The enduring legacy of the "constant-field equation" in membrane ion transport

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.

Electrophysiological properties and structural prediction of the SARS-CoV-2 viroprotein E

COVID-19, the infectious disease caused by the most recently discovered coronavirus SARS- CoV-2, has caused millions of sick people and thousands of deaths all over the world. The viral positive-sense single-stranded RNA encodes 31 proteins among which the spike (S) is undoubtedly the best known. Recently, protein E has been reputed as a potential pharmacological target as well. It is essential for the assembly and release of the virions in the cell. Literature describes protein E as a voltage-dependent channel with preference towards monovalent cations whose intracellular expression, though, alters Ca2+ homeostasis and promotes the activation of the proinflammatory cascades. Due to the extremely high sequence identity of SARS-CoV-2 protein E (E-2) with the previously characterized E-1 (i.e., protein E from SARS-CoV) many data obtained for E-1 were simply adapted to the other. Recent solid state NMR structure revealed that the transmembrane domain (TMD) of E-2 self-assembles into a homo-pentamer, albeit the oligomeric status has not been validated with the full-length protein. Prompted by the lack of a common agreement on the proper structural and functional features of E-2, we investigated the specific mechanism/s of pore-gating and the detailed molecular structure of the most cryptic protein of SARS-CoV-2 by means of MD simulations of the E-2 structure and by expressing, refolding and analyzing the electrophysiological activity of the transmembrane moiety of the protein E-2, in its full length. Our results show a clear agreement between experimental and predictive studies and foresee a mechanism of activity based on Ca2+ affinity.

Bioelectronic Medicine: a multidisciplinary roadmap from biophysics to precision therapies

Bioelectronic Medicine stands as an emerging field that rapidly evolves and offers distinctive clinical benefits, alongside unique challenges. It consists of the modulation of the nervous system by precise delivery of electrical current for the treatment of clinical conditions, such as post-stroke movement recovery or drug-resistant disorders. The unquestionable clinical impact of Bioelectronic Medicine is underscored by the successful translation to humans in the last decades, and the long list of preclinical studies. Given the emergency of accelerating the progress in new neuromodulation treatments (i.e., drug-resistant hypertension, autoimmune and degenerative diseases), collaboration between multiple fields is imperative. This work intends to foster multidisciplinary work and bring together different fields to provide the fundamental basis underlying Bioelectronic Medicine. In this review we will go from the biophysics of the cell membrane, which we consider the inner core of neuromodulation, to patient care. We will discuss the recently discovered mechanism of neurotransmission switching and how it will impact neuromodulation design, and we will provide an update on neuronal and glial basis in health and disease. The advances in biomedical technology have facilitated the collection of large amounts of data, thereby introducing new challenges in data analysis. We will discuss the current approaches and challenges in high throughput data analysis, encompassing big data, networks, artificial intelligence, and internet of things. Emphasis will be placed on understanding the electrochemical properties of neural interfaces, along with the integration of biocompatible and reliable materials and compliance with biomedical regulations for translational applications. Preclinical validation is foundational to the translational process, and we will discuss the critical aspects of such animal studies. Finally, we will focus on the patient point-of-care and challenges in neuromodulation as the ultimate goal of bioelectronic medicine. This review is a call to scientists from different fields to work together with a common endeavor: accelerate the decoding and modulation of the nervous system in a new era of therapeutic possibilities.

Cytoplasmic anion/cation imbalances applied across the membrane capacitance may form a significant component of the resting membrane potential of red blood cells

Electrical aspects of cell function manifest in many ways. The most widely studied is the cell membrane potential, Vm, but others include the conductance and capacitance of the membrane, the conductance of the enclosed cytoplasm, as well as the charge at the cell surface (an electrical double layer) producing an extracellular electrical potential, the ζ-potential. Empirical relationships have been identified between many of these, but not the mechanisms that link them all. Here we examine relationships between Vm and the electrical conductivities of both the cytoplasm and extracellular media, using data from a suspensions of red blood cells. We have identified linear relationships between extracellular medium conductivity, cytoplasm conductivity and Vm. This is in contrast to the standard model of a resting membrane potential which describes a logarithmic relationship between Vm and the concentration of permeable ions in the extracellular medium. The model here suggests that Vm is partially electrostatic in origin, arising from a charge imbalance at an inner electrical double-layer, acting across the membrane and double-layer capacitances to produce a voltage. This model describes an origin for coupling between Vm and ζ, by which cells can alter their electrostatic relationship with their environment, with implications for modulation of membrane ion transport, adhesion of proteins such as antibodies and wider cell-cell interactions.

