Figure 1.
On/Off currents in response to ultrasound in lipid bilayers under voltage-clamp.
A. Diagram of experimental apparatus. Above the transducer are (from bottom to top): a column of distilled water (∼4 mm) held in place by surface tension, a thin mylar film (0.1 mm), a layer of buffered salt solution (5 mm), the lipid bilayer (∼4 nm thick; on the order of 0.1 mm in diameter) and its supporting partition (0.2 mm), and another layer of buffered salt solution (1.7 mm). B. Currents in response to 10-ms (blue) and 6-ms (red) ultrasound applications at 1 MHz and 610 mW/cm2 (estimated power intensity), along with the baseline current in the absence of ultrasound stimulation (black) in a bilayer voltage-clamped at −200 mV. The bilayer was formed from the lipids POPE and POPG (3∶1 by weight). The capacitance of the bilayer was 170 pF. C. Fits of Eq. 1 (black lines) to the On and Off components of the current in A, but showing the average of 20 ultrasound applications. Values of the fit parameters (± SD) are a, 800±7 pA; f, 900±1 Hz; α, 700±9 s−1; φ, −0.21±0.01 radians for the On response and a, −790±7 pA; f, 950±1 Hz; α, 720±9 s−1; φ, −0.25±0.01 radians for the Off response. D. Currents in response to a 10-ms ultrasound application using a focused transducer (∼90 µm focal spot size) at 43 MHz and 5 W/cm2 in another POPE/POPG (3∶1) bilayer, voltage-clamped at −200 mV. The current trace is the average of 16 ultrasound applications. The capacitance of the bilayer was 170 pF. E. Fits of Eq. 1 (black lines) to the On and Off components of the current in C. Values of the fit parameters (± SD) are a, 1700±15 pA; f, 1300±1 Hz; α, 880±10 s−1; φ, −0.27±0.01 radians for the On response and a, −1600±11 pA; f, 1400±1 Hz; α, 1000±9 s−1; φ, −0.04±0.01 radians for the Off response.
Figure 2.
Maximal current response requires alignment of the bilayer and the ultrasound beam.
A. Current recorded from a POPE/POPG bilayer under voltage-clamp at −100 mV in response to a 50-ms, 13-W/cm2 ultrasound pulse from a 43-MHz focused transducer with the focal spot aligned on the bilayer (blue current trace) and with the focal spot moved 2 mm away from the bilayer in the x-y plane (red current trace). The currents are normalized to the peak inward current and the baseline currents have been subtracted. The current scale bar is in normalized units. The peak positive and negative currents were 147 and −157 pA with the focal spot centered on the bilayer, and 15 and −13.7 with the focal spot translated 2 mm in the x-y plane. The capacitance of the bilayer was 153 pF. The currents are the average of 10 ultrasound applications. Mean peak positive and negative currents, relative to the peak current with the bilayer and ultrasound beam aligned, for the On and Off responses (respectively) after moving the transducer were 8.9±0.1% and 9.1±0.1% (mean ± SE, n = 7). B. The Off current response from A. on an expanded time scale. C. Approximate scale drawing indicating the position of the focal spot for the two current traces.
Figure 3.
Voltage changes in response to ultrasound are caused by changes in bilayer capacitance.
A.Voltage changes recorded under “current-clamp”. A 10-ms ultrasound pulse at 1 MHz and 610 mW/cm2 was applied to a POPE/POPG (3∶1) bilayer charged to −194 mV (blue line). The red line shows the voltage changes predicted from the current recorded in voltage-clamp mode (panel B), calculated using Eq. 3. The voltage trace is the average of 20 ultrasound applications. The capacitance of the bilayer was 110 pF. B. Current recorded from the bilayer in A under voltage-clamp at −200 mV, in response to the same ultrasound stimulus as in A. The current trace is the average of 20 ultrasound applications. C. Currents in response to a 10-ms, 1-MHz, 610-mW/cm2 ultrasound application in a POPE/POPG (3∶1) bilayer voltage-clamped at potentials from −200 mV to +200 mV, in 50-mV steps. Current traces are the average of 20 ultrasound applications. The capacitance of the bilayer was 130 pF. D. Mean (± SE) peak negative or positive current following the end of the ultrasound stimulus, as a function of bilayer voltage, normalized to the peak negative current at −200 mV (n = 5). Some error bars are smaller than the symbol size. The black line is a linear fit with slope 5.5±0.1 mV−1 and y-intercept 0.05±0.01 (± SD).
Figure 4.
Ultrasound-induced capacitive currents in solvent-free synthetic bilayers.
