Flexoelectric effects in model and native membranes containing ion channels

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.

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.

A review on ultrasonic neuromodulation of the peripheral nervous system: enhanced or suppressed activities?

Ultrasonic (US) neuromodulation has emerged as a promising therapeutic means by delivering focused energy deep into the tissue. Low-intensity ultrasound (US) directly activates and/or inhibits neurons in the central nervous system (CNS). US neuromodulation of the peripheral nervous system (PNS) is less developed and rarely used clinically. Literature on the neuromodulatory effects of US on the PNS is controversy with some documenting enhanced neural activities, some showing suppressed activities, and others reporting mixed effects. US, with different range of intensity and strength, is likely to generate distinct physical effects in the stimulated neuronal tissues, which underlies different experimental outcomes in the literature. In this review, we summarize all the major reports that documented the effects of US on peripheral nerve endings, axons, and/or somata in the dorsal root ganglion. In particular, we thoroughly discuss the potential impacts by the following key parameters to the study outcomes of PNS neuromodulation by the US: frequency, pulse repetition frequency, duty cycle, intensity, metrics for peripheral neural activities, and type of biological preparations used in the studies. Potential mechanisms of peripheral US neuromodulation are summarized to provide a plausible interpretation to the seemly contradictory effects of enhanced and suppressed neural activities from US neuromodulation.

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.

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.

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.

Electromechanical models of the outer hair cell composite membrane

The outer hair cell (OHC) is an extremely specialized cell and its proper functioning is essential for normal mammalian hearing. This article reviews recent developments in theoretical modeling that have increased our knowledge of the operation of this fascinating cell. The earliest models aimed at capturing experimental observations on voltage-induced cellular length changes and capacitance were based on isotropic elasticity and a two-state Boltzmann function. Recent advances in modeling based on the thermodynamics of orthotropic electroelastic materials better capture the cell's voltage-dependent stiffness, capacitance, interaction with its environment and ability to generate force at high frequencies. While complete models are crucial, simpler continuum models can be derived that retain fidelity over small changes in transmembrane voltage and strains occurring in vivo. By its function in the cochlea, the OHC behaves like a piezoelectric-like actuator, and the main cellular features can be described by piezoelectric models. However, a finer characterization of the cell's composite wall requires understanding the local mechanical and electrical fields. One of the key questions is the relative contribution of the in-plane and bending modes of electromechanical strains and forces (moments). The latter mode is associated with the flexoelectric effect in curved membranes. New data, including a novel experiment with tethers pulled from the cell membrane, can help in estimating the role of different modes of electromechanical coupling. Despite considerable progress, many problems still confound modelers. Thus, this article will conclude with a discussion of unanswered questions and highlight directions for future research.

Dynamic changes in traction forces with DC electric field in osteoblast-like cells

Primary bovine osteoblasts and human osteosarcoma cells exposed to direct-current electric fields undergo processes of retraction and elongation ultimately resulting in the realignment of the long cellular axis perpendicular to the electric field. The time taken for this reorientation was inversely correlated to field strength within a certain range. Cellular force output during reorientation was analyzed using a simple modification of traction force microscopy. The first detectable reaction was an increase in average traction force magnitude occurring between 10 and 30 seconds of electric field exposure. In the following 2 to 15 minutes traction forces at margins tangential to the electric field decreased below their initial values. Phase-contrast microscopy revealed elongating protrusions at these margins several minutes later. We could not correlate the initial traction changes with any change in intracellular free calcium levels measured using the fluorescent dye Fura-2 AM.

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.