Another interpretation of the Goldman-Hodgkin-Katz equation based on Ling's adsorption theory

Explaining neuronal membrane potentials: The Goldman equation vs. Lee's TELC hypothesis

In two recent papers (Curr Trends Neurol 17: 83-98, 2023; J Neurophysiol 124: 1029-1044, 2020), James Lee has argued that his Transmembrane Electrostatically-Localized Cations (TELC) hypothesis offers a model of neuron transmembrane potentials that is superior to Hodgkin-Huxley classic cable theory and the Goldman-Hodgkin-Katz (GHK) equation. Here we examine critically the arguments in these papers, finding key weaknesses and fallacies. We also examine closely the literature cited by Lee, and find (i) strong support for the GHK equation; (ii) published measurements that contradict TELC predictions; and (iii) no convincing support for the TELC hypothesis.

Modifying membrane potential synchronously controls the somite's formation periodicity and growth

Coordination between periodicity of somite formation and somite growth is crucial for regular body pattern formation during somitogenesis. Yet, the specific mechanism that links the two processes remains unclear. Using chick embryos, we demonstrate that both temporal and spatial features can be simultaneously controlled by membrane potential (Vm) of somite-forming cells. Our findings show that somites hyperpolarize as they mature, displaying step-like changes in Vm observed between specific groups of somites, reflecting the reported onset of biochemical and structural changes within them. We modify Vm by changing chemical compositions of the microenvironment of the embryo. Alteration of Vm sets a new pace of somite formation (cell migration and self-assembly) and its concurrent growth (cell proliferation) without disturbing the somite's regular aspect ratio. Our results therefore suggest that Vm has the ability to orchestrate cell proliferation, migration and self-assembly - processes that are hallmarks of embryogenesis, tumorigenesis and tissue regeneration.

The cellular zeta potential: cell electrophysiology beyond the membrane

The standard model of the cell membrane potential Vm describes it as arising from diffusion currents across a membrane with a constant electric field, with zero electric field outside the cell membrane. However, the influence of Vm has been shown to extend into the extracellular space where it alters the cell's ζ-potential, the electrical potential measured a few nm from the cell surface which defines how the cell interacts with charged entities in its environment, including ions, molecules, and other cells. The paradigm arising from surface science is that the ζ-potential arises only from fixed membrane surface charge, and has consequently received little interest. However, if the ζ-potential can mechanistically and dynamically change by alteration of Vm, it allows the cell to dynamically alter cell-cell and cell-molecule interactions and may explain previously unexplained electrophysiological behaviours. Whilst the two potentials Vm and ζ are rarely reported together, they are occasionally described in different studies for the same cell type. By considering published data on these parameters across multiple cell types, as well as incidences of unexplained but seemingly functional Vm changes correlating with changes in cell behaviour, evidence is presented that this may play a functional role in the physiology of red blood cells, macrophages, platelets, sperm, ova, bacteria and cancer. Understanding how these properties will improve understanding of the role of electrical potentials and charges in the regulation of cell function and in the way in which cells interact with their environment. Insight  The zeta (ζ) potential is the electrical potential a few nm beyond the surface of any suspensoid in water. Whilst typically assumed to arise only from fixed charges on the cell surface, recent and historical evidence shows a strong link to the cell's membrane potential Vm, which the cell can alter mechanistically through the use of ion channels. Whilst these two potentials have rarely been studied simultaneously, this review collates data across multiple studies reporting Vm, ζ-potential, electrical properties of changes in cell behaviour. Collectively, this points to Vm-mediated ζ-potential playing a significant role in the physiology and activity of blood cells, immune response, developmental biology and egg fertilization, and cancer among others.

The Membrane Potential Has a Primary Key Equation

It is common to say that the origin of the membrane potential is attributed to transmembrane ion transport, but it is theoretically possible to explain its generation by the mechanism of ion adsorption. It has been previously suggested that the ion adsorption mechanism even leads to potential formulae identical to the famous Nernst equation or the Goldman-Hodgkin-Katz equation. Our further analysis, presented in this paper, indicates that the potential formula based on the ion adsorption mechanism leads to an equation that is a function of the surface charge density of the material and the surface potential of the material. Furthermore, we have confirmed that the equation holds in all the different experimental systems that we have studied. This equation appears to be a key equation that governs the characteristics of the membrane potential in all systems.

