Langmuir 1996, 12, 3743-3746
Effects of an Externally Applied Electric Field on the Static Redistribution of Monolayer Domains Li-Zhi Mi and Sen-Fang Sui* State Key Laboratory of Biomembrane and Membrane Biotechnology, Department of Biological Sciences and Biotechnology, Tsinghua University, Beijing 100084, People’s Republic of China Received October 3, 1995. In Final Form: March 26, 1996
Introduction Lipid monolayers on the air/water interface are extensively studied as a simple model of a biological membrane.1,2 At a certain temperature, lipid monolayers at the air/water interface undergo a phase transition between a liquid and a more condensed gel phase while increasing the surface pressure. In the two-phase region, the gel phase exists as discrete domains within the continuous liquid phase. The domain shape, size, and density can be changed via ionic condition, temperature, and pressure. It was proposed that long-range electrostatic interactions originated from the molecular dipole play an important role in the phase behavior of these two-dimensional systems.3 Therefore, the accurate information about molecular origination of these interactions is helpful for us to understand these phenomena. As the first step, it was necessary to carry out precise measurement of the dipole moment. Some original works had been reported concerning this aspect.4-7 For example, a model of the field gradient electrophoretic mobility of lipid domains was supposed by Mo¨hwald and co-workers,6 and then Klingler and McConnell developed it to be a method in measuring the dipole moment density.7 However, some discrepancies still exist,8 and further work is needed to address this problem. On the other hand, the study of the action of an electric field on the monolayer domains has a potential application in the field of nanotechnology. We hope that this study might help to develop new tools for nanoscope arrangement of molecules in two dimensions. This arrangement is of primary importance in the fields of development of biosensors and molecular devices. The present paper proposes a model for calculation of the equilibrium distribution of lipid domains under the externally applied electric field. On the basis of the model, the difference of dipole moment density between the phases was quantitatively measured.
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Materials and Methods Materials. DPPC (dipalmitoylphosphatidylcholine), DMPE (dimyristoylphosphatidylethanolamine), and DMPA (dimyristoylphosphatidyl acid) were obtained from Sigma Chemical Co. (St. Louis, MO). The dye probe (Rhodamine-DOPC) was purchased from Avanti Polar Lipids, Inc. (Alabaster, AL). The monolayers were spread from a lipid solution in chloroform/ methanol (3:1, v/v) and contained 0.3 mol % of the dye probe. The water used was deionized and the contamination by divalent ions was prevented by adding 10-5 M EDTA to the subphase. The electrolyte concentration in subphase was 2 mM KCl (DPPC, DMPE) or 3 mM NaCl (DMPA). pH was adjusted with NaOH and HCl. Setup. The film balance, which contains a glass window in the bottom, is made of Teflon. Its dimension is 20 × 8 × 0.8 cm3. Monolayers were observed with a Nikon Diaphot fluorescence microscope, equipped with a 40× extremely long working distance objective. The pictures were received with a low light level SIT camera (Hamamatsu c2400) and recorded with VHS video recorder ( Panasonic HD-100). The electrode consists of a metal syringe tip with a tip radius of about 7 µm. A micromanipulator (Nikon Narashige) was used to move the electrode in three orthogonal directions with an accuracy of 5/6 µm.9 A cover was designed to inhibit disturbance of air circulation and slow down the drift of domains. Calculation of Electric Field. The electrode was idealized as follows: A conducting sphere of radius a, which holds a potential V0 against the grounded subphase, is placed above the water surface at the height h. The subphase can be treated as a good conducting medium, due to the high ionic concentration. In this model, the potential V(r,θ,z) generated by the sphere can be derived from the angular conservation transformation
V(r,θ,z) ) V0SW (z + W) W2 W W4r2 + 2 2 W - 2S [r2 + (z + W)2]2 2 r + (z + W)
[
{
]}
2 -1/2
+
2SV0 (1) 2S - W
where
W ) xh2 + 2ah S)
(
)
W2 1 W2 2 W + h W + h + 2a
At the air/water interface, the electric field E(r) is perpendicular to the surface of the subphase, and is given by:
E(r) ) -
|
∂V(r,z) ∂z
) -V0
z)0
4SW (W - 2S)(r2 + W2)
(2)
* Correspondence should be addressed to Dr. Sen-Fang Sui, Department of Biological Science and Biotechnology, Tsinghua University, Beijing 100084, People’s Republic of China: tel, 861062594768; fax, 8610-62568182; e-mail,
[email protected].
