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Langmuir 1998, 14, 3704-3709
Interactions between Membranes Crammed with Gramicidin Pa¨r Wa¨sterby and Per-Ola Quist* Department of Physical Chemistry, Umea˚ University, S-901 87 Umea˚ , Sweden Received December 3, 1997. In Final Form: April 21, 1998 We report an investigation of the lamellar phase of the system N,N-dimethyldodecylamine oxide (DDAO)/ gramicidin D/water. To identify the dominant repulsive interaction between the gramicidin-crammed membranes, we measured the variation (with the membrane volume fraction) of the position of the Bragg peaks in an X-ray diffraction experiment and the 2H NMR quadrupolar splitting of heavy water and of R-deuterated DDAO. Though none of the components are ionic, the results are consistent with an electrostatically stabilized lamellar phase with a low surface charge density ( 10kBT, is too small to sterically stabilize the lamellar phase. This conclusion is also supported by the experimentally determined membrane rigidities of dilute lamellar phases stabilized by membrane undulations (cf. above).29 Hence, the steric repulsion caused by undulating membranes can be ruled out in the present study. Notice that although it is possible to obtain a fairly nice fit with eq 4 in Figure 6, the derived κ values have no physical significance. Electrostatic Repulsion. With steric stabilization by denatured gramicidin and membrane undulations ruled out, it is time to consider electrostatic repulsion between the membranes. The electrostatic repulsion is caused by the reduced mixing entropy of the counterions of the charged membrane: A decreased distance between the charged membranes decreases the entropy of the counterions, resulting in a repulsive force stabilizing the lamellar structure.10 Electrostatic repulsion is one of the major repulsive interactions in ionic lyotropic systems.10 However, in the present system, there are no ionic species. So if the phase is stabilized by an electrostatic repulsion, we expect a low surface charge density, that probably is caused by ionic impurities or by partial protonation of DDAO (cf. below). A simple way to test for electrostatics is to prepare the samples in series 5 and 6 with water replaced by brine, for instance a 0.30 M NaCl solution, where the electrostatic repulsion is effectively screened.10 Preparing and equilibrating these samples in the same way as before (cf. above) yields samples that phase separate some days after the
Wa¨ sterby and Quist
mixing procedure. The samples separate into a clear fluid solution on top of a white precipitate. The precipitate was easy to disperse in the solution by shaking the tubes, but it phase separates again after some days. This indicates that the water-diluted lamellar phase is stabilized by electrostatic repulsion, since the brine solution screens the electrostatics. Since none of the components in the water-diluted samples are ionic, the electrostatic repulsion must be due to either ionic impurities or the weak basicity of the oxide group of DDAO. In the case of ionic impurities, the mouth of the gramicidin A channel is known to act as a strong binding site for some mono- and divalent cations, for instance Na+ or Mn2+,31,32 which produce a positively charged membrane, with a low surface charge density. Another plausible way to obtain a charged membrane is protonation of DDAO due to the weak basicity of the oxide group of DDAO.33 The process was discussed by Hoffmann,33 who estimated that, at neutral pH, only some few tenths of a percent of the DDAO are present in the protonated form. The repulsive force (per unit area) between two charged membranes, with no extra salt added, is analytic and given by (for monovalent counterions)10
Felec )
2(kBT)2r0 e
(d -s δ)
2
2
(5a)
where s is determined by
s tan(s) )
eσ(d - δ) 2kBT0r
(5b)
In eq 5, σ is the surface charge density and the other symbols are defined above or have their usual meaning. If the electrostatic repulsion is the dominant potential, the relation corresponding to eq 4c is given by
F)
x/
π a2
κ
|
d2Velec dl
2
l)d-δ
)
x/
π a2
κ
|
-dFelec dl l)d-δ
(6)
This expression is strictly valid only for flat, rigid membranes but should be a good approximation for weakly undulating membranes, that is membranes with a high κ. By combining eqs 1, 4a, 4b, 5, and 6 it is thus possible to investigate the variation in the quadrupole splitting of R-deuterated DDAO on dilution with water. Equation 5 is easily solved numerically, and so is the derivative in eq 6. Upon fitting eqs 1, 4a, 4b, 5, and 6 to the experimentally observed variation in the quadrupole splitting with the membrane volume fraction, we noticed that the quality of the fit was essentially insensitive to the cutoff length a if a is in the range 50-300 Å. In the following we use a ) 100 Å, which is a physically reasonable value. In addition, we set δ ) 24.4 Å, as determined by the SAXS experiments. Tests showed that δ ) 24.4 Å is not critical; variations of (1 Å hardly influence the outcome of the fit. Hence, with a ) 100 Å and δ ) 24.4 Å, a nonlinear leastsquares fit of eqs 1, 4a, 4b, 5, and 6 to the experimental data yields κ ) (8.3 ( 1.6)kBT and νQ° ) 31 ( 2 kHz for series 5 and κ ) (5.8 ( 0.9)kBT and νQ° ) 30 ( 2 kHz for (31) Golovanov, A. P.; Barsukov, I. L.; Arseniev, A. S.; Bystrov, V. F.; Sukhanov, S. V.; Barsukov, L. I. Biopolymers 1991 31, 425. (32) Jing, N.; Prasad, K. U.; Urry, D. W. Biochim. Biophys. Acta 1995, 1238, 1. (33) Hoffmann, H.; Oetter, G.; Schwandner, B. Prog. Colloid Polym. Sci. 1987, 73, 95.