The significance of bioelectricity on all levels of organization of an organism. Part 1: From the subcellular level to cells

Bioelectricity plays an essential role in the structural and functional organization of biological organisms. In this first article of our three-part series, we summarize the importance of bioelectricity for the basic structural level of biological organization, i.e. from the subcellular level (charges, ion channels, molecules and cell organelles) to cells.

The membrane potential arising from the adsorption of ions at the biological interface

Membrane theory makes it possible to compute the membrane potential of living cells accurately. The principle is that the plasma membrane is selectively permeable to ions and that its permeability to mobile ions determines the characteristics of the membrane potential. However, an artificial experimental cell system with an impermeable membrane can exhibit a nonzero membrane potential, and its characteristics are consistent with the prediction of the Goldman-Hodgkin-Katz eq., which is a noteworthy concept of membrane theory, despite the membrane's impermeability to mobile ions. We noticed this troublesome facet of the membrane theory. We measured the potentials through permeable and impermeable membranes where we used the broad varieties of membranes. Then we concluded that the membrane potential must be primarily, although not wholly, governed by the ion adsorption-desorption process rather than by the passage of ions across the cell membrane. A theory based on the Association-Induction Hypothesis seems to be a more plausible mechanism for the generation of the membrane potential and to explain this unexpected physiological fact. The Association-Induction Hypothesis states that selective ion permeability of the membrane is not a condition for the generation of the membrane potential in living cells, which contradicts the prediction of the membrane theory. Therefore, the Association-Induction Hypothesis is the actual cause of membrane potential. We continued the theoretical analysis by taking into account the Association-Induction Hypothesis and saw that its universality as a cause of potential generation mechanism. We then concluded that the interfacial charge distribution is one of the fundamental causes of the membrane potential.

Nonlinear electric response of the diffuse double layer to an abrupt charge displacement inside a biological membrane

In order to elucidate the old, still unsolved problem of how the diffuse electric double layer responds to an abrupt, intramolecular charge displacement inside a biological membrane, we investigated the fastest components of the light-induced electric signals of bacteriorhodopsin and its mutants, in numerous ionic and buffer solutions. The obtained data for temperature and solute concentration dependence were interpreted as a consequence of changes in the capacity of the diffuse double layer surrounding the purple membrane. The possible physiological consequences of this so far not demonstrated phenomenon are discussed.

Critical analysis of explanations for cellular homeostasis and electrophysiology from murburn perspective

Pursuits in modern cellular electrophysiology are fraught with disagreements at a fundamental level. While the membrane theory of homeostasis deems the cell membrane and proteins embedded therein as the chief players, the association-induction (or sorption/bulk-phase) hypothesis considers the aqueous phase of dissolved proteins (cytoplasm/protoplasm) as the key determinant of cellular composition and ionic fluxes. In the first school of thought, trans-membrane potential (TMP) and selective ion pumps/channels are deemed as key operative principles. In the latter theory, sorption-desorption dynamics and rearrangements of bulk phase determine the outcomes. In both these schools of thought, theorists believe that the macroscopic phase electroneutrality holds, TMP (whether in resting or in activated state) results solely due to ionic concentration differentials across the membrane, and the concerned proteins undergo major conformation changes to affect/effect the noted outcomes. The new entry into the field, murburn concept, builds starting from molecular considerations to macroscopic observations. It moots "effective charge separation" and intricate "molecule-ion-radical" electron transfer equilibriums as a rationale for ionic concentration differentials and TMP variation. After making an unbiased appraisal of the two classical schools of thought, the review makes a point-wise analysis of some hitherto unresolved observations/considerations and suggests the need to rethink the mechanistic perspectives.

What can S-shaped potential profiles tell us about the mechanism of membrane potential generation?