The force exerted on the domain is proportional to the radial gradient of the electric field and the difference in dipole moment density between the gel phase and liquid phase:
(1) McConnell, H. M. Structures And Transitions In Lipid Monolayers At The Air-water Interface. Annu. Rev. Phys. Chem. 1991, 42, 171195. (2) Mo¨hwald, H. Phospholipid And Phospholipid-Protein Monolayers At The Air/Water Interface. Annu. Rev. Phys. Chem. 1990, 41, 441476. (3) McConnell, H. M.; Moy, V. T. Shapes of Finite Two-Dimensional Lipid Domains. J. Phys. Chem. 1988, 92, 4520-4525. (4) Miller, A.; Helm, C. A.; Mo¨hwald, H. The Colloidal Nature of Phospholipid Monolayers. J. Phys. (Paris) 1987, 48, 693-701. (5) McConnell, H. M.; Rice, P. A.; Benvegnu, D. J. Brownian Motion of Lipid Domains in Electrostatic Traps in Monolayers. J. Phys. Chem. 1990, 94, 8965-8968. (6) Heckl, W. M.; Miller, A.; Mo¨hwald, H. Electric-Field-Induced Domain Movement in Phospholipid Monolayers. Thin Solid Films 1988, 159, 125-132. (7) Klingler, J. F.; McConnell, H. M. Field-Gradient Electrophoresis of Lipid Domains. J. Phys. Chem. 1993, 97, 2962-2966. (8) Benvegnu, D. J.; McConnell, H. M. Surface Dipole Densities in Lipid Monolayers. J. Phys. Chem. 1993, 97, 6686-6691.
8SWr F(r) ) µπRd2V0 (W - 2S)(r2 + W2)2
S0743-7463(95)00829-8 CCC: $12.00
(3)
µ is the difference in dipole moment density between the gel phase and liquid phase. The positive direction of µ is defined as along the +z axis. Rd is the radius of a circular lipid domain. Background Theories and Assumptions. Under the action of an inhomogeneous electric field, lipid domains can be attracted to or repelled from the electrode and finally form a certain concentration distribution. In this process, the free energy of the system was changed. One of these changes comes from the external electric field, and another is from the domain redistribution. These two factors counterbalance each other. When (9) Miller, A.; Mo¨hwald, H. Collecting Two-Dimensional Phospholipid Crystals in Inhomogeneous Electric Fields. Europhys. Lett. 1986, 2, (1), 667-74.
© 1996 American Chemical Society
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Langmuir, Vol. 12, No. 15, 1996
Notes
the system reaches equilibrium in the end, the total free energy should be minimal. In this section, we evaluate the difference in dipole moment density between the phases in terms of minimal free energy. The free energy of the system is
F ) ∆Fe + ∆Fd + F0 ∆Fe is the free energy change caused by the external electric field, ∆Fd is the free energy change caused by domain redistribution, and F0 is the primary free energy without external electric field. It can be arbitrarily defined as zero. Considering the experimental results, we introduce a function Φ(r) to represent the area fraction occupied by the dark lipid domains around r. Φ(r) is assumed to be
{
{
S
∫ E(r)‚r‚(φ(V ) - φ) dr + const R
0
(6)
Accurate calculation of ∆Fd is rather complicated. Indeed, ∆Fd reflects the interaction free energy change between domains in the process of domain aggregation or dispersion. We can associate ∆Fd with the difference of two items: first, the energy of domain aggregation or dispersion which can be simplified as a single large domain with radius R suited in a medium without phase separation, second, the energy from the change of domain number within the circle R.
1 2πRµ2(φ(V0) - φ)2 × 4π0
]
2
ln
e2δ |φ(V0) - φ|R Fdomain 4R Rc2
(7)
πRc2 is the mean area of the domains. Fdomain is the electrostatic energy of a single domain. According to McConnell’s theory,10,11 the energy of a domain with a harmonic shape of F ) R0 + rn cos(nφ) can be expressed as
Fdomain ) -2πRcµ2 ln
4Rc -
e2δ 2 µ πrn2 2Rc
{
n2 +
∑a L k
n2 - 1 k
+ 2
k
ln
}
4Rc e2δ
(8)
δ is the distance of the closest neighboring dipoles. For the domains in a circular shape of DMPA or DMPE, the equation can be rewritten as
Fdomain ) -2πRcµ2 ln
(10)
)0
(11)
R)R0
[
µ (φ(V0) - φ) × 4π0
]
2R0 sin(φ(V0) - φ) Fdomain e2δ - (φ(V0) - φ) 4R0 Rc2 2πµ2
(12)
In our experiment, eq 12 can be written as
∫∫E(r)‚µ‚φ(r) dA )
[
}
That can be expressed explicitly
(5)
∆Fe ) -
∆Fd )
{
µ2πrn2 3 4Rc -10 + ln 2 2Rc 2 eδ
|
ln
Here, φ and φ1 are constants that can be measured in experiment, and R indicates the magnitude of domain aggregation or dispersion. Then, ∆Fe can be rewritten as
0
e2δ
-
∂F(R) ∂R
(4)
0 V0 > 0 φ(V0) ) φ1 V0 < 0 φ V0 ) 0
4Rc
In this equation, we select n ) 2. Thus, the value of ∑kakLk is equal to -14.10,11 When the final balance is reached, the free energy should satisfy the following relation.
