Voltage and frequency dependence of prestin-associated charge transfer

Abstract

Membrane protein prestin is a critical component of the motor complex that generates forces and dimensional changes in cells in response to changes in the cell membrane potential. In its native cochlear outer hair cell, prestin is crucial to the amplification and frequency selectivity of the mammalian ear up to frequencies of tens of kHz. Other cells transfected with prestin acquire voltage-dependent properties similar to those of the native cell. The protein performance is critically dependent on chloride ions, and intrinsic protein charges also play a role. We propose an electro-diffusion model to reveal the frequency and voltage dependence of electric charge transfer by prestin. The movement of the combined charge (i.e., anion and protein charges) across the membrane is described with a Fokker-Planck equation coupled to a kinetic equation that describes the binding of chloride ions to prestin. We found a voltage-and frequency-dependent phase shift between the transferred charge and the applied electric field that determines capacitive and resistive components of the transferred charge. The phase shift monotonically decreases from zero to -90 degree as a function of frequency. The capacitive component as a function of voltage is bell-shaped, and decreases with frequency. The resistive component is bell-shaped for both voltage and frequency. The capacitive and resistive components are similar to experimental measurements of charge transfer at high frequencies. The revealed nature of the transferred charge can help reconcile the high-frequency electrical and mechanical observations associated with prestin, and it is important for further analysis of the structure and function of this protein.

MEX-5 enrichment in the C. elegans early embryo mediated by differential diffusion

“…Multi-dimensional solutions to the partial differential equations governing the model described here were obtained using COMSOL v3.5a Multiphysics (FEMLAB) software (Reddy, 1993;Sun et al, 2009). Embryos were simulated using an oval shape with major and minor axes of 50 m and 30 m, respectively.…”

WITHDRAWN: Membrane-based amplification in hearing

“…The large prestin-associated non-ohmic, reactive displacement currents are thought to arise from the movement of cytoplasmic anions such as chloride and bicarbonate into and out the membrane. A model of the electrodiffusion of anions into a model protein is able to quantitatively reproduce several features of this charge movement(Sun et al, 2009). Prestin may help overcome the low-pass problem by facilitating a phase-shifted charge movement that compensates for membrane capacitance in a manner similar to the negative-capacitance circuits found in voltage-clamp amplifier headstages.…”

The potential and electric field in the cochlear outer hair cell membrane

“…Under the dynamic conditions, the amplitude and phase of the prestin mobile charge change significantly with frequency, e.g., the phase of this charge reaches about 60° at 50 kHz and about 75° at 75 kHz [38]. Thus, we investigate this effect on the resulting potential and electric field and, ultimately on the strategically important phase of the active force produced by the outer hair cell.…”

“…Note that the steady state limit of the average position of the mobile charge can be obtained analytically from the Fokker-Planck equation resulting in the following equation $$<z>=L(\frac{e^{\beta L}}{e^{\beta L}-1}-\frac{1}{\beta L})$$ where β = q( ψ–ψ* )/kTL , q= −1.5e, and ψ*=−30 mV. These parameters were previously adjusted [38] based on fitting the data on the voltage dependence of the prestin-associated charge with typical experimental chloride concentrations of about 140mM [36]. We use Eq.…”

“…While the transferred charge was traditionally associated with nonlinear capacitance implying no-phase shift between the transferred charge and applied voltage, recent experiments [31], [10], [26] showed that such a phase shift exists. Further modeling analysis has shown that this phase shift becomes significant for high-frequency regimes [38]. In addition, the amplitude of the transferred charge also depends on frequency and decreases under high-frequency conditions.…”