Membrane Electromechanics in Biology, with a Focus on Hearing

On the Coupling between Mechanical Properties and Electrostatics in Biological Membranes

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

Mapping intrinsic electromechanical responses at the nanoscale via sequential excitation scanning probe microscopy empowered by deep data

Ever-increasing hardware capabilities and computation powers have enabled acquisition and analysis of big scientific data at the nanoscale routine, though much of the data acquired often turn out to be redundant, noisy and/or irrelevant to the problems of interest, and it remains nontrivial to draw clear mechanistic insights from pure data analytics. In this work, we use scanning probe microscopy (SPM) as an example to demonstrate deep data methodology for nanosciences, transitioning from brute-force analytics such as data mining, correlation analysis and unsupervised classification to informed and/or targeted causative data analytics built on sound physical understanding. Three key ingredients of such deep data analytics are presented. A sequential excitation scanning probe microscopy (SE-SPM) technique is first developed to acquire high-quality, efficient and physically relevant data, which can be easily implemented on any standard atomic force microscope (AFM). Brute-force physical analysis is then carried out using a simple harmonic oscillator (SHO) model, enabling us to derive intrinsic electromechanical coupling of interest. Finally, principal component analysis (PCA) is carried out, which not only speeds up the analysis by four orders of magnitude, but also allows a clear physical interpretation of its modes in combination with SHO analysis. A rough piezoelectric material has been probed using such a strategy, enabling us to map its intrinsic electromechanical properties at the nanoscale with high fidelity, where conventional methods fail. The SE in combination with deep data methodology can be easily adapted for other SPM techniques to probe a wide range of functional phenomena at the nanoscale.

Generalized Boussinesq-Scriven surface fluid model with curvature dissipation for liquid surfaces and membranes

Curvature dissipation is relevant in synthetic and biological processes, from fluctuations in semi-flexible polymer solutions, to buckling of liquid columns, tomembrane cell wall functioning. We present a micromechanical model of curvature dissipation relevant to fluid membranes and liquid surfaces based on a parallel surface parameterization and a stress constitutive equation appropriate for anisotropic fluids and fluid membranes.The derived model, aimed at high curvature and high rate of change of curvature in liquid surfaces and membranes, introduces additional viscous modes not included in the widely used 2D Boussinesq-Scriven rheological constitutive equation for surface fluids.The kinematic tensors that emerge from theparallel surface parameterization are the interfacial rate of deformation and the surface co-rotational Zaremba-Jaumann derivative of the curvature, which are used to classify all possibledissipative planar and non-planar modes. The curvature dissipation function that accounts for bending, torsion and twist rates is derived and analyzed under several constraints, including the important inextensional bending mode.A representative application of the curvature dissipation model to the periodic oscillation in nano-wrinkled outer hair cells show how and why curvature dissipation decreases with frequency, and why the 100kHz frequency range is selected. These results contribute to characterize curvature dissipation in membranes and liquid surfaces.

Adaptation Independent Modulation of Auditory Hair Cell Mechanotransduction Channel Open Probability Implicates a Role for the Lipid Bilayer

The auditory system is able to detect movement down to atomic dimensions. This sensitivity comes in part from mechanisms associated with gating of hair cell mechanoelectric transduction (MET) channels. MET channels, located at the tops of stereocilia, are poised to detect tension induced by hair bundle deflection. Hair bundle deflection generates a force by pulling on tip-link proteins connecting adjacent stereocilia. The resting open probability (P(open)) of MET channels determines the linearity and sensitivity to mechanical stimulation. Classically, P(open) is regulated by a calcium-sensitive adaptation mechanism in which lowering extracellular calcium or depolarization increases P(open). Recent data demonstrated that the fast component of adaptation is independent of both calcium and voltage, thus requiring an alternative explanation for the sensitivity of P(open) to calcium and voltage. Using rat auditory hair cells, we characterize a mechanism, separate from fast adaptation, whereby divalent ions interacting with the local lipid environment modulate resting P(open). The specificity of this effect for different divalent ions suggests binding sites that are not an EF-hand or calmodulin model. GsMTx4, a lipid-mediated modifier of cationic stretch-activated channels, eliminated the voltage and divalent sensitivity with minimal effects on adaptation. We hypothesize that the dual mechanisms (lipid modulation and adaptation) extend the dynamic range of the system while maintaining adaptation kinetics at their maximal rates.

