Mechanical surface waves accompany action potential propagation

(2+δ)-dimensional theory of the electromechanics of lipid membranes: Electrostatics

The coupling of electric fields to the mechanics of lipid membranes gives rise to intriguing electromechanical behavior, as, for example, evidenced by the deformation of lipid vesicles in external electric fields. Electromechanical effects are relevant for many biological processes, such as the propagation of action potentials in axons and the activation of mechanically gated ion channels. Currently, a theoretical framework describing the electromechanical behavior of arbitrarily curved and deforming lipid membranes does not exist. Purely mechanical models commonly treat lipid membranes as two-dimensional surfaces, ignoring their finite thickness. While holding analytical and numerical merit, this approach cannot describe the coupling of lipid membranes to electric fields and is thus unsuitable for electromechanical models. In a sequence of articles, we derive an effective surface theory of the electromechanics of lipid membranes, called the (2+δ)-dimensional theory, which has the advantages of surface descriptions while accounting for finite thickness effects. The present article proposes a generic dimension reduction procedure relying on low-order spectral expansions. This procedure is applied to the electrostatics of lipid membranes to obtain the (2+δ)-dimensional theory that captures potential differences across and electric fields within lipid membranes. This model is tested on different geometries relevant for lipid membranes, showing good agreement with the corresponding three-dimensional electrostatics theory.

Neurocomputational mechanisms underlying perception and sentience in the neocortex

The basis for computation in the brain is the quantum threshold of "soliton," which accompanies the ion changes of the action potential, and the refractory membrane at convergences. Here, we provide a logical explanation from the action potential to a neuronal model of the coding and computation of the retina. We also explain how the visual cortex operates through quantum-phase processing. In the small-world network, parallel frequencies collide into definable patterns of distinct objects. Elsewhere, we have shown how many sensory cells are meanly sampled from a single neuron and that convergences of neurons are common. We also demonstrate, using the threshold and refractory period of a quantum-phase pulse, that action potentials diffract across a neural network due to the annulment of parallel collisions in the phase ternary computation (PTC). Thus, PTC applied to neuron convergences results in a collective mean sampled frequency and is the only mathematical solution within the constraints of the brain neural networks (BNN). In the retina and other sensory areas, we discuss how this information is initially coded and then understood in terms of network abstracts within the lateral geniculate nucleus (LGN) and visual cortex. First, by defining neural patterning within a neural network, and then in terms of contextual networks, we demonstrate that the output of frequencies from the visual cortex contains information amounting to abstract representations of objects in increasing detail. We show that nerve tracts from the LGN provide time synchronization to the neocortex (defined as the location of the combination of connections of the visual cortex, motor cortex, auditory cortex, etc.). The full image is therefore combined in the neocortex with other sensory modalities so that it receives information about the object from the eye and all the abstracts that make up the object. Spatial patterns in the visual cortex are formed from individual patterns illuminating the retina, and memory is encoded by reverberatory loops of computational action potentials (CAPs). We demonstrate that a similar process of PTC may take place in the cochlea and associated ganglia, as well as ascending information from the spinal cord, and that this function should be considered universal where convergences of neurons occur.

Biophysical control of plasticity and patterning in regeneration and cancer

Cells and tissues display a remarkable range of plasticity and tissue-patterning activities that are emergent of complex signaling dynamics within their microenvironments. These properties, which when operating normally guide embryogenesis and regeneration, become highly disordered in diseases such as cancer. While morphogens and other molecular factors help determine the shapes of tissues and their patterned cellular organization, the parallel contributions of biophysical control mechanisms must be considered to accurately predict and model important processes such as growth, maturation, injury, repair, and senescence. We now know that mechanical, optical, electric, and electromagnetic signals are integral to cellular plasticity and tissue patterning. Because biophysical modalities underly interactions between cells and their extracellular matrices, including cell cycle, metabolism, migration, and differentiation, their applications as tuning dials for regenerative and anti-cancer therapies are being rapidly exploited. Despite this, the importance of cellular communication through biophysical signaling remains disproportionately underrepresented in the literature. Here, we provide a review of biophysical signaling modalities and known mechanisms that initiate, modulate, or inhibit plasticity and tissue patterning in models of regeneration and cancer. We also discuss current approaches in biomedical engineering that harness biophysical control mechanisms to model, characterize, diagnose, and treat disease states.

Energy optimisation predicts the capacity of ion buffering in the brain

Neurons store energy in the ionic concentration gradients they build across their cell membrane. The amount of energy stored, and hence the work the ions can do by mixing, can be enhanced by the presence of ion buffers in extra- and intracellular space. Buffers act as sources and sinks of ions, however, and unless the buffering capacities for different ion species obey certain relationships, a complete mixing of the ions may be impeded by the physical conditions of charge neutrality and isotonicity. From these conditions, buffering capacities were calculated that enabled each ion species to mix completely. In all valid buffer distributions, the [Formula: see text] ions were buffered most, with a capacity exceeding that of [Formula: see text] and [Formula: see text] buffering by at least an order of magnitude. The similar magnitude of the (oppositely directed) [Formula: see text] and [Formula: see text] gradients made extracellular space behave as a [Formula: see text]-[Formula: see text] exchanger. Anions such as [Formula: see text] were buffered least. The great capacity of the extra- and intracellular [Formula: see text] buffers caused a large influx of [Formula: see text] ions as is typically observed during energy deprivation. These results explain many characteristics of the physiological buffer distributions but raise the question how the brain controls the capacity of its ion buffers. It is suggested that neurons and glial cells, by their great sensitivity to gradients of charge and osmolarity, respectively, sense deviations from electro-neutral and isotonic mixing, and use these signals to tune the chemical composition, and buffering capacity, of the extra- and intracellular matrices.

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.

