Electricity and mechanics of biomembrane systems: Flexoelectricity in living membranes

Advancements and Prospects of Flexoelectricity

The flexoelectric effect, as a novel form of the electromechanical coupling phenomenon, has attracted significant attention in the fields of materials science and electronic devices. It refers to the interaction between strain gradients and electric dipole moments or electric field intensity gradients and strain. In contrast to the traditional piezoelectric effect, the flexoelectric effect is not limited by material symmetry or the Curie temperature and exhibits a stronger effect at the nanoscale. The flexoelectric effect finds widespread applications ranging from energy harvesting to electronic device design. Utilizing the flexoelectric effect, enhanced energy harvesters, sensitive sensors, and high-performance wearable electronic devices can be developed. Additionally, the flexoelectric effect can be utilized to modulate the optoelectronic properties and physical characteristics of materials, holding the potential for significant applications in areas such as optoelectronic devices, energy storage devices, and flexible electronics. This review provides a comprehensive overview of the historical development, measurement of flexoelectric coefficients, enhancement mechanisms, and current research progress of the flexoelectric effect. Additionally, it offers a perspective on future prospects of the flexoelectric effect.

Modeling ultrasound modulation of neural function in a single cell

Background

Low intensity ultrasound stimulation has been shown to non-invasively modulate neural function in the central nervous system (CNS) and peripheral nervous system (PNS) with high precision. Ultrasound sonication is capable of either excitation or inhibition, depending on the ultrasound parameters used. On the other hand, the mode of interaction of ultrasonic waves with the neural tissue for effective neuromodulation remains ambiguous.

New method

Here within we propose a numerical model that incorporates the mechanical effects of ultrasound stimulation on the Hodgkin-Huxley (HH) neuron by incorporating the relation between increased external pressure and the membrane induced tension, with a stress on the flexoelectric effect on the neural membrane. The external pressure causes an increase in the total tension of the membrane thus affecting the probability of the ion channels being open after the conformational changes that those channels undergo.

Results

The interplay between varying the acoustic intensities and frequencies depicts different action potential suppression rates, whereby a combination of low intensity and low frequency ultrasound sonication proved to be the most effective in modulating neural function.Comparison with Existing Methods: Our method solely depends on the HH model of a single neuron and the linear flexoelectric effect of the dielectric neural membrane, when under an ultrasound-induced mechanical strain, while varying the ion-channels conductances based on different sonication frequencies and intensities. We study the effect of ultrasound parameters on the firing rate, latency, and action potential amplitude of a HH neuron for a better understanding of the neuromodulation modality of ultrasound stimulation (in the continuous and pulsed modes).

Conclusions

This simulation work confirms the published experimental data that low intensity and low frequency ultrasound sonication has a higher success rate of modulating neural firing.

The giant flexoelectric effect in a luffa plant-based sponge for green devices and energy harvesters

Soft materials that can produce electrical energy under mechanical stimulus or deform significantly via moderate electrical fields are important for applications ranging from soft robotics to biomedical science. Piezoelectricity, the property that would ostensibly promise such a realization, is notably absent from typical soft matter. Flexoelectricity is an alternative form of electromechanical coupling that universally exists in all dielectrics and can generate electricity under nonuniform deformation such as flexure and conversely, a deformation under inhomogeneous electrical fields. The flexoelectric coupling effect is, however, rather modest for most materials and thus remains a critical bottleneck. In this work, we argue that a significant emergent flexoelectric response can be obtained by leveraging a hierarchical porous structure found in biological materials. We experimentally illustrate our thesis for a natural dry luffa vegetable-based sponge and demonstrate an extraordinarily large mass- and deformability-specific electromechanical response with the highest-density-specific equivalent piezoelectric coefficient known for any material (50 times that of polyvinylidene fluoride and more than 10 times that of lead zirconate titanate). Finally, we demonstrate the application of the fabricated natural sponge as green, biodegradable flexible smart devices in the context of sensing (e.g., for speech, touch pressure) and electrical energy harvesting.

Cations Control Lipid Bilayer Memcapacitance Associated with Long-Term Potentiation

Phospholipid bilayers can be described as capacitors whose capacitance per unit area (specific capacitance, Cm) is determined by their thickness and dielectric constant─independent of applied voltage. It is also widely assumed that the Cm of membranes can be treated as a "biological constant". Recently, using droplet interface bilayers (DIBs), it was shown that zwitterionic phosphatidylcholine (PC) lipid bilayers can act as voltage-dependent, nonlinear memory capacitors, or memcapacitors. When exposed to an electrical "training" stimulation protocol, capacitive energy storage in lipid membranes was enhanced in the form of long-term potentiation (LTP), which enables biological learning and long-term memory. LTP was the result of membrane restructuring and the progressive asymmetric distribution of ions across the lipid bilayer during training, which is analogous, for example, to exponential capacitive energy harvesting from self-powered nanogenerators. Here, we describe how LTP could be produced from a membrane that is continuously pumped into a nonequilibrium steady state, altering its dielectric properties. During this time, the membrane undergoes static and dynamic changes that are fed back to the system's potential energy, ultimately resulting in a membrane whose modified molecular structure supports long-term memory storage and LTP. We also show that LTP is very sensitive to different salts (KCl, NaCl, LiCl, and TmCl3), with LiCl and TmCl3 having the most profound effect in depressing LTP, relative to KCl. This effect is related to how the different cations interact with the bilayer zwitterionic PC lipid headgroups primarily through electric-field-induced changes to the statistically averaged orientations of water dipoles at the bilayer headgroup interface.

