Evidence for two-dimensional solitary sound waves in a lipid controlled interface and its implications for biological signalling

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.

Information propagated by longitudinal pulses near a van der Waals phase transition

Longitudinal pulses that propagate in a medium near a van der Waals phase transition have a sigmoidal dependence on the strength of the stimulus arising from the phase structure. This response resembles the all-or-nothing property of action potentials, which raises the question if an acoustic system near a phase transition can be suitable for material-based neuromorphic computation. Herein, we investigate how information about the stimulus is stored within these pulses. We find that (1) the pulse propagates in parallel both digital and analog information about the stimulus amplitude; (2) the pulse encodes the type of stimulus, for instance, mechanical or thermal; and (3) a collision between two pulses stores information about both stimuli and may be used as a fading memory. Our results unravel a rich encoding of information in a phenomenon that is both common in a plethora of materials and mimics neuronal signaling. In addition, we show that these pulses carry more information than is typically considered by models of neural computation. Therefore, this phenomenon is an excellent candidate for in materio computation.

The excitable fluid mosaic

The Fluid Mosaic Model by Singer & Nicolson proposes that biological membranes consist of a fluid lipid layer into which integral proteins are embedded. The lipid membrane acts as a two-dimensional liquid in which the proteins can diffuse and interact. Until today, this view seems very reasonable and is the predominant picture in the literature. However, there exist broad melting transitions in biomembranes some 10-20 degrees below physiological temperatures that reach up to body temperature. Since they are found below body temperature, Singer & Nicolson did not pay any further attention to the melting process. But this is a valid view only as long as nothing happens. The transition temperature can be influenced by membrane tension, pH, ionic strength and other variables. Therefore, it is not generally correct that the physiological temperature is above this transition. The control over the membrane state by changing the intensive variables renders the membrane as a whole excitable. One expects phase behavior and domain formation that leads to protein sorting and changes in membrane function. Thus, the lipids become an active ingredient of the biological membrane. The melting transition affects the elastic constants of the membrane. This allows for the generation of propagating pulses in nerves and the formation of ion-channel-like pores in the lipid membranes. Here we show that on top of the fluid mosaic concept there exists a wealth of excitable phenomena that go beyond the original picture of Singer & Nicolson.¹.

Evidence for a transition in the cortical membranes of Paramecium

Ever since the pioneering studies in the 1960s and 70s, the importance of order transitions for cell membrane functions has remained a matter of debate. Recently, it has been proposed that the nonlinear stimulus-response curve of excitable cells, which manifests in all-or-none pulses (action potentials (AP)), is due to a transition in the cell membrane. Indeed, evidence for transitions has accumulated in plant cells and neurons, but studies with other excitable cells are expedient in order to show if this finding is of a general nature. Herein, we investigated intact, motile specimens of the "swimming neuron" Paramecium. The cellular membranes were labelled with the solvatochromic fluorophores LAURDAN or Di-4-ANEPPDHQ. Subsequently, a cell was trapped in a microfluidic channel and investigated by fluorescence spectroscopy. The generalized polarization (GP) of the fluorescence emission from cell cortical membranes (probably plasma and alveolar membranes) was extracted by an edge-finding algorithm. The thermo-optical state diagram, i.e. the dependence of GP on temperature, exhibited clear indications for a reversible transition. This transition had a width of ~10-15 °C and a midpoint that was located ~4 °C below the growth temperature. The state diagrams with LAURDAN and Di-4-ANEPPDHQ had widely identical characteristics. These results suggested that the cortical membranes of Paramecium reside in an order transition regime under physiological growth conditions. Based on these findings, membrane potential fluctuations, spontaneous depolarizing spikes, and thermal excitation of Paramecium was interpreted.