On mathematical modeling of the propagation of a wave ensemble within an individual axon

The long history of studying the propagation of an action potential has revealed that an electrical signal is accompanied by mechanical and thermal effects. All these effects together generate an ensemble of waves. The consistent models of such a complex phenomenon can be derived by using properly the fundamental physical principles. In this paper, attention is paid to the analysis of concepts of continuum physics that constitute a basis for deriving the mathematical models which describe the emergence and propagation of a wave ensemble in an axon. Such studies are interdisciplinary and based on biology, physics, mathematics, and chemistry. The governing equations for the action potential together with mechanical and thermal effects are derived starting from basics: Maxwell equations, conservation of momentum, Fourier's law, etc., but modified following experimental studies in electrophysiology. Several ideas from continuum physics like external forces and internal variables can also be used in deriving the corresponding models. Some mathematical concepts used in modeling are also briefly described. A brief overview of several mathematical models is presented that allows us to analyze the present ideas of modeling. Most mathematical models deal with the propagation of signals in a healthy axon. Further analysis is needed for better modeling the pathological situations and the explanation of the influence of the structural details like the myelin sheath or the cytoskeleton in the axoplasm. The future possible trends in improving the models are envisaged.

Flow-driven control of pulse width in excitable media

Models of pulse formation in nerve conduction have provided manifold insight not only into neuronal dynamics but also the nonlinear dynamics of pulse formation in general. Recent observation of neuronal electrochemical pulses also driving mechanical deformation of the tubular neuronal wall, and thereby generating ensuing cytoplasmic flow, now question the impact of flow on the electrochemical dynamics of pulse formation. Here, we theoretically investigate the classical Fitzhugh-Nagumo model, now accounting for advective coupling between the pulse propagator typically describing membrane potential and triggering mechanical deformations, and thus governing flow magnitude, and the pulse controller, a chemical species advected with the ensuing fluid flow. Employing analytical calculations and numerical simulations, we find that advective coupling allows for a linear control of pulse width while leaving pulse velocity unchanged. We therefore uncover an independent control of pulse width by fluid flow coupling.

An Isotonic Model of Neuron Swelling Based on Co-Transport of Salt and Water

Neurons spend most of their energy building ion gradients across the cell membrane. During energy deprivation the neurons swell, and the concomitant mixing of their ions is commonly assumed to lead toward a Donnan equilibrium, at which the concentration gradients of all permeant ion species have the same Nernst potential. This Donnan equilibrium, however, is not isotonic, as the total concentration of solute will be greater inside than outside the neurons. The present theoretical paper, in contrast, proposes that neurons follow a path along which they swell quasi-isotonically by co-transporting water and ions. The final neuronal volume on the path is taken that at which the concentration of impermeant anions in the shrinking extracellular space equals that inside the swelling neurons. At this final state, which is also a Donnan equilibrium, all permeant ions can mix completely, and their Nernst potentials vanish. This final state is isotonic and electro-neutral, as are all intermediate states along this path. The path is in principle reversible, and maximizes the work of mixing.

Electromechanical model for object roughness perception during finger sliding

Touch allows us to gather abundant information in the world around us. However, how sensory cells embedded in the fingers convey texture information into their firing patterns is still poorly understood. Here, we develop an electromechanical model for roughness perception by incorporating main ingredients such as voltage-gated ion channels, active ion pumps, mechanosensitive channels, and cell deformation. The model reveals that sensory cells can convey texture wavelengths into the period of their firing patterns as the finger slides across object surfaces, but they can only convey a limited range of texture wavelengths. We also show that an increase in sliding speed broadens the decoding wavelength range at the cost of reduction of lower perception limits. Thus, a smaller sliding speed and a bigger contact force may be needed to successfully discern a smooth surface, consistent with previous psychophysical observations. Moreover, we show that cells with slowly adapting mechanosensitive channels can still fire action potentials under static loadings, indicating that slowly adapting mechanosensitive channels may contribute to the perception of coarse textures under static touch. Our work thus provides a new theoretical framework to study roughness perception and may have important implications for the design of electronic skin, artificial touch, and haptic interfaces.

In vivo direct imaging of neuronal activity at high temporospatial resolution

There has been a long-standing demand for noninvasive neuroimaging methods that can detect neuronal activity at both high temporal and high spatial resolution. We present a two-dimensional fast line-scan approach that enables direct imaging of neuronal activity with millisecond precision while retaining the high spatial resolution of magnetic resonance imaging (MRI). This approach was demonstrated through in vivo mouse brain imaging at 9.4 tesla during electrical whisker-pad stimulation. In vivo spike recording and optogenetics confirmed the high correlation of the observed MRI signal with neural activity. It also captured the sequential and laminar-specific propagation of neuronal activity along the thalamocortical pathway. This high-resolution, direct imaging of neuronal activity will open up new avenues in brain science by providing a deeper understanding of the brain's functional organization, including the temporospatial dynamics of neural networks.

Emerging Diamond Quantum Sensing in Bio-Membranes

Bio-membranes exhibit complex but unique mechanical properties as communicative regulators in various physiological and pathological processes. Exposed to a dynamic micro-environment, bio-membranes can be seen as an intricate and delicate system. The systematical modeling and detection of their local physical properties are often difficult to achieve, both quantitatively and precisely. The recent emerging diamonds hosting quantum defects (i.e., nitrogen-vacancy (NV) center) demonstrate intriguing optical and spin properties, together with their outstanding photostability and biocompatibility, rendering them ideal candidates for biological applications. Notably, the extraordinary spin-based sensing enable the measurements of localized nanoscale physical quantities such as magnetic fields, electrical fields, temperature, and strain. These nanoscale signals can be optically read out precisely by simple optical microscopy systems. Given these exclusive properties, NV-center-based quantum sensors can be widely applied in exploring bio-membrane-related features and the communicative chemical reaction processes. This review mainly focuses on NV-based quantum sensing in bio-membrane fields. The attempts of applying NV-based quantum sensors in bio-membranes to investigate diverse physical and chemical events such as membrane elasticity, phase change, nanoscale bio-physical signals, and free radical formation are fully overviewed. We also discuss the challenges and future directions of this novel technology to be utilized in bio-membranes.

