The Na+,K+-ATPase and its stoichiometric ratio: some thermodynamic speculations.

 Almost seventy years after its discovery, the sodium-potassium adenosine triphosphatase (the sodium pump) located in the cell plasma membrane remains a source of novel mechanistic and physiologic findings. A noteworthy feature of this enzyme/transporter is its robust stoichiometric ratio under physiological conditions: it sequentially counter-transports three sodium ions and two potassium ions against their electrochemical potential gradients per each hydrolyzed ATP molecule. Here we summarize some present knowledge about the sodium pump and its physiological roles, and speculate whether energetic constraints may have played a role in the evolutionary selection of its characteristic stoichiometric ratio.

Roles of early events in the modifications undergone by bovine corneal endothelial cells during wound healing.

A mechanical injury in bovine corneal endothelial (BCE) cells in culture induces: (1) a fast calcium wave (FCW); (2) slow increases in cytosolic sodium and calcium, critical for the healing process, and (3) a rise in the apoptotic rate with respect to quiescent cells. In order to investigate the nature of the stimuli that determine the ionic changes and apoptotic response, we performed here studies on a non-injury model of tissue restitution in BCE monolayers. For this, we employed cell cultures grown to confluence in the presence of a Parafilm strip. We observed that, previously to strip removal, most of the border cells had already developed the slow ionic modifications, while in the scratch wounds these changes gradually occur after several hours of healing. This finding suggests that, in BCE cells, the presence of a free edge is sufficient to trigger ionic modifications necessary for wound healing and to elicit an augmented apoptotic response. The apoptotic index of the migrating cells in the Parafilm model (PF) was determined to be approximately two-fold the one of scratch wounds, a result that, in agreement with our previous observations, we attributed to the absence of the FCW in the PF experiments. The findings of this work further contribute to the understanding of epithelial wound healing, a crucial adaptive, and homeostatic response.

A mathematical model of wound healing in bovine corneal endothelium.

We developed a mathematical model to describe healing processes in bovine corneal endothelial (BCE) cells in culture, triggered by mechanical wounds with parallel edges. Previous findings from our laboratory show that, in these cases, BCE monolayers exhibit an approximately constant healing velocity. Also, that caspase-dependent apoptosis occurs, with the fraction of apoptotic cells increasing with the distance traveled by the healing edge. In addition, in this study we report the novel findings that, for wound scratch assays performed preserving the basal extracellular matrix: i) the healing cells increase their en face surface area in a characteristic fashion, and ii) the average length of the segments of the cell columns actively participating in the healing process increases linearly with time. These latter observations preclude the utilization of standard traveling wave formalisms to model wound healing in BCE cells. Instead, we developed and studied a simple phenomenological model based on a plausible formula for the spreading dynamics of the individual healing cells, that incorporates original evidence about the process in BCE cells. The model can be simulated to: i) obtain an approximately constant healing velocity; ii) reproduce the profile of the healing cell areas, and iii) obtain approximately linear time dependences of the mean cell area and average length of the front active segments per column. In view of its accuracy to account for the experimental observations, the model can also be acceptably employed to quantify the appearance of apoptotic cells during BCE wound healing. The strategy utilized here could offer a novel formal framework to represent modifications undergone by some epithelial cell lines during wound healing.

A Note of Caution: Gramicidin Affects Signaling Pathways Independently of Its Effects on Plasma Membrane Conductance.

Gramicidin is a thoroughly studied cation ionophore widely used to experimentally manipulate the plasma membrane potential (PMP). In addition, it has been established that the drug, due to its hydrophobic nature, is capable of affecting the organization of membrane lipids. We have previously shown that modifications in the plasma membrane potential of epithelial cells in culture determine reorganizations of the cytoskeleton. To elucidate the molecular mechanisms involved, we explored the effects of PMP depolarization on some putative signaling intermediates. In the course of these studies, we came across some results that could not be interpreted in terms of the properties of gramicidin as an ionic channel. The purpose of the present work is to communicate these results and, in general, to draw attention to the fact that gramicidin effects can be misleadingly attributed to its ionic or electrical properties. In addition, this work also contributes with some novel findings of the modifications provoked on the signaling intermediates by PMP depolarization and hyperpolarization.

Signaling pathways in cytoskeletal responses to plasma membrane depolarization in corneal endothelial cells.