Contribution of the Collective Excitations to the Coupled Proton and Energy Transport along Mitochondrial Cristae Membrane in Oxidative Phosphorylation System

The results of many experimental and theoretical works indicate that after transport of protons across the mitochondrial inner membrane (MIM) in the oxidative phosphorylation (OXPHOS) system, they are retained on the membrane-water interface in nonequilibrium state with free energy excess due to low proton surface-to-bulk release. This well-established phenomenon suggests that proton trapping on the membrane interface ensures vectorial lateral transport of protons from proton pumps to ATP synthases (proton acceptors). Despite the key role of the proton transport in bioenergetics, the molecular mechanism of proton transfer in the OXPHOS system is not yet completely established. Here, we developed a dynamics model of long-range transport of energized protons along the MIM accompanied by collective excitation of localized waves propagating on the membrane surface. Our model is based on the new data on the macromolecular organization of the OXPHOS system showing the well-ordered structure of respirasomes and ATP synthases on the cristae membrane folds. We developed a two-component dynamics model of the proton transport considering two coupled subsystems: the ordered hydrogen bond (HB) chain of water molecules and lipid headgroups of MIM. We analytically obtained a two-component soliton solution in this model, which describes the motion of the proton kink, corresponding to successive proton hops in the HB chain, and coherent motion of a compression soliton in the chain of lipid headgroups. The local deformation in a soliton range facilitates proton jumps due to water molecules approaching each other in the HB chain. We suggested that the proton-conducting structures formed along the cristae membrane surface promote direct lateral proton transfer in the OXPHOS system. Collective excitations at the water-membrane interface in a form of two-component soliton ensure the coupled non-dissipative transport of charge carriers and elastic energy of MIM deformation to ATP synthases that may be utilized in ATP synthesis providing maximal efficiency in mitochondrial bioenergetics.

Unitary Response of Solvatochromic Dye to Pulse Excitation in Lipid and Cell Membranes

The existence of acoustic pulse propagation in lipid monolayers at the air-water interface is well known. These pulses are controlled by the thermodynamic state of the lipid membrane. Nevertheless, the role of acoustic pulses for intra- and inter-cellular communication is still a matter of debate. Herein, we used the dye di-4-ANEPPDHQ, which is known to be sensitive to the physical state and transmembrane potential of membranes, in order to gain insights into compression waves in lipid-based membrane interfaces. The dye was incorporated into lipid monolayers made of phosphatidylserine or phosphatidylcholine at the air-water-interface. A significant blue shift of the emission spectrum was detected when the state of the monolayer was changed from the liquid-expanded (LE) to the liquid-condensed (LC) phase. This "transition sensitivity" of di-4-ANEPPDHQ was generalized in experiments with the bulk solvent dimethyl sulfoxide (DMSO). Upon crystallization of solvent, the emission spectrum also underwent a blue shift. During compression pulses in lipid monolayers, a significant fluorescence response was only observed when the main transition is crossed. The optical signature of these waves─in terms of sign and magnitude─was identical to the response of di-4-ANEPPDHQ during action potentials in neurons and excitable plant cells. These findings corroborated the suggestion that action potentials are nonlinear state changes that propagate in the cell membrane.

The thermodynamic soliton theory of the nervous impulse and possible medical implications

The textbook picture of nerve activity is that of a propagating voltage pulse driven by electrical currents through ion channel proteins, which are gated by changes in voltage, temperature, pressure or by drugs. All function is directly attributed to single molecules. We show that this leaves out many important thermodynamic couplings between different variables. A more recent alternative picture for the nerve pulse is of thermodynamic nature. It considers the nerve pulse as a soliton, i.e., a macroscopic excited region with properties that are influenced by thermodynamic variables including voltage, temperature, pressure and chemical potentials of membrane components. All thermodynamic variables are strictly coupled. We discuss the consequences for medical treatment in a view where one can compensate a maladjustment of one variable by adjusting another variable. For instance, one can explain why anesthesia can be counteracted by hydrostatic pressure and decrease in pH, suggest reasons why lithium over-dose may lead to tremor, and how tremor is related to alcohol intoxication. Lithium action as well as the effect of ethanol and the anesthetic ketamine in bipolar patients may fall in similar thermodynamic patterns. Such couplings remain obscure in a purely molecular picture. Other fields of application are the response of nerve activity to muscle stretching and the possibility of neural stimulation by ultrasound.