Towards Generalizing the Information Theory for Neural Communication

Neuroscience extensively uses the information theory to describe neural communication, among others, to calculate the amount of information transferred in neural communication and to attempt the cracking of its coding. There are fierce debates on how information is represented in the brain and during transmission inside the brain. The neural information theory attempts to use the assumptions of electronic communication; despite the experimental evidence that the neural spikes carry information on non-discrete states, they have shallow communication speed, and the spikes' timing precision matters. Furthermore, in biology, the communication channel is active, which enforces an additional power bandwidth limitation to the neural information transfer. The paper revises the notions needed to describe information transfer in technical and biological communication systems. It argues that biology uses Shannon's idea outside of its range of validity and introduces an adequate interpretation of information. In addition, the presented time-aware approach to the information theory reveals pieces of evidence for the role of processes (as opposed to states) in neural operations. The generalized information theory describes both kinds of communication, and the classic theory is the particular case of the generalized theory.

Current State of Potential Mechanisms Supporting Low Intensity Focused Ultrasound for Neuromodulation

Low intensity focused ultrasound (LIFU) has been gaining traction as a non-invasive neuromodulation technology due to its superior spatial specificity relative to transcranial electrical/magnetic stimulation. Despite a growing literature of LIFU-induced behavioral modifications, the mechanisms of action supporting LIFU's parameter-dependent excitatory and suppressive effects are not fully understood. This review provides a comprehensive introduction to the underlying mechanics of both acoustic energy and neuronal membranes, defining the primary variables for a subsequent review of the field's proposed mechanisms supporting LIFU's neuromodulatory effects. An exhaustive review of the empirical literature was also conducted and studies were grouped based on the sonication parameters used and behavioral effects observed, with the goal of linking empirical findings to the proposed theoretical mechanisms and evaluating which model best fits the existing data. A neuronal intramembrane cavitation excitation model, which accounts for differential effects as a function of cell-type, emerged as a possible explanation for the range of excitatory effects found in the literature. The suppressive and other findings need additional theoretical mechanisms and these theoretical mechanisms need to have established relationships to sonication parameters.

Remote photonic sensing of action potential in mammalian nerve cells via histogram-based analysis of temporal spatial acoustic vibrations

Label free and remote action potential detection in neurons can be of great importance in the neuroscience research field. This paper presents a novel label free imaging modality based on the detection of temporal vibrations of speckle patterns illuminating the sample. We demonstrated the feasibility of detecting action potentials originating from spontaneous and stimulated activity in cortical cell culture. The spatiotemporal vibrations of isolated cortical cells were extracted by illuminating the culture with a laser beam while the vibrations of the random back scattered secondary speckle patterns are captured by a camera. The postulated action potentials were estimated following correlation-based analysis on the captured vibrations, where the variance deviation of the signal from a Gaussian distribution is directly associated with the action potential events. The technique was validated in a series of experiments in which the optical signals were acquired concurrently with microelectrode array (MEA) recordings. Our results demonstrate the ability of detecting action potential events in mammalian cells remotely via extraction of acoustic vibrations.

Intercellular water exchanges trigger soliton-like waves in multicellular systems

Oscillations and waves are ubiquitous in living cellular systems. Generations of these spatio-temporal patterns are generally attributed to some mechanochemical feedbacks. Here, we treat cells as open systems, i.e., water and ions can pass through the cell membrane passively or actively, and reveal a new origin of wave generation. We show that osmotic shocks above a shock threshold will trigger self-sustained cell oscillations and result in long-range waves propagating without decrement, a phenomenon that is analogous to the excitable medium. The travelling wave propagates along intercellular osmotic pressure gradient and its wave speed scales with the magnitude of intercellular water flows. Furthermore, we also find that the travelling wave exhibits several hallmarks of solitary waves. Together, our findings predict a new mechanism of wave generation in living multicellular systems. The ubiquity of intercellular water exchanges implies that this mechanism may be relevant to a broad class of systems.

Collective mechanical responses of cadherin-based adhesive junctions as predicted by simulations

Cadherin-based adherens junctions and desmosomes help stabilize cell-cell contacts with additional function in mechano-signaling, while clustered protocadherin junctions are responsible for directing neuronal circuits assembly. Structural models for adherens junctions formed by epithelial cadherin (CDH1) proteins indicate that their long, curved ectodomains arrange to form a periodic, two-dimensional lattice stabilized by tip-to-tip trans interactions (across junction) and lateral cis contacts. Less is known about the exact architecture of desmosomes, but desmoglein (DSG) and desmocollin (DSC) cadherin proteins are also thought to form ordered junctions. In contrast, clustered protocadherin (PCDH)-based cell-cell contacts in neuronal tissues are thought to be responsible for self-recognition and avoidance, and structural models for clustered PCDH junctions show a linear arrangement in which their long and straight ectodomains form antiparallel overlapped trans complexes. Here, we report all-atom molecular dynamics simulations testing the mechanics of minimalistic adhesive junctions formed by CDH1, DSG2 coupled to DSC1, and PCDHγB4, with systems encompassing up to 3.7 million atoms. Simulations generally predict a favored shearing pathway for the adherens junction model and a two-phased elastic response to tensile forces for the adhesive adherens junction and the desmosome models. Complexes within these junctions first unbend at low tensile force and then become stiff to unbind without unfolding. However, cis interactions in both the CDH1 and DSG2-DSC1 systems dictate varied mechanical responses of individual dimers within the junctions. Conversely, the clustered protocadherin PCDHγB4 junction lacks a distinct two-phased elastic response. Instead, applied tensile force strains trans interactions directly, as there is little unbending of monomers within the junction. Transient intermediates, influenced by new cis interactions, are observed after the main rupture event. We suggest that these collective, complex mechanical responses mediated by cis contacts facilitate distinct functions in robust cell-cell adhesion for classical cadherins and in self-avoidance signaling for clustered PCDHs.

