Steady-state voltages, ion fluxes, and volume regulation in syncytial tissues

Cellular communication among smooth muscle cells: The role of membrane potential via connexins

Communication via action potentials among neurons has been extensively studied. However, effective communication without action potentials is ubiquitous in biological systems, yet it has received much less attention in comparison. Multi-cellular communication among smooth muscles is crucial for regulating blood flow, for example. Understanding the mechanism of this non-action potential communication is critical in many cases, like synchronization of cellular activity, under normal and pathological conditions. In this paper, we employ a multi-scale asymptotic method to derive a macroscopic homogenized bidomain model from the microscopic electro-neutral (EN) model. This is achieved by considering different diffusion coefficients and incorporating nonlinear interface conditions. Subsequently, the homogenized macroscopic model is used to investigate communication in multi-cellular tissues. Our computational simulations reveal that the membrane potential of syncytia, formed by interconnected cells via connexins, plays a crucial role in propagating oscillations from one region to another, providing an effective means for fast cellular communication. Statement of Significance: In this study, we investigated cellular communication and ion transport in vascular smooth muscle cells, shedding light on their mechanisms under normal and abnormal conditions. Our research highlights the potential of mathematical models in understanding complex biological systems. We developed effective macroscale electro-neutral bi-domain ion transport models and examined their behavior in response to different stimuli. Our findings revealed the crucial role of connexinmediated membrane potential changes and demonstrated the effectiveness of cellular communication through syncytium membranes. Despite some limitations, our study provides valuable insights into these processes and emphasizes the importance of mathematical modeling in unraveling the complexities of cellular communication and ion transport.

Spatially Resolved Proteomic Analysis of the Lens Extracellular Diffusion Barrier

Purpose

The presence of a physical barrier to molecular diffusion through lenticular extracellular space has been repeatedly detected. This extracellular diffusion barrier has been proposed to restrict the movement of solutes into the lens and to direct nutrients into the lens core via the sutures at both poles. The purpose of this study is to characterize the molecular components that could contribute to the formation of this barrier.

Methods

Three distinct regions in the bovine lens cortex were captured by laser capture microdissection guided by dye penetration. Proteins were digested by Lys C and trypsin. Mass spectrometry-based proteomic analysis followed by gene ontology and protein interaction network analysis was performed.

Results

Dye penetration showed that fiber cells first shrink the extracellular spaces of the broad sides followed by closure of the extracellular space between narrow sides at a normalized lens distance (r/a) of 0.9. Accompanying the closure of extracellular space of the broad sides, dramatic proteomic changes were detected, including upregulation of several cell junctional proteins. AQP0 and its interacting partners, Ezrin and Radixin, were among a few proteins that were upregulated, accompanying the closure of extracellular space of the narrow sides, suggesting a particularly important role for AQP0 in controlling the narrowing of the extracellular spaces between fiber cells. The results also provided important information related to biological processes that occur during fiber cell differentiation such as organelle degradation, cytoskeletal remodeling, and glutathione synthesis.

Conclusions

The formation of a lens extracellular diffusion barrier is accompanied by significant membrane and cytoskeletal protein remodeling.

Connexin Gap Junctions and Hemichannels in Modulating Lens Redox Homeostasis and Oxidative Stress in Cataractogenesis

The lens is continuously exposed to oxidative stress insults, such as ultraviolet radiation and other oxidative factors, during the aging process. The lens possesses powerful oxidative stress defense systems to maintain its redox homeostasis, one of which employs connexin channels. Connexins are a family of proteins that form: (1) Hemichannels that mediate the communication between the intracellular and extracellular environments, and (2) gap junction channels that mediate cell-cell communication between adjacent cells. The avascular lens transports nutrition and metabolites through an extensive network of connexin channels, which allows the passage of small molecules, including antioxidants and oxidized wastes. Oxidative stress-induced post-translational modifications of connexins, in turn, regulates gap junction and hemichannel permeability. Recent evidence suggests that dysfunction of connexins gap junction channels and hemichannels may induce cataract formation through impaired redox homeostasis. Here, we review the recent advances in the knowledge of connexin channels in lens redox homeostasis and their response to cataract-related oxidative stress by discussing two major aspects: (1) The role of lens connexins and channels in oxidative stress and cataractogenesis, and (2) the impact and underlying mechanism of oxidative stress in regulating connexin channels.

A tridomain model for potassium clearance in optic nerve of Necturus

Complex fluids flow in complex ways in complex structures. Transport of water and various organic and inorganic molecules in the central nervous system are important in a wide range of biological and medical processes. However, the exact driving mechanisms are often not known. In this work, we investigate flows induced by action potentials in an optic nerve as a prototype of the central nervous system. Different from traditional fluid dynamics problems, flows in biological tissues such as the central nervous system are coupled with ion transport. They are driven by osmosis created by concentration gradient of ionic solutions, which in turn influence the transport of ions. Our mathematical model is based on the known structural and biophysical properties of the experimental system used by the Harvard group Orkand et al. Asymptotic analysis and numerical computation show the significant role of water in convective ion transport. The full model (including water) and the electrodiffusion model (excluding water) are compared in detail to reveal an interesting interplay between water and ion transport. In the full model, convection due to water flow dominates inside the glial domain. This water flow in the glia contributes significantly to the spatial buffering of potassium in the extracellular space. Convection in the extracellular domain does not contribute significantly to spatial buffering. Electrodiffusion is the dominant mechanism for flows confined to the extracellular domain.