Modeling of Calcium-dependent Low Intensity Low Frequency Ultrasound Modulation of a Hodgkin-Huxley Neuron

Non-invasive low intensity, low frequency ultrasound is a progressive neuromodulation approach that can reach deep brain areas with peak spatial and temporal resolution for highly-targeted diagnostic and therapeutic purposes. Coupling the ultrasound mechanical effects to the neural membrane comprises different mechanisms that are, to-date, still a topic of debate. The availability of calcium ions in the extracellular medium is of high significance when it comes to the effect of ultrasound on the neural tissue. Whereby the generated calcium influx can directly affect the voltage-gated ion channels, amplifying their action. We modeled the flexoelectric-induced effects of ultrasound to a single firing neuron, taking into consideration the effect of calcium channel embedding into the neural membrane on the neuron's firing rate, latency response, peak-to-peak voltage, and general shape of the action potential.Clinical Relevance- Upon Ultrasound sonication, the mechanical waves interact with the neural membrane and alter the kinetics of the calcium channels, thus changing the neural response.

The effect of the subthreshold oscillation induced by the neurons' resonance upon the electrical stimulation-dependent instability

Repetitive electrical nerve stimulation can induce a long-lasting perturbation of the axon's membrane potential, resulting in unstable stimulus-response relationships. Despite being observed in electrophysiology, the precise mechanism underlying electrical stimulation-dependent (ES-dependent) instability is still an open question. This study proposes a model to reveal a facet of this problem: how threshold fluctuation affects electrical nerve stimulations. This study proposes a new method based on a Circuit-Probability theory (C-P theory) to reveal the interlinkages between the subthreshold oscillation induced by neurons' resonance and ES-dependent instability of neural response. Supported by in-vivo studies, this new model predicts several key characteristics of ES-dependent instability and proposes a stimulation method to minimize the instability. This model provides a powerful tool to improve our understanding of the interaction between the external electric field and the complexity of the biophysical characteristics of axons.

A flexoelectricity-enabled ultrahigh piezoelectric effect of a polymeric composite foam as a strain-gradient electric generator

All dielectric materials including ceramics, semiconductors, biomaterials, and polymers have the property of flexoelectricity, which opens a fertile avenue to sensing, actuation, and energy harvesting by a broad range of materials. However, the flexoelectricity of solids is weak at the macroscale. Here, we achieve an ultrahigh flexoelectric effect via a composite foam based on PDMS and CCTO nanoparticles. The mass- and deformability-specific flexoelectricity of the foam exceeds 10,000 times that of the solid matrix under compression, yielding a density-specific equivalent piezoelectric coefficient 120 times that of PZT. The flexoelectricity output remains stable in 1,000,000 deformation cycles, and a portable sample can power LEDs and charge mobile phones and Bluetooth headsets. Our work provides a route to exploiting flexible and light-weight materials with highly sensitive omnidirectional electromechanical coupling that have applications in sensing, actuation, and scalable energy harvesting.

Label-Free Imaging of Membrane Potentials by Intramembrane Field Modulation, Assessed by Second Harmonic Generation Microscopy

Optical interrogation of cellular electrical activity has proven itself essential for understanding cellular function and communication in complex networks. Voltage-sensitive dyes are important tools for assessing excitability but these highly lipophilic sensors may affect cellular function. Label-free techniques offer a major advantage as they eliminate the need for these external probes. In this work, it is shown that endogenous second-harmonic generation (SHG) from live cells is highly sensitive to changes in transmembrane potential (TMP). Simultaneous electrophysiological control of a living human embryonic kidney (HEK293T) cell, through a whole-cell voltage-clamp reveals a linear relation between the SHG intensity and membrane voltage. The results suggest that due to the high ionic strengths and fast optical response of biofluids, membrane hydration is not the main contributor to the observed field sensitivity. A conceptual framework is further provided that indicates that the SHG voltage sensitivity reflects the electric field within the biological asymmetric lipid bilayer owing to a nonzero χeff(2) tensor. Changing the TMP without surface modifications such as electrolyte screening offers high optical sensitivity to membrane voltage (≈40% per 100 mV), indicating the power of SHG for label-free read-out. These results hold promise for the design of a non-invasive label-free read-out tool for electrogenic cells.

Curvature effects in charge-regulated lipid bilayers

We formulate a theory of electrostatic interactions in lipid bilayer membranes where both monolayer leaflets contain dissociable moieties that are subject to charge regulation. We specifically investigate the coupling between membrane curvature and charge regulation of a lipid bilayer vesicle using both the linear Debye-Hückel (DH) and the non-linear Poisson-Boltzmann (PB) theory. We find that charge regulation of an otherwise symmetric bilayer membrane can induce charge symmetry breaking, non-linear flexoelectricity and anomalous curvature dependence of free energy. The pH effects investigated go beyond the paradigm of electrostatic renormalization of the mechano-elastic properties of membranes.

White matter tract transcranial ultrasound stimulation, a computational study

Low-intensity transcranial ultrasound stimulation (TUS) is poised to become one of the most promising treatments for neurological disorders. However, while recent animal model experiments have successfully quantified the alterations of the functional activity coupling between a sonicated target cortical region and other cortical regions of interest (ROIs), the varying degree of alteration between these different connections remains unexplained. We hypothesise here that the incidental sonication of the tracts leaving the target region towards the different ROIs could participate in explaining these differences. To this end, we propose a tissue level phenomenological numerical model of the coupling between the ultrasound waves and the white matter electrical activity. The model is then used to reproduce in silico the sonication of the anterior cingulate cortex (ACC) of a macaque monkey and measure the neuromodulation power within the white matter tracts leaving the ACC for five cortical ROIs. The results show that the more induced power a white matter tract proximal to the ACC and connected to a secondary ROI receives, the more altered the connectivity fingerprint of the ACC to this region will be after sonication. These results point towards the need to isolate the sonication to the cortical region and minimise the spillage on the neighbouring tracts when aiming at modulating the target region without losing the functional connectivity with other ROIs. Those results further emphasise the potential role of the white matter in TUS and the need to account for white matter topology when designing TUS protocols.