Currents in response to a 10-ms, 1-MHz, 610-mW/cm2 ultrasound application in a bilayer formed from a solution of POPE and POPG (3∶1) in squalene (8.3 mg/mL), under voltage-clamp at −200 mV, along with a fit of Eq. 1 to the Off component of the current. For the example shown here, the fit parameters (±SD) were: a, −140±3 pA; f, 340±1 Hz; α, 300±10 s−1; φ, 0.17±0.02 radians, and the capacitance was 500 pF. The mean (±SE) values were a, −110±30 pA; f, 400±30 Hz; α, 340±50 s−1; φ, 0.19±0.07 radians, and the capacitance ranged from 80 to 560 pF (n = 7).
Figure 5.
The response to ultrasound depends on bilayer curvature.
A. Diagram illustrating changes in bilayer shape in response to ultrasound. The bilayer is a curved surface (shown in cross-section) with base of diameter d. The bilayer displacement u(x, t) is measured relative to the plane u = 0, with positive displacement defined to be in the direction of ultrasound propagation. Under standard experimental conditions, the bilayer is curved opposite the direction of ultrasound propagation in the resting state (blue). In response to ultrasonic radiation force, bilayer curvature is decreased (radius of curvature increased) and bilayer area is decreased (red). The inset summarizes the three types of pressure that determine the bilayer curvature at steady-state: the hydrostatic pressure, P0 (negative); the pressure due to bilayer tension, 2γ(δ2u/δx2) (positive); and the pressure due to radiation force, PUS (positive). The changes in response to ultrasound are exaggerated for the purpose of illustration. B. Capacitive currents at −200 mV in response to a 1-MHz, 610-mW/cm2 ultrasound pulse with different solution volumes in the lower compartment of the bilayer chamber (left), along with illustrations of the inferred resting-state bilayer curvature (right). The lower compartment volumes are 0.45 mL (+0 mL, top), 0.46 mL (+0.01 mL, middle), and 0.47 mL (+0.02 mL, bottom). Currents are the average of 10 ultrasound applications and the baseline currents are subtracted. Bilayer capacitance was 170 pF. C. Mean (±SE) amplitudes for fits of Eq. 1 to the Off capacitive current at −200 mV in response to ultrasound at 1 MHz and 610 mW/cm2 with different solution volumes in the lower compartment of the bilayer chamber, normalized to the amplitude at the initial volume and to bilayer capacitance (see Materials and Methods, “Data Analysis” section) (n = 11–15).
Figure 6.
Changes in capacitance in response to ultrasound are proportional to bilayer capacitance.
Net (steady-state) change in capacitance as a function of resting bilayer capacitance (logarithmic scale) (n = 59). The black line is a linear fit to the net change in capacitance as a function of resting capacitance with a slope of −0.005.4±0.002 pF/pF and y-intercept of 0.48±0.15 pF (± SD). The red line is an alternative fit in which the change in capacitance is assumed to be linearly proportional to the bilayer perimeter. Specifically, the fit function is ΔC = a*p[C]+b, where p[C] is a function which converts the bilayer capacitance (C) to an estimate of the bilayer perimeter (see Materials and Methods, “Data Analysis” section). The values of the fit parameters are a = −11.3±1.1 pF/mm, and b = 4±0.6 pF (± SD). R2 values for the fits are 0.89 for the fit in which capacitance change is linearly proportional to capacitance and 0.64 for the fit in which capacitance change is linearly proportional to perimeter.
Figure 7.
Bilayer tension and fluid dynamics determine the amplitude and time course of the response to ultrasound.
A. Examples of ultrasound-induced currents (Off response) in low-capacitance (30 pF) and high-capacitance (1300 pF) bilayers. The blues lines are the average of 20–50 ultrasound applications and the black lines are fits of Eq. 1. Values of the fit parameters (± SD) are a, −290±5 pA; f, 2680±5 Hz; α, 1370±30 s−1; φ, −0.68±0.01 radians for the 30-pF bilayer; and a, −1570±10 pA; f, 150±0.3 Hz; α, 270±2 s−1; φ, 0.06±0.01 radians for the 1300-pF bilayer. Ultrasound was at 1 MHz and 610 mW/cm2, and the voltage-clamp potential was −200 mV. The baseline currents have been subtracted. B–D. Amplitude (B), frequency (C) and exponential damping constants (D) for the Off component of the capacitive current in response to ultrasound at 1 MHz and 610 mW/cm2, under voltage-clamp at −200 mV, as a function of bilayer capacitance (logarithmic scale) (n = 59). The small squares joined by black lines were obtained from solutions of Eq. 13 with various values of the bilayer diameter, with the solution density ρ = 1000 kg/m3, solution viscosity η = 1 mPa⋅s, bilayer tension γ = 0.8 mN/m, hydrostatic pressure P0 = −70 N/m2, and radiation-force pressure PUS = 0.15 N/m2. E–H. Simulated changes in displacement (u0, measured at the center of the bilayer) (E), changes in area (F), changes in capacitance (G), and capacitive current (H) for the On component of ultrasound response in a 100-pF bilayer, obtained by solving Eq. 13 with a bilayer diameter of 120 µm and other parameters as in part D. The time is relative to the start of the ultrasound application.
