Membranes are thin (≈5 nm) ensembles of lipids, proteins, and other molecules with charged surfaces that work together to drive various biological processes. Living cells expend metabolic energy to sustain electrochemical gradients across their membranes (~ 100 mV). Since membranes are very thin, the associated transmembrane electric field is quite large (> 10 MV/m - compare to the ~ 10 kV/m fields associated with atmospheric lighting). Living cells also expend energy to maintain a characteristic asymmetry in the number of fixed charges on the inner and outer surfaces of their membranes. The Modulation of membrane birefringence by changes in membrane potential may have provided the earliest evidence that membranes were capable of an electromechanical response. The ability of membranes to generate electromechanical force was subsequently demonstrated in axons, mammalian outer hair cells (OHCs), and in cultured mammalian cell. To directly test the effect of the transmembrane electric field on cellular membranes, we have developed a technique that combines optical trapping with cell voltage clamping. An optically trapped bead is used to detach the cell plasma membrane from the cytoskeleton and pull them into long (10-60 µm) thin (50-300 nm) tubes or tethers, and the force production by membrane tether in response to changes in the transmembrane electric field, imposed by the voltage clamp apparatus, is measured by optical monitoring of the displacement of the trapped bead. We have measured electromechanical responses from tethers formed from outer hair cells (OHCs) obtained from the cochlea of guinea pigs, and cultured human embryonic kidney (HEK) cells. Our data demonstrate that tether force during elongation and relaxation is a function of the holding potential. The electric field across the membrane affects the mechanical properties of the HEK plasma membrane with hyperpolarizing potentials resulting in greater membrane tension. To test the effect of changing the transmembrane electric field on tether force generation, sinusoidal electrical stimuli are administered after the tether force reaches equilibrium Stimulation with a sinusoidal waveform generates an electromechanical force (EMF) such that hyperpolarization relative to the holding potential increases and depolarization decreases the force exerted by the tether. The electromechanical gain (~ 0.3 pN/mV) measured for the OHC tether in response to 1 Hz sinusoidal excitation is about 5 times that of the HEK tether. The EMF generated by a membrane tether also tracks sinusoidal electrical stimuli through acoustic frequencies where the OHC's EMF is about 6 times that of the HEK's EMF at 1 kHz. Hyperpolarizating holding potentials results in an increase in the amplitude of the tether's EMF and depolarization decreases the EMF. The EMF is largest at –120 mV holding potential and is reduced by a factor of three as the membrane becomes increasingly depolarized. To test the effect of changes in tether diameter on EMF, we have monitored EMF while increasing the tether length. Morphometric analysis of tether diameter in non-voltage clamped HEK cells reveal that increases in the equilibrium tether force are accompanied by decreases in tether diameter. While the HEK tethers can be visualized, OHC lateral wall tethers cannot. The greater diameter of HEK tethers is consistent with their having a smaller tether force and EMF than the OHC tethers. The fact that a smaller tether diameter is associated with a larger EMF suggests the increase in EMF observed with hyperpolarization may also be associated with a decrease in tether diameter. To test for changes in tether cable properties, we monitor the effect of changing tether length. Our results demonstrate that EMF increases with a microscopically confirmed decrease in tether diameter (an increase in membrane curvature). However, EMF begins to decrease after reaching a length dependent peak. The decrease in EMF most likely reflects the cable properties of the tether dominating the increased contribution of the tether membrane area and increasing tether curvature as the tether gets longer. The data are all consistent with sustained hyperpolarization leading to an increase in tether curvature (nominally a decrease in tether diameter). The high-frequency electrically-evoked tether displacements most likely represent a converse flexoelectric response. Flexoelectricity is the change in electrical polarization that results from bending a membrane. Converse flexoelectricity describes a change in membrane curvature resulting from a change in the transmembrane potential. Several factors are thought responsible, including molecular reorientation of electrical dipoles in conjunction with changes in interfacial or surface tension. Surface tension holds the membrane bilayer together. A transmembrane electric field increases surface tension on one side of the membrane while reducing it on the other. This differential surface tension becomes even more important when membranes display high curvature (as in the small radii membrane tethers that we pull from cells). Membrane curvature in a tether is usually determined by a consideration of force equilibrium. Our results demonstrate that force equilibrium in a biological membrane must also include the contribution of the electrically generated force.

An EMF increase and decrease correspond to tether shortening and elongation respectively. We interpret the tether shortening and elongation associated with hyperpolarizing and depolarizing sinusoidal potentials to result from a decrease and increase respectively in the tether curvature. Tether elongation and shortening may be compensatory responses to diameter change because the tether volume will remain essentially constant during the period of the sinusoid. A converse flexoelectric origin for the tether EMF opens the possibility that similar forces are produced in highly curved biological membranes. Examples of highly curved biological membranes abound. Intercellular tunneling nanotubes between adjacent HEK cells in culture have geometries resembling our tethers. The stereocilia of hair cells are typically 200 nm in diameter and can reach lengths of > 30 mm. The stereocilia bundle is known to produce voltage dependent “flicks”. The crenellated membrane of the OHC displays high curvature and a strong mechanical coupling with the cell's cytoskeleton that can explain the mechanical force underlying OHC electromotility. Peripheral dendrites and dendritic spines have smaller radii than HEK tethers as do mitochondrial cristae, synaptic vesicles, and membrane fusion pores . Dendritic spines, synaptic vesicles, and membrane fusion pores are all structures that might be able to utilize the change in energy in the transmembrane electric field during an action potential to modulate membrane mechanics. It has long been assumed that modulation of the transmembrane electric field exerts a force on the charged portions of some membrane proteins (voltage gated ion channels) and the resulting electromechanical response has been called voltage sensing. Local bending of the membrane has been suggested as a mechanism for gating ion channels. A role for membrane mechanics in channel gating is supported by the fact that the kinetics of a variety of voltage gated ion channels are modulated by membrane tension. The ability of the membrane to sense the transmembrane electric field and do work opens the possibility that voltage sensing by ion channels may involve membrane electromechanics. The crystal structure of several voltage gated ion channels reveals they are truncated cones. Truncated cones would contribute to a local curvature of the membrane around the protein and flexure of these nanodomes in response to the transmembrane potential could contribute to the gating of the ion channel. It is possible that the conformation change that opens and closes voltage gated ion channels benefits from the ability of the membrane surrounding the protein to sense the transmembrane electric field and deform. The membrane protein prestin in the OHC lateral wall modifies membrane electromechanics. HEK membranes with prestin show a modest increase (2-3X) in force production over those without it. On the other hand there is more than a three order of magnitude increase in charge movement. The strong influence on charge movement most likely reflects prestin's membership in the Slc26A family of anion transporters. These transporters might benefit from flexoelectric membrane bending since such bending leads to a differential tension between the leaflets of the bilayer, which could facilitate the conformational changes of the protein. We provide the first direct evidence for the ability of biological membranes from living cells to perform work in response to changes in the transmembrane electric field. There are numerous membrane proteins that perform functions essential for life, making it important to determine how lipid-protein interactions might allow them to take advantage of the work performed by the membrane and thereby benefit both the cell and the organism. Acknowledgments This work was supported by research grants R01 DC02775 from the National Institute of Deafness and other Communication Disorders at the National Institutes of Health (WEB, BA), BES-0522862 from the National Science Foundation (BA), and a fellowship from the Keck Center Nanobiology Training Program of the Gulf Coast Consortia, NIH Grant No.1 R90 DK071504-01 (FQ), and the Jake and Nina Kamin Chair of Otorhinolaryngology (WEB).

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