Gender differences in cell volume fraction (CVF): a structural parameter reflecting the energy efficiency of maintaining the resting membrane potential

The cell volume fraction (CVF) of the human brain is high (~82%) and is preserved across healthy aging while the brain declines in volume. These two observations, supported by several independent techniques, suggest that CVF is an important structural parameter. A new biophysical model is presented that incorporates CVF into the Goldman equation of classical membrane electrophysiology. The Goldman equation contains few structural constraints beyond two compartments separated by a semipermeable membrane supporting ion gradients. As potassium is the most permeable ion in the resting state, the resting membrane potential is determined by the potassium ion gradient. This biophysical model indicates that the sodium-potassium ion pumps use less energy at high CVF to maintain the resting membrane potential, explaining the high value of CVF and its conservation with healthy aging. CVF is measured to be statistically significantly higher in the brains of males compared with females, suggesting a structural requirement for higher energy efficiency in the larger male brain to support the greater number of neurons and synapses. As CVF can be measured in humans using quantitative sodium MRI and has potential implications for brain health, CVF may be a quantitative parameter that is useful for assessment of brain health, especially in patients with diseases such as dementia and psychiatric disease that do not have anatomical correlates detectable by clinical proton MRI.

Can two wrongs make a right? F508del-CFTR ion channel rescue by second-site mutations in its transmembrane domains

Deletion of phenylalanine 508 (F508del) in the cystic fibrosis transmembrane conductance regulator (CFTR) anion channel is the most common cause of cystic fibrosis. The F508 residue is located on nucleotide-binding domain 1 (NBD1) in contact with the cytosolic extensions of the transmembrane helices, in particular intracellular loop 4 (ICL4). To investigate how absence of F508 at this interface impacts the CFTR protein, we carried out a mutagenesis scan of ICL4 by introducing second-site mutations at 11 positions in cis with F508del. Using an image-based fluorescence assay, we measured how each mutation affected membrane proximity and ion-channel function. The scan strongly validated the effectiveness of R1070W at rescuing F508del defects. Molecular dynamics simulations highlighted two features characterizing the ICL4/NBD1 interface of F508del/R1070W-CFTR: flexibility, with frequent transient formation of interdomain hydrogen bonds, and loosely stacked aromatic sidechains (F1068, R1070W, and F1074, mimicking F1068, F508, and F1074 in WT CFTR). F508del-CFTR displayed a distorted aromatic stack, with F1068 displaced toward the space vacated by F508, while in F508del/R1070F-CFTR, which largely retained F508del defects, R1070F could not form hydrogen bonds and the interface was less flexible. Other ICL4 second-site mutations which partially rescued F508del-CFTR included F1068M and F1074M. Methionine side chains allow hydrophobic interactions without the steric rigidity of aromatic rings, possibly conferring flexibility to accommodate the absence of F508 and retain a dynamic interface. These studies highlight how both hydrophobic interactions and conformational flexibility might be important at the ICL4/NBD1 interface, suggesting possible structural underpinnings of F508del-induced dysfunction.

Effects of ionic strength on gating and permeation of TREK-2 K2P channels

In addition to the classical voltage-dependent behavior mediated by the voltage-sensing-domains (VSD) of ion channels, a growing number of voltage-dependent gating behaviors are being described in channels that lack canonical VSDs. A common thread in their mechanism of action is the contribution of the permeating ion to this voltage sensing process. The polymodal K2P K⁺ channel, TREK2 responds to membrane voltage through a gating process mediated by the interaction of K⁺ with its selectivity filter. Recently, we found that this action can be modulated by small molecule agonists (e.g. BL1249) which appear to have an electrostatic influence on K⁺ binding within the inner cavity and produce an increase in the single-channel conductance of TREK-2 channels. Here, we directly probed this K⁺-dependent gating process by recording both macroscopic and single-channel currents of TREK-2 in the presence of high concentrations of internal K⁺. Surprisingly we found TREK-2 is inhibited by high internal K⁺ concentrations and that this is mediated by the concomitant increase in ionic-strength. However, we were still able to determine that the increase in single channel conductance in the presence of BL1249 was blunted in high ionic-strength, whilst its activatory effect (on channel open probability) persisted. These effects are consistent with an electrostatic mechanism of action of negatively charged activators such as BL1249 on permeation, but also suggest that their influence on channel gating is complex.

Fusion pores with low conductance are cation selective

Many neurotransmitters are organic ions that carry a net charge, and their release from secretory vesicles is therefore an electrodiffusion process. The selectivity of early exocytotic fusion pores is investigated by combining electrodiffusion theory, measurements of amperometric foot signals from chromaffin cells with anion substitution, and molecular dynamics simulation. The results reveal that very narrow fusion pores are cation selective, but more dilated fusion pores become anion permeable. The transition occurs around a fusion pore conductance of ~300 pS. The cation selectivity of a narrow fusion pore accelerates the release of positively charged transmitters such as dopamine, noradrenaline, adrenaline, serotonin, and acetylcholine, while glutamate release may require a more dilated fusion pore.