The activity of the intrinsically water-soluble enzyme ADAMTS13 correlates with the membrane state when bound to a phospholipid bilayer

Membrane-associated enzymes have been found to behave differently qualitatively and quantitatively in terms of activity. These findings were highly debated in the 1970s and many general correlations and reaction specific models have been proposed, reviewed, and discarded. However, new biological applications brought up the need for clarification and elucidation. To address literature shortcomings, we chose the intrinsically water-soluble enzyme a disintegrin and metalloproteinase with a thrombospondin type 1 motif, member 13 (ADAMTS13) and large unilamellar vesicles with a relative broad phase transition. We here present activity measurements of ADAMTS13 in the freely dissolved state and the membrane associated state for phosphocholine lipids with different acyl-chain lengths (13:0, 14:0 and 15:0) and thus main phase transition temperatures. While the freely dissolved enzyme shows a simple Arrhenius behavior, the activity of membrane associated ADAMTS13 in addition shows a peak. This peak temperature correlates with the main phase transition temperature of the used lipids. These findings support an alternative theory of catalysis. This theory predicts a correlation of the membrane associated activity and the heat capacity, as both are susceptibilities of the same surface Gibb's free energy, since the enzyme is attached to the membrane.

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.

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.

Membrane-Mediated Activity of Local Anesthetics

The activity of local anesthetics (LAs) has been attributed to the inhibition of ion channels, causing anesthesia. However, there is a growing body of research showing that LAs act on a wide range of receptors and channel proteins far beyond simple analgesia. The current concept of ligand recognition may no longer explain the multitude of protein targets influenced by LAs. We hypothesize that LAs can cause anesthesia without directly binding to the receptor proteins just by changing the physical properties of the lipid bilayer surrounding these proteins and ion channels based on LAs' amphiphilicity. It is possible that LAs act in one of the following ways: They 1) dissolve raft-like membrane microdomains, 2) impede nerve impulse propagation by lowering the lipid phase transition temperature, or 3) modulate the lateral pressure profile of the lipid bilayer. This could also explain the numerous additional effects of LAs besides anesthesia. Furthermore, the concepts of membrane-mediated activity and binding to ion channels do not have to exclude each other. If we were to consider LA as the middle part of a continuum between unspecific membrane-mediated activity on one end and highly specific ligand binding on the other end, we could describe LA as the link between the unspecific action of general anesthetics and toxins with their highly specific receptor binding. This comprehensive membrane-mediated model offers a fresh perspective to clinical and pharmaceutical research and therapeutic applications of local anesthetics. SIGNIFICANCE STATEMENT: Local anesthetics, according to the World Health Organization, belong to the most important drugs available to mankind. Their rediscovery as therapeutics and not only anesthetics marks a milestone in global pain therapy. The membrane-mediated mechanism of action proposed in this review can explain their puzzling variety of target proteins and their thus far inexplicable therapeutic effects. The new concept presented here places LAs on a continuum of structures and molecular mechanisms in between small general anesthetics and the more complex molecular toxins.

On the Coupling between Mechanical Properties and Electrostatics in Biological Membranes

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

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 multiple biological roles of the cholinesterases

It is tacitly assumed that the biological role of acetylcholinesterase is termination of synaptic transmission at cholinergic synapses. However, together with its structural homolog, butyrylcholinesterase, it is widely distributed both within and outside the nervous system, and, in many cases, the role of both enzymes remains obscure. The transient appearance of the cholinesterases in embryonic tissues is especially enigmatic. The two enzymes' extra-synaptic roles, which are known as 'non-classical' roles, are the topic of this review. Strong evidence has been presented that AChE and BChE play morphogenetic roles in a variety of eukaryotic systems, and they do so either by acting as adhesion proteins, or as trophic factors. As trophic factors, one mode of action is to directly regulate morphogenesis, such as neurite outgrowth, by poorly understood mechanisms. The other mode is by regulating levels of acetylcholine, which acts as the direct trophic factor. Alternate substrates have been sought for the cholinesterases. Quite recently, it was shown that levels of the aggression hormone, ghrelin, which also controls appetite, are regulated by butyrylcholinesterase. The rapid hydrolysis of acetylcholine by acetylcholinesterase generates high local proton concentrations. The possible biophysical and biological consequences of this effect are discussed. The biological significance of the acetylcholinesterases secreted by parasitic nematodes is reviewed, and, finally, the involvement of acetylcholinesterase in apoptosis is considered.

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.

