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.

Questioning rotary functionality in the bacterial flagellar system and proposing a murburn model for motility.

Bacterial flagellar system (BFS) was the primary example of a purported 'rotary-motor' functionality in a natural assembly. This mandates the translation of a circular motion of components inside into a linear displacement of the cell body outside, which is supposedly orchestrated with the following features of the BFS: (i) A chemical/electrical differential generates proton motive force (pmf, including a trans-membrane potential, TMP), which is electro-mechanically transduced by inward movement of protons via BFS. (ii) Membrane-bound proteins of BFS serve as stators and the slender filament acts as an external propeller, culminating into a hook-rod that pierces the membrane to connect to a 'broader assembly of deterministically movable rotor'. We had disclaimed the purported pmf/TMP-based respiratory/photosynthetic physiology involving Complex V, which was also perceived as a 'rotary machine' earlier. We pointed out that the murburn redox logic was operative therein. We pursue the following similar perspectives in BFS-context: (i) Low probability for the evolutionary attainment of an ordered/synchronized teaming of about two dozen types of proteins (assembled across five-seven distinct phases) towards the singular agendum of rotary motility. (ii) Vital redox activity (not the gambit of pmf/TMP!) powers the molecular and macroscopic activities of cells, including flagella. (iii) Flagellar movement is noted even in ambiances lacking/countering the directionality mandates sought by pmf/TMP. (iv) Structural features of BFS lack component(s) capable of harnessing/achieving pmf/TMP and functional rotation. A viable murburn model for conversion of molecular/biochemical activity into macroscopic/mechanical outcomes is proposed herein for understanding BFS-assisted motility. HIGHLIGHTSThe motor-like functionalism of bacterial flagellar system (BFS) is analyzedProton/Ion-differential based powering of BFS is unviable in bacteriaUncouplers-sponsored effects were misinterpreted, resulting in a detour in BFS researchThese findings mandate new explanation for nano-bio-mechanical movements in BFSA minimalist murburn model for the bacterial flagella-aided movement is proposedCommunicated by Ramaswamy H. Sarma.

Na,K-ATPase: A murzyme facilitating thermodynamic equilibriums at the membrane-interface.

The redox metabolic paradigm of murburn concept advocates that diffusible reactive species (DRS, particularly oxygen-centric radicals) are mainstays of physiology, and not mere pathological manifestations. The murburn purview of cellular function also integrates the essential principles of bioenergetics, thermogenesis, homeostasis, electrophysiology, and coherence. In this context, any enzyme that generates/modulates/utilizes/sustains DRS functionality is called a murzyme. We have demonstrated that several water-soluble (peroxidases, lactate dehydrogenase, hemogoblin, etc.) and membrane-embedded (Complexes I-V in mitochondria, Photosystems I/II in chloroplasts, rhodopsin/transducin in rod cells, etc.) proteins serve as murzymes. The membrane protein of Na,K-ATPase (NKA, also known as sodium-potassium pump) is the focus of this article, owing to its centrality in neuro-cardio-musculo electrophysiology. Herein, via a series of critical queries starting from the geometric/spatio-temporal considerations of diffusion/mass transfer of solutes in cells to an update on structural/distributional features of NKA in diverse cellular systems, and from various mechanistic aspects of ion-transport (thermodynamics, osmoregulation, evolutionary dictates, etc.) to assays/explanations of inhibitory principles like cardiotonic steroids (CTS), we first highlight some unresolved problems in the field. Thereafter, we propose and apply a minimalist murburn model of trans-membrane ion-differentiation by NKA to address the physiological inhibitory effects of trans-dermal peptide, lithium ion, volatile anesthetics, confirmed interfacial DRS + proton modulators like nitrophenolics and unsaturated fatty acid, and the diverse classes of molecules like CTS, arginine, oximes, etc. These explanations find a pan-systemic connectivity with the inhibitions/uncouplings of other membrane proteins in cells.

The physiological role of complex V in ATP synthesis: Murzyme functioning is viable whereas rotary conformation change model is untenable.

