Collision of two action potentials in a single excitable cell

Advances in using ultrasound to regulate the nervous system

Ultrasound is a mechanical vibration with a frequency greater than 20 kHz. Due to its high spatial resolution, good directionality, and convenient operation in neural regulation, it has recently received increasing attention from scientists. However, the mechanism by which ultrasound regulates the nervous system is still unclear. This article mainly explores the possible mechanisms of ultrasound's mechanical effects, cavitation effects, thermal effects, and the rise of sonogenetics. In addition, the essence of action potential and its relationship with ultrasound were also discussed. Traditional theory treats nerve impulses as pure electrical signals, similar to cable theory. However, this theory cannot explain the phenomenon of inductance and cell membrane bulging out during the propagation of action potential. Therefore, the flexoelectric effect of cell membrane and soliton model reveal that action potential may also be a mechanical wave. Finally, we also elaborated the therapeutic effect of ultrasound on nervous system disease such as epilepsy, Parkinson's disease, and Alzheimer's disease.

Thinking about the action potential: the nerve signal as a window to the physical principles guiding neuronal excitability

Ever since the work of Edgar Adrian, the neuronal action potential has been considered as an electric signal, modeled and interpreted using concepts and theories lent from electronic engineering. Accordingly, the electric action potential, as the prime manifestation of neuronal excitability, serving processing and reliable "long distance" communication of the information contained in the signal, was defined as a non-linear, self-propagating, regenerative, wave of electrical activity that travels along the surface of nerve cells. Thus, in the ground-breaking theory and mathematical model of Hodgkin and Huxley (HH), linking Nernst's treatment of the electrochemistry of semi-permeable membranes to the physical laws of electricity and Kelvin's cable theory, the electrical characteristics of the action potential are presented as the result of the depolarization-induced, voltage- and time-dependent opening and closure of ion channels in the membrane allowing the passive flow of charge, particularly in the form of Na+ and K+ -ions, into and out of the neuronal cytoplasm along the respective electrochemical ion gradient. In the model, which treats the membrane as a capacitor and ion channels as resistors, these changes in ionic conductance across the membrane cause a sudden and transient alteration of the transmembrane potential, i.e., the action potential, which is then carried forward and spreads over long(er) distances by means of both active and passive conduction dependent on local current flow by diffusion of Na+ ion in the neuronal cytoplasm. However, although highly successful in predicting and explaining many of the electric characteristics of the action potential, the HH model, nevertheless cannot accommodate the various non-electrical physical manifestations (mechanical, thermal and optical changes) that accompany action potential propagation, and for which there is ample experimental evidence. As such, the electrical conception of neuronal excitability appears to be incomplete and alternatives, aiming to improve, extend or even replace it, have been sought for. Commonly misunderstood as to their basic premises and the physical principles they are built on, and mistakenly perceived as a threat to the generally acknowledged explanatory power of the "classical" HH framework, these attempts to present a more complete picture of neuronal physiology, have met with fierce opposition from mainstream neuroscience and, as a consequence, currently remain underdeveloped and insufficiently tested. Here we present our perspective that this may be an unfortunate state of affairs as these different biophysics-informed approaches to incorporate also non-electrical signs of the action potential into the modeling and explanation of the nerve signal, in our view, are well suited to foster a new, more complete and better integrated understanding of the (multi)physical nature of neuronal excitability and signal transport and, hence, of neuronal function. In doing so, we will emphasize attempts to derive the different physical manifestations of the action potential from one common, macroscopic thermodynamics-based, framework treating the multiphysics of the nerve signal as the inevitable result of the collective material, i.e., physico-chemical, properties of the lipid bilayer neuronal membrane (in particular, the axolemma) and/or the so-called ectoplasm or membrane skeleton consisting of cytoskeletal protein polymers, in particular, actin fibrils. Potential consequences for our view of action potential physiology and role in neuronal function are identified and discussed.

Bioelectricity in Developmental Patterning and Size Control: Evidence and Genetically Encoded Tools in the Zebrafish Model

Developmental patterning is essential for regulating cellular events such as axial patterning, segmentation, tissue formation, and organ size determination during embryogenesis. Understanding the patterning mechanisms remains a central challenge and fundamental interest in developmental biology. Ion-channel-regulated bioelectric signals have emerged as a player of the patterning mechanism, which may interact with morphogens. Evidence from multiple model organisms reveals the roles of bioelectricity in embryonic development, regeneration, and cancers. The Zebrafish model is the second most used vertebrate model, next to the mouse model. The zebrafish model has great potential for elucidating the functions of bioelectricity due to many advantages such as external development, transparent early embryogenesis, and tractable genetics. Here, we review genetic evidence from zebrafish mutants with fin-size and pigment changes related to ion channels and bioelectricity. In addition, we review the cell membrane voltage reporting and chemogenetic tools that have already been used or have great potential to be implemented in zebrafish models. Finally, new perspectives and opportunities for bioelectricity research with zebrafish are discussed.

