control of temperature and flow rate in a shower. The model brings recent findings and theory concerning the role of aquaporins in epithelia together with measurements of epithelial paracellular flow into a single scheme. It is not based upon osmotic equilibration across the epithelium but rather on the function of aquaporins as osmotic sensors that control the tonicity of the transported fluid by mixing cellular and paracellular flows, which may be regarded individually as hyper- and hypo-tonic fluids, to achieve near-isotonicity. The system is built on a simple feedback loop and the quasi-isotonic behavior is robust to the precise values of most parameters. Although the two flows are separate, the overall fluid transport rate is governed by the rate of salt pumping through the cell. The model explains many things: how cell pumping and paracellular flow can be coupled via control of the tight junctions; how osmolarity is controlled without depending upon the precise magnitude of membrane osmotic permeability; and why many epithelia have different aquaporins at the two membranes.The model reproduces all the salient features of epithelial fluid transport seen over many years but also indicates novel behavior that may provide a subject for future research and serve to distinguish it from other schemes such as simple osmotic equilibration. Isotonic transport is freed from constraints due to limited permeability of the membranes and the precise geometry of the system. It achieves near-isotonicity in epithelia in which partial water transport by co-transporters may be present, and shows apparent electro-osmotic effects. The model has been developed with a minimum of parameters, some of which require measurement, but the model is flexible enough for the basic idea to be extended both to complex systems of water and salt transport that still await a clear explanation, such as intestine and airway, and to systems that may lack aquaporins or use other sensors.     

Characterization of a carbohydrate epitope defined by the monoclonal antibody H185: sialic acid O-acetylation on epithelial cell-surface mucins

Sialic acids comprise a large family of derivatives of neuraminic acid containing methyl, acetyl, sulfate, and phosphate among other groups, which confer specific physicochemical properties (e.g., hydrophobicity and resistance to hydrolases) to the molecules carrying them. Several years ago, a monoclonal antibody, designated H185, was developed, which binds to cell membranes of human corneal, conjunctival, laryngeal, and vaginal epithelia and whose distribution is altered on the ocular surface of patients with keratinizing disease. Recent findings using immunoprecipitation and immunodepletion techniques have demonstrated that, in human corneal epithelial cells, the H185 antigen is carried by the membrane-associated mucin MUC16. In this study, we show that the H185 epitope on human corneal cells and in tear fluid is an O-acetylated sialic acid epitope that can be selectively hydrolyzed in an enzyme-concentration-dependent manner by sialidase from Arthrobacter ureafaciens and to a lesser extent by sialidases from Newcastle disease virus, Clostridium perfringens, and Streptococcus pneumoniae. Binding of the H185 antibody was impaired by treatment of tear fluid with a recombinant 9-O-acetylesterase from influenza C virus. Two O-acetyl derivatives, Neu5,7Ac(2) and Neu5,9Ac(2), were identified in human tear fluid by fluorometric high-performance liquid chromatography (HPLC) and electrospray mass spectrometry (MS). Immunoprecipitation of the H185 epitope from human corneal epithelial cells revealed that Neu5,9Ac(2) was the major derivative on the mucin isolate. These results indicate that exposed wet-surfaced epithelia are decorated with O-acetyl sialic acid derivatives on membrane-associated mucins and suggest that O-acetylation on cell surfaces may protect against pathogen infection by preventing degradation of membrane-associated mucins.     

Aquaporin deletion in mice reduces corneal water permeability and delays restoration of transparency after swelling

Two aquaporin (AQP)-type water channels are expressed in mammalian cornea, AQP1 in endothelial cells and AQP5 in epithelial cells. To test whether these aquaporins are involved in corneal fluid transport and transparency, we compared corneal thickness, water permeability, and response to experimental swelling in wild type mice and transgenic null mice lacking AQP1 and AQP5. Corneal thickness in fixed sections was remarkably reduced in AQP1 null mice and increased in AQP5 null mice. By z-scanning confocal microscopy, corneal thickness in vivo was (in microm, mean +/- S.E., n = 5 mice) 123 +/- 1 (wild type), 101 +/- 2 (AQP1 null), and 144 +/- 2 (AQP5 null). After exposure of the external corneal surface to hypotonic saline (100 mosm), the rate of corneal swelling (5.0 +/- 0.3 microm/min, wild type) was reduced by AQP5 deletion (2.7 +/- 0.1 microm/min). After exposure of the endothelial surface to hypotonic saline by anterior chamber perfusion, the rate of corneal swelling (7.1 +/- 1.0 microm/min, wild type) was reduced by AQP1 deletion (1.6 +/- 0.4 microm/min). Base-line corneal transparency was not impaired by AQP1 or AQP5 deletion. However, the recovery of corneal transparency and thickness after hypotonic swelling (10-min exposure of corneal surface to hypotonic saline) was remarkably delayed in AQP1 null mice with approximately 75% recovery at 7 min in wild type mice compared with 5% recovery in AQP1 null mice. Our data indicate that AQP1 and AQP5 provide the principal routes for corneal water transport across the endothelial and epithelial barriers, respectively. The impaired recovery of corneal transparency in AQP1 null mice provides evidence for the involvement of AQP1 in active extrusion of fluid from the corneal stroma across the corneal endothelium. The up-regulation of AQP1 expression and/or function in corneal endothelium may reduce corneal swelling and opacification following injury.     