It sounds like an action potential: unification of electrical, chemical and mechanical aspects of acoustic pulses in lipids

In an ongoing debate on the physical nature of the action potential (AP), one group adheres to the electrical model of Hodgkin and Huxley, while the other describes the AP as a nonlinear acoustic pulse propagating within an interface near a transition. However, despite remarkable similarities, acoustics remains a non-intuitive mechanism for APs for the following reason. While acoustic pulses are typically associated with the propagation of density, pressure and temperature variation, APs are most commonly measured electrically. Here, we show that this discrepancy is lifted upon considering the electrical and chemical aspects of the interface, in addition to its mechanical properties. Specifically, we demonstrate how electrical and pH aspects of acoustic pulses emerge from an idealized description of the lipid interface, which is based on classical physical principles and contains no fit parameters. The pulses that emerge from the model show similarities to APs not only in qualitative shape and scales (time, velocity and voltage), but also demonstrate saturation of amplitude and annihilation upon collision.

Nonlinear pulses at the interface and its relation to state and temperature

Environmental temperature has a well-conserved effect on the pulse velocity and excitability of excitable biological systems. The consistency suggests that the cause originates from a fundamental principle. A physical (hydrodynamic) approach has proposed that the thermodynamic state of the hydrated interface (e.g., plasma membrane) determines the pulse behavior. This implies that the temperature effect happens because the environmental temperature affects the state of the interface in any given system. To test the hypothesis, we measured temperature-dependent phase diagrams of a lipid monolayer and studied the properties of nonlinear acoustic pulses excited along the membrane. We observed that the membrane in the fluid-gel transition regime exhibited lower compressibility (i.e., stiffer) overall with increasing temperature. Nonlinear pulses excited near the transition state propagated with greater velocity with increasing temperature, and these observations were consistent with the compressibility profiles. Excitability was suppressed significantly or ceased completely when the state departed too far from the transition regime either by cooling or by heating. The overall correlation between the pulses in the membrane and in living systems as a function of temperature supports the view that the thermodynamic state of the interface and phase transition are the key to understanding pulse propagation in excitable systems.

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.

Ultrasound Neuromodulation: A Review of Results, Mechanisms and Safety

Ultrasonic neuromodulation is a rapidly growing field, in which low-intensity ultrasound (US) is delivered to nervous system tissue, resulting in transient modulation of neural activity. This review summarizes the findings in the central and peripheral nervous systems from mechanistic studies in cell culture to cognitive behavioral studies in humans. The mechanisms by which US mechanically interacts with neurons and could affect firing are presented. An in-depth safety assessment of current studies shows that parameters for the human studies fall within the safety envelope for US imaging. Challenges associated with accurately targeting US and monitoring the response are described. In conclusion, the literature supports the use of US as a safe, non-invasive brain stimulation modality with improved spatial localization and depth targeting compared with alternative methods. US neurostimulation has the potential to be used both as a scientific instrument to investigate brain function and as a therapeutic modality to modulate brain activity.

Similarities between action potentials and acoustic pulses in a van der Waals fluid

An action potential is typically described as a purely electrical change that propagates along the membrane of excitable cells. However, recent experiments have demonstrated that non-linear acoustic pulses that propagate along lipid interfaces and traverse the melting transition, share many similar properties with action potentials. Despite the striking experimental similarities, a comprehensive theoretical study of acoustic pulses in lipid systems is still lacking. Here we demonstrate that an idealized description of an interface near phase transition captures many properties of acoustic pulses in lipid monolayers, as well as action potentials in living cells. The possibility that action potentials may better be described as acoustic pulses in soft interfaces near phase transition is illustrated by the following similar properties: correspondence of time and velocity scales, qualitative pulse shape, sigmoidal response to stimulation amplitude (an 'all-or-none' behavior), appearance in multiple observables (particularly, an adiabatic change of temperature), excitation by many types of stimulations, as well as annihilation upon collision. An implication of this work is that crucial functional information of the cell may be overlooked by focusing only on electrical measurements.

Cell Surface Deformation during an Action Potential

The excitation of many cells and tissues is associated with cell mechanical changes. The evidence presented herein corroborates that single cells deform during an action potential. It is demonstrated that excitation of plant cells (Chara braunii internodes) is accompanied by out-of-plane displacements of the cell surface in the micrometer range (∼1-10 μm). The onset of cellular deformation coincides with the depolarization phase of the action potential. The mechanical pulse: 1) propagates with the same velocity as the electrical pulse (within experimental accuracy, ∼10 mm s^-1), 2) is reversible, 3) in most cases is of biphasic nature (109 out of 152 experiments), and 4) is presumably independent of actin-myosin-motility. The existence of transient mechanical changes in the cell cortex is confirmed by micropipette aspiration experiments. A theoretical analysis demonstrates that this observation can be explained by a reversible change in the mechanical properties of the cell surface (transmembrane pressure, surface tension, and bending rigidity). Taken together, these findings contribute to the ongoing debate about the physical nature of cellular excitability.

