Mathematical modeling of intracellular osmolarity and cell volume stabilization: The Donnan effect and ion transport.

The presence of impermeant molecules within a cell can lead to an increase in cell volume through the influx of water driven by osmosis. This phenomenon is known as the Donnan (or Gibbs-Donnan) effect. Animal cells actively transport ions to counteract the Donnan effect and regulate their volume, actively pumping Na+ out and K+ into their cytosol using the Na+/K+ ATPase (NKA) pump. The pump-leak equations (PLEs) are a system of algebraic-differential equations to model the membrane potential, ion (Na+, K+, and Cl-), and water flux across the cell membrane, which provide insight into how the combination of passive ions fluxes and active transport contribute to stabilizing cell volume. Our broad objective is to provide analytical insight into the PLEs through three lines of investigation: (1) we show that the provision of impermeant extracellular molecules can stabilize the volume of a passive cell; (2) we demonstrate that the mathematical form of the NKA pump is not as important as the stoichiometry for cell stabilization; and (3) we investigate the interaction between the NKA pump and cation-chloride co-transporters (CCCs) on cell stabilization, showing that NCC can destabilize a cell while NKCC and KCC can stabilize it. We incorporate extracellular impermeant molecules, NKA pump, and CCCs into the PLEs and derive the exact formula for the steady states in terms of all the parameters. This analytical expression enables us to easily explore the effect of each of the system parameters on the existence and stability of the steady states.

The physical basis of osmosis.

Osmosis is an important force in all living organisms, yet the molecular basis of osmosis is widely misunderstood as arising from diffusion of water across a membrane separating solutions of differing osmolarities, and hence different water concentrations. In 1923, Peter Debye proposed a physical model for a semipermeable membrane emphasizing the repulsive forces between solute molecules and membrane that prevent the solute from entering the membrane. His work was hardly noticed at the time and slipped out of view. We show that Debye's analysis of van 't Hoff's law for osmotic equilibrium also provides a consistent and plausible mechanism for osmotic flow. A difference in osmolyte concentrations in solutions separated by a semipermeable membrane leads to different pressures at the two water-membrane interfaces because the total repulsive force between solute molecules and the membrane is different at the two interfaces. Water is therefore driven through the membrane for exactly the same reason that pure water flows in response to an imposed hydrostatic pressure difference. In this paper, we present the Debye model in both equilibrium and flow conditions. We point out its applicability regardless of the nature of the membrane with examples ranging from the predominantly convective flow of water through synthetic membranes and capillary walls to the purely diffusive flow of independent water molecules through a lipid bilayer and the flow of a single-file column of water molecules in narrow protein channels.

A sensitive and specific genetically-encoded potassium ion biosensor for in vivo applications across the tree of life.

Potassium ion (K+) plays a critical role as an essential electrolyte in all biological systems. Genetically-encoded fluorescent K+ biosensors are promising tools to further improve our understanding of K+-dependent processes under normal and pathological conditions. Here, we report the crystal structure of a previously reported genetically-encoded fluorescent K+ biosensor, GINKO1, in the K+-bound state. Using structure-guided optimization and directed evolution, we have engineered an improved K+ biosensor, designated GINKO2, with higher sensitivity and specificity. We have demonstrated the utility of GINKO2 for in vivo detection and imaging of K+ dynamics in multiple model organisms, including bacteria, plants, and mice.

Myogenic contraction of a somatic muscle powers rhythmic flow of hemolymph through Drosophila antennae and generates brain pulsations.

Hemolymph is driven through the antennae of Drosophila melanogaster by the rhythmic contraction of muscle 16 (m16), which runs through the brain. Contraction of m16 results in the expansion of an elastic ampulla, opening ostia and filling the ampulla. Relaxation of the ampullary membrane forces hemolymph through vessels into the antennae. We show that m16 is an auto-active rhythmic somatic muscle. The activity of m16 leads to the rapid perfusion of the antenna by hemolymph. In addition, it leads to the rhythmic agitation of the brain, which could be important for clearing the interstitial space.

Improving Management of Limb Injuries in Disasters and Conflicts.