On the Effects of Mechanical Stress of Biological Membranes in Modeling of Swelling Dynamics of Biological Systems

We highlight mechanical stretching and bending of membranes and the importance of membrane deformations in the analysis of swelling dynamics of biological systems, including cells and subcellular organelles. Membrane deformation upon swelling generates tensile stress and internal pressure, contributing to volume changes in biological systems. Therefore, in addition to physical (internal/external) and chemical factors, mechanical properties of the membranes should be considered in modeling analysis of cellular swelling. Here we describe an approach that considers mechanical properties of the membranes in the analysis of swelling dynamics of biological systems. This approach includes membrane bending and stretching deformations into the model, producing a more realistic description of swelling. We also discuss the effects of membrane stretching on swelling dynamics. We report that additional pressure generated by membrane bending is negligible, compared to pressures generated by membrane stretching, when both membrane surface area and volume are variable parameters. Note that bending deformations are reversible, while stretching deformation may be irreversible, leading to membrane disruption when they exceed a certain threshold level. Therefore, bending deformations need only be considered in reversible physiological swelling, whereas stretching deformations should also be considered in pathological irreversible swelling. Thus, the currently proposed approach may be used to develop a detailed biophysical model describing the transition from physiological to pathological swelling mode.

A Bidomain Model for Lens Microcirculation

There exists a large body of research on the lens of the mammalian eye over the past several decades. The objective of this work is to provide a link between the most recent computational models and some of the pioneering work in the 1970s and 80s. We introduce a general nonelectroneutral model to study the microcirculation in the lens of the eye. It describes the steady-state relationships among ion fluxes, between water flow and electric field inside cells, and in the narrow extracellular spaces between cells in the lens. Using asymptotic analysis, we derive a simplified model based on physiological data and compare our results with those in the literature. We show that our simplified model can be reduced further to the first-generation models, whereas our full model is consistent with the most recent computational models. In addition, our simplified model captures in its equations the main features of the full computational models. Our results serve as a useful link intermediate between the computational models and the first-generation analytical models. Simplified models of this sort may be particularly helpful as the roles of similar osmotic pumps of microcirculation are examined in other tissues with narrow extracellular spaces, such as cardiac and skeletal muscle, liver, kidney, epithelia in general, and the narrow extracellular spaces of the central nervous system, the "brain." Simplified models may reveal the general functional plan of these systems before full computational models become feasible and specific.

Electroneutral models for dynamic Poisson-Nernst-Planck systems

The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layers poses both modeling and computational challenges. In this paper, we derive simplified electroneutral (EN) models where the thin boundary layers are replaced by effective boundary conditions. There are two major advantages of EN models. First, it is much cheaper to solve them numerically. Second, EN models are easier to deal with compared to the original PNP system; therefore, it would also be easier to derive macroscopic models for cellular structures using EN models. Even though the approach used here is applicable to higher-dimensional cases, this paper mainly focuses on the one-dimensional system, including the general multi-ion case. Using systematic asymptotic analysis, we derive a variety of effective boundary conditions directly applicable to the EN system for the bulk region. This EN system can be solved directly and efficiently without computing the solution in the boundary layer. The derivation is based on matched asymptotics, and the key idea is to bring back higher-order contributions into the effective boundary conditions. For Dirichlet boundary conditions, the higher-order terms can be neglected and the classical results (continuity of electrochemical potential) are recovered. For flux boundary conditions, higher-order terms account for the accumulation of ions in boundary layer and neglecting them leads to physically incorrect solutions. To validate the EN model, numerical computations are carried out for several examples. Our results show that solving the EN model is much more efficient than the original PNP system. Implemented with the Hodgkin-Huxley model, the computational time for solving the EN model is significantly reduced without sacrificing the accuracy of the solution due to the fact that it allows for relatively large mesh and time-step sizes.

Feedback Regulation of Intracellular Hydrostatic Pressure in Surface Cells of the Lens

In wild-type lenses from various species, an intracellular hydrostatic pressure gradient goes from ∼340 mmHg in central fiber cells to 0 mmHg in surface cells. This gradient drives a center-to-surface flow of intracellular fluid. In lenses in which gap-junction coupling is increased, the central pressure is lower, whereas if gap-junction coupling is reduced, the central pressure is higher but surface pressure is always zero. Recently, we found that surface cell pressure was elevated in PTEN null lenses. This suggested disruption of a feedback control system that normally maintained zero surface cell pressure. Our purpose in this study was to investigate and characterize this feedback control system. We measured intracellular hydrostatic pressures in mouse lenses using a microelectrode/manometer-based system. We found that all feedback went through transport by the Na/K ATPase, which adjusted surface cell osmolarity such that pressure was maintained at zero. We traced the regulation of Na/K ATPase activity back to either TRPV4, which sensed positive pressure and stimulated activity, or TRPV1, which sensed negative pressure and inhibited activity. The inhibitory effect of TRPV1 on Na/K pumps was shown to signal through activation of the PI3K/AKT axis. The stimulatory effect of TRPV4 was shown in previous studies to go through a different signal transduction path. Thus, there is a local two-legged feedback control system for pressure in lens surface cells. The surface pressure provides a pedestal on which the pressure gradient sits, so surface pressure determines the absolute value of pressure at each radial location. We speculate that the absolute value of intracellular pressure may set the radial gradient in the refractive index, which is essential for visual acuity.