Periodic soliton trains and informational code structures in an improved soliton model for biomembranes and nerves

Many experiments have shown that the action potential propagating in a nerve fiber is an electromechanical density pulse. A mathematical model proposed by Heimburg and Jackson is an important step in explaining the propagation of electromechanical pulses in nerves. In this work, we consider the dynamics of modulated waves in an improved soliton model for nerve pulses. Application of the reductive perturbation method on the resulting generalized Boussinesq equation in the low-amplitude and weak damping limit yields a damped nonlinear Schrödinger equation that is shown to admit soliton trains. This solution contains an undershoot beneath the baseline ("hyperpolarization") and a "refractory period," i.e., a minimum distance between pulses, and therefore it represents typical nerve profiles. Likewise, the linear stability of wave trains is analyzed. It is shown that the amplitude of the fourth-order mixed dispersive term introduced here can be used to control the amount of information transmitted along the nerve fiber. The results from the linear stability analysis show that, in addition to the main periodic wave trains observed in most nerve experiments, five other localized background modes can copropagate along the nerve. These modes could eventually be responsible for various fundamental processes in the nerve, such as phase transitions and electrical and mechanical changes. Furthermore, analytical and numerical analyses show that increasing the fourth-order mixed dispersion coefficient improves the stability of the nerve signal.

Wide-Field Functional Microscopy of Peripheral Nerve Injury and Regeneration

Severe peripheral nerve injuries often result in partial repair and lifelong disabilities in patients. New surgical techniques and better graft tissues are being studied to accelerate regeneration and improve functional recovery. Currently, limited tools are available to provide in vivo monitoring of changes in nerve physiology such as myelination and vascularization, and this has impeded the development of new therapeutic options. We have developed a wide-field and label-free functional microscopy platform based on angiographic and vectorial birefringence methods in optical coherence tomography (OCT). By incorporating the directionality of the birefringence, which was neglected in the previously reported polarization-sensitive OCT techniques for nerve imaging, vectorial birefringence contrast reveals internal nerve microanatomy and allows for quantification of local myelination with superior sensitivity. Advanced OCT angiography is applied in parallel to image the three-dimensional vascular networks within the nerve over wide-fields. Furthermore, by combining vectorial birefringence and angiography, intraneural vessels can be discriminated from those of the surrounding tissues. The technique is used to provide longitudinal imaging of myelination and revascularization in the rodent sciatic nerve model, i.e. imaged at certain sequential time-points during regeneration. The animals were exposed to either crush or transection injuries, and in the case of transection, were repaired using an autologous nerve graft or acellular nerve allograft. Such label-free functional imaging by the platform can provide new insights into the mechanisms that limit regeneration and functional recovery, and may ultimately provide intraoperative assessment in human subjects.

Bio-soliton model that predicts non-thermal electromagnetic frequency bands, that either stabilize or destabilize living cells

Solitons, as self-reinforcing solitary waves, interact with complex biological phenomena such as cellular self-organization. A soliton model is able to describe a spectrum of electromagnetism modalities that can be applied to understand the physical principles of biological effects in living cells, as caused by endogenous and exogenous electromagnetic fields and is compatible with quantum coherence. A bio-soliton model is proposed, that enables to predict which eigen-frequencies of non-thermal electromagnetic waves are life-sustaining and which are, in contrast, detrimental for living cells. The particular effects are exerted by a range of electromagnetic wave eigen-frequencies of one-tenth of a Hertz till Peta Hertz that show a pattern of 12 bands, and can be positioned on an acoustic reference frequency scale. The model was substantiated by a meta-analysis of 240 published articles of biological electromagnetic experiments, in which a spectrum of non-thermal electromagnetic waves were exposed to living cells and intact organisms. These data support the concept of coherent quantized electromagnetic states in living organisms and the theories of Fröhlich, Davydov and Pang. It is envisioned that a rational control of shape by soliton-waves and related to a morphogenetic field and parametric resonance provides positional information and cues to regulate organism-wide systems properties like anatomy, control of reproduction and repair.

