Virgilio L. Lew

Calcium Transport and the Properties of a Calcium-Activated Potassium Channel in Red Cell Membranes

Publisher Summary This chapter concentrates on the Ca-sensitive K permeability mechanism of red cells. Although the functional role of this process is completely unknown in these cells, the red cell membrane represents an extremely convenient experimental model for the study of such a mechanism. Ca-induced K flux is so easy to measure and so richly responsive to all sorts of treatments that it has stimulated more extensive than analytical research. The chapter explores that as an experimental model, the red cell has clear advantages in that Ca 2+ can be assessed and controlled better than in any other cell, and in that even minute selective changes in K permeability can be unambiguously determined by relatively simple methods. Furthermore, investigation of the molecular nature of the Ca-sensitive K channel is still at a very early stage. Moreover, a few attempts have been made to search for specific high affinity inhibitors with which the channels can be “labeled,” their surface density can be measured, but the results so far are not very promising.

Volume, pH, and Ion-Content Regulation in Human Red Cells: Analysis of Transient Behavior with an Integrated Model

SummaryA basic mathematical model of human red cells is presented which integrates the charge and nonideal osmotic behavior of hemoglobin and of other impermeant cell solutes with the ion transport properties of the red cell membrane. The computing strategy was designed to predict the behavior of all measurable variables in time in ways that optimize comparison with experimentally determined behavior. The need and applications of such a model are illustrated in three separate examples covering different areas of experimentation in the physiology and pathophysiology of red cells.

Evidence for a direct reticulocyte origin of dense red cells in sickle cell anemia.

To explore our hypothesis of a direct reticulocyte origin of irreversibly sickled cells (ISCs), we fractionated light, reticulocyte-rich, and discocyte-rich sickle anemia red cells on Stractan gradients, and examined the effects of deoxygenation-induced sickling, external Ca2+, acidification, and replacing external Na+ by impermeant N-methyl-D-glucamine (NMG+). Sickling permeabilized light reticulocyte-rich cells to cations (Na+, K+, and Ca2+) more than discocytes; without external Ca2+, Na+ influx matched K+ efflux, with stable cell volume; with Ca2+, many light, low hemoglobin (Hb) F reticulocytes dehydrated rapidly (preventable by quinine, a Ca2(+)-dependent K+ channel inhibitor). Acidification of oxygenated discocytes (high mean Hb F) and reticulocyte-rich fractions yielded denser, reticulocyte-enriched cells with lower Hb F (as in light reticulocyte or dense ISC-rich fractions). Light cells shrank when NMG+ replaced Na+, supporting predictions of a Na(+)-dependent volume control system. Demonstration of sickling-induced, Ca2(+)-dependent dehydration of Hb F-free reticulocytes, and conservation of acid-stimulated K:Cl cotransport among low Hb F, reticulocyte-enriched cells in discocyte fractions support the hypothesis. Ancillary new findings included heparin stimulation of sickling-induced Na+ and K+ permeabilizations, and Ca2+ inhibition of the Na+ leak.

Irreversible ATP depletion caused by low concentrations of formaldehyde and of calcium-chelator esters in intact human red cells

Calcium chelators which can be incorporated inside small cells without disruption have become useful tools to investigate the role of intracellular ionized calcium in the processes of cell activation and signal-effect mediation. In experiments designed to investigate further Ca2+ pump function in chelator-loaded human red cells we found that the chelator-loading procedure itself caused delayed Ca2+-pump inhibition when pump function was explored by increasing the intracellular Ca2+ levels with the aid of the divalent cation ionophore A23187. Ca2+-pump inhibition was found to be secondary to ATP-depletion, and ATP-depletion, in turn, could be attributed to formaldehyde, which was released during the hydrolytic incorporation of free chelator, from the cleavage of the four ester groups which anchor it to cell membranes on addition to cell suspensions. The evidence suggests that the formaldehyde released stays largely within the cells. Formaldehyde, in concentrations of up to 20 mmol/l cells had no direct effects on Ca2+ transport in red cells, other than through ATP depletion. Procedures to circumvent the difficulties arising from the formaldehyde effects are outlined and discussed.

Systems Dynamic Modeling of the Stomatal Guard Cell Predicts Emergent Behaviors in Transport, Signaling, and Volume Control

The dynamics of stomatal movements and their consequences for photosynthesis and transpirational water loss have long been incorporated into mathematical models, but none have been developed from the bottom up that are widely applicable in predicting stomatal behavior at a cellular level. We previously established a systems dynamic model incorporating explicitly the wealth of biophysical and kinetic knowledge available for guard cell transport, signaling, and homeostasis. Here we describe the behavior of the model in response to experimentally documented changes in primary pump activities and malate (Mal) synthesis imposed over a diurnal cycle. We show that the model successfully recapitulates the cyclic variations in H+, K+, Cl−, and Mal concentrations in the cytosol and vacuole known for guard cells. It also yields a number of unexpected and counterintuitive outputs. Among these, we report a diurnal elevation in cytosolic-free Ca2+ concentration and an exchange of vacuolar Cl− with Mal, both of which find substantiation in the literature but had previously been suggested to require additional and complex levels of regulation. These findings highlight the true predictive power of the OnGuard model in providing a framework for systems analysis of stomatal guard cells, and they demonstrate the utility of the OnGuard software and HoTSig library in exploring fundamental problems in cellular physiology and homeostasis.