Towards understanding specific ion effects in aqueous media using thermodiffusion

Specific ion effects play an important role in scientific and technological processes. According to Hofmeister, the influence on the hydrogen bond network depends on the ion and leads to a specific order of the ions. Also thermodiffusion the mass transport caused by a temperature gradient is very sensitive to changes of the hydrogen bond network leading to a ranking according to hydrophilicity of the salt. Hence, we investigate various salt solutions in order to compare with the Hofmeister concept. We have studied three different sodium salts in water as a function of temperature (25-45[Formula: see text]C) and concentration (0.5-5 mol kg[Formula: see text]) using Thermal Diffusion Forced Rayleigh Scattering (TDFRS). The three anions studied, carbonate, acetate and thiocyanate, span the entire range of the Hofmeister series from hydrophilic to hydrophobic. We compare the results with the recent measurements of the corresponding potassium salts to see to what extent the cation changes the thermodiffusion of the salt.

Holistic idealization: An artifactual standpoint

Idealization is commonly understood as distortion: representing things differently than how they actually are. In this paper, we outline an alternative artifactual approach that does not make misrepresentation central for the analysis of idealization. We examine the contrast between the Hodgkin-Huxley (1952a, b, c) and the Heimburg-Jackson (2005, 2006) models of the nerve impulse from the artifactual perspective, and argue that, since the two models draw upon different epistemic resources and research programs, it is often difficult to tell which features of a system the central assumptions involved are supposed to distort. Many idealizations are holistic in nature. They cannot be locally undone without dismantling the model, as they occupy a central position in the entire research program. Nor is their holistic character mainly related to the use of mathematical and statistical modeling techniques as portrayed by Rice (2018, 2019). We suggest that holistic idealizations are implicit theoretical and representational assumptions that can only be understood in relation to the conceptual and representational tools exploited in modeling and experimental practices. Such holistic idealizations play a pivotal role not just in individual models, but also in defining research programs.

Neuromechanical modulation of transmembrane voltage in a model of a nerve

Despite substantial evidence that mechanical variables play a crucial role in transmembrane voltage regulation, most research efforts focus mostly on the nerve cell's biochemical or electrophysiological activities. We propose an electromechanical model of a nerve in order to advance our understanding of how mechanical forces and thermodynamics also regulate neural electrical activities. We explore the spatiotemporal dynamics of the transmembrane potential using the proposed nonlinear model with a sinusoid as the initial transmembrane potential and periodic boundary conditions. The localized wave from our numerical simulation and transmembrane potentials in nerves are solitary and show the three stages of action potential (depolarization, repolarization, and hyperpolarization), as well as threshold and saturation effects. We show that the mechanical properties of membranes affect the localization of the transmembrane potential. According to simulation data, mechanical pulses of sufficient magnitude can modulate a transmembrane voltage. The current model could be used to describe the dynamics of a transmembrane potential modulated by sound. Mechanical perturbations that modulate an electrical signal have a lot of clinical potential for treating pain and other neurological diseases.

Hyperbolic equations for neuronal membrane deformation waves accompanying an action potential

Experiments show that the propagation of an action potential along an axon is accompanied by mechanical deformations. We describe the mechanisms of the effect using fluid dynamic equations, Laplace's and Hook's laws for surface tension, and Lippmann's law, which relates membrane tension to membrane potential. We derived a minimal, 1-D model, which is a hyperbolic system of equations. Our model qualitatively reproduces the membrane's mechanical deformation evoked by either the propagation of an action potential or the stepwise change of membrane potential. The understanding of the relationship between electrical activity and mechanical deformation provides guidance toward non-invasive imaging of neuronal activity.

Improved alpha-beta power reduction via combined electrical and ultrasonic stimulation in a parkinsonian cortex-basal ganglia-thalamus computational model

Objective. To investigate computationally the interaction of combined electrical and ultrasonic modulation of isolated neurons and of the parkinsonian cortex-basal ganglia-thalamus loop.Approach. Continuous-wave or pulsed electrical and ultrasonic neuromodulation is applied to isolated Otsuka plateau-potential generating subthalamic nucleus (STN) and Pospischil regular, fast and low-threshold spiking cortical cells in a temporally alternating or simultaneous manner. Similar combinations of electrical/ultrasonic waveforms are applied to a parkinsonian biophysical cortex-basal ganglia-thalamus neuronal network. Ultrasound-neuron interaction is modelled respectively for isolated neurons and the neuronal network with the NICE and SONIC implementations of the bilayer sonophore underlying mechanism. Reduction inα-βspectral energy is used as a proxy to express improvement in Parkinson's disease by insonication and electrostimulation.Main results. Simultaneous electro-acoustic stimulation achieves a given level of neuronal activity at lower intensities compared to the separate stimulation modalities. Conversely, temporally alternating stimulation with50 Hzelectrical and ultrasound pulses is capable of eliciting100 HzSTN firing rates. Furthermore, combination of ultrasound with hyperpolarizing currents can alter cortical cell relative spiking regimes. In the parkinsonian neuronal network, continuous-wave and pulsed ultrasound reduce pathological oscillations by different mechanisms. High-frequency pulsed separated electrical and ultrasonic deep brain stimulation (DBS) reduce pathologicalα-βpower by entraining STN-neurons. In contrast, continuous-wave ultrasound reduces pathological oscillations by silencing the STN. Compared to the separated stimulation modalities, temporally simultaneous or alternating electro-acoustic stimulation can achieve higher reductions inα-βpower for the same safety contraints on electrical/ultrasonic intensity.Significance. Focused ultrasound has the potential of becoming a non-invasive alternative of conventional DBS for the treatment of Parkinson's disease. Here, we elaborate on proposed benefits of combined electro-acoustic stimulation in terms of improved dynamic range, efficiency, spatial resolution, and neuronal selectivity.