In previous work, we reported that plasma membrane potential depolarization (PMPD) provokes cortical F-actin remodeling in bovine corneal endothelial (BCE) cells in culture, which eventually leads to the appearance of intercellular gaps. In kidney epithelial cells it has been shown that PMPD determines an extracellular-signal-regulated kinase (ERK)/Rho-dependent increase in diphosphorylated myosin light chain (ppMLC). The present study investigated the signaling pathways involved in the response of BCE cells to PMPD. Differently to renal epithelial cells, we observed that PMPD leads to a decrease in monophosphorylated MLC (pMLC) without affecting diphosphorylated MLC. Also, that the pMLC reduction is a consequence of cyclic adenosine 3',5'-monophosphate (cAMP)/protein kinase A (PKA) activation. In addition, we found evidence that the cAMP increase mostly depends on soluble adenylyl cyclase activity. Inhibition of this enzyme reduces the effect of PMPD on the cAMP rise, F-actin remodeling, and pMLC decrease. No changes in phosho-ERK were observed, although we could determine that RhoA undergoes activation. Our results suggested that active RhoA is not involved in the intercellular gap formation. Overall, the findings of this study support the view that, differently to renal epithelial cells, in BCE cells PMPD determines cytoskeletal reorganization via activation of the cAMP/PKA pathway.

Calcium Oscillatory Behavior and Its Possible Role during Wound Healing in Bovine Corneal Endothelial Cells in Culture.

In epithelial layers in culture, immediately after an injury a fast calcium wave (FCW) propagates from the wound borders toward the rest of the monolayer. We show here that similarly to other tissues, during the FCW in bovine corneal endothelial (BCE) cells in culture many cells exhibit calcium oscillations mediated by IP3 signaling. In this study we perform a detailed characterization of this oscillatory behavior and explore its possible role in the process of wound healing. In previous work we showed that, in BCE cells in culture, the healing cells undergo two stages of caspase-dependent apoptosis, at approximately two and eight hours after wounding. We determined that inhibition of the FCW greatly increases the apoptotic rate of the two stages, suggesting that the wave prevents excessive apoptosis of the healing cells. Taking this into account, we investigated the possible participation of the calcium oscillations during the FCW in apoptosis of the healing cells. For this, we employed ARL-67156 (ARL), a weak competitive inhibitor of ecto-ATPases, and the calcium chelator EGTA. We show here that, in healing BCE cells, ARL enhances cellular calcium oscillations during the FCW, while EGTA decreases oscillations. We found that ARL produces a significant decrease (to about half the control value) in the apoptotic index of the first stage of apoptosis, while EGTA increases it. Neither drug noticeably affects the second stage. We have interpreted the effect of ARL on apoptosis as due to the maintenance of moderately risen ATP levels during the FCW, which is in turn the cause for the enhancement of ATP-dependent calcium oscillations. Correspondingly, EGTA would increase the apoptotic index of the first stage by promoting a decrease in the calcium oscillatory rate. The fact that the second stage of apoptosis is not affected by the drugs suggests that the two stages are at least partially subject to different signaling pathways.

Epithelial Fluid Transport is Due to Electro-osmosis (80%), Plus Osmosis (20%).

Epithelial fluid transport, an important physiological process shrouded in a long-standing enigma, may finally be moving closer to a solution. We propose that, for the corneal endothelium, relative proportions for the driving forces for fluid transport are 80% of paracellular electro-osmosis, and 20% classical transcellular osmosis. These operate in a cyclical process with a period of 9.2 s, which is dictated by the decrease and exhaustion of cellular Na+. Paracellular electro-osmosis is sketched here, and partially discussed as much as the subject still allows; transcellular osmosis is presented at length.

The Epithelial Sodium Channel and the Processes of Wound Healing.

The epithelial sodium channel (ENaC) mediates passive sodium transport across the apical membranes of sodium absorbing epithelia, like the distal nephron, the intestine, and the lung airways. Additionally, the channel has been involved in the transduction of mechanical stimuli, such as hydrostatic pressure, membrane stretch, and shear stress from fluid flow. Thus, in vascular endothelium, it participates in the control of the vascular tone via its activity both as a sodium channel and as a shear stress transducer. Rather recently, ENaC has been shown to participate in the processes of wound healing, a role that may also involve its activities as sodium transporter and as mechanotransducer. Its presence as the sole channel mediating sodium transport in many tissues and the diversity of its functions probably underlie the complexity of its regulation. This brief review describes some aspects of ENaC regulation, comments on evidence about ENaC participation in wound healing, and suggests possible regulatory mechanisms involved in this participation.