The thermodynamic theory of action potential propagation: a sound basis for unification of the physics of nerve impulses

The thermodynamic theory of action potential propagation challenges the conventional understanding of the nerve signal as an exclusively electrical phenomenon. Often misunderstood as to its basic tenets and predictions, the thermodynamic theory is virtually ignored in mainstream neuroscience. Addressing a broad audience of neuroscientists, we here attempt to stimulate interest in the theory. We do this by providing a concise overview of its background, discussion of its intimate connection to Albert Einstein's treatment of the thermodynamics of interfaces and outlining its potential contribution to the building of a physical brain theory firmly grounded in first principles and the biophysical reality of individual nerve cells. As such, the paper does not attempt to advocate the superiority of the thermodynamic theory over any other approach to model the nerve impulse, but is meant as an open invitation to the neuroscience community to experimentally test the assumptions and predictions of the theory on their validity.

Shock and detonation waves at an interface and the collision of action potentials

Action potentials in neurons are known to annihilate each other upon collision, while there are cases where they might penetrate each other. The fate of two waves upon collision is critically dependent on the underlying mechanism of propagation and therefore an understanding of possible outcomes of collision under different conditions is important. Previously, compression waves that travel within the plasma membrane of a neuron have been proposed as a thermodynamic basis for the propagation of action potentials. In this context, it was recently shown that two-dimensional compressive shock waves in the model system of lipid monolayers behave strikingly similar to action potentials in neurons and can even annihilate each other upon head-on collision. However, even a qualitative mechanism remained unclear. To this end, we summarise the fundamentals of shock physics as applied to an interface and recap how it explained the observation of threshold and saturation of shockwaves in the lipid monolayer (all - or - none). We then compare the theory with the soliton model that has the same fundamental premise, i.e. the conservation laws and thermodynamics, and was previously proposed as a model for the nerve pulse propagation. We elaborate on how the two approaches make different predictions with regards to collisions and the detailed structure of the wave-front. As a case study and a new qualitative result, we finally show that previously unexplained annihilation of shock waves in the lipid monolayer is a direct consequence of the nature of state changes, i.e. jump conditions, within these shockwaves.

The living state: How cellular excitability is controlled by the thermodynamic state of the membrane

The thermodynamic (TD) properties of biological membranes play a central role for living systems. It has been suggested, for instance, that nonlinear pulses such as action potentials (APs) can only exist if the membrane state is in vicinity of a TD transition. Herein, two membrane properties in living systems - excitability and velocity - are analyzed for a broad spectrum of conditions (temperature (T), 3D-pressure (p) and pH-dependence). Based on experimental data from Characean cells and a review of literature we predict parameter ranges in which a transition of the membrane is located (15-35°C below growth temperature; 1-3pH units below pH7; at ∼800atm) and propose the corresponding phase diagrams. The latter explain: (i) changes of AP velocity with T,p and pH.(ii) The existence and origin of two qualitatively different forms of loss of nonlinear excitability ("nerve block", anesthesia). (iii) The type and quantity of parameter changes that trigger APs. Finally, a quantitative comparison between the TD behavior of 2D-lipid model membranes with living systems is attempted. The typical shifts in transition temperature with pH and p of model membranes agree with values obtained from cell physiological measurements. Taken together, these results suggest that it is not specific molecules that control the excitability of living systems but rather the TD properties of the membrane interface. The approach as proposed herein can be extended to other quantities (membrane potential, calcium concentration, etc.) and makes falsifiable predictions, for example, that a transition exists within the specified parameter ranges in excitable cells.

Electrophysiological-mechanical coupling in the neuronal membrane and its role in ultrasound neuromodulation and general anaesthesia

The current understanding of the role of the cell membrane is in a state of flux. Recent experiments show that conventional models, considering only electrophysiological properties of a passive membrane, are incomplete. The neuronal membrane is an active structure with mechanical properties that modulate electrophysiology. Protein transport, lipid bilayer phase, membrane pressure and stiffness can all influence membrane capacitance and action potential propagation. A mounting body of evidence indicates that neuronal mechanics and electrophysiology are coupled, and together shape the membrane potential in tight coordination with other physical properties. In this review, we summarise recent updates concerning electrophysiological-mechanical coupling in neuronal function. In particular, we aim at making the link with two relevant yet often disconnected fields with strong clinical potential: the use of mechanical vibrations-ultrasound-to alter the electrophysiogical state of neurons, e.g., in neuromodulation, and the theories attempting to explain the action of general anaesthetics. STATEMENT OF SIGNIFICANCE: General anaesthetics revolutionised medical practice; now an apparently unrelated technique, ultrasound neuromodulation-aimed at controlling neuronal activity by means of ultrasound-is poised to achieve a similar level of impact. While both technologies are known to alter the electrophysiology of neurons, the way they achieve it is still largely unknown. In this review, we argue that in order to explain their mechanisms/effects, the neuronal membrane must be considered as a coupled mechano-electrophysiological system that consists of multiple physical processes occurring concurrently and collaboratively, as opposed to sequentially and independently. In this framework the behaviour of the cell membrane is not the result of stereotypical mechanisms in isolation but instead emerges from the integrative behaviour of a complexly coupled multiphysics system.

