First Observation of the Converse Flexoelectric Effect in Bilayer Lipid Membranes

Analysis of outer hair cell electromechanics reveals power delivery at the upper-frequency limits of hearing

Outer hair cells are the cellular motors in the mammalian inner ear responsible for sensitive high-frequency hearing. Motor function over the frequency range of human hearing requires expression of the protein prestin in the OHC lateral membrane, which imparts piezoelectric properties to the cell membrane. In the present report, electrical power consumption and mechanical power output of the OHC membrane–motor complex are determined using previously published voltage-clamp data from isolated OHCs and membrane patches. Results reveal that power output peaks at a best frequency much higher than implied by the low-pass character of nonlinear capacitance, and much higher than the whole-cell resistive–capacitive corner frequency. High frequency power output is enabled by a −90° shift in the phase of electrical charge displacement in the membrane, manifested electrically as emergence of imaginary-valued nonlinear capacitance.

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.

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.

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.

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.

Flexoelectricity in two-dimensional crystalline and biological membranes

The ability of a material to convert electrical stimuli into mechanical deformation, i.e. piezoelectricity, is a remarkable property of a rather small subset of insulating materials. The phenomenon of flexoelectricity, on the other hand, is universal. All dielectrics exhibit the flexoelectric effect whereby non-uniform strain (or strain gradients) can polarize the material and conversely non-uniform electric fields may cause mechanical deformation. The flexoelectric effect is strongly enhanced at the nanoscale and accordingly, all two-dimensional membranes of atomistic scale thickness exhibit a strong two-way coupling between the curvature and electric field. In this review, we highlight the recent advances made in our understanding of flexoelectricity in two-dimensional (2D) membranes-whether the crystalline ones such as dielectric graphene nanoribbons or the soft lipid bilayer membranes that are ubiquitous in biology. Aside from the fundamental mechanisms, phenomenology, and recent findings, we focus on rapidly emerging directions in this field and discuss applications such as energy harvesting, understanding of the mammalian hearing mechanism and ion transport among others.

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.

Voltage control of droplet interface bilayer lipid membrane dimensions

A novel approach to control the area of anchor-free droplet interface bilayer (DIB) lipid membranes is presented. Unsupported DIB lipid membranes are formed at the interface of phospholipid-coated aqueous droplets dispensed in dodecane oil. Using electrodes inserted into the droplets, an external voltage is applied which modulates the effective DIB area. Electrical (capacitance or current) and optical (imaging of DIB lateral length) recordings were simultaneously performed. Alpha-hemolysin (αHL) single channel insertions into the DIB were recorded. Currents across the DIB were measured as a function of voltage and αHL concentration in the droplets. Nonlinear response is observed for current, DIB lateral length and area, and capacitance with respect to voltage. Voltage induced changes in interfacial tension modulated the DIB-oil contact angle and the membrane contact length, which provided control of membrane dimensions. Comparison of these results is made to the electrowetting effect, which is also governed by effect of voltage on the interfacial tension. This approach provides active control of the number of ion channels inserted into the DIB.

Cell membrane tethers generate mechanical force in response to electrical stimulation

Living cells maintain a huge transmembrane electric field across their membranes. This electric field exerts a force on the membrane because the membrane surfaces are highly charged. We have measured electromechanical force generation by cell membranes using optically trapped beads to detach the plasma membrane from the cytoskeleton and form long thin cylinders (tethers). Hyperpolarizing potentials increased and depolarizing potentials decreased the force required to pull a tether. The membrane tether force in response to sinusoidal voltage signals was a function of holding potential, tether diameter, and tether length. Membrane electromechanical force production can occur at speeds exceeding those of ATP-based protein motors. By harnessing the energy in the transmembrane electric field, cell membranes may contribute to processes as diverse as outer hair cell electromotility, ion channel gating, and transport.

Voltage-induced bending and electromechanical coupling in lipid bilayers

The electrical properties of the cellular membrane are important for ion transport across cells and electrophysiology. Plasma membranes also resist bending and stretching, and mechanical properties of the membrane influence cell shape and forces in membrane tethers pulled from cells. There exists a coupling between the electrical and mechanical properties of the membrane. Previous work has shown that applied voltages can induce forces and movements in the lipid bilayer. We present a theory that computes membrane bending deformations and forces as the applied voltage is changed. We discover that electromechanical coupling in lipid bilayers depends on the voltage-dependent adsorption of ions into the region occupied by the phospholipid head groups. A simple model of counter-ion absorption is investigated. We show that electromechanical coupling can be measured using membrane tethers and we use our model to predict the membrane tether tension as a function of applied voltage. We also discuss how electromechanical coupling in membranes may influence transmembrane protein function.