The cause and consequence of fiber cell compaction in the vertebrate lens

Fiber cells of the ocular lens are arranged in a series of concentric shells. New growth shells are added continuously to the lens surface and, as a consequence, the preexisting shells are buried. To focus light, the refractive index of the lens cytoplasm must exceed that of the surrounding aqueous and vitreous humors, and to that end, lens cells synthesize high concentrations of soluble proteins, the crystallins. To correct for spherical aberration, it is necessary that the crystallin concentration varies from shell-to-shell, such that cellular protein content is greatest in the center of the lens. The radial variation in protein content underlies the critical gradient index (GRIN) structure of the lens. Only the outermost shells of lens fibers contain the cellular machinery necessary for protein synthesis. It is likely, therefore, that the GRIN (which spans the synthetically inactive, organelle-free zone of the lens) does not result from increased levels of protein synthesis in the core of the lens but is instead generated through loss of volume by inner fiber cells. Because volume is lost primarily in the form of cell water, the residual proteins in the central lens fibers can be concentrated to levels of >500 mg/ml. In this short review, we describe the process of fiber cell compaction, its relationship to lens growth and GRIN formation, and offer some thoughts on the likely nature of the underlying mechanism.

A computer model of lens structure and function predicts experimental changes to steady state properties and circulating currents

BACKGROUND

In a previous study (Vaghefi et al. 2012) we described a 3D computer model that used finite element modeling to capture the structure and function of the ocular lens. This model accurately predicted the steady state properties of the lens including the circulating ionic and fluid fluxes that are believed to underpin the lens internal microcirculation system. In the absence of a blood supply, this system brings nutrients to the core of the lens and removes waste products faster than would be achieved by passive diffusion alone. Here we test the predictive properties of our model by investigating whether it can accurately mimic the experimentally measured changes to lens steady-state properties induced by either depolarising the lens potential or reducing Na+ pump rate.

METHODS

To mimic experimental manipulations reported in the literature, the boundary conditions of the model were progressively altered and the model resolved for each new set of conditions. Depolarisation of lens potential was implemented by increasing the extracellular [K+], while inhibition of the Na+ pump was stimulated by utilising the inherent temperature sensitivity of the pump and changing the temperature at which the model was solved.

RESULTS

Our model correctly predicted that increasing extracellular [K+] depolarizes the lens potential, reducing and then reversing the magnitude of net current densities around the lens. While lowering the temperature reduced Na+ pump activity and caused a reduction in circulating current, it had a minimal effect on the lens potential, a result consistent with published experimental data.

CONCLUSION

We have shown that our model is capable of accurately simulating the effects of two known experimental manipulations on lens steady-state properties. Our results suggest that the model will be a valuable predictive tool to support ongoing studies of lens structure and function.

The effect of size and species on lens intracellular hydrostatic pressure

PURPOSE

Previous experiments showed that mouse lenses have an intracellular hydrostatic pressure that varied from 335 mm Hg in central fibers to 0 mm Hg in surface cells. Model calculations predicted that in larger lenses, all else equal, pressure should increase as the lens radius squared. To test this prediction, lenses of different radii from different species were studied.

METHODS

All studies were done in intact lenses. Intracellular hydrostatic pressures were measured with a microelectrode-manometer-based system. Membrane conductances were measured by frequency domain impedance analysis. Intracellular Na(+) concentrations were measured by injecting the Na(+)-sensitive dye sodium-binding benzofuran isophthalate.

RESULTS

Intracellular hydrostatic pressures were measured in lenses from mice, rats, rabbits, and dogs with radii (cm) 0.11, 0.22, 0.49, and 0.57, respectively. In each species, pressure varied from 335 ± 6 mm Hg in central fiber cells to 0 mm Hg in surface cells. Further characterization of transport in lenses from mice and rats showed that the density of fiber cell gap junction channels was approximately the same, intracellular Na(+) concentrations varied from 17 mM in central fiber cells to 7 mM in surface cells, and intracellular voltages varied from -45 mV in central fiber cells to -60 mV in surface cells. Fiber cell membrane conductance was a factor of 2.7 times larger in mouse than in rat lenses.

CONCLUSIONS

Intracellular hydrostatic pressure is an important physiological parameter that is regulated in lenses from these different species. The most likely mechanism of regulation is to reduce the density of open Na(+)-leak channels in fiber cells of larger lenses.