For transmission, a fusion pore forms when vesicle and target membranes are brought together by SNARE proteins. Delacruz et al. demonstrate that selectivity of the pore accelerates release of positively charged transmitters such as dopamine, noradrenaline, adrenaline, serotonin, and acetylcholine, while glutamate release may require a more dilated fusion pore.

Trans-epithelial potential (TEP) response as an indicator of major ion toxicity in rainbow trout and goldfish exposed to 10 different salts in ion-poor water

Freshwater ecosystems are facing increasing contamination by major ions. The Multi-Ion Toxicity (MIT) model, a new tool for risk assessment and regulation, predicts major ion toxicity to aquatic organisms by relating it to a critical disturbance of the trans-epithelial potential (TEP) across the gills, as predicted by electrochemical theory. The model is based on unproven assumptions. We tested some of these by directly measuring the acute TEP responses to a geometric series of 10 different single salts (NaCl, Na₂SO₄, KCl, K₂SO₄, CaCl₂, CaSO₄, MgCl₂, MgSO₄, NaHCO₃, KHCO₃) in the euryhaline rainbow trout (Oncorhynchus mykiss) and the stenohaline goldfish (Carassius auratus) acclimated to very soft, ion-poor water (hardness 10 mg CaCO₃/L). Results were compared to 24-h and 96-h LC50 data from the literature, mainly from fathead minnow (Pimephales promelas). All salts caused concentration-dependent increases in TEP to less negative/more positive values, in patterns well-described by the Michaelis-Menten equation, or a modified version incorporating substrate inhibition. The ΔTEP above baseline became close to a maximum at the 96-h LC50, except for the HCO₃^- salts. Furthermore, the range of ΔTEP values at the LC50 within one species was much more consistent (1.6- to 2.1-fold variation) than the molar concentrations of the different salts at the LC50 (19- to 25-fold variation). ΔTEP responses were related to cation rather than anion concentrations. Overall patterns were qualitatively similar between trout and goldfish, with some quantitative differences, and also in general accord with recently published data on three other species in harder water where ΔTEP responses were much smaller. Blood plasma Na⁺ and K⁺ concentrations were minimally affected by the exposures. The results are in accord with most but not all of the assumptions of the MIT model and support its further development as a predictive tool.

Imaging the electrical activity of organelles in living cells

Eukaryotic cells are complex systems compartmentalized in membrane-bound organelles. Visualization of organellar electrical activity in living cells requires both a suitable reporter and non-invasive imaging at high spatiotemporal resolution. Here we present hVoSorg, an optical method to monitor changes in the membrane potential of subcellular membranes. This method takes advantage of a FRET pair consisting of a membrane-bound voltage-insensitive fluorescent donor and a non-fluorescent voltage-dependent acceptor that rapidly moves across the membrane in response to changes in polarity. Compared to the currently available techniques, hVoSorg has advantages including simple and precise subcellular targeting, the ability to record from individual organelles, and the potential for optical multiplexing of organellar activity.

Climbing aboard

Welcome from new Editor-in-Chief

SLC4A11 function: evidence for H+(OH-) and NH3-H+ transport

Whether SLC4A11 transports ammonia and its potential mode of ammonia transport (NH4+, NH₃, or NH₃-2H⁺ transport have been proposed) are controversial. In the absence of ammonia, whether SLC4A11 mediates significant conductive H⁺(OH^-) transport is also controversial. The present study was performed to determine the mechanism of human SLC4A11 ammonia transport and whether the transporter mediates conductive H⁺(OH^-) transport in the absence of ammonia. We quantitated H⁺ flux by monitoring changes in intracellular pH (pH_i) and measured whole cell currents in patch-clamp studies of HEK293 cells expressing the transporter in the absence and presence of NH₄Cl. Our results demonstrate that SLC4A11 mediated conductive H⁺(OH^-) transport that was stimulated by raising the extracellular pH (pH_e). Ammonia-induced HEK293 whole cell currents were also stimulated by an increase in pH_e. In studies using increasing NH₄Cl concentrations with equal NH4+ extracellular and intracellular concentrations, the shift in the reversal potential (E_rev) due to the addition of ammonia was compatible with NH₃-H⁺ transport competing with H⁺(OH^-) rather than NH₃-nH⁺ (n ≥ 2) transport. The increase in equivalent H⁺(OH^-) flux observed in the presence of a transcellular H⁺ gradient was also compatible with SLC4A11-mediated NH₃-H⁺ flux. The NH₃ versus E_rev data fit a theoretical model suggesting that NH₃-H⁺ and H⁺(OH^-) competitively interact with the transporter. Studies of mutant SLC4A11 constructs in the putative SLC4A11 ion coordination site showed that both H⁺(OH^-) transport and ammonia-induced whole cell currents were blocked suggesting that the H⁺(OH^-) and NH₃-H⁺ transport processes share common features involving the SLC4A11 transport mechanism.

