1. Volume 80, Issue 5, Pages 2298-2309 (May 2001)
Microelectrophoresis of a Bilayer-Coated Silica Bead in an Optical Trap: Application to Enzymology 
R. Galneder, V. Kahl, A. Arbuzova, M. Rebecchi, J.O. Rädler, S. McLaughlin 
Biophysical Journal 
Volume 80, Issue 5, Pages (May 2001)
DOI: /S (01)
Copyright © 2001 The Biophysical Society Terms and Conditions

2. Figure 1
Principle of operation of the field/trap apparatus. (A) Sketch of a bilayer-coated silica bead (blue sphere) in a laser trap (yellow) exposed to an electric field. Applying an electric field via the electrodes (black rectangles with+and−signs) produces an electrophoretic force (Fel) on the bead due to the fixed negative charges (PIP2) on the outer leaflet of the bilayer. This force causes a displacement (Δx=10–100nm) of the bead from its equilibrium position in the tightly focused laser beam. (B) Sketch of a small portion of the 500-nm-radius silica bead (blue) coated with a phospholipid bilayer consisting of 98% PC (zwitterionic lipids with white polar headgroups) and 2% PIP2 (acidic lipids with red headgroups). The bilayer thickness is ∼5nm, and the adsorbed PLC-δ1 enzyme (green) is drawn to scale from the known structures of the PH domain and the remainder of the molecule, which contains a catalytic (Cat) domain. The hydrolysis of negatively charged PIP2 produces electrically neutral diacylglycerol (decapitated lipid below arrow), which remains in the membrane. The negatively charged headgroup, inositol 1,4,5-trisphosphate (IP3; red circle in aqueous phase), diffuses away from the bead.
Biophysical Journal  , DOI: ( /S (01) )
Copyright © 2001 The Biophysical Society Terms and Conditions

3. Figure 2 Sketch of the field trap apparatus. See text for details.
Biophysical Journal  , DOI: ( /S (01) )
Copyright © 2001 The Biophysical Society Terms and Conditions

4. Figure 3
Calibration of the laser trap. (A) A typical power spectrum (average of s spectra) due to the Brownian motion of a 500-nm-radius bead in the laser trap. The power spectral density is obtained from the voltage output of the quadrant diode illustrated in Fig. 2. As described in the text, analysis of a power spectrum allows us to obtain values for both the detector sensitivity, β, and the trap stiffness, κ. (B) Determination of zeta potential. Applying a 160-Hz AC field to a coated bead in the calibrated laser trap produces this typical displacement power spectrum. The field-induced oscillation of the bead in the trap manifests itself as the peak in the power spectrum at 160Hz. As we discuss in the text, the square root of the peak height is proportional to the zeta potential and, thus, the number of PIP2 molecules on the bead. This figure depicts the average of 15 spectra, but we typically averaged only 3 spectra to improve the time resolution of our on-line measurement of the zeta potential (e.g., Fig. 6 C). The beads used to generate the data in Figs. 3, 4, 6, 7, and 8 were coated with a PC/PIP2 bilayer (2% PIP2) and suspended in a solution containing 10mM HEPES, pH 7.0, 300μM EGTA, 200μM calcium, ∼0.5μM free Ca2+.
Biophysical Journal  , DOI: ( /S (01) )
Copyright © 2001 The Biophysical Society Terms and Conditions

5. Figure 4
The amplitude of the voltage-induced displacement of a bilayer coated silica bead versus applied voltage. We used data averaged from 15 power spectra, as illustrated in Fig. 3 B, to obtain the displacement, which is proportional to the applied voltage (correlation coefficient>0.99). The size of the square symbols is equal to the average SD of 10 measurements. We estimate we can deduce the displacement (or zeta potential) to an accuracy of ∼1–2% by applying a voltage of 100V to our coated beads and averaging 3 power spectra, a process that takes ∼3s.
Biophysical Journal  , DOI: ( /S (01) )
Copyright © 2001 The Biophysical Society Terms and Conditions