Identification of a nonselective cation channel in isolated lens fiber cells that is activated by cell shrinkage

The initiation of lens cataract has long been associated with the development of a membrane "leak" in lens fiber cells that depolarizes the lens intracellular potential and elevates intracellular Na(+) and Ca(2+) concentrations. It has been proposed that the leak observed in cataractous lenses is due to the activation of a nonselective cation (NSC) conductance in the normal electrically tight fiber cells. Studies of the membrane properties of isolated fiber cells using the patch-clamp technique have demonstrated a differentiation-dependent shift in membrane permeability from K(+)-dominated in epithelial and short fiber cells toward larger contributions from anion and NSC conductances as fiber cells elongate. In this study, the NSC conductances in elongating lens fiber cells are demonstrated to be due to at least two distinct classes: a Gd(3+)-sensitive, mechanosensitive channel whose blockade is essential for obtaining viable isolated fiber cells, and a second Gd(3+)-insensitive, La(3+)-sensitive conductance that appears to be activated by cell shrinkage. This second conductance was eliminated by the replacement of extracellular Na(+) with the impermeant cation N-methyl-d-glucamine and was potentiated by both hypertonic stress and isosmotic cell shrinkage evoked by the replacement of extracellular Cl(-) with the impermeant anion gluconate. This additional cation conductance may play a role in normal lens physiology by mediating regulatory volume increase under osmotic or other physiological challenges. Since the inappropriate activation of NSC channels is implicated in the initiation of lens cataract, they represent potential targets for the development of novel anticataract therapies.

Development of a 3D finite element model of lens microcirculation

BACKGROUND

It has been proposed that in the absence of a blood supply, the ocular lens operates an internal microcirculation system. This system delivers nutrients, removes waste products and maintains ionic homeostasis in the lens. The microcirculation is generated by spatial differences in membrane transport properties; and previously has been modelled by an equivalent electrical circuit and solved analytically. While effective, this approach did not fully account for all the anatomical and functional complexities of the lens. To encapsulate these complexities we have created a 3D finite element computer model of the lens.

METHODS

Initially, we created an anatomically-correct representative mesh of the lens. We then implemented the Stokes and advective Nernst-Plank equations, in order to model the water and ion fluxes respectively. Next we complemented the model with experimentally-measured surface ionic concentrations as boundary conditions and solved it.

RESULTS

Our model calculated the standing ionic concentrations and electrical potential gradients in the lens. Furthermore, it generated vector maps of intra- and extracellular space ion and water fluxes that are proposed to circulate throughout the lens. These fields have only been measured on the surface of the lens and our calculations are the first 3D representation of their direction and magnitude in the lens.

CONCLUSION

Values for steady state standing fields for concentration and electrical potential plus ionic and fluid fluxes calculated by our model exhibited broad agreement with observed experimental values. Our model of lens function represents a platform to integrate new experimental data as they emerge and assist us to understand how the integrated structure and function of the lens contributes to the maintenance of its transparency.

Magnetic resonance and confocal imaging of solute penetration into the lens reveals a zone of restricted extracellular space diffusion

It has been proposed that in the absence of blood supply, the ocular lens operates an internal microcirculation system that delivers nutrients to internalized fiber cells faster and more efficiently than would occur by passive diffusion alone. To visualize the extracellular space solute fluxes potentially generated by this system, bovine lenses were organ cultured in artificial aqueous humor (AAH) for 4 h in the presence or absence of two gadolinium-based contrast agents, ionic Gd3+, or a chelated form of Gd3+, Gd-diethylenetriamine penta-acetic acid (Gd-DTPA; mol mass = 590 Da). Contrast reagent penetration into the lens core was monitored in real time using inversion recovery-spin echo (IR-SE) magnetic resonance imaging (MRI), while steady-state accumulation of [Gd-DTPA]−2 was also determined by calculating T1 values. After incubation, lenses were fixed and cryosectioned, and sections were labeled with the membrane marker wheat germ agglutinin (WGA). Sections were imaged by confocal microscopy using standard and reflectance imaging modalities to visualize the fluorescent WGA label and gadolinium reagents, respectively. Real-time IR-SE MRI showed rapid penetration of Gd3+ into the outer cortex of the lens and a subsequent bloom of signal in the core. These two areas of signal were separated by an area in the inner cortex that limited entry of Gd3+. Similar results were obtained for Gd-DTPA, but the penetration of the larger negatively charged molecule into the core could only be detected by calculating T1 values. The presence of Gd-DTPA in the extracellular space of the outer cortex and core, but its apparent absence from the inner cortex was confirmed using reflectance imaging of equatorial sections. In axial sections, Gd-DTPA was associated with the sutures, suggesting these structures provide a pathway from the surface, across the inner cortex barrier to the lens core. Our studies have revealed inner and outer boundaries of a zone within which a narrowing of the extracellular space restricts solute diffusion and acts to direct fluxes into the lens core via the sutures.