E(R0)R0 )
φ(V0) |r| e R φ(r) ) φ |r| > R
-2πµ
Fdomain ) -2πRcµ2 ln
4Rc e2δ
(9)
For the domains in a shape like DPPC (as shown in Figure 1), (10) McConnell, H. M. Harmonic Shape Transitions in Lipid Monolayer Domains. J. Phys. Chem. 1990, 94, 4728-4731. (11) Vanderlik, T. K.; Mo¨hwald, H. Mode Selection and Shape Transitions of Phospholipid Monolayer Domains. J. Phys. Chem. 1990, 94, 886-890.
µ)-
[
16V0SW π0R0 e2δ (φ(V0) - φ) ln 2 2 W - 2S R0 + W 4R0 2R0 sign(φ(V0) - φ) Fdomain (φ(V0) - φ) Rc2 2πµ2
]
-1
(13)
Therefore, we can use this equation to calculate the difference of dipole moment density between the phases.
Results Three systems (DMPA, DMPE, DPPC) have been investigated. We observed that the monolayer domains were repelled from the electrode when the voltage applied was positive and attracted to the electrode when the voltage was negative. This phenomenon indicates that the difference in dipole moment density between the phases is inherent. Its direction was pointing from the subphase to the air. Figure 1 and Figure 2 were taken from fluorescence microscopy after the voltage has been applied for at least 20 min. This duration excluded further movement of domains caused by the electric field. It is shown that DPPC domains were repelled from the electrode under voltage of +30 V (Figure 1). The surface pressure was 5.1 mN/m, which located on the second turn of the pressure/area isotherm. It is evident that the shape of DPPC monolayer domains is not a regular circle but has two or three branches. We also observed the action of the electric field on DMPA monolayer. (The photographs are not displayed.) The voltage applied was +30 V, at a pH of 8.0 in the subphase. The ionic strength was 3 mM NaCl. However, this concentration was not accurate due to the introduction of a small amount of Na+ and Cl- while adjusting the pH. The measurement pressure was 3.8 mN/m located at the linear portion of the two-phase region of the pressure/ area isotherm. The voltages applied on the DMPE sample were +30 and -30 V, respectively. Pressure was 7.8 mN/m. This pressure was just at the beginning of the first turn of the pressure/area isotherm. The concentration gradient of lipid domains aggregated around the electrode (Figure 2a). When the equilibrium was reached, a large aggregation area of lipid domain was observed at the bottom of the electrode; the domains beyond this area still had some mobility caused by the air circulation or thermal motion. Considering this observation and the definition of eqs 4 and 5, we used a radius R0 to indicate this aggregation amplitude. In our experiment, this radius was about 215
Notes
Langmuir, Vol. 12, No. 15, 1996 3745 Table 1. Dipole Moment Density Differences (µ) for Three Different Lipids sample temp (°C) DPPCa
22.3-22.5 DMPAa 21.6-22.8 a DMPE 26.2-26.8 DMPEa 26.2-26.8
pressure (mN/m) ion conditionc pH 5.1 3.8 7.9 7.9
2 mM KCl 3 mM NaCld 2 mM KCl 2 mM KCl
4.7 8.0 4.7 4.7
µ (D/nm2 ) 0.73 ( 0.10 0.089 ( 0.012 0.052 ( 0.007 0.049 ( 0.012
a The voltage applied for measurement was +30 V. b The voltage applied for measurement was -30 V. c In order to prevent the condemnation of divalent ions, we added 10-5 M EDTA in all measurements. d The ionic concentration was not accurate because of the introduction of NaOH and HCl while adjusting the pH of the subphase.