On the Physical Basis of Biological Signaling by Interface Pulses

Currently, biological signaling is envisaged as a combination of activation and movement, triggered by local molecular interactions and molecular diffusion, respectively. However, here, we suggest that other fundamental physical mechanisms might play an at least equally important role. We have recently shown that lipid interfaces permit the excitation and propagation of sound pulses. Here, we demonstrate that these reversible perturbations can control the activity of membrane-embedded enzymes without a requirement for molecular transport. They can thus facilitate rapid communication between distant biological entities at the speed of sound, which is here on the order of 1 m/s within the membrane. The mechanism described provides a new physical framework for biological signaling that is fundamentally different from the molecular approach that currently dominates the textbooks.

Surface deformation during an action potential in pearled cells

Electric pulses in biological cells (action potentials) have been reported to be accompanied by a propagating cell-surface deformation with a nanoscale amplitude. Typically, this cell surface is covered by external layers of polymer material (extracellular matrix, cell wall material, etc.). It was recently demonstrated in excitable plant cells (Chara braunii) that the rigid external layer (cell wall) hinders the underlying deformation. When the cell membrane was separated from the cell wall by osmosis, a mechanical deformation, in the micrometer range, was observed upon excitation of the cell. The underlying mechanism of this mechanical pulse has, to date, remained elusive. Herein we report that Chara cells can undergo a pearling instability, and when the pearled fragments were excited even larger and more regular cell shape changes were observed (∼10-100μm in amplitude). These transient cellular deformations were captured by a curvature model that is based on three parameters: surface tension, bending rigidity, and pressure difference across the surface. In this paper these parameters are extracted by curve-fitting to the experimental cellular shapes at rest and during excitation. This is a necessary step to identify the mechanical parameters that change during an action potential.

Nerve conduction models in myelinated and unmyelinated nerves based on three-dimensional electrostatic interaction

Until now, nerve conduction has been described on the basis of equivalent circuit model and cable theory, both of which supposed closed electric circuits spreading inside and outside the axoplasm. With these conventional models, we can simulate the propagating pattern of action potential along the axonal membrane based on Ohm’s law and Kirchhoff’s law. However, we could not fully explain the different conductive patterns in unmyelinated and myelinated nerves with these theories. Also, whether we can really suppose closed electrical circuits in the actual site of the nerves or not has not been fully discussed yet. In this report, a recently introduced new theoretical model of nerve conduction based on electrostatic molecular interactions within the axoplsm will be reviewed. With this new approach, we can explain the different conductive patterns in unmyelinated and myelinated nerves. This new mathematical conductive model based on electrostatic compressional wave in the intracellular fluid may also be able to explain the signal integration in the neuronal cell body and the back-propagation mechanism from the axons to the dendrites. With this new mathematical nerve conduction model based on electrostatic molecular interactions within the intracellular fluid, we may be able to achieve an integrated explanation for the physiological phenomena taking place in the nervous system.

Collision of two action potentials in a single excitable cell

BACKGROUND

It is a common incident in nature, that two waves or pulses run into each other head-on. The outcome of such an event is of special interest, because it allows conclusions about the underlying physical nature of the pulses. The present experimental study dealt with the head-on meeting of two action potentials (AP) in a single excitable plant cell (Chara braunii internode).

METHODS

The membrane potential was monitored with multiple sensors along a single excitable cell. In control experiments, an AP was excited electrically at either end of the cell cylinder. Subsequently, stimuli were applied simultaneously at both ends of the cell in order to generate two APs that met each other head-on.

RESULTS

When two action potentials propagated into each other, the pulses did not penetrate but annihilated (N=26 experiments in n=10 cells).

CONCLUSIONS

APs in excitable plant cells did not penetrate upon meeting head-on. In the classical electrical model, this behavior is specifically attributed to relaxation of ion channel proteins. From an acoustic point of view, annihilation can be viewed as a result of nonlinear material properties (e.g. a phase change).

GENERAL SIGNIFICANCE

The present results suggest that APs in excitable animal and plant cells belong to a similar class of nonlinear phenomena. Intriguingly, other excitation waves in biology (intracellular waves, cortical spreading depression, etc.) also annihilate upon collision and are thus expected to follow the same underlying principles as the observed action potentials.