Mass Transfer in the Cornea: II. Ion Transport and Electrical Properties of a Series Membrane Tissue

The electrical and active transport properties of isolated rabbit cornea are investigated by computer experimentation. The tissue is modeled as a series membrane system and the passive ion fluxes through it are described by the frictional formulation of irreversible thermodynamics. From short-circuit current (SCC) data, it is found that the epithelial sodium pump rate (P) is not appreciably changed when much of the sodium in the solution bathing the anterior corneal surface (concentration = c₁₁) is replaced by choline, with choline-free medium posteriorly. Simulations of open-circuited corneas, using the mean P computed from the SCC data, yield corneal and stromal potentials in agreement with experiment. The stromal fluid is calculated to become more hypotonic as c₁₁ is diminished, a result consistent with posttest measurements of the sodium content of experimental stromata. The apparent decrease in “bound sodium” which accompanies the reduction of c₁₁ is a result of the associated changes in steady stromal hydration; the epithelial sodium pump does not contribute to corneal deturgescence. The inclusion of a simple epithelial structure in the computations changes the value of P but affects neither its constancy nor the calculated behavior of the cornea under open-circuit conditions. A general algebraic relation among pump rates and ion fluxes in short-circuited series membrane systems bathed in complex media is derived and used to construct a relation between P and SCC for the cornea. This equation yields pump rates in good agreement with the computer results and is used to show that (a) P is independent of c₁₁ if d(SCC)/dc₁₁ is a constant related to the over-all corneal permeability to sodium, and (b) a Lineweaver-Burke plot of 1/SCC vs. 1/c₁₁ can appear to be linear at constant P.     

Regeneration of the Cornea in Adult Newts: Overall Process and Behavior of Epithelial Cells

Regeneration of the cornea in adult newts was studied by means of light- and electron-microscopic techniques. We focused our analysis particularly on the behavior of epithelial cells during the initial process of wound healing after we had excised a central disk about 0.5 mm in diameter through the entire thickness of the cornea. Fine fibrous material, assumed to be fibrin, appeared within 30 min to form an acellular layer of mucous consistency which sealed the wound opening completely. The cut edge of corneal epithelium moved centripetally on this layer by coordinate movement of individual epithelial cells. Almost all cells of the remained epithelium were completely rearranged within 5 h after excision. Some desmosomes among the epithelial cells persisted during the process of cellular rearrangement. Thus, the wound opening was covered completely within 24 h by the epithelium alone without cell proliferation. Cytochalasin B or D completely inhibited movement of the corneal epithelium on the stroma in conditions in vitro, suggesting active participation of intracellular contractile microfilaments in such movement of the epithelium. Active growth of cells in the epithelium started on day 3 and the epithelium recovered its normal thickness by day 10 after excision.
After the recovery of the epithelium, keratocytes moved out from the wounded edge of the remained corneal stroma. These keratocytes actively proliferated in the wound area under the newly formed epithelium and participated in the stromal reconstitution, which proceeded gradually for more than 5 weeks.     

Dipeptidyl peptidase IV (DPPIV) activity in the tear fluid as an indicator of the severity of corneal injury: a histochemical and biochemical study

Comparative histochemical and biochemical studies on the catalytically active protease Dipeptidyl peptidase IV (DPPIV), have been performed in the rabbit cornea and the tear fluid using a sensitive fluorogenic substrate, Gly-Pro-7-amino-4-Trifluoromethyl Coumarine (AFC). In both normal and experimentally injured corneas, DPPIV activity was detected histochemically and in the tear fluid biochemically. In contrast to the normal cornea where DPPIV activity was absent and in the tear fluid where it was low, during continuous wearing of contact lenses or repeated irradiation of the cornea with UVB rays, slight DPPIV activity appeared first in the superficial layers of the corneal epithelium, while later increased activity was present in the whole epithelium. This paralleled elevated DPPIV activity in the tear fluid. Moreover, during continuous contact lens wear, the increased DPPIV activity in the tear fluid was, in many cases, coincidental with the presence of capillaries in the limbal part of the corneal stroma. After severe alkali burns when corneal ulcers appeared, collagen fragments were active for DPPIV, which was associated with high DPPIV activity in the tear fluid. In conclusion, Gly-Pro-AFC was found to be useful for comparative histochemical and biochemical studies on DPPIV activity in the experimentally injured rabbit eye. Using the method of the tear film collection by a short touch of substrate punches to the respective site of the cornea or conjunctiva we can show that in experimental injuries (wearing of contact lenses, irradiation of the cornea with UVB rays), the damaged corneal cells were the main source for DPPIV activity in the tear fluid. It is suggested that the activity of DPPIV measured in the tear fluid might serve as an indicator of early corneal disorders, e.g. corneal vascularization related to contact lens wear.     

A triphasic analysis of corneal swelling and hydration control.

Physiological studies strongly support the view that hydration control in the cornea is dependent on active ion transport at the corneal endothelium. However, the mechanism by which endothelial ion transport regulates corneal thickness has not been elaborated in detail. In this study, the corneal stroma is modeled as a triphasic material under steady-state conditions. An ion flux boundary condition is developed to represent active transport at the endothelium. The equations are solved in cylindrical coordinates for confined compression and in spherical coordinates to represent an intact cornea. The model provides a mechanism by which active ion transport at the endothelium regulates corneal hydration and provides a basis for explaining the origin of the "imbibition pressure" and stromal "swelling pressure." The model encapsulates the Donnan view of corneal swelling as well as the "pump-leak hypothesis."