Mechanisms and Applications of Neuromodulation Using Surface Acoustic Waves-A Mini-Review

The study of neurons is fundamental for basic neuroscience research and treatment of neurological disorders. In recent years ultrasound has been increasingly recognized as a viable method to stimulate neurons. However, traditional ultrasound transducers are limited in the scope of their application by self-heating effects, limited frequency range and cavitation effects during neuromodulation. In contrast, surface acoustic wave (SAW) devices, which are producing wavemodes with increasing application in biomedical devices, generate less self-heating, are smaller and create less cavitation. SAW devices thus have the potential to address some of the drawbacks of traditional ultrasound transducers and could be implemented as miniaturized wearable or implantable devices. In this mini review, we discuss the potential mechanisms of SAW-based neuromodulation, including mechanical displacement, electromagnetic fields, thermal effects, and acoustic streaming. We also review the application of SAW actuation for neuronal stimulation, including growth and neuromodulation. Finally, we propose future directions for SAW-based neuromodulation.

Non-linear Conductance, Rectification, and Mechanosensitive Channel Formation of Lipid Membranes

There is mounting evidence that lipid bilayers display conductive properties. However, when interpreting the electrical response of biological membranes to voltage changes, they are commonly considered as inert insulators. Lipid bilayers under voltage-clamp conditions display current traces with discrete conduction-steps, which are indistinguishable from those attributed to the presence of protein channels. In current-voltage (I-V) plots they may also display outward rectification, i.e., voltage-gating. Surprisingly, this has even been observed in chemically symmetric lipid bilayers. Here, we investigate this phenomenon using a theoretical framework that models the electrostrictive effect of voltage on lipid membranes in the presence of a spontaneous polarization, which can be recognized by a voltage offset in electrical measurements. It can arise from an asymmetry of the membrane, for example from a non-zero spontaneous curvature of the membrane. This curvature can be caused by voltage via the flexoelectric effect, or by hydrostatic pressure differences across the membrane. Here, we describe I-V relations for lipid membranes formed at the tip of patch pipettes situated close to an aqueous surface. We measured at different depths relative to air/water surface, resulting in different pressure gradients across the membrane. Both linear and non-linear I-V profiles were observed. Non-linear conduction consistently takes the form of outward rectified currents. We explain the conductance properties by two mechanisms: One leak current with constant conductance without pores, and a second process that is due to voltage-gated pore opening correlating with the appearance of channel-like conduction steps. In some instances, these non-linear I-V relations display a voltage regime in which dI/dV is negative. This has also been previously observed in the presence of sodium channels. Experiments at different depths reveal channel formation that depends on pressure gradients. Therefore, we find that the channels in the lipid membrane are both voltage-gated and mechanosensitive. We also report measurements on black lipid membranes that also display rectification. In contrast to the patch experiments they are always symmetric and do not display a voltage offset.

A Physical Perspective to the Inductive Function of Myelin-A Missing Piece of Neuroscience

Starting from the inductance in neurons, two physical origins are discussed, which are the coil inductance of myelin and the piezoelectric effect of the cell membrane. The direct evidence of the coil inductance of myelin is the opposite spiraling phenomenon between adjacent myelin sheaths confirmed by previous studies. As for the piezoelectric effect of the cell membrane, which has been well-known in physics, the direct evidence is the mechanical wave accompany with action potential. Therefore, a more complete physical nature of neural signals is provided. In conventional neuroscience, the neural signal is a pure electrical signal. In our new theory, the neural signal is an energy pulse containing electrical, magnetic, and mechanical components. Such a physical understanding of the neural signal and neural systems significantly improve the knowledge of the neurons. On the one hand, we achieve a corrected neural circuit of an inductor-capacitor-capacitor (LCC) form, whose frequency response and electrical characteristics have been validated by previous studies and the modeling fitting of artifacts in our experiments. On the other hand, a number of phenomena observed in neural experiments are explained. In particular, they are the mechanism of magnetic nerve stimulations and ultrasound nerve stimulations, the MRI image contrast issue and Anode Break Excitation. At last, the biological function of myelin is summarized. It is to provide inductance in the process of neural signal, which can enhance the signal speed in peripheral nervous systems and provide frequency modulation function in central nervous systems.

Topological-Defect-Induced Surface Charge Heterogeneities in Nematic Electrolytes

We show that topological defects in an ion-doped nematic liquid crystal can be used to manipulate the surface charge distribution on chemically homogeneous, charge-regulating external surfaces, using a minimal theoretical model. In particular, the location and type of the defect encodes the precise distribution of surface charges and the effect is enhanced when the liquid crystal is flexoelectric. We demonstrate the principle for patterned surfaces and charged colloidal spheres. More generally, our results indicate an interesting approach to control surface charges on external surfaces without changing the surface chemistry.

Ultrasound neuromodulation: mechanisms and the potential of multimodal stimulation for neuronal function assessment

Focused ultrasound (FUS) neuromodulation has shown that mechanical waves can interact with cell membranes and mechanosensitive ion channels, causing changes in neuronal activity. However, the thorough understanding of the mechanisms involved in these interactions are hindered by different experimental conditions for a variety of animal scales and models. While the lack of complete understanding of FUS neuromodulation mechanisms does not impede benefiting from the current known advantages and potential of this technique, a precise characterization of its mechanisms of action and their dependence on experimental setup (e.g., tuning acoustic parameters and characterizing safety ranges) has the potential to exponentially improve its efficacy as well as spatial and functional selectivity. This could potentially reach the cell type specificity typical of other, more invasive techniques e.g., opto- and chemogenetics or at least orientation-specific selectivity afforded by transcranial magnetic stimulation. Here, the mechanisms and their potential overlap are reviewed along with discussions on the potential insights into mechanisms that magnetic resonance imaging sequences along with a multimodal stimulation approach involving electrical, magnetic, chemical, light, and mechanical stimuli can provide.