Complex V or FoF1-ATPase is a multimeric protein found in bioenergetic membranes of cells and organelles like mitochondria/chloroplasts. The popular perception on Complex V deems it as a reversible molecular motor, working bi-directionally (breaking or making ATP) via a conformation-change based chemiosmotic rotary ATP synthesis (CRAS) mechanism, driven by proton-gradients or trans-membrane potential (TMP). In continuance of our pursuits against the CRAS model of cellular bioenergetics, herein we demonstrate the validity of the murburn model based in diffusible reactive (oxygen) species (DRS/DROS). Supported by new in silico derived data (that there are ∼12 adenosine nucleotide binding sites on the F1 bulb and not merely 3 sites, as perceived earlier), available structural information, known experimental observations, and thermodynamic/kinetic considerations (that de-solvation of protons from hydronium ions is facile), we deduce that Complex V serves as a physiological chemostat and a murzyme (enzyme working via murburn scheme, employing DRS). That is- Complex V uses ATP (via consumption at ε or proteins of F1 module) as a Michaelis-Menten substrate to serve as a pH-stat by inletting protons via the c-ring of Fo module. Physiologically, Complex V also functions as a murzyme by presenting ADP/Pi (or their reaction intermediates) on the αß bulb, thereby enabling greater opportunities for DRS/proton-assisted ATP formation. Thus, the murburn paradigm succeeds the CRAS hypothesis for explaining the role of oxygen in mitochondrial physiologies of oxidative phosphorylation, thermogenesis, TMP and homeostasis.Communicated by Ramaswamy H. Sarma.

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.

Murburn model of vision: Precepts and proof of concept.

The classical paradigm of visual physiology comprises of the following features: (i) rod/cone cells located at the rear end of the retina serve as the primary transducers of incoming photo-information, (ii) cis-trans retinal (C20 H28 O) transformations on rhodopsin act as the transduction switch to generate a transmittable signal, (iii) signal amplification occurs via GDP-GTP exchange at transducin, and (iv) the amplified signal is relayed (as an action potential) as a flux-based ripple of Na-K ions along the axons of neurons. Fundamental physical principles, chemical kinetics, and awareness of architecture of eye/retina prompt a questioning of these classical assumptions. In lieu, based on experimental and in silico findings, a simple space-time resolved murburn model for the physiology of phototransduction in the retina is presented wherein molecular oxygen plays key roles. It is advocated that: (a) photo-induced oxygen to superoxide conversion serves as the key step in signal transduction in the visual cycle, (b) all photoactive cells of the retina serve as photoreceptors and rods/cones serve as the ultimate electron source in the retina (deriving oxygen and nutrients from retinal pigmented epithelium), (c) signal amplification is through superoxide mediated phosphorylation of GDP bound to inactive transducin, thereby activating a GDP-based cascade (a new mechanism for trimeric G-proteins), and (d) signal relay is primarily an electron movement along the neuron, from dendritic source to synaptic sink. In particular, we specify the roles for the various modules of transducin and GDP-based activation of phosphodiesterase-6 in the physiology of visual transduction.

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.

The murburn precepts for cellular ionic homeostasis and electrophysiology.

Starting from the basic molecular structure and redox properties of its components, we build a macroscopic cellular electrophysiological model. We first present a murburn purview that could explain ion distribution in bulk-milieu/membrane-interface and support the origin of trans-membrane potential (TMP) in cells. In particular, the discussion focuses on how cells achieve disparity in the distribution of monovalent and divalent cations within (K+ > Na+ > Mg2+ > Ca2+ ) and outside (Na+ > K+ > Ca2+ > Mg2+ ). We explore how TMP could vary for resting/graded/action potentials generation and project a model for impulse conduction in neurons. Outcomes based on murburn bioenergetic equilibriums leading to solubilization of ion-pairs, membrane's permittivity, protein channels' fluxes, and proteins' innate ability to bind/adsorb ions selectively are projected as the integral rationale. We also provide experimental modalities to ratify the projections.

Analyses of HH and GHK equations with another perspective: Can ion adsorption also govern trans-membrane potential?