Optical coherence tomography phase measurement of transient changes in squid giant axons during activity

Noncontact optical measurements reveal that transient changes in squid giant axons are associated with action potential propagation and altered under different environmental (i.e., temperature) and physiological (i.e., ionic concentrations) conditions. Using a spectral-domain optical coherence tomography system, which produces real-time cross-sectional images of the axon in a nerve chamber, axonal surfaces along a depth profile are monitored. Differential phase analyses show transient changes around the membrane on a millisecond timescale, and the response is coincident with the arrival of the action potential at the optical measurement area. Cooling the axon slows the electrical and optical responses and increases the magnitude of the transient signals. Increasing the NaCl concentration bathing the axon, whose diameter is decreased in the hypertonic solution, results in significantly larger transient signals during action potential propagation. While monophasic and biphasic behaviors are observed, biphasic behavior dominates the results. The initial phase detected was constant for a single location but alternated for different locations; therefore, these transient signals acquired around the membrane appear to have local characteristics.

Membrane Electromechanics in Biology, with a Focus on Hearing

Cells are ion conductive gels surrounded by a ~5-nm-thick insulating membrane, and molecular ionic pumps in the membrane establish an internal potential of approximately -90 mV. This electrical energy store is used for high-speed communication in nerve and muscle and other cells. Nature also has used this electric field for high-speed motor activity, most notably in the ear, where transduction and detection can function as high as 120 kHz. In the ear, there are two sets of sensory cells: the "inner hair cells" that generate an electrical output to the nervous system and the more numerous "outer hair cells" that use electromotility to counteract viscosity and thus sharpen resonance to improve frequency resolution. Nature, in a remarkable exhibition of nanomechanics, has made out of soft, aqueous materials a microphone and high-speed decoder capable of functioning at 120 kHz, limited only by thermal noise. Both physics and biology are only now becoming aware of the material properties of biomembranes and their ability to perform work and sense the environment. We anticipate new examples of this biopiezoelectricity will be forthcoming.

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.

Electromechanical effects on tether formation from lipid membranes: a theoretical analysis

The material properties of biomembranes can be measured by forming a tether, a thin bilayer tube that extends from the membrane surface. Recent experiments have demonstrated that the force required to maintain a tether is sensitive to the transmembrane potential. As a first approach towards understanding this phenomenon, a thermodynamic analysis of the influence of electrical fields on tether formation from an aspirated lipid vesicle is developed. The analysis considers contributions from Maxwell stresses as well as two forms of electromechanical coupling: coupling between the electric field and curvature strain (flexoelectric coupling) and between the electric field and areal strain (piezoelectric coupling). Predictions of equilibrium tether conformations are obtained numerically. For expected values of the dimensionless coupling parameters, flexoelectric coupling alters the force required to form a tether of a given length, while piezoelectric coupling and Maxwell forces do not greatly change the force versus tether length behavior. The results of this analysis indicate that tether experiments have the potential to characterize electromechanical coupling in both synthetic and cellular membranes.

Flexoelectricity of model and living membranes

The theory and experiments on model and biomembrane flexoelectricity are reviewed. Biological implications of flexoelectricity are underlined. Molecular machinery and molecular electronics applications are pointed out.

Molecular basis of mechanotransduction in living cells

The simplest cell-like structure, the lipid bilayer vesicle, can respond to mechanical deformation by elastic membrane dilation/thinning and curvature changes. When a protein is inserted in the lipid bilayer, an energetic cost may arise because of hydrophobic mismatch between the protein and bilayer. Localized changes in bilayer thickness and curvature may compensate for this mismatch. The peptides alamethicin and gramicidin and the bacterial membrane protein MscL form mechanically gated (MG) channels when inserted in lipid bilayers. Their mechanosensitivity may arise because channel opening is associated with a change in the protein's membrane-occupied area, its hydrophobic mismatch with the bilayer, excluded water volume, or a combination of these effects. As a consequence, bilayer dilation/thinning or changes in local membrane curvature may shift the equilibrium between channel conformations. Recent evidence indicates that MG channels in specific animal cell types (e.g., Xenopus oocytes) are also gated directly by bilayer tension. However, animal cells lack the rigid cell wall that protects bacteria and plants cells from excessive expansion of their bilayer. Instead, a cortical cytoskeleton (CSK) provides a structural framework that allows the animal cell to maintain a stable excess membrane area (i.e., for its volume occupied by a sphere) in the form of membrane folds, ruffles, and microvilli. This excess membrane provides an immediate membrane reserve that may protect the bilayer from sudden changes in bilayer tension. Contractile elements within the CSK may locally slacken or tighten bilayer tension to regulate mechanosensitivity, whereas membrane blebbing and tight seal patch formation, by using up membrane reserves, may increase membrane mechanosensitivity. In specific cases, extracellular and/or CSK proteins (i.e., tethers) may transmit mechanical forces to the process (e.g., hair cell MG channels, MS intracellular Ca(2+) release, and transmitter release) without increasing tension in the lipid bilayer.

