Figure 4.9: Two dimensional radial distribution function of lipid bilayers at 310 K.
In the DPPC lipid bilayer, the two dimensional ordering is observed up to 25 Å while in the POPC lipid bilayer it is lost after 15 Å. These curves also reveal that the lipid-lipid distance in a monolayer is larger with POPC lipids than with DPPC lipids.
bilayer where it is 0.2810Åagainst 0.1762Åin the DPPC lipid bilayers (computed over 100 ps). If we know go back to Figure 4.8, we can notice the charges are mostly located in the hydrophilic heads of the lipids. The POPC lipids being more mobile, we think the angular fluctuations bring those dipoles in more perpendicular positions than the DPPC lipids. Indeed, when computing the ratio of the out-of-plane polarisation over the in-plane polarisation,
in the monolayers, we find 0.0309 for POPC lipids and 0.0017 for the DPPC lipids. This difference, due to the space between lipids reducing the dipole-dipole interaction, explains that the electric capacity is larger with POPC lipids than with DPPC lipids.
The in-plane dielectric permittivity being larger in the POPC lipid bilayer (Figure 4.6) means that the fluctuations of the dipoles in the plane of the POPC lipid bilayer are larger than in the DPPC lipid bilayer. This could also come from the larger distance between POPC lipids and the smaller the dipole-dipole interactions, inducing more dipole-dipole fluctuations. The slight decrease of the permittivity with the temperature is a sign that the temperature is screening the dipole-dipole interactions between the lipids.
Going back to Figure 4.8, we see that the charges, and thus the dipoles are mostly in the heads of the lipids. Thus according to our analysis of the static permittivity and the polarisability, we can consider the lipids as big dipoles interacting with each other. The distance between those dipoles, and thus their mobility, is driven by the mostly uncharged lipid tails. Those tails give the general structure of the bilayer that will change the behaviour of the charges in the lipid heads and thus change the dielectric properties.
4.4.2 The effect of the structure and the infra-red absorption In the case of the infra-red absorption, Figure 4.7 shows that the absorption spectra of both bilayers are very similar. This is quite surprising after having seen the morphological differences of the two bilayers but then where is this absorption occurring? By computing the absorption spectra as function of the axis perpendicular to the bilayer’s plane with a 2 Å resolution, we were able to address this question with Figure4.10.
The top of Figure 4.10 represents the local absorption averaged on the whole spectrum part available to our simulation. This Figure shows that the absorp-tion in the DPPC lipid bilayer occurs mainly in the heads of the lipids (at about 40 and 85 Å), where the curve is maximal but in the bilayer made of POPC, the absorption is spread more homogeneously. The bottom part of Figure4.10 represents the absorption at 53 THz as function of the position in the bilayers.
We have chosen this frequency because it is he frequency of the C-C bond, which lie in the center of the bilayers so that we expect to have more homoge-neous curves than with the total absorption. This is what we actually find but with several differences between both bilayers. These curves can be explain by noticing they mainly follow the charge density represented on Figure4.8.
0 1 2 3 4 5
< α ’’( ω )>
ωDPPC bilayer POPC bilayer
40 50 60 70 80 90
Position (Å) 0
0.5 1 1.5 2
α ’’( ω =53THz)
Figure 4.10: Average absorption (top) and absorption at 53 THz (bottom) as function of the position in the bilayers. The absorption in the bilayers different structures and are driven by the charges density profiles. Thus the absorption in the DPPC lipid bilayer is localised in the heads even at 53 THz which is the frequency of the C-C bonds. Oppositely the absorption in the POPC lipid bilayer is more homogeneous in the bilayer.
4.5 Conclusion
In summary, this work presents a first attempt to theoretically predict the IR-THz absorption properties of two types of lipid bilayer. We have based our approach on the fluctuation-dissipation theorem using molecular dynamics simulations. Our calculations have been compared with experiments. A good agreement is reported for the static and frequency dependent polarizability for the range of frequencies available in the literature. In addition, our analysis provides spectral data at lower frequencies (below 40 THZ) where no experi-ments have been conducted so far. The physical origin of the polarizability has been further investigated:
• The temperature is found to have no effect on the static polarizability that differs by a factor of three between POPC and DPPC layers. This feature is explained by different structural configurations that allow more dipole fluctuations at the POPC hydrophilic heads.
• For the case of the IR spectra, both structures exhibit the same broad-band absorption, ranging from 10 to 100 THz where the full vibrational spectrum is IR-active. Surprisingly, we found that for the case of the DPPC bilayer, IR absorption is strongly localized at the hydrophilic heads whereas for the case of the POPC bilayer, the absorption occurs more uniformly. This has been explained by the charge distribution. This ap-proach opens the field to the study of the heating properties of biological systems when IR radiation plays a dominant role.