Fast calcium wave inhibits excessive apoptosis during epithelial wound healing.

Successful wound closure is mainly the result of two cellular processes: migration and proliferation. Apoptosis has also been suggested to play a role in the mechanisms of wound healing. The fast calcium wave (FCW), triggered immediately after a wound is produced, has been proposed to be involved in determining healing responses in epithelia. We have explored the effects of the reversible inhibition of FCW on the apoptotic and proliferative responses of healing bovine corneal endothelial (BCE) cells in culture. The most important findings of this study are that caspase-dependent apoptosis occurs during the healing process, that the amount of apoptosis has a linear dependence on the migrated distance, and that FCW inhibition greatly increases the apoptotic index. We have further been able to establish that FCW plays a role in the control of cell proliferation during BCE wound healing. These results indicate that one of the main roles of the wave is to inhibit an excessive apoptotic response of the healing migrating cells. This property might represent a basic mechanism to allow sufficient migration and proliferation of the healing cells to assure proper restitution of the injured tissue.

Diagrammatic analysis of nonhomogeneous diffusion.

By virtue of its complexity, realistic approaches to describe diffusion in cellular media require the employment of computational methods. Among others, this type of studies has shown that the apparent diffusion coefficient of a macromolecular solute through a cytoplasmic-like medium exhibits a power-law dependence with the excluded volume. Power laws are ubiquitous findings in diverse systems, such as metabolic processes, population dynamics, and communication networks, and have been the object of many interpretative formal approaches. This study introduces a diagrammatic algorithm, inspired in previous ones employed to analyze multicyclic chemical systems, to derive expressions for nonhomogeneous diffusion coefficients and to study the effects of volume exclusion. A most noteworthy result of this work is that midsize diagrams of nonhomogeneous diffusion are already able to exhibit an approximate power-law dependence of the diffusion coefficient with the excluded volume. The employment of the diagrammatic method for the analysis of simple situations may thus prove useful to interpret some properties of larger network systems.

ENaC contribution to epithelial wound healing is independent of the healing mode and of any increased expression in the channel.

Previous work from our laboratory and others has shown that, in some epithelia, the epithelial sodium channel (ENaC) increases its expression during wound healing. In these cases, inhibition of the channel determines a decrease in the healing rate, a result suggesting a role for ENaC in the overall healing process. To understand further this role of ENaC in epithelia, we explored the participation of ENaC in wound healing in four cultured epithelial cell lines selected on the basis of their different embryonic origins, function and modality of healing, i.e., by lamellipodial cell crawling or by actin cable formation. Three of the cell lines (bovine corneal endothelial cells, rabbit corneal epithelial cells and Madin-Darby canine kidney cells) exhibited an increase in ENaC expression and consequent membrane potential depolarization and an increase in cytosolic sodium and calcium, whereas one line (bovine aortal endothelial cells, BAEC) did not exhibit any of these changes. In all of the cell lines, however, ENaC inhibition determined a similar decrease in the rate of wound healing. In BAEC monolayers, the increase in ENaC activity produced plasma membrane depolarization, increased cytosolic sodium and calcium, and augmented the velocity of healing. These novel findings contribute to the idea that ENaC plays a critical role in wound healing in various epithelia, independently of the modality of healing and of any increase in the expression of the channel.

Reduced dynamic models in epithelial transport.

Most models developed to represent transport across epithelia assume that the cell interior constitutes a homogeneous compartment, characterized by a single concentration value of the transported species. This conception differs significantly from the current view, in which the cellular compartment is regarded as a highly crowded media of marked structural heterogeneity. Can the finding of relatively simple dynamic properties of transport processes in epithelia be compatible with this complex structural conception of the cell interior? The purpose of this work is to contribute with one simple theoretical approach to answer this question. For this, the techniques of model reduction are utilized to obtain a two-state reduced model from more complex linear models of transcellular transport with a larger number of intermediate states. In these complex models, each state corresponds to the solute concentration in an intermediate intracellular compartment. In addition, the numerical studies reveal that it is possible to approximate a general two-state model under conditions where strict reduction of the complex models cannot be performed. These results contribute with arguments to reconcile the current conception of the cell interior as a highly complex medium with the finding of relatively simple dynamic properties of transport across epithelial cells.