Figure 1. A picture reprinted from the video recorder indicating the action of the electric field on the lipid monolayer. It was the DPPC sample under a voltage of +30 V. Temperature was 22.322.5 °C. Pressure was 5.1 mN/m.
Figure 3. Diagram of the V-R2 plot calculated from eq 13. This curve indicated that V is proportional to R2.
measured difference of the dipole moment density was an effective value. The value measured for DMPE under the voltage of -30 V (µ ) 0.049 D/nm2) was smaller than that under the voltage of +30 V (µ ) 0.052 D/nm2) (Table 1). This small difference could be attributed to the ignorance of the concentration gradient in the calculation. Discussion
Figure 2. Photographs displaying a comparison of the redistribution of the domain densities under the different electric fields. The sample was DMPE. Part a was taken under the voltage of -30 V, and part b was taken under a voltage of +30 V. Temperature was 26.2-26.8 °C. Pressure was 7.8 mN/ m.
µm, which is little larger than the radius of dispersion (205 µm) (Figure 2b). As mentioned above, domain distribution patterns under electric fields can be used to calculate the difference of the dipole moment density. Table 1 lists our experimental results. For charged lipids such as DMPA, the effect of surface charges and that of the intrinsic dipole moment could not be discriminated. Therefore, the
(1) In the case of a specified sample and specified measurement condition, eq 12 gives the relationship between the applied electric field and the radius of domain redistribution (R0). To verify our theoretical model, we could observe the corresponding changes of the radius (R0) under different magnitude and different distribution of electric fields. Two kinds of electric field distributions were discussed below. First, we consider the electric field generated by a syringe electrode. This kind of electrode has also been used in the experiments reported by Heckl et al.6 The spatial distribution of the field has been given in eq 2. For the convenience of comparison, we use eq 13 to calculate the radius (R0) under different voltages (Figure 3). One can see that V0 is proportional to R02. This relationship agreed with the published experimental results.6 In another case, the electric field generated by an infinitely extended conducting cylinder has been used.12 Klingler et al. also deduced a precise expression of this field.7 Moreover, over a wide range of their experimental values, the electric field is approximately to be E(r) ≈ const‚(V0/r). Replacing E(r) in eq 12 by this relation, we conclude that V0 is proportional to R0. It also agrees with Lee’s experiments.12 (2) A method was developed by Miller et al.4 to extrapolate the µ from the potential/area curve. The (12) Lee, K. Y. C.; Klingler, J. F.; McConnell, H. M. Electric FieldInduced Concentration Gradients in Lipid Monolayers. Science 1994, 263, 655-658.
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Langmuir, Vol. 12, No. 15, 1996
values they deduced for DMPA (µ ) 0.06-0.11 D/nm2) and DMPE (µ ) 0.05 D/nm2) can be compared with ours (Table 1). However, when their method is applied to the data of DPPC given by Mu¨ller-Landau et al.,13 a discrepancy appears. The value obtained by extrapolation is µ ) 0.2-0.3 D/nm2, which was about half of the value calculated from eq 13. When examining the pressure/ area isotherm, the measurement pressure of DMPA or DMPE was located in the linear region of the isotherm, but the pressure of DPPC was beyond that region. In other words, the extrapolation method was valid only in the linear region. Klingler et al. derived the value (µ ) 0.64 ( 0.2 D/nm2) for DPPC from a microscopic dynamic study.7 It had excellent agreement with ours, and the small difference might come from the different pressure. (They measured at pressures 5.5-6.0 mN/m.) Unfortunately, the value they reported for DMPE was µ ) 0.31 ( 0.1 D/nm2; the reason for this discrepancy is still under investigation. (13) Mu¨ller-Landau, F.; Cadenhead, D. A. Molecular packing in steroid-lecithin monolayers. Chem. Phys. Lipids 1979, II, 315-328.
Notes
(3) When domains were attracted to the electrode, a concentration gradient of domain distribution was often observed. We should take this effect into account. Because the electric field generated by the electrode was inhomogeneous, the concentration gradient of domain distribution will give rise to an additional free energy change in eq 12. This change will make the magnitude of aggregation (R0) larger than that assumed in eq 5. Under this condition, we need to revise the assumption in eq 5 and introduce a factor in eq 12. In some practical cases, however, apparent difference concentrates on a limited area just below the electrode; this difference could be neglected (Table 1). (4) Because molecules in the gel-like domain have different mobility around their liquid surroundings, monolayer domain redistribution induced by the electric field changes these local characteristics of the membrane. This phenomenon may relate to some physiological activities. LA9508295