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

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

Analytical Electromechanical Modeling of Nanoscale Flexoelectric Energy Harvesting

With the attention focused on harvesting energy from the ambient environment for nanoscale electronic devices, electromechanical coupling effects in materials have been studied for many potential applications. Flexoelectricity can be observed in all dielectric materials, coupling the strain gradients and polarization, and may lead to strong size-dependent effects at the nanoscale. This paper investigates the flexoelectric energy harvesting under the harmonic mechanical excitation, based on a model similar to the classical Euler–Bernoulli beam theory. The electric Gibbs free energy and the generalized Hamilton’s variational principle for a flexoelectric body are used to derive the coupled governing equations for flexoelectric beams. The closed-form electromechanical expressions are obtained for the steady-state response to the harmonic mechanical excitation in the flexoelectric cantilever beams. The results show that the voltage output, power density, and mechanical vibration response exhibit significant scale effects at the nanoscale. Especially, the output power density for energy harvesting has an optimal value at an intrinsic length scale. This intrinsic length is proportional to the material flexoelectric coefficient. Moreover, it is found that the optimal load resistance for peak power density depends on the beam thickness at the small scale with a critical thickness. Our research indicates that flexoelectric energy harvesting could be a valid alternative to piezoelectric energy harvesting at micro- or nanoscales.

Flexoelectret: An Electret with a Tunable Flexoelectriclike Response

Because of the flexoelectric effect, dielectric materials usually polarize in response to a strain gradient. Soft materials are good candidates for developing a large strain gradient because of their good deformability. However, they always suffer from lower flexoelectric coefficients compared to ceramics. In this work, a flexoelectriclike effect is introduced to enhance the effective flexoelectricity of a polydimethylsiloxane bar. The flexoelectriclike effect is realized by depositing a layer of net charges on the middle plane of the bar to form an electret. Experiments show that the enhancement of flexoelectricity depends on the density of inserted net charges. It is found that a charged layer with surface potential of -5723  V results in a 100 times increase of the material's flexoelectric coefficient. We also show that the enhancement is proportional to the thickness of electrets. This work provides a new way of enhancing flexoelectricity in soft materials and further prompts the application of soft materials in electromechanical transducers.

Nonlinear bending deformation of soft electrets and prospects for engineering flexoelectricity and transverse (d31) piezoelectricity

Soft materials that exhibit electromechanical coupling are an important element in the development of soft robotics, flexible and stretchable electronics, energy harvesters, sensor and actuators. Truly soft natural piezoelectrics essentially do not exist and typical dielectric elastomers, predicated on electrostriction and the Maxwell stress effect, exhibit only a one-way electromechanical coupling. Extensive research however has shown that soft electrets i.e. materials with embedded immobile charges and dipoles, can be artificially engineered to exhibit a rather large piezoelectric-like effect. Unfortunately, this piezoelectric effect-large as it may be-is primarily restricted to an electromechanical coupling in the longitudinal direction or what is referred colloquially as the d33 piezoelectric coefficient. In sharp contrast, the transverse piezoelectric property (the so-called d31 coefficient) is rather small. This distinction has profound implications since these soft electrets exhibit negligible electromechanical coupling under bending deformation. As a result, the typically engineered soft electrets are rendered substantively ill-suited for energy harvesting as well as actuation/sensing of flexure motion that plays a critical role in applications like soft robotics. In this work, we analyze nonlinear bending deformation of a soft electret structure and examine the precise conditions that may lead to a strong emergent piezoelectric response under bending. Furthermore, we show that non-uniformly distributed dipoles and charges in the soft electrets lead to an apparent electromechanical response that may be ambiguously and interchangeably interpreted as either transverse piezoelectricity or flexoelectricity. We suggest pragmatic routes to engineer a large transverse piezoelectric (d31) and flexoelectric coefficient in soft electrets. Finally, we show that in an appropriately designed soft electret, even a uniform external electric field can induce curvature in the structure thus enabling its application as a bending actuator.

Detection of Curvature-Radius-Dependent Interfacial pH/Polarity for Amphiphilic Self-Assemblies: Positive versus Negative Curvature

It is possible that a defined curvature at the membrane interface controls its pH/polarity to exhibit specific bioactivity. By utilizing an interface-interacting spiro-rhodamine pH probe and the Schiff base polarity probe, we have shown that the pH deviation from the bulk phase to the interface (ΔpH)/interfacial dielectric constant (κ(i)) for amphiphilic self-assemblies can be regulated by the curvature geometry (positive/negative) and its radius. According to ¹H NMR and fluorescence anisotropy investigations, the probes selectively interact with an anionic interfacial Stern layer. The ΔpH/κ(i) values for the Stern layer are estimated by UV-vis absorption and fluorescence studies. For the anionic sodium bis-2-ethylhexyl-sulfosuccinate (AOT) inverted micellar (IM) negative interface, the highly restricted water and proton penetration into the Stern layer owing to tight surfactant packing or a reduced water-exposed headgroup area may be responsible for the much lower ΔpH ≈ -0.45 and κ(i) ≈ 28 in comparison to ∼-2.35 and ∼44, respectively, for the anionic sodium dodecyl sulfate (SDS) micellar positive interface with a close similar Stern layer. With increasing AOT IM water-pool radius (1.7-9.5 nm) or [water]/[AOT] ratio ( w₀) (8.0-43.0), the ΔpH and κ(i) increase maximally up to ∼-1.22 and ∼45, respectively, due to a greater water-exposed headgroup area. However, the unchanged ΔpH ≈ -0.65 and κ(i) ≈ 53.0 within radii ∼3.5-8.0 nm for the positive interface of a mixed Triton X-100 (TX-100)/SDS (4:1) micelle justify its packing flexibility. Interestingly, the continuously increasing ΔpH trend for IM up to its largest possible water-pool radius of ∼9.5 nm may rationalize the increase in ΔpH (∼-1.4 to -1.6) with the change in the curvature radii (∼15 to 50 nm) for sodium 1,2-dimyristoyl- sn-glycero-3-phosphorylglycerol (DMPG)/1,2-dimyristoyl- sn-glycero-3-phosphocholine (DMPC) (2:1) large unilamellar vesicles (LUV) owing to its negative interface. Whereas, similar to the micellar positive interface, the unchanged ΔpH at the positive LUV interface was confirmed by fluorescence microscopic studies with giant unilamellar vesicles of identical lipids composition. The present study offers a unique and simple method of monitoring the curvature-radius-dependent interfacial pH/polarity for biologically related membranes.