Figure 8.
On/Off current in response to ultrasound in cholesterol membranes.
A.. Current in response to a 10-ms ultrasound application at 1 MHz and 610 mW/cm2 in a cholesterol membrane voltage-clamped at −200 mV. The current trace is the average of 50 ultrasound applications. The capacitance of the membrane was 130 pF and the peak negative current is −11 pA. The mean (± SE) peak negative current was −18±3 pA (n = 10, capacitance range 70–130 pF). This small current response was not seen when the aperture on the bilayer partition was occluded with a drop of lipid/decane solution, indicating that it depends on the presence of a nanometer-scale lipid film. B. Off current responses for the cholesterol membrane in A (blue current trace) and in a POPE/POPG bilayer with the same capacitance in response to the same ultrasound stimulus (red current trace), normalized to the peak negative current. The current scale bar is in normalized units.
Figure 9.
Similar time courses of ultrasound-induced capacitive currents and bilayer velocity measured by laser Doppler vibrometry.
A. Bilayer velocity (blue) and current (red) in response to a 10-ms ultrasound application with a focused transducer at 43 MHz and 5 W/cm2, under voltage-clamp at −200 mV. The current and velocity traces are the average of 20 ultrasound applications. The capacitance of the bilayer was 380 pF. B. Fits of Eq. 1 (black lines) to the Off components of the velocity and current for the bilayer in A. For velocity, values of the fit parameters (± SD) are a, −24±1 mm/s; f, 1600±5 Hz; α, 980±30 s−1; φ, −1.10±0.02 radians. For current, values of the fit parameters (± SD) are a, −5700±40 pA; f, 1600±2 Hz; α, 1200±10 s−1; φ, −0.42±0.01 radians. C. Mean (±SE) amplitude (left), and frequency (f) and damping constant (α) (right) from fits of Eq. 1 to the Off velocity (blue) and current (red) in response to ultrasound at 43 MHz and 5 W/cm2, under voltage-clamp at −200 mV.
Figure 10.
Part of the radiation force on the bilayer is due to a direct interaction with ultrasound.
A. Mean (±SE) capacitive current response amplitude as a function of the thickness of the solution layer between the bilayer and the solution/air interface, normalized to the response amplitude at the reference thickness (1.7 mm, corresponding to the standard solution volume of 300 µL in the upper compartment of the chamber) and to the bilayer capacitance (see Materials and Methods, “Data Analysis” section), for ultrasound at 1 MHz and 610 mW/cm2 (n = 2–8). The solid blue line is an exponential fit with amplitude of 2.7±0.2, exponential decay constant of 0.84±0.14, and baseline value of 0.38±0.08 (parameters ± SD). B. As in A, but for focused ultrasound at 43 MHz and 13 W/cm2 (intensity at focal spot, located on the bilayer) (n = 3–8). The solid blue line is an exponential fit with amplitude of 17±14, exponential decay constant of 2.3±0.8, and baseline value of 0.53±0.10 (parameters ± SD). C. Currents in response to ultrasound at 43 MHz and 13 W/cm2, under voltage-clamp at −100 mV, with an ∼8 mm thick solution layer between the bilayer and the solution air interface (blue current trace), and in response to the same ultrasound stimulus with the reflective solution/air interface replaced by an acoustic absorber (red current trace). The red current trace is the average of 10 ultrasound applications, and the blue current trace is the average of the currents before putting the acoustic absorber in place and after removing it, each the average of 10 ultrasound applications. The capacitance of the bilayer was 180 pF. D. Mean (±SE) capacitive current response frequency (red circles) and damping constant (blue circles) as a function of the thickness of the solution layer between the bilayer and the solution/air interface, for ultrasound at 1 MHz and 610 mW/cm2 or at 43 MHz and 13 W/cm2 (combined data sets from A and B, n = 9–15). The solid lines are linear fits with slope and intercept of −14±2 Hz/mm and 480±9 Hz (frequency), and 2.7±4.3 s−1/mm and 440±20 s−1 (damping constant) (parameters ± SD).