Visualizing ocular lens fluid dynamics using MRI: manipulation of steady state water content and water fluxes

Studies using various MRI techniques have shown that a water-protein concentration gradient exists in the ocular lens. Because this concentration is higher in the core relative to the lens periphery, a gradient in refractive index is established in the lens. To investigate how the water-protein concentration profile is maintained, bovine lenses were incubated in different solutions, and changes in water-protein concentration ratio monitored using proton density weighted (PD-weighted) imaging in the absence and presence of heavy water (D2O). Lenses incubated in artificial aqueous humor (AAH) maintained the steady state water-protein concentration gradient, but incubating lenses in high extracellular potassium (KCl-AAH) or low temperature (Low T-AAH) caused a collapse of the gradient due to a rise in water content in the core of the lens. To visualize water fluxes, lenses were incubated in D2O, which acts as a contrast agent. Incubation in KCl-AAH and low T-AAH dramatically slowed the movement of D2O into the core but did not affect the movement of D2O into the outer cortex. D2O seemed to preferentially enter the lens cortex at the anterior and posterior poles before moving circumferentially toward the equatorial regions. This directionality of D2O influx into the lens cortex was abolished by incubating lenses in high KCl-AAH or low T-AAH, and resulted in homogenous influx of D2O into the outer cortex. Taken together, our results show that the water-protein concentration ratio is actively maintained in the core of the lens and that water fluxes preferentially enter the lens at the poles.

Lens intracellular hydrostatic pressure is generated by the circulation of sodium and modulated by gap junction coupling

We recently modeled fluid flow through gap junction channels coupling the pigmented and nonpigmented layers of the ciliary body. The model suggested the channels could transport the secretion of aqueous humor, but flow would be driven by hydrostatic pressure rather than osmosis. The pressure required to drive fluid through a single layer of gap junctions might be just a few mmHg and difficult to measure. In the lens, however, there is a circulation of Na(+) that may be coupled to intracellular fluid flow. Based on this hypothesis, the fluid would cross hundreds of layers of gap junctions, and this might require a large hydrostatic gradient. Therefore, we measured hydrostatic pressure as a function of distance from the center of the lens using an intracellular microelectrode-based pressure-sensing system. In wild-type mouse lenses, intracellular pressure varied from ∼330 mmHg at the center to zero at the surface. We have several knockout/knock-in mouse models with differing levels of expression of gap junction channels coupling lens fiber cells. Intracellular hydrostatic pressure in lenses from these mouse models varied inversely with the number of channels. When the lens' circulation of Na(+) was either blocked or reduced, intracellular hydrostatic pressure in central fiber cells was either eliminated or reduced proportionally. These data are consistent with our hypotheses: fluid circulates through the lens; the intracellular leg of fluid circulation is through gap junction channels and is driven by hydrostatic pressure; and the fluid flow is generated by membrane transport of sodium.

Gap junctions

Gap junctions are aggregates of intercellular channels that permit direct cell-cell transfer of ions and small molecules. Initially described as low-resistance ion pathways joining excitable cells (nerve and muscle), gap junctions are found joining virtually all cells in solid tissues. Their long evolutionary history has permitted adaptation of gap-junctional intercellular communication to a variety of functions, with multiple regulatory mechanisms. Gap-junctional channels are composed of hexamers of medium-sized families of integral proteins: connexins in chordates and innexins in precordates. The functions of gap junctions have been explored by studying mutations in flies, worms, and humans, and targeted gene disruption in mice. These studies have revealed a wide diversity of function in tissue and organ biology.

The effects of GPX-1 knockout on membrane transport and intracellular homeostasis in the lens

Glutathione peroxidase-1 (GPX-1) is an enzyme that protects the lens against H2O2-mediated oxidative damage. The purpose of the present study was to determine the effects of GPX-1 knockout (KO) on lens transport and intracellular homeostasis. To investigate these lenses we used (1) whole lens impedance studies to measure membrane conductance, resting voltage and fiber cell gap junction coupling conductance; (2) osmotic swelling of fiber cell membrane vesicles to determine water permeability; and (3) injection of Fura2 and Na+-binding benzofuran isophthalate (SBFI) into fiber cells to measure [Ca2+]i and [Na+]i, respectively, in intact lenses. These approaches were used to compare wild-type (WT) and GPX-1 KO lenses from mice around 2 months of age. There were no significant differences in clarity, size, resting voltage, membrane conductance or fiber cell membrane water permeability between WT and GPX-1 KO lenses. However, in GPX-1 KO lenses, coupling conductance was 72% of normal in the outer shell of differentiating fibers and 45% of normal in the inner core of mature fibers. Quantitative Western blots showed that GPX-1 KO lenses had about 50% as much labeled Cx46 and Cx50 protein as WT, whereas they had equivalent labeled AQP0 protein as WT. Both Ca2+ and Na+ accumulated significantly in the core of GPX-1 KO lenses. In summary, the major effect on lens transport of GPX-1 KO was a reduction in gap junction coupling conductance. This reduction affected the lens normal circulation by causing [Na+]i and [Ca2+]i to increase, which could increase cataract susceptibility in GPX-1 KO lenses.