The plasma membrane potential and the organization of the actin cytoskeleton of epithelial cells.

The establishment and maintenance of the polarized epithelial phenotype require a characteristic organization of the cytoskeletal components. There are many cellular effectors involved in the regulation of the cytoskeleton of epithelial cells. Recently, modifications in the plasma membrane potential (PMP) have been suggested to participate in the modulation of the cytoskeletal organization of epithelia. Here, we review evidence showing that changes in the PMP of diverse epithelial cells promote characteristic modifications in the cytoskeletal organization, with a focus on the actin cytoskeleton. The molecular paths mediating these effects may include voltage-sensitive integral membrane proteins and/or peripheral proteins sensitive to surface potentials. The voltage dependence of the cytoskeletal organization seems to have implications in several physiological processes, including epithelial wound healing and apoptosis.

Early and late calcium waves during wound healing in corneal endothelial cells.

Immediately after wounding, bovine corneal endothelial cells develop a fast calcium wave that propagates from the wound border to the rest of the monolayer and extinguishes in approximately 5 minutes. One hour after wounding, a late, slow calcium wave (SCW) develops concomitantly to the depolarization of the plasma membrane potential of the border cells. The incorporation of inhibitors of the epithelial sodium channel and of the sodium-calcium exchanger produces inhibition of the membrane depolarization and the SCW, and diminishes the rate of wound healing. The L-type calcium channel blocker nimodipine does not have any effect on the SCW. The reversible inhibition of the fast calcium wave does not affect the SCW and only slightly decreases the velocity of healing. Our results suggest that the SCW is at least partially produced by the coupling of the epithelial sodium channel and the sodium-calcium exchanger functioning in reverse mode. They also suggest that the SCW may play a role in the overall healing process.

Regulatory design in a simple system integrating membrane potential generation and metabolic ATP consumption. Robustness and the role of energy dissipating processes.

Bacterial physiological responses integrate energy-coupling processes at the membrane level with metabolic energy demand. The regulatory design behind these responses remains largely unexplored. Propionigenium modestum is an adequate organism to study these responses because it presents the simplest scheme known integrating membrane potential generation and metabolic ATP consumption. A hypothetical sodium leak is added to the scheme as the sole regulatory site. Allosteric regulation is assumed to be absent. Information of the rate equations is not available. However, relevant features of the patterns of responses may be obtained using Metabolic Control Analysis (MCA) and Metabolic Control Design (MCD). With these tools, we show that membrane potential disturbances can be compensated by adjusting the leak flux, without significant perturbations of ATP consumption. Perturbations of membrane potential by ATP demand are inevitable and also require compensatory changes in the leak. Numerical simulations were performed with a kinetic model exhibiting the responses for small changes obtained with MCA and MCD. A modest leak (10% of input) was assumed for the reference state. We found that disturbances in membrane potential and ATP consumption, produced by environmental perturbations of the cation concentration, may be reverted to the reference state adjusting the leak. Leak changes can also compensate for undesirable effects on membrane potential produced by changes in nutrient availability or ATP demand, in a wide range of values. The system is highly robust to parameter fluctuations. The regulatory role of energy dissipating processes and the trade-off between energetic efficiency and regulatory capacity are discussed.

Minimal models of electric potential oscillations in non-excitable membranes.

Sustained oscillations in the membrane potential have been observed in a variety of cellular and subcellular systems, including several types of non-excitable cells and mitochondria. For the plasma membrane, these electrical oscillations have frequently been related to oscillations in intracellular calcium. For the inner mitochondrial membrane, in several cases the electrical oscillations have been attributed to modifications in calcium dynamics. As an alternative, some authors have suggested that the sustained oscillations in the mitochondrial membrane potential induced by some metabolic intermediates depends on the direct effect of internal protons on proton conductance. Most theoretical models developed to interpret oscillations in the membrane potential integrate several transport and biochemical processes. Here we evaluate whether three simple dynamic models may constitute plausible representations of electric oscillations in non-excitable membranes. The basic mechanism considered in the derivation of the models is based upon evidence obtained by Hattori et al. for mitochondria and assumes that an ionic species (i.e., the proton) is transported via passive and active transport systems between an external and an internal compartment and that the ion affects the kinetic properties of transport by feedback regulation. The membrane potential is incorporated via its effects on kinetic properties. The dynamic properties of two of the models enable us to conclude that they may represent alternatives enabling description of the generation of electrical oscillations in membranes that depend on the transport of a single ionic species.