Imaging Action Potential in Single Mammalian Neurons by Tracking the Accompanying Sub-Nanometer Mechanical Motion

Action potentials in neurons have been studied traditionally by intracellular electrophysiological recordings and more recently by the fluorescence detection methods. Here we describe a label-free optical imaging method that can measure mechanical motion in single cells with a sub-nanometer detection limit. Using the method, we have observed sub-nanometer mechanical motion accompanying the action potential in single mammalian neurons by averaging the repeated action potential spikes. The shape and width of the transient displacement are similar to those of the electrically recorded action potential, but the amplitude varies from neuron to neuron, and from one region of a neuron to another, ranging from 0.2-0.4 nm. The work indicates that action potentials may be studied noninvasively in single mammalian neurons by label-free imaging of the accompanying sub-nanometer mechanical motion.

Toward a Reasoned Classification of Diseases Using Physico-Chemical Based Phenotypes

Background: Diseases and health conditions have been classified according to anatomical site, etiological, and clinical criteria. Physico-chemical mechanisms underlying the biology of diseases, such as the flow of energy through cells and tissues, have been often overlooked in classification systems.

Objective: We propose a conceptual framework toward the development of an energy-oriented classification of diseases, based on the principles of physical chemistry.

Methods: A review of literature on the physical chemistry of biological interactions in a number of diseases is traced from the point of view of the fluid and solid mechanics, electricity, and chemistry.

Results: We found consistent evidence in literature of decreased and/or increased physical and chemical forces intertwined with biological processes of numerous diseases, which allowed the identification of mechanical, electric and chemical phenotypes of diseases.

Discussion: Biological mechanisms of diseases need to be evaluated and integrated into more comprehensive theories that should account with principles of physics and chemistry. A hypothetical model is proposed relating the natural history of diseases to mechanical stress, electric field, and chemical equilibria (ATP) changes. The present perspective toward an innovative disease classification may improve drug-repurposing strategies in the future.

Control of electro-chemical processes using energy harvesting materials and devices

Energy harvesting is a topic of intense interest that aims to convert ambient forms of energy such as mechanical motion, light and heat, which are otherwise wasted, into useful energy. In many cases the energy harvester or nanogenerator converts motion, heat or light into electrical energy, which is subsequently rectified and stored within capacitors for applications such as wireless and self-powered sensors or low-power electronics. This review covers the new and emerging area that aims to directly couple energy harvesting materials and devices with electro-chemical systems. The harvesting approaches to be covered include pyroelectric, piezoelectric, triboelectric, flexoelectric, thermoelectric and photovoltaic effects. These are used to influence a variety of electro-chemical systems such as applications related to water splitting, catalysis, corrosion protection, degradation of pollutants, disinfection of bacteria and material synthesis. Comparisons are made between the range harvesting approaches and the modes of operation are described. Future directions for the development of electro-chemical harvesting systems are highlighted and the potential for new applications and hybrid approaches are discussed.

Physical forces modulate cell differentiation and proliferation processes

Currently, the predominant hypothesis explains cellular differentiation and behaviour as an essentially genetically driven intracellular process, suggesting a gene-centrism paradigm. However, although many living species genetic has now been described, there is still a large gap between the genetic information interpretation and cell behaviour prediction. Indeed, the physical mechanisms underlying the cell differentiation and proliferation, which are now known or suspected to guide such as the flow of energy through cells and tissues, have been often overlooked. We thus here propose a complementary conceptual framework towards the development of an energy-oriented classification of cell properties, that is, a mitochondria-centrism hypothesis based on physical forces-driven principles. A literature review on the physical-biological interactions in a number of various biological processes is analysed from the point of view of the fluid and solid mechanics, electricity and thermodynamics. There is consistent evidence that physical forces control cell proliferation and differentiation. We propose that physical forces interfere with the cell metabolism mostly at the level of the mitochondria, which in turn control gene expression. The present perspective points towards a paradigm shift complement in biology.

Acoustic neuromodulation from a basic science prospective

We present here biophysical models to gain deeper insights into how an acoustic stimulus might influence or modulate neuronal activity. There is clear evidence that neural activity is not only associated with electrical and chemical changes but that an electro-mechanical coupling is also involved. Currently, there is no theory that unifies the electrical, chemical, and mechanical aspects of neuronal activity. Here, we discuss biophysical models and hypotheses that can explain some of the mechanical aspects associated with neuronal activity: the soliton model, the neuronal intramembrane cavitation excitation model, and the flexoelectricity hypothesis. We analyze these models and discuss their implications on stimulation and modulation of neuronal activity by ultrasound.