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.

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.

Mechanical transduction by ion channels: A cautionary tale

Mechanical transduction by ion channels occurs in all cells. The physiological functions of these channels have just begun to be elaborated, but if we focus on the upper animal kingdom, these channels serve the common sensory services such as hearing and touch, provide the central nervous system with information on the force and position of muscles and joints, and they provide the autonomic system with information about the filling of hollow organs such as blood vessels. However, all cells of the body have mechanosensitive channels (MSCs), including red cells. Most of these channels are cation selective and are activated by bilayer tension. There are also K⁺ selective MSCs found commonly in neurons where they may be responsible for both general anesthesia and knockout punches in the boxing ring by hyperpolarizing neurons to reduce excitability. The cationic MSCs are typically inactive under normal mechanical stress, but open under pathologic stress. The channels are normally inactive because they are shielded from stress by the cytoskeleton. The cationic MSCs are specifically blocked by the externally applied peptide GsMtx4 (aka, AT-300). This is the first drug of its class and provides a new approach to many pathologies since it is nontoxic, non-immunogenic, stable in a biological environment and has a long pharmacokinetic lifetime. Pathologies involving excessive stress are common. They produce cardiac arrhythmias, contraction in stretched dystrophic muscle, xerocytotic and sickled red cells, etc. The channels seem to function primarily as “fire alarms”, providing feedback to the cytoskeleton that a region of the bilayer is under excessive tension and needs reinforcing. The eukaryotic forms of MSCs have only been cloned in recent years and few people have experience working with them. “Newbies” need to become aware of the technology, potential artifacts, and the fundamentals of mechanics. The most difficult problem in studying MSCs is that the actual stimulus, the force applied to the channel, is not known. We don’t have direct access to the channels themselves but only to larger regions of the membrane as seen in patches. Cortical forces are shared by the bilayer, the cytoskeleton and the extracellular matrix. How much of an applied stimulus reaches the channel is unknown. Furthermore, many of these channels exist in spatial domains where the forces within a domain are different from forces outside the domain, although we often hope they are proportional. This review is intended to be a guide for new investigators who want to study mechanosensitive ion channels.

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.

Glucose suppresses biological ferroelectricity in aortic elastin

Elastin is an intriguing extracellular matrix protein present in all connective tissues of vertebrates, rendering essential elasticity to connective tissues subjected to repeated physiological stresses. Using piezoresponse force microscopy, we show that the polarity of aortic elastin is switchable by an electrical field, which may be associated with the recently discovered biological ferroelectricity in the aorta. More interestingly, it is discovered that the switching in aortic elastin is largely suppressed by glucose treatment, which appears to freeze the internal asymmetric polar structures of elastin, making it much harder to switch, or suppressing the switching completely. Such loss of ferroelectricity could have important physiological and pathological implications from aging to arteriosclerosis that are closely related to glycation of elastin.

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.

Electromechanical and elastic probing of bacteria in a cell culture medium

Rapid phenotype characterization and identification of cultured cells, which is needed for progress in tissue engineering and drug testing, requires an experimental technique that measures physical properties of cells with sub-micron resolution. Recently, band excitation piezoresponse force microscopy (BEPFM) has been proven useful for recognition and imaging of bacteria of different types in pure water. Here, the BEPFM method is performed for the first time on physiologically relevant electrolyte media, such as Dulbecco's phosphate-buffered saline (DPBS) and Dulbecco's modified Eagle's medium (DMEM). Distinct electromechanical responses for Micrococcus lysodeikticus (Gram-positive) and Pseudomonas fluorescens (Gram-negative) bacteria in DPBS are demonstrated. The results suggest that mechanical properties of the outer surface coating each bacterium, as well as the electrical double layer around them, are responsible for the BEPFM image formation mechanism in electrolyte media.

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.

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.

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