Hyperpolarization of the plasma membrane potential provokes reorganization of the actin cytoskeleton and increases the stability of adherens junctions in bovine corneal endothelial cells in culture.

In previous works we showed that the depolarization of the plasma membrane potential (PMP) determines a reorganization of the cytoskeleton of diverse epithelia in culture, consisting mainly of a reallocation of peripheral actin toward the cell center, ultimately provoking intercellular disruption. In view of this evidence, we explored in this study the possible effects of membrane potential hyperpolarization on the cytoskeletal organization and adherens junction (AJ) morphology and the stability of confluent bovine corneal endothelial cells in culture. For this purpose, hyperpolarization was achieved by substitution of extracellular sodium by nondiffusible cations or via the incorporation of valinomycin to the control solution. Actin compactness at the cell periphery was assessed by quantitative analysis of fluorescence microscopy images. The stability of the AJ was challenged by calcium deprivation or temperature decrease. Our results showed that plasma membrane hyperpolarization provokes a compaction of AJ-associated actin filaments toward the plasma membrane and an increase in the stability of the AJs. We also observed that the hyperpolarizing procedures determined similar modifications in the actin cytoskeleton of endothelial cells in whole bovine corneas. Together with our previous work, the results of this study contribute to the idea that modifications in the PMP of nonexcitable cells participate in cellular adaptive responses involving reorganization of cytoskeletal components.

Roles of wound geometry, wound size, and extracellular matrix in the healing response of bovine corneal endothelial cells in culture.

It has classically been accepted that the healing of narrow wounds in epithelia occurs by the formation of a contractile actin cable, while wide wounds are resurfaced by lamellipodia-dependent migration of border cells into the denuded area. To further investigate the general validity of this idea, we performed systematic experiments of the roles of wound geometry, wound size, and extracellular matrix (ECM) in wound healing in monolayers of bovine corneal endothelial cells, a system shown here to predominantly display any of the two healing mechanisms according to the experimental conditions. We found that, in this system, it is the absence or presence of the ECM on the wound surface that determines the specific healing mode. Our observations demonstrate that, independent of their size and geometry, wounds created maintaining the ECM heal by migration of cells into the wound area, while ECM removal from the wound surface determines the predominant formation of an actin cable. While the latter mechanism is slower, the actin cable permits the maintainance of the epithelial phenotype to a larger extent during the healing process, as also confirmed by our finding of a more conserved localization of cadherin and vinculin. We also introduce a model that simulates experimental findings about the dynamics of healing mechanisms, both for the maintenance or removal of the ECM on the wound surface. The findings of this study may contribute to the understanding of physiological and pathological aspects of epithelial wound healing and to the design of therapeutic strategies.

A general model for the dynamics of the cell volume.

The conservation of the cell volume within values compatible with the overall cell functions represents an ubiquitous property, shared by cells comprising the whole biological world. Water transport across membranes constitutes the main process associated to the dynamics of the cell volume, its chronic and acute regulations therefore represent crucial aspects of cell homeostasis. In spite of the biological diversity, the dynamics of the cell volume exhibits common basic features in the diverse types of cells. The purpose of this study is to show that there is a general model capable to describe the basic aspects of the dynamics of the cell volume. It is demonstrated here that the steady states of this model represent asymptotically stable configurations. As illustrations, several cases of non-polarized (i.e., symmetrical) and polarized (e.g., epithelial) cells performing water transport are shown here to represent particular cases of the general model. From a biological perspective, the existence of a general model for the dynamics of the cell volume reveals that, in spite of physiological and morphological peculiarities, there is a basic common design of the membrane transport processes. In view of its stability properties, this basic design may represent an ancestral property that has proven to be successful regarding the overall homeostatic properties of cells.