Membrane theory attributes the generation mechanism of the membrane potential to transmembrane ion transport, while Cheng's ISE (Ion selective electrode) mechanism attributes the ISE potential generation to ion adsorption on to the ISE surface. Although the membrane potential generation mechanism is different from the ISE potential generation mechanism, both the membrane potential and the ISE potential exhibit quite similar characteristics. For instance, both become indifferent to the variation of the ion concentration in both the high and the low ion concentration environment. Our experimental and theoretical investigations suggest that such a characteristic membrane potential behavior could be explained by the ion adsorption mechanism called Ling's adsorption theory (LA theory) instead of by membrane theory. If the membrane potential generation mechanism is explained by the LA theory, then the significant similarity between the membrane potential and the ISE potential is understandable, since both the LA theory and Cheng's ISE mechanism rely on the ion adsorption process. Although the LA theory is not acknowledged as the mechanism for the membrane potential generation in the mainstream physiology community, it does not have any serious defect in principle as a membrane potential generation mechanism. Hence, it is worth investigating if the current membrane potential generation mechanism needs reevaluation in light of evidence presented here. We conclude that the LA theory is a quite plausible membrane potential generation mechanism, suggesting that it may contribute to it.

On the Coupling between Mechanical Properties and Electrostatics in Biological Membranes

Cell membrane structure is proposed as a lipid matrix with embedded proteins, and thus, their emerging mechanical and electrostatic properties are commanded by lipid behavior and their interconnection with the included and absorbed proteins, cytoskeleton, extracellular matrix and ionic media. Structures formed by lipids are soft, dynamic and viscoelastic, and their properties depend on the lipid composition and on the general conditions, such as temperature, pH, ionic strength and electrostatic potentials. The dielectric constant of the apolar region of the lipid bilayer contrasts with that of the polar region, which also differs from the aqueous milieu, and these changes happen in the nanometer scale. Besides, an important percentage of the lipids are anionic, and the rest are dipoles or higher multipoles, and the polar regions are highly hydrated, with these water molecules forming an active part of the membrane. Therefore, electric fields (both, internal and external) affects membrane thickness, density, tension and curvature, and conversely, mechanical deformations modify membrane electrostatics. As a consequence, interfacial electrostatics appears as a highly important parameter, affecting the membrane properties in general and mechanical features in particular. In this review we focus on the electromechanical behavior of lipid and cell membranes, the physicochemical origin and the biological implications, with emphasis in signal propagation in nerve cells.

Protonic conductor: better understanding neural resting and action potential

With the employment of the transmembrane electrostatic proton localization theory with a new membrane potential equation, neural resting and action potential is now much better understood as the voltage contributed by the localized protons/cations at a neural liquid- membrane interface. Accordingly, the neural resting/action potential is essentially a protonic/cationic membrane capacitor behavior. It is now understood with a newly formulated action potential equation: when action potential is <0 (negative number), the localized protons/cations charge density at the liquid-membrane interface along the periplasmic side is >0 (positive number); when the action potential is >0, the concentration of the localized protons and localized nonproton cations is <0, indicating a "depolarization" state. The nonlinear curve of the localized protons/cations charge density in the real-time domain of an action potential spike appears as an inverse mirror image to the action potential. The newly formulated action potential equation provides biophysical insights for neuron electrophysiology, which may represent a complementary development to the classic Goldman-Hodgkin-Katz equation. With the use of the action potential equation, the biological significance of axon myelination is now also elucidated as to provide protonic insulation and prevent any ions both inside and outside of the neuron from interfering with the action potential signal, so that the action potential can quickly propagate along the axon with minimal (e.g., 40 times less) energy requirement.NEW & NOTEWORTHY The newly formulated action potential equation provides biophysical insights for neuron electrophysiology, which may represent a complementary development to the classic Goldman-Hodgkin-Katz equation. The nonlinear curve of the localized protons/cations charge density in the real-time domain of an action potential spike appears as an inverse mirror image to the action potential. The biological significance of axon myelination is now elucidated as to provide protonic insulation and prevent any ions from interfering with action potential signal.

Discrete Helmholtz model: a single layer of correlated counter-ions. Metal oxides and silica interfaces, ion-exchange and biological membranes

The mechanism by which interfaces in solution can be polarised depends on the nature of the charge carriers. In the case of a conductor, the charge carriers are electrons and the polarisation is homogeneous in the plane of the electrode. In the case of an insulator covered by ionic moieties, the polarisation is inhomogeneous and discrete in the plane of the interface. Despite these fundamental differences, these systems are usually treated in the same theoretical framework that relies on the Poisson-Boltzmann equation for the solution side. In this perspective, we show that interfaces polarised by discrete charge distributions are rather ubiquitous and that their associated potential drop significantly differs from those of conductor-electrolyte interfaces. We show that these configurations, spanning liquid-liquid interfaces, charged silica-water interfaces, metal oxide interfaces, supercapacitors, ion-exchange membranes and even biological membranes can be uniformly treated under a common "Discrete Helmholtz" model where the discrete charges are compensated by a single layer of correlated counter-ions, thereby generating a sharp potential drop at the interface.