Dielectric relaxations on erythrocyte membrane as revealed by spectrin denaturation

We studied the effect of spectrin denaturation at 49.5°C (TA) on the dielectric relaxations and related changes in the complex impedance, Z*, complex capacitance, C*, and dielectric loss curve of suspensions containing human erythrocytes, erythrocyte ghost membranes (EMs) and Triton-X-100 residues of EMs. The loss curve prior to, minus the loss curve after TA, resulted in a bell-shaped peak at 1.5MHz. The changes in the real and imaginary components of Z* and C* at TA, i.e., ΔZre, ΔZim, ΔCre and ΔCim, calculated in the same way, strongly varied with frequency. Between 1.0 and 12MHz the -ΔZim vs ΔZre, and ΔCim vs ΔCre plots depicted semicircles with critical frequencies, fcr, at 2.5MHz expressing recently reported relaxation of spectrin dipoles. Between 0.02 and 1.0MHz the -ΔZim vs ΔZre plot exhibited another relaxation whose fcr mirrored that of beta relaxation. This relaxation was absent on Triton-X-shells, while on erythrocytes and EMs it was inhibited by selective dissociation of either attachment sites between spectrin and bilayer. Considering above findings and inaccessibility of cytosole to outside field at such frequencies, the latter relaxation was assumed originating from a piezoelectric effect on the highly deformable spectrin filaments.

Voltage-morphology coupling in biomimetic membranes: dynamics of giant vesicles in applied electric fields

An electric potential difference across the plasma membrane is common to all living cells and is essential to physiological functions such as the generation of action potentials for cell-to-cell communication. While the basics of cell electrical activity are well established (e.g. the Hodgkin-Huxley model of the action potential), the reciprocal coupling of voltage and membrane deformation has received limited attention. In recent years, studies of biomimetic membranes in externally applied electric fields have revealed a plethora of intriguing dynamics (formation of edges, pearling, and phase separation) that challenge the current understanding of membrane electromechanics.

Actuation of flexoelectric membranes in viscoelastic fluids with applications to outer hair cells

Liquid crystal flexoelectric actuation uses an imposed electric field to create membrane bending, and it is used by the outer hair cells (OHCs) located in the inner ear, whose role is to amplify sound through generation of mechanical power. Oscillations in the OHC membranes create periodic viscoelastic flows in the contacting fluid media. A key objective of this work on flexoelectric actuation relevant to OHCs is to find the relations and impact of the electromechanical properties of the membrane, the rheological properties of the viscoelastic media, and the frequency response of the generated mechanical power output. The model developed and used in this work is based on the integration of: (i) the flexoelectric membrane shape equation applied to a circular membrane attached to the inner surface of a circular capillary and (ii) the coupled capillary flow of contacting viscoelastic phases, such that the membrane flexoelectric oscillations drive periodic viscoelastic capillary flows, as in OHCs. By applying the Fourier transform formalism to the governing equation, analytical expressions for the transfer function associated with the curvature and electrical field and for the power dissipation of elastic storage energy were found.

Mechanosensitive Channels Activity in a Droplet Interface Bilayer System

This paper presents the first attempts to study the large conductance mechano-sensitive channel (MscL) activity in an artificial droplet interface bilayer (DIB) system. A novel and simple technique is developed to characterize the behavior of an artificial lipid bilayer interface containing mechano-sensitive (MS) channels. The experimental setup is assembled on an inverted microscope and consists of two micropipettes filled with PEG-DMA hydrogel and containing Ag/AgCl wires, a cylindrical oil reservoir glued on top of a thin acrylic sheet, and a piezoelectric oscillator actuator. By using this technique, dynamic tension can be applied by oscillating axial motion of one droplet, producing deformation of both droplets and area changes of the DIB interface. The tension in the artificial membrane will cause the MS channels to gate, resulting in an increase in the conductance levels of the membrane. The results show that the MS channels are able to gate under an applied dynamic tension. Moreover, it can be concluded that the response of channel activity to mechanical stimuli is voltage-dependent and highly related to the frequency and amplitude of oscillations.

Direct cortical hemodynamic mapping of somatotopy of pig nostril sensation by functional near-infrared cortical imaging (fNCI)

Functional near-infrared spectroscopy (fNIRS) is a neuroimaging technique for the noninvasive monitoring of human brain activation states utilizing the coupling between neural activity and regional cerebral hemodynamics. Illuminators and detectors, together constituting optodes, are placed on the scalp, but due to the presence of head tissues, an inter-optode distance of more than 2.5cm is necessary to detect cortical signals. Although direct cortical monitoring with fNIRS has been pursued, a high-resolution visualization of hemodynamic changes associated with sensory, motor and cognitive neural responses directly from the cortical surface has yet to be realized. To acquire robust information on the hemodynamics of the cortex, devoid of signal complications in transcranial measurement, we devised a functional near-infrared cortical imaging (fNCI) technique. Here we demonstrate the first direct functional measurement of temporal and spatial patterns of cortical hemodynamics using the fNCI technique. For fNCI, inter-optode distance was set at 5mm, and light leakage from illuminators was prevented by a special optode holder made of a light-shielding rubber sheet. fNCI successfully detected the somatotopy of pig nostril sensation, as assessed in comparison with concurrent and sequential somatosensory-evoked potential (SEP) measurements on the same stimulation sites. Accordingly, the fNCI system realized a direct cortical hemodynamic measurement with a spatial resolution comparable to that of SEP mapping on the rostral region of the pig brain. This study provides an important initial step toward realizing functional cortical hemodynamic monitoring during neurosurgery of human brains.

Apparent flexoelectricity in lipid bilayer membranes due to external charge and dipolar distributions

In this Rapid Communication we show that the interplay between the deformation geometric-nonlinearity and distributions of external charges and dipoles lead to the renormalization of the membrane's native flexoelectric response. Our work provides a framework for a mesoscopic interpretation of flexoelectricity and if necessary, artificially "design" tailored flexoelectricity in membranes. Comparisons with experiments indicate reasonable quantitative agreement.