Collision and annihilation of nonlinear sound waves and action potentials in interfaces

Nerve impulses, previously proposed as manifestations of nonlinear acoustic pulses localized at the plasma membrane, can annihilate upon collision. However, whether annihilation of acoustic waves at interfaces takes place is unclear. We previously showed the propagation of nonlinear sound waves that propagate as solitary waves above a threshold (super-threshold) excitation in a lipid monolayer near a phase transition. Here we investigate the interaction of these waves. Sound waves were excited mechanically via a piezo cantilever in a lipid monolayer at the air-water interface and their amplitude is reported before and after a collision. The compression amplitude was observed via Förster resonance energy transfer between donor and acceptor dyes, measured at fixed points along the propagation path in the lipid monolayer. We provide direct experimental evidence for the annihilation of two super-threshold interfacial pulses upon head-on collision in a lipid monolayer and conclude that sound waves propagating in a lipid interface can interact linearly, nonlinearly, or annihilate upon collision depending on the state of the system. Thus we show that the main characteristics of nerve impulses, i.e. solitary character, velocity, couplings, all-or-none behaviour, threshold and even annihilation are also demonstrated by nonlinear sound waves in a lipid monolayer, where they follow directly from the thermodynamic principles applied to an interface. As these principles are equally unavoidable in a nerve membrane, our observations strongly suggest that the underlying physical basis of action potentials and the observed nonlinear-pules is identical.

Computational model of the mechanoelectrophysiological coupling in axons with application to neuromodulation

For more than half a century, the action potential (AP) has been considered a purely electrical phenomenon. However, experimental observations of membrane deformations occurring during APs have revealed that this process also involves mechanical features. This discovery has recently fuelled a controversy on the real nature of APs: whether they are mechanical or electrical. In order to examine some of the modern hypotheses regarding APs, we propose here a coupled mechanoelectrophysiological membrane finite-element model for neuronal axons. The axon is modeled as an axisymmetric thin-wall cylindrical tube. The electrophysiology of the membrane is modeled using the classic Hodgkin-Huxley (H-H) equations for the Nodes of Ranvier or unmyelinated axons and the cable theory for the internodal regions, whereas the axonal mechanics is modeled by means of viscoelasticity theory. Membrane potential changes induce a strain gradient field via reverse flexoelectricity, whereas mechanical pulses result in an electrical self-polarization field following the direct flexoelectric effect, in turn influencing the membrane potential. Moreover, membrane deformation also alters the values of membrane capacitance and resistance in the H-H equation. These three effects serve as the fundamental coupling mechanisms between the APs and mechanical pulses in the model. A series of numerical studies was systematically conducted to investigate the consequences of interaction between the APs and mechanical waves on both myelinated and unmyelinated axons. Simulation results illustrate that the AP is always accompanied by an in-phase propagating membrane displacement of ≈1nm, whereas mechanical pulses with enough magnitude can also trigger APs. The model demonstrates that mechanical vibrations, such as the ones arising from ultrasound stimulations, can either annihilate or enhance axonal electrophysiology depending on their respective directionality and frequency. It also shows that frequency of pulse repetition can also enhance signal propagation independently of the amplitude of the signal. This result not only reconciles the mechanical and electrical natures of the APs but also provides an explanation for the experimentally observed mechanoelectrophysiological phenomena in axons, especially in the context of ultrasound neuromodulation.

Experimental and Computational Studies on the Basic Transmission Properties of Electromagnetic Waves in Softmaterial Waveguides

Conventional waveguides are usually made of metallic materials, and they are effective pathways for the transmission of electromagnetic waves. A “Softmaterial waveguide”, by contrast, is supposed to be made of dielectric material and ionic fluids. In this work, by means of both experiment and computational simulation we examined one kind of softmaterial waveguide, which has the configuration of ionic fluids filled in and out of a dielectric tube. We investigated configurations with varied parameters, i.e., tube thickness from 0.2 mm to 5.0 mm, tube length of 2.0–12.0 cm, ionic concentration covering 4 orders of magnitude from 0.0002–2.0 mol/L, frequency of 10 Hz to 100 MHz for sine wave excitations, pulse duration of 5 ns to 100 ms for excitation pulses. We also mimicked the myelin sheath structure in myelinated axons in simulation. Both experimental and simulation results consistently showed a clear confinement effect for the energy flux of transmitting electromagnetic waves inside the dielectric tube, strongly supporting the model of softmaterail waveguide. The results revealed that the softmaterial waveguide had a low-pass nature, where the intensity of transmitted signals saturated at a duration of 10–100 μs for pulses, or cut off at frequency of 10–100 kHz for sine waves. And, the transmission efficiency increased with the thickness of the dielectric layer, as well as ion concentration of the solution. The results may help for a better understanding various electrical communication behaviors observed in biosystems, where a natural lipid membrane with bilateral fluids was suggested as the efficient pathway for pulsed neural impulses in a way similar to soliton-like electromagnetic pulses transmitting in a softmaterial waveguide.