Nucleotides in ocular secretions: their role in ocular physiology

The eye is the sense organ that permits the detection of light owing to the existence of a sophisticated neuronal array, called the retina, which is responsive to photons. The correct functioning of this complex system requires the coordination of several intraocular structures that ultimately permit the perfect focusing of images on the neural retina. Light has to pass through different media: the tear, the cornea, aqueous humour, lens, and vitreous humour before it reaches the retina. Moreover, the composition and structure of some of these media can change due to several physiological mechanisms. Nucleotides are active components of the humours bathing relevant ocular structures. The tear contains nucleotides and dinucleotides that control the process of tearing, wound healing and protects of superficial infections. In the inner eye, the aqueous humour also presents a collection of mono and dinucleotides that affect pupil contraction, aqueous humour production and accommodation. Behind the lens and between this structure and the retina the vitreous humour can modify the physiology of the retinal cells, mostly the ganglion cells. By investigating the actions of nucleotides and dinucleotide present in the ocular humours we will be able not only to understand the functioning of the ocular structures but also to develop new pharmacological therapies for pathologies such as dry eye, glaucoma or retinal detachment.

The lens: local transport and global transparency

The perception of the lens changed remarkably during the career of David Maurice. The early view was that it was an inert sack of protein that assisted the cornea in focusing light on the retina. As investigators looked more carefully, more and more complexity was revealed and today we know the lens is a living, dynamic organ that carries out a host of biochemical and physiological processes necessary for homeostasis. We have worked on the lens over this period and have provided a small part of the data on lens physiology. This paper is an overview of our own contributions, in the context of the ever evolving view of the lens. Given this is a brief tribute to the career of David Maurice, there is not enough space nor is it appropriate to provide a complete review of all the work that has contributed to this evolving

Transport of fluid by lens epithelium

We report for the first time that cultured lens epithelial cell layers and rabbit lenses in vitro transport fluid. Layers of the alphaTN4 mouse cell line and bovine cell cultures were grown to confluence on permeable membrane inserts. Fluid movement across cultured layers and excised rabbit lenses was determined by volume clamp (37 degrees C). Cultured layers transported fluid from their basal to their apical sides against a pressure head of 3 cmH2O. Rates were (in microliter. h-1. cm-2) 3.3 +/- 0.3 for alphaTN4 cells (n = 27) and 4.7 +/- 1.0 for bovine layers (n = 6). Quinidine, a blocker of K+ channels, and p-chloromercuribenzenesulfonate and HgCl2, inhibitors of aquaporins, inhibited fluid transport. Rabbit lenses transported fluid from their anterior to their posterior sides against a 2.5-cmH2O pressure head at 10.3 +/- 0.62 microliter. h-1. lens-1 (n = 5) and along the same pressure head at 12.5 +/- 1.1 microliter. h-1. lens-1 (n = 6). We calculate that this flow could wash the lens extracellular space by convection about once every 2 h and therefore might contribute to lens homeostasis and transparency.

Multifunctional transporter models: lessons from the transport of water, sugars, and ring compounds by GLUTs

Facilitative glucose transporters (GLUTs) have recently been shown to be multifunctional, transporting substrates other than sugars, such as water and ring compounds as large as nitrobenzene-diazol-aminoglucose. Other membrane proteins, including transporters and cystic fibrosis transmembrane conductance regulator, have also revealed a finite permeability to water. We compare the alpha-helical and beta-barrel models for the structure of GLUTs, discuss recent evidence, and argue that a beta-barrel fold explains it better. We show a model for GLUTs consisting of a relatively rigid beta-barrel translocation unit ("channel") of diameter ample enough to allow permeation of the above substrates (approximately 20 A) but gated shut by mobile loops at both ends. Such gates would open only after aromatic interactions would lead to binding of the ring substrates for GLUTs; water would, however, traverse crevices in the closed gates. Using the insights gained from GLUTs, we propose that other transporters may share with GLUTs the motif of a beta-barrel channel and would be permeable to water due to the presence of such channels together with similarly behaving gates.

Diffusion of extracellular K+ can synchronize bursting oscillations in a model islet of Langerhans

Electrical bursting oscillations of mammalian pancreatic beta-cells are synchronous among cells within an islet. While electrical coupling among cells via gap junctions has been demonstrated, its extent and topology are unclear. The beta-cells also share an extracellular compartment in which oscillations of K+ concentration have been measured (Perez-Armendariz and Atwater, 1985). These oscillations (1-2 mM) are synchronous with the burst pattern, and apparently are caused by the oscillating voltage-dependent membrane currents: Extracellular K+ concentration (Ke) rises during the depolarized active (spiking) phase and falls during the hyperpolarized silent phase. Because raising Ke depolarizes the cell membrane by increasing the potassium reversal potential (VK), any cell in the active phase should recruit nonspiking cells into the active phase. The opposite is predicted for the silent phase. This positive feedback system might couple the cells' electrical activity and synchronize bursting. We have explored this possibility using a theoretical model for bursting of beta-cells (Sherman et al., 1988) and K+ diffusion in the extracellular space of an islet. Computer simulations demonstrate that the bursts synchronize very quickly (within one burst) without gap junctional coupling among the cells. The shape and amplitude of computed Ke oscillations resemble those seen in experiments for certain parameter ranges. The model cells synchronize with exterior cells leading, though incorporating heterogeneous cell properties can allow interior cells to lead. The model islet can also be forced to oscillate at both faster and slower frequencies using periodic pulses of higher K+ in the medium surrounding the islet. Phase plane analysis was used to understand the synchronization mechanism. The results of our model suggest that diffusion of extracellular K+ may contribute to coupling and synchronization of electrical oscillations in beta-cells within an islet.