Evolution equation for nonlinear Lucassen waves, with application to a threshold phenomenon

A nonlinear, fractional, surface wave equation with a spatial derivative of second order was developed by Kappler, Shrivastava, Schneider, and Netz [Phys. Rev. Fluids 2, 114804 (2017)] for propagation along an elastic interface coupled to a viscous incompressible liquid. Linear theory for the attenuation and dispersion was developed originally by Lucassen [Trans. Faraday Soc. 64, 2221 (1968)]. Kappler et al. introduced a fractional time derivative to account for the Lucassen wave attenuation and dispersion, and they included quadratic and cubic nonlinearity associated with compression of the elastic interface. Presented here is an integrated form of their time domain equation for progressive waves that is first order in the spatial derivative. Solutions of this evolution equation capture the main features of waveforms predicted by the full model equation of Kappler et al., especially the formation and propagation of shocks, while the evolution equation can be solved numerically with substantially less computational cost. Approximate analytical expressions obtained from the evolution equation for the nonlinear propagation speed and attenuation of a compression pulse reveal that a threshold phenomenon discussed by Kappler et al. is due to competition between quadratic and cubic nonlinearity associated with a lipid monolayer interface.

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.

Focused ultrasound neuromodulation

Focused ultrasound (FUS) is an emerging modality for performing incisionless neurosurgical procedures including thermoablation and blood-brain barrier (BBB) modulation. Emerging evidence suggests that low intensity FUS can also be used for neuromodulation with several benefits, including high spatial precision and the possibility of targeting deep brain regions. Here we review the existing data regarding the biological mechanisms of FUS neuromodulation, the characteristics of neuronal activity altered by FUS, emerging indications for FUS neuromodulation, as well as the strengths and limitations of this approach.

Optical Electrophysiology: Toward the Goal of Label-Free Voltage Imaging

Measuring and monitoring the electrical signals transmitted between neurons is key to understanding the communication between neurons that underlies human perception, information processing, and decision-making. While electrode-based electrophysiology has been the gold standard, optical electrophysiology has opened up a new area in the past decade. Voltage-dependent fluorescent reporters enable voltage imaging with high spatial resolution and flexibility to choose recording locations. However, they exhibit photobleaching as well as phototoxicity and may perturb the physiology of the cell. Label-free optical electrophysiology seeks to overcome these hurdles by detecting electrical activities optically, without the incorporation of exogenous fluorophores in cells. For example, electrochromic optical recording detects neuroelectrical signals via a voltage-dependent color change of extracellular materials, and interferometric optical recording monitors membrane deformations that accompany electrical activities. Label-free optical electrophysiology, however, is in an early stage, and often has limited sensitivity and temporal resolution. In this Perspective, we review the recent progress to overcome these hurdles. We hope this Perspective will inspire developments of label-free optical electrophysiology techniques with high recording sensitivity and temporal resolution in the near future.

Mechanical Principles Governing the Shapes of Dendritic Spines

Dendritic spines are small, bulbous protrusions along the dendrites of neurons and are sites of excitatory postsynaptic activity. The morphology of spines has been implicated in their function in synaptic plasticity and their shapes have been well-characterized, but the potential mechanics underlying their shape development and maintenance have not yet been fully understood. In this work, we explore the mechanical principles that could underlie specific shapes using a minimal biophysical model of membrane-actin interactions. Using this model, we first identify the possible force regimes that give rise to the classic spine shapes-stubby, filopodia, thin, and mushroom-shaped spines. We also use this model to investigate how the spine neck might be stabilized using periodic rings of actin or associated proteins. Finally, we use this model to predict that the cooperation between force generation and ring structures can regulate the energy landscape of spine shapes across a wide range of tensions. Thus, our study provides insights into how mechanical aspects of actin-mediated force generation and tension can play critical roles in spine shape maintenance.

A rapid-onset diffusion functional MRI signal reflects neuromorphological coupling dynamics

Functional Magnetic Resonance Imaging (fMRI) has transformed our understanding of brain function in-vivo. However, the neurovascular coupling mechanisms underlying fMRI are somewhat "distant" from neural activity. Interestingly, evidence from Intrinsic Optical Signals (IOSs) indicates that neural activity is also coupled to (sub)cellular morphological modulations. Diffusion-weighted functional MRI (dfMRI) experiments have been previously proposed to probe such neuromorphological couplings, but the underlying mechanisms have remained highly contested. Here, we provide the first direct link between in vivo ultrafast dfMRI signals upon rat forepaw stimulation and IOSs in acute slices stimulated optogenetically. We reveal a hitherto unreported rapid onset (<100 ms) dfMRI signal component which (i) agrees with fast-rising IOSs dynamics; (ii) evidences a punctate quantitative correspondence to the stimulation period; and (iii) is rather insensitive to a vascular challenge. Our findings suggest that neuromorphological coupling can be detected via dfMRI signals, auguring well for future mapping of neural activity more directly compared with blood-oxygenation-level-dependent mechanisms.

The trigeminocardiac reflex: Does the activation pathway of its efferent arc affect the intensity of the hemodynamic drop during the management of maxillofacial fractures?

The study aimed to correlate between the stimulated nerve, intensity of trigeminovagal reflex (TVR), and neuropathophysiological pathway by which the efferent arc is activated. Material and methods: A retrospective study included patients who developed TVR during the surgical management of mandibular, midface, and orbital fractures. The reflex was divided into type I, II, III, and IV-TVR according to the following nerves: ophthalmic, maxillary, mandibular, and non-trigeminal nerves, respectively. The magnitude of hemodynamic drops was identified at the intraoperative baseline, during reflex, and postoperatively. The needed time to elicit the reflex, frequency and duration, need for medical intervention, and sequence of the drop were also recorded. P - values < 0.05 was considered significant. Out of 260 patients' files were reviewed, the TVR was observed in only 30 (11.55 %) patients. The ophthalmic nerve activation significantly caused the greatest intensity and magnitude of hemodynamic drop, followed by maxillary nerve, then mandibular division, and the lowest one was non-trigeminal nerves. The highest mean of drops in the mean arterial blood pressure (MABP) was 62.92 ± 2.39 with the type ITVR, whereas those of the type II, III, and IV were 75.5 ±3.98, 81.02±1.31, and 82.22±1.85, respectively. Also, the type I-TVR led to the greatest decrease in the heart rate (HR) with the mean equaled to 52.31± 3.91. The drop percentage in the MABP was -30.5, -17.5, -12, -10.08 for type I, II, III, and IV, whereas those of the HR were - 33.9, -27.13, -26.6, and -25 with type I, II, III, and IV, respectively. All results showed highly significant differences with p-values less than 0.001 when comparing between the baseline and intraoperative values of each TVR type. There is a positive correlation between the activated pathway of the TVR and the intensity of its efferent arc response due to the neural pathway of each division in the brainstem circuitry. Understanding of the pathophysiology and mechanism of the TVR, together with the rapid recognition and treatment could prevent serious negative outcomes, especially when the ophthalmic nerve is stimulated. 1Introduction.