It has become clear that disaster relief needs to transition from good intentions or a charity-based approach to a professional, outcome-oriented response. The practice of medicine in disaster and conflict is a profession practiced in environments where lack of resources, chaos, and unpredictability are the norm rather than the exception. With this consideration in mind, the World Health Organization (WHO; Geneva, Switzerland) and its partners set out to improve the disaster response systems. The resulting Emergency Medical Team (EMT) classification system requires that teams planning on engaging in disaster response follow common standards for the delivery of care in resource-constraint environments. In order to clarify these standards, the WHO EMT Secretariat collaborated with the International Committee of the Red Cross (ICRC; Geneva, Switzerland) and leading experts from other stakeholder non-governmental organizations (NGOs) to produce a guide to the management of limb injuries in disaster and conflict.The resulting text is a free and open-access resource to provide guidance for national and international EMTs caring for patients in disasters and conflicts. The content is a result of expert consensus, literature review, and an iterative process designed to encourage debate and resolution of existing open questions within the field of disaster and conflict medical response.The end result of this process is a text providing guidance to providers seeking to deliver safe, effective care within the EMT framework that is now part of the EMT training and verification system and is being distributed to ICRC teams deploying to the field.This work seeks to encourage professionalization of the field of disaster and conflict response, and to contribute to the existing EMT framework, in order to provide for better care for future victims of disaster and conflict.Jensen G, Bar-On E, Wiedler JT, Hautz SC, Veen H, Kay AR, Norton I, Gosselin RA, von Schreeb J. Improving management of limb injuries in disasters and conflicts. Prehosp Disaster Med. 2019;34(3):330-334.

Evolution of our understanding of cell volume regulation by the pump-leak mechanism.

All animal cells are surrounded by a flexible plasma membrane that is permeable to water and to small ions. Cells thus face a fundamental problem: the considerable tension that their membranes would experience if the osmotic influx of water, driven by the presence of impermeant intracellular ions, was left unopposed. The pivotal study that described the cell's remedy for this impending osmotic catastrophe-the "pump-leak mechanism" (PLM)-was published in the Journal of General Physiology by Tosteson and Hoffman in 1960. Their work revealed how the sodium pump stabilizes cell volume by eliminating the osmotic gradient. Here we describe the mechanistic basis of the PLM, trace the history of its discovery, and place it into the context of our current understanding.

Biophysical models reveal the relative importance of transporter proteins and impermeant anions in chloride homeostasis.

Fast synaptic inhibition in the nervous system depends on the transmembrane flux of Cl- ions based on the neuronal Cl- driving force. Established theories regarding the determinants of Cl- driving force have recently been questioned. Here, we present biophysical models of Cl- homeostasis using the pump-leak model. Using numerical and novel analytic solutions, we demonstrate that the Na+/K+-ATPase, ion conductances, impermeant anions, electrodiffusion, water fluxes and cation-chloride cotransporters (CCCs) play roles in setting the Cl- driving force. Our models, together with experimental validation, show that while impermeant anions can contribute to setting [Cl-]i in neurons, they have a negligible effect on the driving force for Cl- locally and cell-wide. In contrast, we demonstrate that CCCs are well-suited for modulating Cl- driving force and hence inhibitory signaling in neurons. Our findings reconcile recent experimental findings and provide a framework for understanding the interplay of different chloride regulatory processes in neurons.

How Cells Can Control Their Size by Pumping Ions.

The ability of all cells to set and regulate their size is a fundamental aspect of cellular physiology. It has been known for sometime but not widely so, that size stability in animal cells is dependent upon the operation of the sodium pump, through the so-called pump-leak mechanism (Tosteson and Hoffman, 1960). Impermeant molecules in cells establish an unstable osmotic condition, the Donnan effect, which is counteracted by the operation of the sodium pump, creating an asymmetry in the distribution of Na+ and K+ staving off water inundation. In this paper, which is in part a tutorial, I show how to model quantitatively the ion and water fluxes in a cell that determine the cell volume and membrane potential. The movement of water and ions is constrained by both osmotic and charge balance, and is driven by ion and voltage gradients and active ion transport. Transforming these constraints and forces into a set of coupled differential equations allows us to model how the ion distributions, volume and voltage change with time. I introduce an analytical solution to these equations that clarifies the influence of ion conductances, pump rates and water permeability in this multidimensional system. I show that the number of impermeant ions (x) and their average charge have a powerful influence on the distribution of ions and voltage in a cell. Moreover, I demonstrate that in a cell where the operation of active ion transport eliminates an osmotic gradient, the size of the cell is directly proportional to x. In addition, I use graphics to reveal how the physico-chemical constraints and chemical forces interact with one another in apportioning ions inside the cell. The form of model used here is applicable to all membrane systems, including mitochondria and bacteria, and I show how pumps other than the sodium pump can be used to stabilize cells. Cell biologists may think of electrophysiology as the exclusive domain of neuroscience, however the electrical effects of ion fluxes need to become an intimate part of cell biology if we are to understand a fundamental process like cell size regulation.