OnGuard, a Computational Platform for Quantitative Kinetic Modeling of Guard Cell Physiology

Stomatal guard cells play a key role in gas exchange for photosynthesis while minimizing transpirational water loss from plants by opening and closing the stomatal pore. Foliar gas exchange has long been incorporated into mathematical models, several of which are robust enough to recapitulate transpirational characteristics at the whole-plant and community levels. Few models of stomata have been developed from the bottom up, however, and none are sufficiently generalized to be widely applicable in predicting stomatal behavior at a cellular level. We describe here the construction of computational models for the guard cell, building on the wealth of biophysical and kinetic knowledge available for guard cell transport, signaling, and homeostasis. The OnGuard software was constructed with the HoTSig library to incorporate explicitly all of the fundamental properties for transporters at the plasma membrane and tonoplast, the salient features of osmolite metabolism, and the major controls of cytosolic-free Ca2+ concentration and pH. The library engenders a structured approach to tier and interrelate computational elements, and the OnGuard software allows ready access to parameters and equations ‘on the fly’ while enabling the network of components within each model to interact computationally. We show that an OnGuard model readily achieves stability in a set of physiologically sensible baseline or Reference States; we also show the robustness of these Reference States in adjusting to changes in environmental parameters and the activities of major groups of transporters both at the tonoplast and plasma membrane. The following article addresses the predictive power of the OnGuard model to generate unexpected and counterintuitive outputs.

Effects of deoxygenation on active and passive Ca2+ transport and on the cytoplasmic Ca2+ levels of sickle cell anemia red cells.

Elevated [Ca2+]i in deoxygenated sickle cell anemia (SS) red cells (RBCs) could trigger a major dehydration pathway via the Ca(2+)-sensitive K+ channel. But apart from an increase in calcium permeability, the effects of deoxygenation on the Ca2+ metabolism of sickle cells have not been previously documented. With the application of 45Ca(2+)-tracer flux methods and the combined use of the ionophore A23187, Co2+ ions, and intracellular incorporation of the Ca2+ chelator benz-2, in density-fractionated SS RBCs, we show here for the first time that upon deoxygenation, the mean [Ca2+]i level of SS discocytes was significantly increased, two- to threefold, from a normal range of 9.4 to 11.4 nM in the oxygenated cells, to a range of 21.8 to 31.7 nM in the deoxygenated cells, closer to K+ channel activatory levels. Unlike normal RBCs, deoxygenated SS RBCs showed a two- to fourfold increase in pump-leak Ca2+ turnover. Deoxygenation of the SS RBCs reduced their Ca2+ pump Vmax, more so in reticulocyte- and discocyte-rich than in dense cell fractions, and decreased their cytoplasmic Ca2+ buffering. Analysis of these results suggests that both increased Ca2+ influx and reduced Ca2+ pump extrusion contribute to the [Ca2+]i elevation.

A mathematical model of the volume, pH, and ion content regulation in reticulocytes. Application to the pathophysiology of sickle cell dehydration.

We developed a mathematical model of the reticulocyte, seeking to explain how a cell with similar volume but much higher ionic traffic than the mature red cell (RBC) regulates its volume, pH, and ion content in physiological and abnormal conditions. Analysis of the fluxbalance required by reticulocytes to conserve volume and composition predicted the existence of previously unsuspected Na(+)-dependent Cl- entry mechanisms. Unlike mature RBCs, reticulocytes did not tend to return to their original state after brief perturbations. The model predicted hysteresis and drift in cell pH, volume, and ion contents after transient alterations in membrane permeability or medium composition; irreversible cell dehydration could thus occur by brief K+ permeabilization, transient medium acidification, or the replacement of external Na+ with an impermeant cation. Both the hysteresis and drift after perturbations were shown to depend on the pHi dependence of the K:Cl cotransport, a major reticulocyte transporter. This behavior suggested a novel mechanism for the generation of irreversibly sickled cells directly from reticulocytes, rather than in a stepwise, progressive manner from discocytes. Experimental tests of the models predictions and the hypothesis are described in the following paper.

The magnesium dependence of sodium‐pump‐mediated sodium—potassium and sodium—sodium exchange in intact human red cells

1. The magnesium content of human red blood cells was controlled by varying the magnesium concentration in the medium in the presence of the ionophore A23187. The new magnesium levels attained were very stable, which allowed the magnesium dependence of the sodium pump to be investigated.

The Homeostasis of Plasmodium falciparum-Infected Red Blood Cells

The asexual reproduction cycle of Plasmodium falciparum, the parasite responsible for severe malaria, occurs within red blood cells. A merozoite invades a red cell in the circulation, develops and multiplies, and after about 48 hours ruptures the host cell, releasing 15–32 merozoites ready to invade new red blood cells. During this cycle, the parasite increases the host cell permeability so much that when similar permeabilization was simulated on uninfected red cells, lysis occurred before ∼48 h. So how could infected cells, with a growing parasite inside, prevent lysis before the parasite has completed its developmental cycle? A mathematical model of the homeostasis of infected red cells suggested that it is the wasteful consumption of host cell hemoglobin that prevents early lysis by the progressive reduction in the colloid-osmotic pressure within the host (the colloid-osmotic hypothesis). However, two critical model predictions, that infected cells would swell to near prelytic sphericity and that the hemoglobin concentration would become progressively reduced, remained controversial. In this paper, we are able for the first time to correlate model predictions with recent experimental data in the literature and explore the fine details of the homeostasis of infected red blood cells during five model-defined periods of parasite development. The conclusions suggest that infected red cells do reach proximity to lytic rupture regardless of their actual volume, thus requiring a progressive reduction in their hemoglobin concentration to prevent premature lysis.