A membrane bending model of outer hair cell electromotility

We propose a new mechanism for outer hair cell electromotility based on electrically induced localized changes in the curvature of the plasma membrane (flexoelectricity). Electromechanical coupling in the cell's lateral wall is modeled in terms of linear constitutive equations for a flexoelectric membrane and then extended to nonlinear coupling based on the Langevin function. The Langevin function, which describes the fraction of dipoles aligned with an applied electric field, is shown to be capable of predicting the electromotility voltage displacement function. We calculate the electrical and mechanical contributions to the force balance and show that the model is consistent with experimentally measured values for electromechanical properties. The model rationalizes several experimental observations associated with outer hair cell electromotility and provides for constant surface area of the plasma membrane. The model accounts for the isometric force generated by the cell and explains the observation that the disruption of spectrin by diamide reduces force generation in the cell. We discuss the relation of this mechanism to other proposed models of outer hair cell electromotility. Our analysis suggests that rotation of membrane dipoles and the accompanying mechanical deformation may be the molecular mechanism of electromotility.

Voltage-induced membrane displacement in patch pipettes activates mechanosensitive channels

The patch-clamp technique allows currents to be recorded through single ion channels in patches of cell membrane in the tips of glass pipettes. When recording, voltage is typically applied across the membrane patch to drive ions through open channels and to probe the voltage-sensitivity of channel activity. In this study, we used video microscopy and single-channel recording to show that prolonged depolarization of a membrane patch in borosilicate pipettes results in delayed slow displacement of the membrane into the pipette and that this displacement is associated with the activation of mechanosensitive (MS) channels in the same patch. The membrane displacement, approximately 1 micrometer with each prolonged depolarization, occurs after variable delays ranging from tens of milliseconds to many seconds and is correlated in time with activation of MS channels. Increasing the voltage step shortens both the delay to membrane displacement and the delay to activation. Preventing depolarization-induced membrane displacement by applying positive pressure to the shank of the pipette or by coating the tips of the borosilicate pipettes with soft glass prevents the depolarization-induced activation of MS channels. The correlation between depolarization-induced membrane displacement and activation of MS channels indicates that the membrane displacement is associated with sufficient membrane tension to activate MS channels. Because membrane tension can modulate the activity of various ligand and voltage-activated ion channels as well as some transporters, an apparent voltage dependence of a channel or transporter in a membrane patch in a borosilicate pipette may result from voltage-induced tension rather than from direct modulation by voltage.

Membrane-pipette interactions underlie delayed voltage activation of mechanosensitive channels in Xenopus oocytes

To investigate the mechanism for the delayed activation by voltage of the predominant mechanosensitive (MS) channel in Xenopus oocytes, currents were recorded from on-cell and excised patches of membrane with the patch clamp technique and from intact oocytes with the two-electrode voltage clamp technique. MS channels could be activated by stretch in inside-out, on-cell, and outside-out patch configurations, using pipettes formed of either borosilicate or soft glass. In inside-out patches formed with borosilicate glass pipettes, depolarizing voltage steps activated MS channels in a cooperative manner after delays of seconds. This voltage-dependent activation was not observed for outside-out patches. Voltage-dependent activation was also not observed when the borosilicate pipettes were either replaced with soft glass pipettes or coated with soft glass. When depolarizing voltage steps were applied to the whole oocyte with a two-electrode voltage clamp, currents that could be attributed to MS channels were not observed. Yet the same depolarizing steps activated MS channels in on-cell patches formed with borosilicate pipettes on the same oocyte. These observations suggest that the delayed cooperative activation of MS channels by depolarization is not an intrinsic property of the channels, but requires interaction between the membrane and patch pipette.

Voltage-dependent membrane displacements measured by atomic force microscopy

Cells use polar molecules in the membrane to sense changes in the transmembrane potential. The opening of voltage-gated ion channels and membrane bending due to the inverse flexoelectric effect are two examples of such electromechanical coupling. We have looked for membrane motions in an electric field using atomic (or scanning) force microscopy (AFM) with the intent of studying voltage-dependent conformational changes of ion channels. Voltage-clamped HEK293 cells were either untransfected controls or transfected with Shaker K+ channels. Using a +/- 10-mV peak-peak AC carrier stimulus, untransfected cells moved 0.5-15 nm normal to the plane of the membrane. These movements tracked the voltage at frequencies >1 kHz with a phase lead of 60-120 degrees, as expected of a displacement current. The movement was outward with depolarization, but the holding potential only weakly influenced the amplitude of the movement. In contrast, cells transfected with a noninactivating mutant of Shaker K+channels showed similar movements, but these were sensitive to the holding potential; decreasing with depolarization between -80 and 0 mV. Searching for artifactual origins of these movements, we used open or sealed pipettes and AFM cantilever placements just above the cells. These results were negative, suggesting that the observed movements were produced by the cell membrane rather than by movement of the patch pipette, or by acoustic or electrical interactions of the membrane with the AFM tip. In control cells, the electrical motor may arise from the flexoelectric effect, where changes in potential induce changes in curvature. In transfected cells, it appears that channel-specific movements also occurred. These experiments demonstrate that the AFM may be able to exploit voltage-dependent movements as a source of contrast for imaging membrane components. The electrically induced motility will cause twitching during action potentials, and may have physiological consequences.