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.

Touch inhibits touch: sanshool-induced paradoxical tingling reveals perceptual interaction between somatosensory submodalities

Human perception of touch is mediated by inputs from multiple channels. Classical theories postulate independent contributions of each channel to each tactile feature, with little or no interaction between channels. In contrast to this view, we show that inputs from two sub-modalities of mechanical input channels interact to determine tactile perception. The flutter-range vibration channel was activated anomalously using hydroxy-α-sanshool, a bioactive compound of Szechuan pepper, which chemically induces vibration-like tingling sensations. We tested whether this tingling sensation on the lips was modulated by sustained mechanical pressure. Across four experiments, we show that sustained touch inhibits sanshool tingling sensations in a location-specific, pressure-level and time-dependent manner. Additional experiments ruled out the mediation of this interaction by nociceptive or affective (C-tactile) channels. These results reveal novel inhibitory influence from steady pressure onto flutter-range tactile perceptual channels, consistent with early-stage interactions between mechanoreceptor inputs within the somatosensory pathway.

How is information transmitted in a nerve?

In the last 15 years, a debate has emerged about the validity of the famous Hodgkin-Huxley model for nerve impulse. Mechanical models have been proposed. This note reviews the experimental properties of the nerve impulse and discusses the proposed alternatives. The experimental data, which rule out some of the alternative suggestions, show that while the Hodgkin-Huxley model may not be complete, it nevertheless includes essential features that should not be overlooked in the attempts made to improve, or supersede, it.

Acoustic Waves in Axonal Membrane and Caveolins are the New Targets for Pain Treatment with High Frequency Ultrasound

Reciprocal interaction between electrical and mechanical waves observed in axonal membrane during its excitation leads to a paradigm shift in pain research making the uncoupling of electro-mechanical signals an interesting target in pain treatment. This uncoupling can be realized either through direct disturbance of the mechanical surface waves in axonal membrane or through shifting of the thermodynamic state of this membrane far from its phase transition point. Both effects can be effectively realized through application of the very high frequency ultrasound waves. Additional target for application of ultrasound in pain treatment is the caveolin-1, which is abundantly present in Schwann cells as well as in the non-axonal tissues. Both targets demonstrate frequency-dependent reactions, thus making a very high frequency ultrasound a promising treatment modality in pain treatment.

Displacement Imaging for Focused Ultrasound Peripheral Nerve Neuromodulation

Focused ultrasound (FUS) is an emerging technique for neuromodulation due to its noninvasive application and high depth penetration. Recent studies have reported success in modulation of brain circuits, peripheral nerves, ion channels, and organ structures. In particular, neuromodulation of peripheral nerves and the underlying mechanisms remain comparatively unexplored in vivo. Lack of methodologies for FUS targeting and monitoring impede further research in in vivo studies. Thus, we developed a method that non-invasively measures nerve engagement, via tissue displacement, during FUS neuromodulation of in vivo nerves using simultaneous high frame-rate ultrasound imaging. Using this system, we can validate, in real-time, FUS targeting of the nerve and characterize subsequent compound muscle action potentials (CMAPs) elicited from sciatic nerve activation in mice using 0.5 to 5 ms pulse durations and 22 - 28 MPa peak positive stimulus pressures at 4 MHz. Interestingly, successful motor excitation from FUS neuromodulation required a minimum interframe nerve displacement of 18 μm without any displacement incurred at the skin or muscle levels. Moreover, CMAPs detected in mice monotonically increased with interframe nerve displacements within the range of 18 to 300 μm . Thus, correlation between nerve displacement and motor activation constitutes strong evidence FUS neuromodulation is driven by a mechanical effect given that tissue deflection is a result of highly focused acoustic radiation force.

SECONIC: Towards multi-compartmental models for ultrasonic brain stimulation by intramembrane cavitation

OBJECTIVE

To design a computationally efficient model for ultrasonic neuromodulation (UNMOD) of morphologically realistic multi-compartmental neurons based on intramembrane cavitation.

APPROACH

A Spatially Extended Neuronal Intramembrane Cavitation model that accurately predicts observed fast Charge Oscillations (SECONIC) is designed. A regular spiking cortical Hodgkin-Huxley type nanoscale neuron model of the bilayer sonophore and surrounding proteins is used. The accuracy and computational efficiency of SECONIC is compared with the Neuronal Intramembrane Cavitation Excitation (NICE) and multiScale Optimized model of Neuronal Intramembrane Cavitation (SONIC).

MAIN RESULTS

Membrane charge redistribution between different compartments should be taken into account via fourier series analysis in an accurate multi-compartmental UNMOD-model. Approximating charge and voltage traces with the harmonic term and first two overtones results in reasonable goodness-of-fit, except for high ultrasonic pressure (adjusted R-squared ≥0.61). Taking into account the first eight overtones results in a very good fourier series fit (adjusted R-squared ≥0.96) up to 600 kPa. Next, the dependency of effective voltage and rate parameters on charge oscillations is investigated. The two-tone SECONIC-model is one to two orders of magnitude faster than the NICE-model and demonstrates accurate results for ultrasonic pressure up to 100 kPa.

SIGNIFICANCE

Up to now, the underlying mechanism of UNMOD is not well understood. Here, the extension of the bilayer sonophore model to spatially extended neurons via the design of a multi-compartmental UNMOD-model, will result in more detailed predictions that can be used to validate or falsify this tentative mechanism. Furthermore, a multi-compartmental model for UNMOD is required for neural engineering studies that couple finite difference time domain simulations with neuronal models. Here, we propose the SECONIC-model, extending the SONIC-model by taking into account charge redistribution between compartments.