Potassium currents from isolated frog lens epithelial cells

Using the perforated patch version of whole-cell recording, we have measured currents from isolated frog lens epithelial cells. Three types of currents were seen. A time-independent outwardly rectifying potassium current was identified that sets the resting voltage. This potassium current differs significantly from any of the potassium currents recorded with the whole-cell technique in mammalian lens epithelial cells. In addition to the potassium current, the two other currents present were both outwardly rectifying: one was time-independent while the other showed distinct activation.

Membrane architecture as a function of lens fibre maturation: a freeze fracture and scanning electron microscopic study in the human lens

The ultrastructure of fibre membranes in human lenses, varying in age from premature to 40 years, was investigated using a strict protocol regarding their localization within the lens. The ultrastructural approaches used were scanning electron microscopy (SEM), and transmission electron microscopy (TEM) of ultrathin sections and freeze-fracture replicas. Irrespective of the age of the lens, superficial fibre membranes are characterized by a high density of intramembrane particles (IMPs) and numerous gap junctions (GJs). In contrast deep cortical fibres, at the SEM-level characterized by grooves and ridges, are largely free of IMPs but still contain numerous GJs. In between these regions a transitional zone was observed. At the SEM-level the transitional fibres are characterized by wrinkled membranes and formation of grooves and ridges. In freeze-fracture replicas the presence of numerous square arrays (SAs) associated with GJs is most remarkable. It is concluded that at all ages studied, the maturation and compaction of lens fibres results in a transformation of membrane architecture leading to clear-cut ultrastructural differences between superficial and deep cortical membranes. It is argued that this ultrastructural heterogeneity parallels the gradients observed biochemically for intrinsic membrane proteins and cholesterol:phospholipid ratios. The observations confirm the electrophysiological view that superficial membranes have an 'average' permeability and that deep cortical membranes are 'degenerate' or 'non-leaky'.

The crystalline lens. A system networked by gap junctional intercellular communication

The vertebrate eye lens is a solid cyst of cells which grows throughout life by addition of new cells at the surface. The older cells, buried by the newer generations, differentiate into long, prismatic fibers, losing their cellular organelles and filling their cytoplasms with high concentrations of soluble proteins, the crystallins. The long-lived lens fibers are interconnected by gap junctions, both with themselves and with an anterior layer of simple cuboidal epithelial cells at the lens surface. This network of gap junctions joins the lens cells into a syncytium with respect to small molecules, permitting metabolic co-operation: intercellular diffusion of ions, metabolites, and water. In contact with nutrients at the lens surface, the epithelial cells retain their cellular organelles, and are able to provide the metabolic energy to maintain correct ion and metabolite concentrations within the lens fiber cytoplasms, such that the crystallins remain in solution and do not aggregate (cataract). Gap junctions are formed by a family of integral membrane channel-forming proteins called connexins. Gap junctions between lens epithelial cells are composed of a connexin which is common between many different cell types, notably myocardial cells and connective tissue fibroblasts. The gap junctions between epithelial cells and lens fibers have not yet been biochemically characterized. The gap junctions formed between lens fibers are composed of at least two different connexins, one of which has not been detected between other cell types. The unusual physiology and longevity of the lens fibers may require the special set of connexins which are found joining these cells.

Inwardly rectifying potassium current in mammalian lens epithelial cells

Lens potassium conductance is essential for the maintenance of lens volume and transparency. Recent work has identified three major potassium currents in lens: 1) an outwardly rectifying current, 2) an inwardly rectifying current, and 3) a calcium-activated current. This paper presents a study of the lens inward rectifier using whole cell and single-channel patch-clamp techniques. Inwardly rectifying potassium current is present in isolated human, rabbit, rat, and mouse lens epithelia. The voltage about which rectification occurs depends on the external potassium concentration. Internal magnesium is not necessary for rectification. In physiological saline, a time-dependent decrease in current during sustained hyperpolarization is seen. This "droop" is due to voltage-dependent block by external sodium. The inward rectifier is also effectively blocked by external cesium or barium but not by tetraethylammonium or 4-aminopyridine. The mouse lens inward rectifier has a single-channel conductance of 32 pS (measured on-cell with 150 mM potassium in the pipette). The single-channel current-voltage relationship is linear in the inward direction. In contrast to the macroscopic case, no outward current was measurable. The inward rectifier in lens has the necessary properties to be involved in setting resting voltage.

Electrostatic properties of fiber cell membranes from the frog lens

The electrostatic properties of lens fiber cell membranes have been investigated by recording the electrophoretic mobility of membrane vesicles formed from isolated fiber cells. The vesicles appear to be sealed and have external surfaces that are representative of the extracellular surface of fiber cells. The average mobility of a vesicle in normal Ringer's solution was 0.9 microns/s per v/cm, which gives a zeta potential of -9 mV, a value similar to that reported for other cells (McLaughlin, S. 1989. Annu. Rev. Biophys. Biophys. Chem. 18:113-136.). There was no significant difference in the mobility of vesicles formed from peripheral, middle cortical, or nuclear fiber cells. Vesicle surface changes were titrated using Ca and Mg and each had a pK of approximately 2, which is similar to that for the most common phospholipids. We also titrated these charges with varying pH and found the most significant changes in mobility at pH values between 5 and 6. The majority of lipids found in biological membranes are not titratable in this pH range, so the pH effect is probably through a membrane protein charged group. These experimental data in conjunction with the previously measured extracellular voltage gradient (Mathias, R. T., and J. L. Rae. 1985. Am. J. Physiol. 249:C181-C190) imply that electroosmosis can generate a fluid velocity of approximately 0.6 mm/h, directed from the aqueous or vitreous toward the center of the lens, along intercellular clefts.