Goggatomy: A Method for Opening Small Cuticular Compartments in Arthropods for Physiological Experiments.

Most sense organs of arthropods are ensconced in small exoskeletal compartments that hinder direct access to plasma membranes. We have developed a method for exposing live sensory and supporting cells in such structures. The technique uses a viscous light cured resin to embed and support the structure, which is then sliced with a sharp blade. We term the procedure a "goggatomy," from the Khoisan word for a bug, gogga. To demonstrate the utility of the method we show that it can be used to expose the auditory chordotonal organs in the second antennal segment and the olfactory receptor neurons in the third antennal segment of Drosophila melanogaster, preserving the transduction machinery. The procedure can also be used on other small arthropods, like mosquitoes and mites to expose a variety of cells.

Evidence for an extracellular zinc-veneer in rodent brains from experiments with Zn-ionophores and ZnT3 knockouts.

Ionic zinc is found at a high concentration in some glutamatergic vesicles of the mammalian brain. Ionic zinc is also found chelated to macromolecules in the extracellular space, constituting what has been called the "zinc veneer". In this communication we show that the zinc ionophore, pyrithione, can be used to demonstrate the presence of the veneer. Application of pyrithione without added ionic zinc to rodent hippocampal slices mobilizes extracellular zinc, which can be detected intracellularly by the zinc probe FluoZin-3. In addition, we show that ZnT3 null mice, which lack the transporter responsible for stocking synaptic vesicles, nevertheless do have a zinc veneer, albeit diminished compared to wild type animals. The presence of the zinc veneer in ZnT3 null mice may account for the absence of any marked deficit in these animals.

A method for detecting molecular transport within the cerebral ventricles of live zebrafish (Danio rerio) larvae.

The production and flow of cerebrospinal fluid performs an important role in the development and homeostasis of the central nervous system.However, these processes are difficult to study in the mammalian brain because the ventricles are situated deep within the parenchyma.In this communication we introduce the zebrafish larva as an in vivo model for studying cerebral ventricle and blood­brain barrier function. Using confocal microscopy we show that zebrafish ventricles are topologically similar to those of the mammalian brain.We describe a new method for measuring the dynamics of molecular transport within the ventricles of live zebrafish by means of the uncaging of a fluorescein derivative. Furthermore, we determine that in 5­6 days post-fertilization zebrafish, the dispersal of molecules in the ventricles is driven by a combination of ciliary motion and diffusion. The zebrafish presents a tractable system with the advantage of genetics, size and transparency for exploring ventricular physiology and for mounting large-scale high throughput experiments.

Differential transition metal uptake and fluorescent probe localization in hippocampal slices.

Metals are taken up by the combined action of metal transporters and ion channels. In this communication we have measured the uptake of the biologically important transition metals Mn, Fe, Co, Ni, Cu, Zn and Cd by rat and mouse hippocampal slices using the fluorescent probes FluoZin-3 (FZ3) and Newport Green (NPG), introduced by acetoxymethyl ester (AM) loading. The combination of metals and probes is also used to attempt to localize cellular sites into which metals translocate. We show that FZ3 and NPG partition into different cellular compartments; FZ3 into neuropil, whereas NPG localizes in neuropil and compartments within the cell bodies of neurons. Ni, Zn and Cd pass across the plasma membrane and then accumulate in intracellular vesicles and within intracellular membranes of cell bodies. The latter accumulate Cd, while synaptic vesicles take up Co. The passage of Mn, Cu and Fe into cells can be detected but there is some uncertainty about their disposition within the cell. All of our experiments are consistent with metals accumulating in intracellular compartments rather than the cytoplasm. Whether and to what extent there are transient elevations of free zinc levels in the cytoplasm remains unclear.

Pediatric superficial scald burns--reassessment of our follow-up protocol.