Two mathematically distinct physiological concepts, the Goldman-Hodgkin-Katz eq. (GHK eq.) and the Hodgkin-Huxley model (HH model) were successfully associated with each other in a prior work. The previous work was performed on the following premises (i) The membrane potential is generated by ion adsorption, as opposed to the classical ion transport mechanisms, (ii) The living cell is a thermodynamically real system rather than an ideal system, and (iii) The conductance employed in the HH model is replaced by the ion activity coefficient, which is weighted with the role of conductance. Consequently, the GHK eq. was mathematically associated with the HH model through the intermediary of Boltzmann ion distribution and mass action law. To verify if our theoretical formularization could afford a physiologically, physically and chemically viable model, we performed computational analysis using the formulae (quantitative correlations between various variables) we derived in the previous work. The computational results obtained through associating the GHK eq. with the HH model validated our model and its predictions. This outcome suggests that the current prevailing physiological concepts could be expanded further, to incorporate the newly proposed mechanisms. That is, GHK eq. and HH model could be interpreted via another set of founding principles that incorporate the ubiquitous phenomena of ion-adsorption.

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.

The need for reconsideration of a mechanism of membrane potential generation using Ling's adsorption theory.

Membrane theory attributes the mechanism of generation of membrane potential to transmembrane ion transport, and is typified by the Goldman-Hodgkin-Katz equation (GHK eq.). Despite broad acceptance of the GHK eq. in physiology, it seems unable to explain some characteristics of the membrane potential. The long-underrated Ling's adsorption theory (LA theory) is another mechanism for membrane potential generation. The LA theory attributes the generation mechanism of the membrane potential to an ion adsorption-desorption process. Although the LA theory has not been seriously considered up until today, there are no serious defects in it as a membrane potential generation mechanism. In this work, the authors explain problematic facets of membrane theory from the view of the GHK eq. We propose an alternative concept based on the LA theory that addresses problematic issues with membrane theory. Consequently, an ion adsorption-desorption process could be a genuine mechanism of membrane potential generation as predicted by the LA theory.

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.

Mathematical expression of membrane potential based on Ling's adsorption theory is approximately the same as the Goldman-Hodgkin-Katz equation.

The Goldman-Hodgkin-Katz equation (GHK equation), one of the most successful achievements of membrane theory in electrophysiology, can precisely predict the membrane potential. Its conceptual foundation lies in the idea that the transmembrane ion transport across the plasma membrane is responsible for the membrane potential generation. However, the potential virtually equivalent to the membrane potential is generated even across the impermeable membrane. In this work, I discus the membrane potential generation mechanism and find that the potential formula based on the long-dismissed Ling's adsorption theory, which attributes the membrane potential generation to the mobile ion adsorption rather than the transmembrane ion transport, is the same as the GHK equation. Based on this finding, I derive a conclusion that the membrane potential is generated by the ion adsorption against the existing electrophysiological concept.

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

According to standard membrane theory, the generation of membrane potential is attributed to transmembrane ion transport. However, there have been a number of reports of membrane behavior in conflict with the membrane theory of cellular potential. Putting aside the membrane theory, we scrutinized the generation mechanism of membrane potential from the view of the long-dismissed adsorption theory of Ling. Ling's adsorption theory attributes the membrane potential generation to mobile ion adsorption. Although Ling's adsorption theory conflicts with the broadly accepted membrane theory, we found that it well reproduces experimentally observed membrane potential behavior. Our theoretical analysis finds that the potential formula based on the GHK eq., which is a fundamental concept of membrane theory, coincides with the potential formula based on Ling's adsorption theory. Reinterpreting the permeability coefficient in the GHK eq. as the association constant between the mobile ion and adsorption site, the GHK eq. turns into the potential formula from Ling's adsorption theory. We conclude that the membrane potential is generated by ion adsorption as Ling's adsorption theory states and that the membrane theory of cellular potential should be amended even if not discarded.

Generation of membrane potential beyond the conceptual range of Donnan theory and Goldman-Hodgkin-Katz equation.

Donnan theory and Goldman-Hodgkin-Katz equation (GHK eq.) state that the nonzero membrane potential is generated by the asymmetric ion distribution between two solutions separated by a semipermeable membrane and/or by the continuous ion transport across the semipermeable membrane. However, there have been a number of reports of the membrane potential generation behaviors in conflict with those theories. The authors of this paper performed the experimental and theoretical investigation of membrane potential and found that (1) Donnan theory is valid only when the macroscopic electroneutrality is sufficed and (2) Potential behavior across a certain type of membrane appears to be inexplicable on the concept of GHK eq. Consequently, the authors derived a conclusion that the existing theories have some limitations for predicting the membrane potential behavior and we need to find a theory to overcome those limitations. The authors suggest that the ion adsorption theory named Ling's adsorption theory, which attributes the membrane potential generation to the mobile ion adsorption onto the adsorption sites, could overcome those problems.