6. Figure 5
Effect of calcium ions on the zeta potential of PC/PIP2 multilamellar vesicles. These measurements were conducted in a conventional DC microelectrophoresis apparatus described by Bangham et al. (1958). The three data points at the left of the graph (free [Ca2+]<10−7M) demonstrate that the zeta potential of a PC/PIP2 vesicle depends, to a first approximation, linearly on the mole fraction of PIP2 in the vesicle over the range 0–2% PIP2. The relationship is given more exactly by the Gouy equation, Eq. 9. ▿, ●, and ○, measurements with vesicles formed from PC, PC/PIP2 with 1% PIP2, and PC/PIP2 with 2% PIP2, respectively. The figure also illustrates that free [Ca2+]>1μM significantly deceases the zeta potential of the PC/PIP2 (2% PIP2) vesicles by binding to PIP2. The aqueous solutions contained 10mM HEPES (ionic strength ∼3mM), pH 7.0, 150μM EGTA, at 25°C, and Ca2+ to bring the free [Ca2+] to the indicated value, as measured directly by a calcium electrode.
Biophysical Journal  , DOI: ( /S (01) )
Copyright © 2001 The Biophysical Society Terms and Conditions

7. Figure 6
Effect of PLC-δ on the zeta potential of bilayer-coated silica beads as measured in the field/trap apparatus. The experimental approach is described in detail in Materials and Methods. Briefly, we used a tightly focused laser beam to trap a 500-nm-radius silica bead coated with a PC/PIP2 bilayer (Fig. 1 A), then applied an AC electric field and monitored the displacement of the bead (Δx in Fig. 1 A) using a fast quadrant diode (Fig. 2). Using our calibrations of the stiffness of the trap and the sensitivity of the diode detector (Fig. 3 A), we calculated the net electrophoretic force on the coated bead (Fel in Fig. 1 A) from the displacement, Δx (Fig. 3 B). Fel is proportional to the zeta potential, ζ (Eq. 8), which is approximately proportional to the number of PIP2 molecules on the outer leaflet coating the bead (Eq. 9). We follow the decline of ζ as a function of time as the bead is exposed to PLC-δ, which hydrolyzes the negatively charged lipid PIP2 to produce the neutral lipid diacylglycerol (Fig. 1 B). (A) Power spectrum of a bead coated with PC/PIP2, 2% PIP2, when an AC field of 160Hz is applied. The square root of the height of the peak at 160Hz is proportional to the zeta potential. (B) Power spectrum of the same bead after exposure to 9nM PLC-δ for 500s. (C) Online measurements of the zeta potential of coated beads exposed to 1nM, 3nM, or 9nM PLC-δ. The cross-channel containing the enzyme solution (Fig. 2) was opened at t=0, allowing the solution to flow past the bead. The zeta potential was calculated from the height of the peak at 160Hz from power spectra like those shown in A and B. Two beads coated with a PC/PIP2 bilayer (2% PIP2) were measured at each of the three PLC-δ concentrations.
Biophysical Journal  , DOI: ( /S (01) )
Copyright © 2001 The Biophysical Society Terms and Conditions

8. Figure 7
Enzyme kinetics measured on a single bilayer-coated silica bead. The zeta potentials (○) determined experimentally from one of the coated beads exposed to 9nM PLC-δ (Fig. 6 C) are plotted as a function of time. An analysis using a single-exponential fit (— — —) does not describe the data well. An equation based on second-order kinetic theory (see Eq. 12) predicts that the zeta potential should decay as α/(c+kt), where α, c, and k are constants. This equation provides a better fit to the data (——).
Biophysical Journal  , DOI: ( /S (01) )
Copyright © 2001 The Biophysical Society Terms and Conditions

9. Figure 8
Relationship between the initial slope of the kinetic curves and enzyme concentration. As expected theoretically, the initial slopes of the kinetic curves (○), determined by fitting Eq. 12 to the data in Fig. 6 C, are proportional to the [PLC]. The straight line is the least-squares best fit to the data. Analysis of data from these and other similar experiments (not shown) gives an average slope ∼−0.1mV/s per nM PLC.
Biophysical Journal  , DOI: ( /S (01) )
Copyright © 2001 The Biophysical Society Terms and Conditions