Fundamentals of flexoelectricity in solids

The flexoelectric effect is the response of electric polarization to a mechanical strain gradient. It can be viewed as a higher-order effect with respect to piezoelectricity, which is the response of polarization to strain itself. However, at the nanoscale, where large strain gradients are expected, the flexoelectric effect becomes appreciable. Besides, in contrast to the piezoelectric effect, flexoelectricity is allowed by symmetry in any material. Due to these qualities flexoelectricity has attracted growing interest during the past decade. Presently, its role in the physics of dielectrics and semiconductors is widely recognized and the effect is viewed as promising for practical applications. On the other hand, the available theoretical and experimental results are rather contradictory, attesting to a limited understanding in the field. This review paper presents a critical analysis of the current knowledge on the flexoelectricity in common solids, excluding organic materials and liquid crystals.

Nanoscale flexoelectricity

Electromechanical effects are ubiquitous in biological and materials systems. Understanding the fundamentals of these coupling phenomena is critical to devising next-generation electromechanical transducers. Piezoelectricity has been studied in detail, in both the bulk and at mesoscopic scales. Recently, an increasing amount of attention has been paid to flexoelectricity: electrical polarization induced by a strain gradient. While piezoelectricity requires crystalline structures with no inversion symmetry, flexoelectricity does not carry this requirement, since the effect is caused by inhomogeneous strains. Flexoelectricity explains many interesting electromechanical behaviors in hard crystalline materials and underpins core mechanoelectric transduction phenomena in soft biomaterials. Most excitingly, flexoelectricity is a size-dependent effect which becomes more significant in nanoscale systems. With increasing interest in nanoscale and nano-bio hybrid materials, flexoelectricity will continue to gain prominence. This Review summarizes work in this area. First, methods to amplify or manipulate the flexoelectric effect to enhance material properties will be investigated, particularly at nanometer scales. Next, the nature and history of these effects in soft biomaterials will be explored. Finally, some theoretical interpretations for the effect will be presented. Overall, flexoelectricity represents an exciting phenomenon which is expected to become more considerable as materials continue to shrink.

The capacitance and electromechanical coupling of lipid membranes close to transitions: the effect of electrostriction

Biomembranes are thin capacitors with the unique feature of displaying phase transitions in a physiologically relevant regime. We investigate the voltage and lateral pressure dependence of their capacitance close to their chain melting transition. Because the gel and the fluid membrane have different area and thickness, the capacitance of the two membrane phases is different. In the presence of external fields, charges exert forces that can influence the state of the membrane, thereby influencing the transition temperature. This phenomenon is called "electrostriction". We show that this effect allows us to introduce a capacitive susceptibility that assumes a maximum in the melting transition with an associated excess charge. As a consequence, voltage regimes exist in which a small change in voltage can lead to a large uptake of charge and a large capacitive current. Furthermore, we consider electromechanical behavior such as pressure-induced changes in capacitance, and the application of such concepts in biology.

The effect of oxidative stress on the membrane dipole potential of human red blood cells

The membrane dipole potential (ψ(d)) is an important biophysical determinant of membrane function and a sensitive indicator of lipid organisation. In this study we have used the environmentally sensitive probe di-8-anepps to explore the effects of oxidative stress on the membrane dipole potential of human erythrocytes. Cells suspended in 0.15mM phosphate buffered saline containing 0.1mg/ml albumin maintained a mean value for ψ(d) of 270 (±20) mV over the course of 1hour. In the presence of 0.4mM cumene hydroperoxide there was an increase in ψ(d) of 14 (±7)%, accompanied by a decrease in cell diameter of ~14 (±2)%. Exposure of the cells to 0.4mM hydrogen peroxide caused ψ(d) to decrease by 13 (±8)% at the centre of the cell and 8 (±5)% at the edge whilst the diameter remained constant. In both cases the changes were equivalent to a change in transmembrane electric field of a magnitude of ~10MVm(-1), sufficient to influence membrane function. Raman microspectrometry supported the conclusion that cumene exerts its effect primarily on membrane lipids whilst hydrogen peroxide causes the formation of spectrin-haemoglobin complexes which stiffen the membrane.

Piezo- and Flexoelectric Membrane Materials Underlie Fast Biological Motors in the Ear

The mammalian inner ear is remarkably sensitive to quiet sounds, exhibits over 100dB dynamic range, and has the exquisite ability to discriminate closely spaced tones even in the presence of noise. This performance is achieved, in part, through active mechanical amplification of vibrations by sensory hair cells within the inner ear. All hair cells are endowed with a bundle of motile microvilli, stereocilia, located at the apical end of the cell, and the more specialized outer hair cells (OHC's) are also endowed with somatic electromotility responsible for changes in cell length in response to perturbations in membrane potential. Both hair bundle and somatic motors are known to feed energy into the mechanical vibrations in the inner ear. The biophysical origin and relative significance of the motors remains a subject of intense research. Several biological motors have been identified in hair cells that might underlie the motor(s), including a cousin of the classical ATP driven actin-myosin motor found in skeletal muscle. Hydrolysis of ATP, however, is much too slow to be viable at audio frequencies on a cycle-by-cycle basis. Heuristically, the OHC somatic motor behaves as if the OHC lateral wall membrane were a piezoelectric material and the hair bundle motor behaves as if the plasma membrane were a flexoelectric material. We propose these observations from a continuum materials perspective are literally true. To examine this idea, we formulated mathematical models of the OHC lateral wall "piezoelectric" motor and the more ubiquitous "flexoelectric" hair bundle motor. Plausible biophysical mechanisms underlying piezo- and flexoelectricity were established. Model predictions were compared extensively to the available data. The models were then applied to study the power conversion efficiency of the motors. Results show that the material properties of the complex membranes in hair cells provide them with the ability to convert electrical power available in the inner ear cochlea into useful mechanical amplification of sound induced vibrations at auditory frequencies. We also examined how hair cell amplification might be controlled by the brain through efferent synaptic contacts on hair cells and found a simple mechanism to tune hearing to signals of interest to the listener by electrical control of these motors.