The important consequences of the reversible heat production in nerves and the adiabaticity of the action potential

It has long been known that there is no measurable heat production associated with the nerve pulse. Rather, one finds that heat production is biphasic, and a heat release during the first phase of the action potential is followed by the reabsorption of a similar amount of heat during the second phase. We review the long history the measurement of heat production in nerves and provide a new analysis of these findings focusing on the thermodynamics of adiabatic and isentropic processes. We begin by considering adiabatic oscillations in gases, waves in layers, oscillations of springs and the reversible (or irreversible) charging and discharging of capacitors. We then apply these ideas to the heat signature of nerve pulses. Finally, we compare the temperature changes expected from the Hodgkin-Huxley model and the soliton theory for nerves. We demonstrate that heat production in nerves cannot be explained as an irreversible charging and discharging of a membrane capacitor as it is proposed in the Hodgkin-Huxley model. Instead, we conclude that it is consistent with an adiabatic pulse. However, if the nerve pulse is adiabatic, completely different physics is required to explain its features. Membrane processes must then be reversible and resemble the oscillation of springs more than resembling "a burning fuse of gunpowder" (quote A. L. Hodgkin). Theories acknowledging the adiabatic nature of the nerve pulse have recently been discussed by various authors. It forms the central core of the soliton model, which considers the nerve pulse as a localized sound pulse.

Modelling of processes in nerve fibres at the interface of physiology and mathematics

The in silico simulations are widely used in contemporary systems biology including the analysis of nerve pulse propagation. As known from numerous experiments, the propagation of an action potential is accompanied by mechanical and thermal effects. This calls for an analysis at the interface of physics, physiology and mathematics. In this paper, the background of the model equations governing the effects in nerve fibres is analysed from a physical viewpoint and then discussed how to unite them into a system by using the coupling forces. The leading hypothesis associates the coupling to the changes of variables, not to their values or amplitudes. This hypothesis models actually the physiological mechanisms of energy transductions in a fibre. The general assumptions in modelling the processes and the properties of the coupled system of equations are described. The dimensionless mathematical model which couples the action potential with mechanical waves together with temperature effects is presented in "Appendix". This model generates an ensemble of waves including the electrical signal and mechanical and thermal effects.

Excitation of Faraday-like body waves in vibrated living earthworms

Biological cells and many living organisms are mostly made of liquids and therefore, by analogy with liquid drops, they should exhibit a range of fundamental nonlinear phenomena such as the onset of standing surface waves. Here, we test four common species of earthworm to demonstrate that vertical vibration of living worms lying horizontally on a flat solid surface results in the onset of subharmonic Faraday-like body waves, which is possible because earthworms have a hydrostatic skeleton with a flexible skin and a liquid-filled body cavity. Our findings are supported by theoretical analysis based on a model of parametrically excited vibrations in liquid-filled elastic cylinders using material parameters of the worm's body reported in the literature. The ability to excite nonlinear subharmonic body waves in a living organism could be used to probe, and potentially to control, important biophysical processes such as the propagation of nerve impulses, thereby opening up avenues for addressing biological questions of fundamental impact.

High-speed interferometric imaging reveals dynamics of neuronal deformation during the action potential

Neurons undergo nanometer-scale deformations during action potentials, and the underlying mechanism has been actively debated for decades. Previous observations were limited to a single spot or the cell boundary, while movement across the entire neuron during the action potential remained unclear. Here we report full-field imaging of cellular deformations accompanying the action potential in mammalian neuron somas (-1.8 to 1.4 nm) and neurites (-0.7 to 0.9 nm), using high-speed quantitative phase imaging with a temporal resolution of 0.1 ms and an optical path length sensitivity of <4 pm per pixel. The spike-triggered average, synchronized to electrical recording, demonstrates that the time course of the optical phase changes closely matches the dynamics of the electrical signal. Utilizing the spatial and temporal correlations of the phase signals across the cell, we enhance the detection and segmentation of spiking cells compared to the shot-noise-limited performance of single pixels. Using three-dimensional (3D) cellular morphology extracted via confocal microscopy, we demonstrate that the voltage-dependent changes in the membrane tension induced by ionic repulsion can explain the magnitude, time course, and spatial features of the phase imaging. Our full-field observations of the spike-induced deformations shed light upon the electromechanical coupling mechanism in electrogenic cells and open the door to noninvasive label-free imaging of neural signaling.

Action Potential: A Vortex Phenomena; Driving Membrane Oscillations

Hodgkin-Huxley (HH) model has been one of the most successful electrical interpretation of nerve membrane which led to revolutions in the field of computational neuroscience. On the contrary, experimental observations indicate that, an Action Potential (AP) is accompanied with certain physiological changes in the nerve membrane such as, production and absorption of heat; variation of axon diameter, pressure and length. Although, in the early 1900's a Pressure Wave Theory was proposed by E. Wilke, but, due to lack of sophisticated experimental techniques it was left uncharted. Until recently, when Heimburg-Jackson, Hady-Machta and Rvachev, independently proposed Soliton Theory (thermodynamic interpretation of nerve membrane), Mechanical Surface Waves theory (electro-mechanical interpretation) and Rvachev Model (mechano-electrical activation of voltage gated sodium ion channels) respectively; encouraging a deviation from the traditional HH interpretation with justification for the physical changes in the nerve membrane observed experimentally. But, these theories lead to a “hit and miss” scenario because, they do explain certain features (increase/decrease in axon diameter) but miss to explain, correlation between the strength of stimuli and spike rate of AP. Bio-physical models of nerve membrane are thus important for enhancing our understanding regarding the governing dynamics of neural activities encompassing the experimental observations. A novel theory is proposed here which, unravels vortex ring formation due to ion currents in the intracellular and extracellular region leading to variation of pressure causing the increment/decrement in axon diameter. These formations manifest as membrane oscillations which are used to establish a correlation between the strength of stimuli and spike rate of AP. The theory proposed in this paper, brings a paradigm shift in our understanding of neural dynamics from a thorough bio-physical and physiological perspective with promising applications.

