State dependent effects on the frequency response of prestin’s real and imaginary components of nonlinear capacitance

The outer hair cell (OHC) membrane harbors a voltage-dependent protein, prestin (SLC26a5), in high density, whose charge movement is evidenced as a nonlinear capacitance (NLC). NLC is bell-shaped, with its peak occurring at a voltage, Vh, where sensor charge is equally distributed across the plasma membrane. Thus, Vh provides information on the conformational state of prestin. Vh is sensitive to membrane tension, shifting to positive voltage as tension increases and is the basis for considering prestin piezoelectric (PZE). NLC can be deconstructed into real and imaginary components that report on charge movements in phase or 90 degrees out of phase with AC voltage. Here we show in membrane macro-patches of the OHC that there is a partial trade-off in the magnitude of real and imaginary components as interrogation frequency increases, as predicted by a recent PZE model (Rabbitt in Proc Natl Acad Sci USA 17:21880–21888, 2020). However, we find similar behavior in a simple 2-state voltage-dependent kinetic model of prestin that lacks piezoelectric coupling. At a particular frequency, Fis, the complex component magnitudes intersect. Using this metric, Fis, which depends on the frequency response of each complex component, we find that initial Vh influences Fis; thus, by categorizing patches into groups of different Vh, (above and below − 30 mV) we find that Fis is lower for the negative Vh group. We also find that the effect of membrane tension on complex NLC is dependent, but differentially so, on initial Vh. Whereas the negative group exhibits shifts to higher frequencies for increasing tension, the opposite occurs for the positive group. Despite complex component trade-offs, the low-pass roll-off in absolute magnitude of NLC, which varies little with our perturbations and is indicative of diminishing total charge movement, poses a challenge for a role of voltage-driven prestin in cochlear amplification at very high frequencies.

Position Estimator Design for a MEMS Top-Drive Electrostatic Rotary Actuator

The capacitance and rotor angle of a MEMS top-drive electrostatic rotary actuator do not have a linear relationship due to the non-ignorable fringe effect and low aspect ratio of the electrodes. Therefore, the position estimation is not as straightforward as that for a comb-drive linear actuator or a side-drive rotary actuator. The reason is that the capacitance is a nonlinear and periodic function of the rotor angle and is affected by the three-phase input voltages. Therefore, it cannot be approximated as a simple two-plate capacitor. Sensing the capacitance between a rotor and a stator is another challenge. The capacitance can be measured in the electrodes (stators), but the electrodes also have to perform actuation, so a method is needed to combine actuation and sensing. In this study, a nonlinear capacitance model was derived as a data-driven model that effectively represents the nonlinear capacitance with sufficient accuracy. To measure the capacitance accurately, the stator parts for actuation and those for sensing are separated. Using the nonlinear model and the capacitance measurement, an unscented Kalman filter was designed to mitigate the large estimation error due to the periodic nonlinearity. The proposed method shows stable and accurate estimation that cannot be achieved with a simple two-plate capacitor model. The proposed approach can be applied to a similar system with highly nonlinear capacitance.

CREATING MOSFET NONLINEAR CAPACITANCE MODEL

The problems of model creating for nonlinear gate-drain capacitance of MOSFET are considered. A circuit is proposed for measuring this capacitance in the region of negative drain-gate voltages. The dependence of the gate-drain capacitance on voltage for the IRF540N transistor is constructed and an approximating function that can be used to create a model of a MOS-transistor is proposed.

Outer hair cell electromotility is low-pass filtered relative to the molecular conformational changes that produce nonlinear capacitance

The outer hair cell (OHC) of the organ of Corti underlies a process that enhances hearing, termed cochlear amplification. The cell possesses a unique voltage-sensing protein, prestin, that changes conformation to cause cell length changes, a process termed electromotility (eM). The prestin voltage sensor generates a capacitance that is both voltage- and frequency-dependent, peaking at a characteristic membrane voltage (Vh), which can be greater than the linear capacitance of the OHC. Accordingly, the OHC membrane time constant depends upon resting potential and the frequency of AC stimulation. The confounding influence of this multifarious time constant on eM frequency response has never been addressed. After correcting for this influence on the whole-cell voltage clamp time constant, we find that both guinea pig and mouse OHC eM is low pass, substantially attenuating in magnitude within the frequency bandwidth of human speech. The frequency response is slowest at Vh, with a cut-off, approximated by single Lorentzian fits within that bandwidth, near 1.5 kHz for the guinea pig OHC and near 4.3 kHz for the mouse OHC, each increasing in a U-shaped manner as holding voltage deviates from Vh. Nonlinear capacitance (NLC) measurements follow this pattern, with cut-offs about double that for eM. Macro-patch experiments on OHC lateral membranes, where voltage delivery has high fidelity, confirms low pass roll-off for NLC. The U-shaped voltage dependence of the eM roll-off frequency is consistent with prestin’s voltage-dependent transition rates. Modeling indicates that the disparity in frequency cut-offs between eM and NLC may be attributed to viscoelastic coupling between prestin’s molecular conformations and nanoscale movements of the cell, possibly via the cytoskeleton, indicating that eM is limited by the OHC’s internal environment, as well as the external environment. Our data suggest that the influence of OHC eM on cochlear amplification at higher frequencies needs reassessment.