The remarkable cochlear amplifier

This composite article is intended to give the experts in the field of cochlear mechanics an opportunity to voice their personal opinion on the one mechanism they believe dominates cochlear amplification in mammals. A collection of these ideas are presented here for the auditory community and others interested in the cochlear amplifier. Each expert has given their own personal view on the topic and at the end of their commentary they have suggested several experiments that would be required for the decisive mechanism underlying the cochlear amplifier. These experiments are presently lacking but if successfully performed would have an enormous impact on our understanding of the cochlear amplifier.

WITHDRAWN: Membrane-based amplification in hearing

This article has been withdrawn at the request of the author(s) and/or editor. The Publisher apologizes for any inconvenience this may cause. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy.

Electrohydrodynamic model of vesicle deformation in alternating electric fields

We develop an analytical theory to explain the experimentally observed morphological transitions of quasispherical giant vesicles induced by alternating electric fields. The model treats the inner and suspending media as lossy dielectrics, and the membrane as an impermeable flexible incompressible-fluid sheet. The vesicle shape is obtained by balancing electric, hydrodynamic, bending, and tension stresses exerted on the membrane. Our approach, which is based on force balance, also allows us to describe the time evolution of the vesicle deformation, in contrast to earlier works based on energy minimization, which are able to predict only stationary shapes. Our theoretical predictions for vesicle deformation are consistent with experiment. If the inner fluid is more conducting than the suspending medium, the vesicle always adopts a prolate shape. In the opposite case, the vesicle undergoes a transition from a prolate to oblate ellipsoid at a critical frequency, which the theory identifies with the inverse membrane charging time. At frequencies higher than the inverse Maxwell-Wagner polarization time, the electrohydrodynamic stresses become too small to alter the vesicle's quasispherical rest shape. The model can be used to rationalize the transient and steady deformation of biological cells in electric fields.

Chirality of lipids makes fluid lamellar phases piezoelectric

The role of chirality in membrane-forming lipids is not well appreciated at present. Here we demonstrate that the chirality of phospholipids makes fluid lipid bilayers piezoelectric. Thus, chiral lipids would play a central role in the functioning of cell membranes as active mechanotransducers. By periodically shearing and compressing nonaqueous lamellar phases of left ( L-alpha -phosphatidylcholine), right (D- alpha -phosphatidylcholine), and racemic (DL- alpha -phosphatidylcholine) lipids, we induced a tilt of the molecules with respect to the bilayer's normal and produced electric current perpendicular to the tilt plane, with the chiral lipids only. This effect is due to the Sm-A;{*} phase liquid crystal structure of the bilayers, which under molecular tilt becomes a ferroelectric Sm-C;{*} phase, where the polarization is normal to the tilt plane. This coupling allows for a wide variety of sensory possibilities of cell membranes such as mechanoreception, magnetosensitivity, as well as in-plane proton membrane transport and related phenomena such as adenosine triphosphate (ATP) synthesis, soft molecular machine performance, etc.

Electromagnetic effects - From cell biology to medicine

In this review we compile and discuss the published plethora of cell biological effects which are ascribed to electric fields (EF), magnetic fields (MF) and electromagnetic fields (EMF). In recent years, a change in paradigm took place concerning the endogenously produced static EF of cells and tissues. Here, modern molecular biology could link the action of ion transporters and ion channels to the "electric" action of cells and tissues. Also, sensing of these mainly EF could be demonstrated in studies of cell migration and wound healing. The triggers exerted by ion concentrations and concomitant electric field gradients have been traced along signaling cascades till gene expression changes in the nucleus. Far more enigmatic is the way of action of static MF which come in most cases from outside (e.g. earth magnetic field). All systems in an organism from the molecular to the organ level are more or less in motion. Thus, in living tissue we mostly find alternating fields as well as combination of EF and MF normally in the range of extremely low-frequency EMF. Because a bewildering array of model systems and clinical devices exits in the EMF field we concentrate on cell biological findings and look for basic principles in the EF, MF and EMF action. As an outlook for future research topics, this review tries to link areas of EF, MF and EMF research to thermodynamics and quantum physics, approaches that will produce novel insights into cell biology.

Converse flexoelectric effect in a bent-core nematic liquid crystal

Flexoelectricity is a unique property of liquid crystals; it is a linear coupling between electric polarizations and bend and/or splay distortions of the direction of average molecular orientation. Recently it was shown [J. Harden, Phys. Rev. Lett. 97, 157802 (2006)] that the bend flexoelectric coefficient in bent-core nematic liquid crystals can be three orders of magnitude higher than the effect with calamitic (rod-shaped) molecular shape. Here we report the converse of the flexoelectric effect: An electric field applied across a bent-core liquid crystal sandwiched between thin flexible substrates produces a director distortion which is manifested as a polarity-dependent flexing of the substrates. The flex magnitude is shown to be consistent with predictions based upon both the measured value of the bend flexoelectric constant and the elastic properties of the substrates. Converse flexoelectricity makes possible a new class of microactuators with no internal moving parts, which offers applications as diverse as optical beam steering to artificial muscles.

Spontaneous corrugation of dipolar membranes

We present a simple model for dipolar elastic membranes that gives lattice-bound point dipoles complete orientational freedom as well as translational freedom along one coordinate (out of the plane of the membrane). There is an additional harmonic term which binds each of the dipoles to the six nearest neighbors on either triangular or distorted lattices. The translational freedom of the dipoles allows triangular lattices to find states that break out of the normal orientational disorder of frustrated configurations and which are stabilized by long-range antiferroelectric ordering. In order to break out of the frustrated states, the dipolar membranes form corrugated or "rippled" phases that make the lattices effectively nontriangular. We observe three common features of the corrugated dipolar membranes: (1) the corrugated phases develop easily when hosted on triangular lattices, (2) the wave vectors for the surface ripples are always found to be perpendicular to the dipole director axis, and (3) on triangular lattices, the dipole director axis is found to be parallel to any of the three equivalent lattice directions.