Ling's Adsorption Theory as a Mechanism of Membrane Potential Generation Observed in Both Living and Nonliving Systems.

The potential between two electrolytic solutions separated by a membrane impermeable to ions was measured and the generation mechanism of potential measured was investigated. From the physiological point of view, a nonzero membrane potential or action potential cannot be observed across the impermeable membrane. However, a nonzero membrane potential including action potential-like potential was clearly observed. Those observations gave rise to a doubt concerning the validity of currently accepted generation mechanism of membrane potential and action potential of cell. As an alternative theory, we found that the long-forgotten Ling's adsorption theory was the most plausible theory. Ling's adsorption theory suggests that the membrane potential and action potential of a living cell is due to the adsorption of mobile ions onto the adsorption site of cell, and this theory is applicable even to nonliving (or non-biological) system as well as living system. Through this paper, the authors emphasize that it is necessary to reconsider the validity of current membrane theory and also would like to urge the readers to pay keen attention to the Ling's adsorption theory which has for long years been forgotten in the history of physiology.

Membrane potential generated by ion adsorption.

It has been widely acknowledged that the Goldman-Hodgkin-Katz (GHK) equation fully explains membrane potential behavior. The fundamental facet of the GHK equation lies in its consideration of permeability of membrane to ions, when the membrane serves as a separator for separating two electrolytic solutions. The GHK equation describes that: variation of membrane permeability to ion in accordance with ion species results in the variation of the membrane potential. However, nonzero potential was observed even across the impermeable membrane (or separator) separating two electrolytic solutions. It gave rise to a question concerning the validity of the GHK equation for explaining the membrane potential generation. In this work, an alternative theory was proposed. It is the adsorption theory. The adsorption theory attributes the membrane potential generation to the ion adsorption onto the membrane (or separator) surface not to the ion passage through the membrane (or separator). The computationally obtained potential behavior based on the adsorption theory was in good agreement with the experimentally observed potential whether the membrane (or separator) was permeable to ions or not. It was strongly speculated that the membrane potential origin could lie primarily in the ion adsorption on the membrane (or separator) rather than the membrane permeability to ions. It might be necessary to reconsider the origin of membrane potential which has been so far believed explicable by the GHK equation.

Experimental estimate of viscoelastic properties for ionic polymer-metal composites.

We propose an experimental method for estimating the general time-dependent elastic moduli of ionic polymer-metal composites (IPMCs). The materials exhibit fast and large bending motion even when a small voltage about 1 V is applied, and are expected to be used for polymer actuators. Experimental measurements for an IPMC beam of silver plated Nafion are given to demonstrate the usefulness of the proposed method. For the IPMC beam we also present a viscoelastic model, which describes the experimental results successfully.

An interpretation of amphoteric gel hardness variation through potential and hardness measurement.

The hardness variation of amphoteric gel according to the surrounding solution conditions is quite unique. It hardens and softens reversibly regardless of its molecular network density. But this has been understood merely qualitatively. For the purpose of elucidation of the details of its behavior, we performed quantitative potential and hardness measurements on it. We observed the constant potential of amphoteric gels, approximately -60 mV, regardless of their swelling ratio and hardness. Such observations can be interpreted as the maintenance of the constant charge density of *COO- for any amphoteric gel, and they are further interpreted as intermolecular salt-linkage formation/disruption dominating the hardness of amphoteric gels.

Extension of Colacicco's experiment supporting the adsorption theory.

The pervasive concept of the cause of the potential occurring across a semipermeable membrane intervening between two ionic solutions is called the membrane theory; hence, this potential is called the membrane potential. Although almost nobody has doubted its validity, research results defying it have been continuously reported by a small number of researchers. They have claimed that the cause the potential lies in the adsorption of ions onto adsorption sites, which is the adsorption theory. One such research report by G. Colacicco (Nature 207 (1965) 936) was employed for our experimental work reported in this paper in order to examine the validity of the membrane theory and the adsorption theory. The results we obtained are in conflict with the membrane theory but appear to be in full agreement with the long dismissed adsorption theory. This paper urges the reexamination of the membrane theory and the reconsideration of the adsorption theory from a nonbiased standpoint.