Membrane and junctional properties of dissociated frog lens epithelial cells

Individual cells and cell pairs were isolated from frog lens epithelium. Individual cells were whole cell voltage clamped and the current-voltage relationship was determined. The cells had a mean resting voltage of -54.3 mV and a mean input resistance of 1.4 G omega. The current-voltage relationship was linear near the cell resting voltage, but showed decreased resistance with large depolarization or hyperpolarization. Junctional currents between pairs of cells were recorded using the dual whole cell voltage-clamp technique. The corrected junctional resistance was 15.5 M omega (64.5 nS). The junctional current-voltage relationship was linear. A combination of ATP and cAMP, in the electrodes, stabilized junctional resistance. Currents recorded when uncoupling was nearly complete, showed evidence of single connexion gating events. A single-channel conductance of about 100 pS was prominent. Dye spread between isolated cell pairs was demonstrated using Lucifer Yellow CH in a whole cell configuration. Photodamage to the cells due to the dye was apparent. Dye loaded cells, in the presence of exciting light, showed decreased resting voltages, decreased input resistances and morphological changes. Glutathione (20 mM) delayed this damage.

Steady-state current flow through gap junctions. Effects on intracellular ion concentrations and fluid movement

Double voltage clamp studies were performed on gap junctions contained in septal membranes of the earthworm median giant axon. The gap junctions exhibited no conductance changes in response to voltages imposed across either the septal membrane or the plasma membrane. However, the trans-septal current displayed a slow (10 s) relaxation in response to transjunctional voltage steps. The experimental evidence suggests that this relaxation is a polarization of the septum due to local accumulation/depletion of permeant ions. A theoretical analysis of this observation suggests that the applied electric field causes accumulation of impermeant anions on one side of the junction and depletion on the other, which leads to a change in concentration of permeant ions to maintain macroscopic electroneutrality. The change in concentration of permeant ions generates a transjunctional equilibrium potential that opposes junctional current flow. These results indicate that currents flowing through gap junctions can have an influence on the distribution of intracellular ions. Moreover, the theoretical analysis suggests that such currents will be accompanied by significant intracellular and intercellular water flow.

A cation channel in frog lens epithelia responsive to pressure and calcium

Patch-clamp recording from the apical surface of the epithelium of frog lens reveals a cation-selective channel after pressure (about +/- 30 mm Hg) is applied to the pipette. The open state of this channel has a conductance of some 50 pS near the resting potential (-56.1 +/- 2.3 mV) when 107 mM NaCl and 10 HEPES (pH 7.3) is outside the channel. The probability of the channel being open depends strongly on pressure but the current-voltage relation of the open state does not. With minimal Ca2+ (55 +/- 2 microM) outside the channel, the current-voltage relation is nonlinear even in symmetrical salt solutions, allowing more current to flow into the cell than out. The channel, in minimal Ca2+ solution, is selective among the monovalent cations in the following sequence K+ greater than Rb+ greater than Cs+ greater than Na+ greater than Li+. The conductance depends monotonically on the mole fraction of K+ when the other ion present is Li+ or Na+. The single-channel current is a saturating function of [K+] when K+ is the permeant ion, for [K+] less than or equal to 214 mM. When [Ca2+] = 2 mM, the current-voltage relation is linearized and the channel cannot distinguish Na+ and K+.

The localization of transport properties in the frog lens

The selectivity of fiber-cell membranes and surface-cell membranes in the frog lens is examined using a combination of ion substitutions and impedance studies. We replace bath sodium and chloride, one at a time, with less permeant substitute ions and we increase bath potassium at the expense of sodium. We then record the time course and steady-state value of the intracellular potential. Once a new steady state has been reached, we perform a small signal-frequency-domain impedance study. The impedance study allows us to separately determine the values of inner fiber-cell membrane conductance and surface-cell membrane conductance. If a membrane is permeable to a particular ion, we presume that the conductance of that membrane will change with the concentration of the permeant ion. Thus, the impedance studies allow us to localize the site of permeability to inner or surface membranes. Similarly, the time course of the change in intracellular potential will be rapid if surface membranes are the site of permeation whereas it will be slow if the new solution has to diffuse into the intercellular space to cause voltage changes. Lastly, the value of steady-state voltage change provides an estimate of the lens' permeability, at least for chloride and potassium. The results for sodium are complex and not well understood. From the above studies we conclude: (a) surface membranes are dominated by potassium permeability; (b) inner fiber-cell membranes are permeable to sodium and chloride, in approximately equal amounts; and (c) inner fiber-cell membranes have a rather small permeability to potassium.