Heat of nervous conduction: A thermodynamic framework

Early recordings of nervous conduction revealed a notable thermal signature associated with the electrical signal. The observed production and subsequent absorption of heat arise from physicochemical processes that occur at the cell membrane level during the conduction of the action potential. In particular, the reversible release of electrostatic energy stored as a difference of potential across the cell membrane appears as a simple yet consistent explanation for the heat production, as proposed in the "Condenser Theory." However, the Condenser Theory has not been analyzed beyond the analogy between the cell membrane and a parallel-plate capacitor, i.e., a condenser, and cannot account for the magnitude of the heat signature. In this work, we use a detailed electrostatic model of the cell membrane to revisit the Condenser Theory. We derive expressions for free energy and entropy changes associated with the depolarization of the membrane by the action potential, which give a direct measure of the heat produced and absorbed by neurons. We show how the density of surface charges on both sides of the membrane impacts the energy changes. Finally, considering a typical action potential, we show that if the membrane holds a bias of surface charges, such that the internal side of the membrane is 0.05Cm^{-2} more negative than the external side, the size of the heat predicted by the model reaches the range of experimental values. Based on our study, we identify the release of electrostatic energy by the membrane as the primary mechanism of heat production and absorption by neurons during nervous conduction.

Nerve impulse propagation: Mechanical wave model and HH model

The Hodgkin-Huxley model (HH model) of nerve propagation from the middle of the 20th century has not remained untouched by criticism. Complementary as well as ambivalent views of this model have been published. A real breakthrough of another model does not exist yet. Many similarities as well as contradictions between the HH model and the alternative mechanical impulse model are shown.

Mechanical regulation of oligodendrocyte biology

Oligodendrocytes (OL) are a subset of glial cells in the central nervous system (CNS) comprising the brain and spinal cord. The CNS environment is defined by complex biochemical and biophysical cues during development and response to injury or disease. In the last decade, significant progress has been made in understanding some of the key biophysical factors in the CNS that modulate OL biology, including their key role in myelination of neurons. Taken together, those studies offer translational implications for remyelination therapies, pharmacological research, identification of novel drug targets, and improvements in methods to generate human oligodendrocyte progenitor cells (OPCs) and OLs from donor stem cells in vitro. This review summarizes current knowledge of how various physical and mechanical cues affect OL biology and its implications for disease, therapeutic approaches, and generation of human OPCs and OLs.

Label-free Optical Imaging of Membrane Potential

Offering high temporal resolution, voltage imaging is an important and essential technique in neuroscience. Among different optical imaging approaches, the label-free approach remains attractive due to its unique value coming from free of exogenous chromophores. The intrinsic voltage-indicating signals arising from membrane deformation, membrane spectral change, phase shift, light scattering, and membrane hydration haven been reported. First demonstrated 70 years ago, label-free optical imaging of membrane potential is still at an early stage and the field is challenged by the relatively small signals generated by the intrinsic optical properties. We review major contrast mechanisms used for label-free voltage imaging and discuss several recent exciting advances that could potentially enable membrane potential imaging in mammalian neurons at high speed and high sensitivity.

The mechanosensitive ion channel TRAAK is localized to the mammalian node of Ranvier

TRAAK is a membrane tension-activated K⁺ channel that has been associated through behavioral studies to mechanical nociception. We used specific monoclonal antibodies in mice to show that TRAAK is localized exclusively to nodes of Ranvier, the action potential propagating elements of myelinated nerve fibers. Approximately 80 percent of myelinated nerve fibers throughout the central and peripheral nervous system contain TRAAK in what is likely an all-nodes or no-nodes per axon fashion. TRAAK is not observed at the axon initial segment where action potentials are first generated. We used polyclonal antibodies, the TRAAK inhibitor RU2 and node clamp amplifiers to demonstrate the presence and functional properties of TRAAK in rat nerve fibers. TRAAK contributes to the ‘leak’ K⁺ current in mammalian nerve fiber conduction by hyperpolarizing the resting membrane potential, thereby increasing Na⁺ channel availability for action potential propagation. We speculate on why nodes of Ranvier contain a mechanosensitive K⁺ channel.

Axonal Computations

Axons functionally link the somato-dendritic compartment to synaptic terminals. Structurally and functionally diverse, they accomplish a central role in determining the delays and reliability with which neuronal ensembles communicate. By combining their active and passive biophysical properties, they ensure a plethora of physiological computations. In this review, we revisit the biophysics of generation and propagation of electrical signals in the axon and their dynamics. We further place the computational abilities of axons in the context of intracellular and intercellular coupling. We discuss how, by means of sophisticated biophysical mechanisms, axons expand the repertoire of axonal computation, and thereby, of neural computation.

Mechanical characterization of squid giant axon membrane sheath and influence of the collagenous endoneurium on its properties

To understand traumas to the nervous system, the relation between mechanical load and functional impairment needs to be explained. Cellular-level computational models are being used to capture the mechanism behind mechanically-induced injuries and possibly predict these events. However, uncertainties in the material properties used in computational models undermine the validity of their predictions. For this reason, in this study the squid giant axon was used as a model to provide a description of the axonal mechanical behavior in a large strain and high strain rate regime [Formula: see text], which is relevant for injury investigations. More importantly, squid giant axon membrane sheaths were isolated and tested under dynamic uniaxial tension and relaxation. From the lumen outward, the membrane sheath presents: an axolemma, a layer of Schwann cells followed by the basement membrane and a prominent layer of loose connective tissue consisting of fibroblasts and collagen. Our results highlight the load-bearing role of this enwrapping structure and provide a constitutive description that could in turn be used in computational models. Furthermore, tests performed on collagen-depleted membrane sheaths reveal both the substantial contribution of the endoneurium to the total sheath's response and an interesting increase in material nonlinearity when the collagen in this connective layer is digested. All in all, our results provide useful insights for modelling the axonal mechanical response and in turn will lead to a better understanding of the relationship between mechanical insult and electrophysiological outcome.