Interactions between Membranes Crammed with Gramicidin
Langmuir, Vol. 14, No. 13, 1998 3709
Finally, it is worth mentioning that the bending rigidity of the membrane κ appears to decrease on addition of DDAO to the gramicidin-crammed membrane. However, the decrease is hardly significant, and we are lacking data to be sure of a significant trend. In a recent paper, Freed finds that addition of gramicidin to phospholipid membranes, up to 1 gramicidin per 5 lipids, has only a small effect on the order of fluctuations of the membranes.34 However, according to mean-field theories, addition of the flexible DDAO molecule to the rigid membrane is expected to decrease the bending rigidity of the membrane.35
Figure 7. Best fit of eqs 1, 4a, 4b, 5, and 6, for an electrostatic potential, to the variation of the quadrupolar splitting with the membrane volume fraction. The data correspond to the samples in series 5. The error bars are based on a maximum estimated error of (0.2 in the quadrupolar splitting. The best fit yields κ ) (8 ( 2)kBT, νQ° ) 31 ( 2 kHz, and a surface charge density σ ≈ 10-4 C/m2 or less.
series 6. For both series, the surface charge density σ was determined to be about 10-4 C/m2 or less. In Figure 7, we show the best fit to series 5. Unfortunately, the variation in νQ with σ when σ < 10-3 C/m2 is rather weak, which results in a fairly large uncertainty in σ. Hence, we can only determine an upper limit for σ. In Figure 4, where the basic unit in the membrane is 1 gramicidin + 6 DDAO, the area covered by this unit is about 450 Å2. This means that a surface charge density of 10-4 C/m2 corresponds to about one elementary charge per 400 units of 1 gramicidin + 6 DDAO. As mentioned above, the surface charge density is likely an effect either of ionic impurities that bind to the mouth of the gramicidin channel or of partial protonation of DDAO in the membrane. The derived value of the surface charge density supports this interpretation.
Conclusions A lamellar phase with membranes of DDAO and gramicidin D in water was studied with SAXS and 2H quadrupolar echo NMR experiments on heavy water and R-deuterated DDAO. The results show that the lamellar phase is not stabilized by steric repulsion due to denatured gramicidin or membrane undulations. Rather it is stabilized by a repulsive electrostatic interaction, which is due either to ionic impurities that bind to the mouth of the gramicidin channel or to partial protonation of DDAO in the membrane. By analyzing the variation of the quadrupole splitting with the membrane volume fraction, we show that it is possible to determine the bending rigidity of these weakly charged membranes to be in the range κ ) (5-10)kBT. Acknowledgment. We are grateful to Dr. Patrick Williams and Dr. Eva Selstam for kindly sharing their experimental time at the CLRC’s Synchrotron Radiation Source (SRS) in Daresbury with us and to Dr. Greger Ora¨dd for a helping hand with the SAXS experiments. Eva Vikstro¨m’s assistance at the sample preparation has also been of importance. The financial support from the Swedish Research Council for Engineering Sciences (TFR) is also acknowledged. LA971332T (34) Patyal, B.; Creeau, R. H.; Freed, J. H. Biophys. J. 1997, 73, 2201. (35) Szleifer, I.; Kramer, D.; Ben-Shaul, A.; Gelbart, W. M.; Safran, S. A. J. Chem. Phys. 1990, 92, 6800.