Relationship between inorganic ion distribution, resting membrane potential, and the ΔG' of ATP hydrolysis: a new paradigm

Cell membrane potential and inorganic ion distributions are currently viewed from a kinetic electric paradigm, which ignores thermodynamics. The resting membrane potential is viewed as a diffusion potential. The 9 major inorganic ions found in blood plasma (Ca²⁺, Na⁺, Mg²⁺, K⁺, H⁺, Cl^-, HCO₃^-, H₂PO₄^-, and HPO₄^2-) are distributed unequally across the plasma membrane. This unequal distribution requires the energy of ATP hydrolysis through the action of the Na⁺-K⁺ ATPase. The cell resting membrane potential in each of 3 different tissues with widely different resting membrane potentials has been shown to be equal to the Nernst equilibrium potential of the most permeant inorganic ion. The energy of the measured distribution of the 9 major inorganic ions between extra- and intracellular phases was essentially equal to the independently measured energy of ATP hydrolysis, showing that the distribution of these 9 major ions was in near-equilibrium with the ΔG' of ATP. Therefore, thermodynamics does appear to play an essential role in the determination of the cell resting membrane potential and the inorganic ion distribution across the plasma membrane.-Veech, R. L., King, M. T., Pawlosky, R., Bradshaw, P. C., Curtis, W. Relationship between inorganic ion distribution, resting membrane potential, and the ΔG' of ATP hydrolysis: a new paradigm.

Role of Carbonic Anhydrases and Inhibitors in Acid-Base Physiology: Insights from Mathematical Modeling

Carbonic anhydrases (CAs) catalyze a reaction fundamental for life: the bidirectional conversion of carbon dioxide (CO2) and water (H2O) into bicarbonate (HCO3-) and protons (H+). These enzymes impact numerous physiological processes that occur within and across the many compartments in the body. Within compartments, CAs promote rapid H+ buffering and thus the stability of pH-sensitive processes. Between compartments, CAs promote movements of H+, CO2, HCO3-, and related species. This traffic is central to respiration, digestion, and whole-body/cellular pH regulation. Here, we focus on the role of mathematical modeling in understanding how CA enhances buffering as well as gradients that drive fluxes of CO2 and other solutes (facilitated diffusion). We also examine urinary acid secretion and the carriage of CO2 by the respiratory system. We propose that the broad physiological impact of CAs stem from three fundamental actions: promoting H+ buffering, enhancing H+ exchange between buffer systems, and facilitating diffusion. Mathematical modeling can be a powerful tool for: (1) clarifying the complex interdependencies among reaction, diffusion, and protein-mediated components of physiological processes; (2) formulating hypotheses and making predictions to be tested in wet-lab experiments; and (3) inferring data that are impossible to measure.

The yin and yang of KV channels in cerebral small vessel pathologies

Cerebral SVDs encompass a group of genetic and sporadic pathological processes leading to brain lesions, cognitive decline, and stroke. There is no specific treatment for SVDs, which progress silently for years before becoming clinically symptomatic. Here, we examine parallels in the functional defects of PAs in CADASIL, a monogenic form of SVD, and in response to SAH, a common type of hemorrhagic stroke that also targets the brain microvasculature. Both animal models exhibit dysregulation of the voltage-gated potassium channel, K_V 1, in arteriolar myocytes, an impairment that compromises responses to vasoactive stimuli and impacts CBF autoregulation and local dilatory responses to neuronal activity (NVC). However, the extent to which this channelopathy-like defect ultimately contributes to these pathologies is unknown. Combining experimental data with computational modeling, we describe the role of K_V 1 channels in the regulation of myocyte membrane potential at rest and during the modest increase in extracellular potassium associated with NVC. We conclude that PA resting membrane potential and myogenic tone depend strongly on K_V 1.2/1.5 channel density, and that reciprocal changes in K_V channel density in CADASIL and SAH produce opposite effects on extracellular potassium-mediated dilation during NVC.

The founding of Journal of General Physiology: Membrane permeation and ion selectivity

Hille recounts the founding years of JGP, including key articles that advanced the field of membrane permeation and ion selectivity.

This essay begins with a description of the founding years of Journal of General Physiology (JGP) and a historical overview of the content of the journal. It then turns to key conceptual articles published in JGP that advanced the field of membrane permeation and ion selectivity. Much of this information comes from reading the online archives of JGP and searches in PubMed.

100 years and counting: JGP celebrates its centenary

As JGP approaches its 100th year, dissemination of science is more important than ever.

As JGP approaches its 100th year, dissemination of science is more important than ever.