Propagation of a thermo-mechanical perturbation on a lipid membrane

The propagation of sound waves on lipid monolayers supported on water has been previously studied during the melting transition. Since changes in volume, area, and compressibility in lipid membranes have biological relevance, the observed sound propagation is of paramount importance. However, it is unknown what would occur on a lipid bilayer, which is a more approximate model of a cell membrane. With the aim to answer this relevant question, we built an experimental setup to assemble long artificial lipid membranes. We found that if these membranes are heated in order to force local melting, a thermo-mechanical perturbation propagates a long distance. Our findings may support the existence of solitary waves, postulated to explain the propagation of isentropic signals together with the action potential in neurons.

Stress Propagation through Biological Lipid Bilayers in Silico

Membrane tension plays various critical roles in the cell. We here asked how fast and how far localized pulses of mechanical stress dynamically propagate through biological lipid bilayers. In both coarse-grained and all-atom molecular dynamics simulations of a dipalmitoylphosphatidylcholine lipid bilayer, we observed nanometer-wide stress pulses, propagating very efficiently longitudinally at a velocity of approximately 1.4 ± 0.5 nm/ps (km/s), in close agreement with the expected speed of sound from experiments. Remarkably, the predicted characteristic attenuation time of the pulses was in the order of tens of picoseconds, implying longitudinal stress propagation over length scales up to several tens of nanometers before damping. Furthermore, the computed dispersion relation leading to such damping was consistent with proposed continuum viscoelastic models of propagation. We suggest this mode of stress propagation as a potential ultrafast mechanism of signaling that may quickly couple mechanosensitive elements in crowded biological membranes.

Label-free optical detection of action potential in mammalian neurons

We describe an optical technique for label-free detection of the action potential in cultured mammalian neurons. Induced morphological changes due to action potential propagation in neurons are optically interrogated with a phase sensitive interferometric technique. Optical recordings composed of signal pulses mirror the electrical spike train activity of individual neurons in a network. The optical pulses are transient nanoscale oscillatory changes in the optical path length of varying peak magnitude and temporal width. Exogenous application of glutamate to cortical neuronal cultures produced coincident increase in the electrical and optical activity; both were blocked by application of a Na-channel blocker, Tetrodotoxin. The observed transient change in optical path length in a single optical pulse is primarily due to physical fluctuations of the neuronal cell membrane mediated by a yet unknown electromechanical transduction phenomenon. Our analysis suggests a traveling surface wave in the neuronal cell membrane is responsible for the measured optical signal pulses.

Protons at the speed of sound: Predicting specific biological signaling from physics

Local changes in pH are known to significantly alter the state and activity of proteins and enzymes. pH variations induced by pulses propagating along soft interfaces (e.g. membranes) would therefore constitute an important pillar towards a physical mechanism of biological signaling. Here we investigate the pH-induced physical perturbation of a lipid interface and the physicochemical nature of the subsequent acoustic propagation. Pulses are stimulated by local acidification and propagate - in analogy to sound - at velocities controlled by the interface's compressibility. With transient local pH changes of 0.6 directly observed at the interface and velocities up to 1.4 m/s this represents hitherto the fastest protonic communication observed. Furthermore simultaneously propagating mechanical and electrical changes in the lipid interface are detected, exposing the thermodynamic nature of these pulses. Finally, these pulses are excitable only beyond a threshold for protonation, determined by the pKa of the lipid head groups. This protonation-transition plus the existence of an enzymatic pH-optimum offer a physical basis for intra- and intercellular signaling via sound waves at interfaces, where not molecular structure and mechano-enyzmatic couplings, but interface thermodynamics and thermodynamic transitions are the origin of the observations.

Solitary shock waves and adiabatic phase transition in lipid interfaces and nerves

This study shows that the stability of solitary waves excited in a lipid monolayer near a phase transition requires positive curvature of the adiabats, a known necessary condition in shock compression science. It is further shown that the condition results in a threshold for excitation, saturation of the wave's amplitude, and the splitting of the wave at the phase boundaries. Splitting in particular confirms that a hydrated lipid interface can undergo condensation on adiabatic heating, thus showing retrograde behavior. Finally, using the theoretical insights and state dependence of conduction velocity in nerves, the curvature of the adiabatic state diagram is shown to be closely tied to the thermodynamic blockage of nerve pulse propagation.