Cells in New Light: Ion Concentration, Voltage, and Pressure Gradients across a Hydrogel Membrane

The ionic compositions of the intra- and extracellular environments are distinct from one another, with K⁺ being the main cation in the cytosol and Na⁺ being the most abundant cation outside of the cell. Specific ions can permeate into and out of the cell at different rates, bringing about uneven distribution of charges and development of negative electric potential inside the cell. Each healthy cell must maintain a specific ion concentration gradient and voltage. To account for these functions, various ionic pumps and channels located within the cell membrane have been invoked. In this work, we use a porous alginate hydrogel as a model gelatinous network representing the plant cell wall or cytoskeleton of the animal cell. We show that the gel barrier is able to maintain a stable separation of ionic solutions of different ionic strengths and chemical compositions without any pumping activity. For the Na⁺/K⁺ concentration gradient sustained across the barrier, a negative electric potential develops within the K⁺-rich side. The situation is reminiscent of that in the cell. Furthermore, also the advective flow of water molecules across the gel barrier is restricted, despite the gel's large pores and the osmotic or hydrostatic pressure gradients across it. This feature has important implications for osmoregulation. We propose a mechanism in which charge separation and electric fields developing across the permselective (gel) membrane prevent ion and bulk fluid flows ordinarily driven by chemical and pressure gradients.

GHK eq. and HH eq. for a real system is mathematically associable to each other but their physiological interpretation needs a reconsideration

Despite the long and broad acceptance of the Goldman - Hodgkin - Katz equation (GHK eq.) and the Hodgkin - Huxley equation (HH eq.) as strong tools for the quantitative analysis of the membrane potential behavior, for a long time they have been utilized as separate concepts. That is the GHK eq. and the HH eq. have not been associated with each other mathematically. In this paper, an attempt to associate these equations to each other mathematically was demonstrated and was successful by viewing the system in question as a thermodynamically real system rather than an ideal system. For achieving that, two fundamental physical chemistry concepts, the mass action law, and the Boltzmann distribution were employed. Hence, this paper's achievement is completely within the framework of common thermodynamics. Through this work, the origin of the membrane potential generation attributed to the ion adsorption-desorption process and governed by the mass action law and the Boltzmann distribution is expressed to be plausible, whereas the existing membrane potential generation mechanism states that membrane potential is generated by transmembrane ion transport. As at this moment, this work does not intend to deny the transmembrane ion transport as a membrane potential generation mechanism but urges the readers to reconsider its validity, since this work suggests that the ion adsorption-desorption mechanism is as plausible as the transmembrane ion transport mechanism as a cause of membrane potential generation.

Cellular metabolism and colloids: Realistically linking physiology and biological physical chemistry

Important concepts from colloidal physical chemistry such as coacervation, phase transitions, emergent properties and ionic association, are currently emerging in the lexicon of cellular biology, prompted mostly by recent experimental observations of liquid phase coexistence in the cell cytosol. Nevertheless, from an historical point of view, the application of these concepts in cell biology is not new. They were key concepts into the so-called protoplasmic doctrine, an alternative (and largely forgotten) approach to cell physiology. The most complete theory originating from this line of thinking was the Association-Induction Hypothesis (AIH), introduced by Gilbert N. Ling in 1962. The AIH, which envisions living cells as complex dynamical colloidal systems, provides ample theory and experimental evidence to call into question the now dominant view of living cells as fluid-filled vesicles. This review attempts to present and discuss the usefulness of the AIH to understand a series of experimental observations from our laboratory from living suspensions of the yeast Saccharomyces cerevisiae exhibiting glycolytic oscillations. Particularly, the AIH helped us integrate, in a mechanistic sense, the basis of a strong temporal coupling observed between ATP and a series of cellular properties such as intracellular water dipolar relaxation, intracellular K⁺ concentration, among many others, where the colloidal physical chemistry of the cell interior plays a fundamental role.