The most common pediatric burn injury is a superficial scald. The current follow-up protocol for such burns includes review of the patient at 2 weeks postinjury and then 2 months later. The authors decided to review the protocol to assess the need for this second follow-up. A retrospective study reviewed the case notes of patients younger than 16 years at the time of their injury presenting with a scald over 5% TBSA. The progress of healing and scar development up to 5 years follow-up was assessed. This study showed that scalds healing within 2 weeks following injury rarely became hypertrophic. A prospective study was performed over a 10-month period. All children who suffered a superficial partial-thickness scald injury were included. At the 2-week appointment, the need for further follow-up was predicted. The accuracy of this prediction was assessed 2 months later. This study showed that an experienced member of the burns team could reliably predict at 2-week appointment those children who could be safely discharged with no subsequent need for scar management. This study suggests that it will be safe to modify the follow-up protocol, reducing the number of clinic attendances.

Zinc is externalized rather than released during synaptic transmission.

The synaptic vesicles of some glutamatergic terminals contain a high concentration of zinc that serves functions that remain obscure. In this publication we have used the membrane permeant zinc fluophore, ZnAF-2 to determine if zinc is released during the course of synaptic transmission. Stimulation of the slices with either high potassium or electrically, leads to an increase in fluorescence that long outlasts the stimulus and remains elevated for many minutes. We demonstrate that this response is inconsistent with the free release of zinc but is with the presentation of zinc coordinated to macromolecules within the exocytosed vesicles to the extracellular space; a process we term 'externalization'. Our data suggests a novel mechanism of synaptic transmission at zinc-rich glutamatergic terminals that distinguishes them from their metal free counterparts.

The interplay between inorganic phosphate and amino acids determines zinc solubility in brain slices.

Inorganic phosphate (Pi) is an important polyanion needed for ATP synthesis and bone formation. As it is found at millimolar levels in plasma, it is usually incorporated as a constituent of artificial CSF formulations for maintaining brain slices. In this paper, we show that Pi limits the extracellular zinc concentration by inducing metal precipitation. We present data suggesting that amino acids like histidine may counteract the Pi-induced zinc precipitation by the formation of soluble zinc complexes. We propose that the interplay between Pi and amino acids in the extracellular space may influence the availability of metals for cellular uptake.

The interaction of biological and noxious transition metals with the zinc probes FluoZin-3 and Newport Green.

Zinc-sensitive fluorescent probes have become increasingly important in the investigation of the cellular roles of zinc. There is, however, little information on how the other transition metals in cells may influence the measurement of zinc. We have characterized in vitro the interaction of the nominal zinc indicators FluoZin-3 and Newport Green with all the cationic transition metals found within cells, Cr, Mn, Fe, Co, and Cu, as well as Ni and Cd, by measuring their dissociation constants. In addition, we have shown how FluoZin-3 can be used to quantify the concentration of copper in a cell-free assay and report that the fluorescence of Newport Green is boosted by both Cu(I) and Fe(II). Furthermore, we have introduced diagnostics for detecting the interference of metals other than zinc with its measurement within cells.

Is zinc a neuromodulator?

The vesicles of certain glutamatergic terminals in the mammalian forebrain are replete with ionic zinc. It is believed that during synaptic transmission zinc is released, binds to receptors on the pre- or postsynaptic membranes, and hence acts as a neuromodulator. Although exogenous zinc modulates a wide variety of channels, whether synaptic zinc transits across the synaptic cleft and alters the response of channels has been difficult to establish. We will review the evidence for zinc as a neuromodulator and propose diagnostic criteria for establishing whether it is indeed one. Moreover, we will delineate alternative ways in which zinc might act at synapses.

The zinc indicator FluoZin-3 is not perturbed significantly by physiological levels of calcium or magnesium.

There has been some dispute in the literature as to the sensitivity of the zinc indicator FluoZin-3 to calcium, with suggestions that physiological levels of calcium and magnesium effectively occlude the response of the probe to zinc. In this communication we demonstrate that calcium concentrations as high as 10 mM do not prevent FluoZin-3 from detecting zinc elevations as low as 100 pM. Moreover, the inclusion of a few microM Ca-EDTA does not prevent FluoZin-3 from responding to increases in zinc concentration but does extend the dynamic range of the probe by reducing contaminating zinc levels and allowing the probe to respond to multiple zinc additions. In addition, we have derived a mathematical model to account for the kinetics of FluoZin-3 response to zinc in the presence of an additional zinc and calcium chelator.