Mesoscopic models of lipid bilayers and bilayers with embedded ...

7.3 Results and discussion 109
that this is also the case for the other values of positive mismatch. The derived values
of ξP (using equation 7.3) as function of protein size and hydrophobic mismatch,
which are shown in Table 7.2, indicate that there is a mismatch dependence of the
perturbation caused by the protein on the surrounding lipids. For a given protein
size, NP, if the mismatch is negative, the correlation length increases with decreasing
mismatch (absolute value), while for positive mismatch the opposite happens,
and the correlation length increases with increasing mismatch. Also, in the case of
negative mismatch the decay length increases by increasing the protein size. Instead
there is no detectable ξP dependence on NP in the case of ∆d > 0, at least at the considered
temperature, i.e. well above the melting temperature of the pure system. The
scenario is somehow different when the temperature decreases and approaches the
transition temperature, as it is discussed in the next section.
Figure 7.4f shows that, for the large protein (NP=43), the lipid thickness profile
dL(r) differs from an exponential one. The effect is even more pronounced at lower
temperatures (data not shown), at least in the case of negative mismatch (since lower
temperature means larger negative mismatch). This non-exponential behavior, and
the possible reason for it, will be discussed later.
Table 7.2 also gives the values of the pure lipid bilayer hydrophobic thickness d o L
obtained from the best fit of dL(r) using equation 7.3. For all the considered cases, the
(fitted) compare well with the value of the pure lipid bilayer hydrophobic
values of do L
thickness, do L =23.6 ˚A, obtained directly from the simulation at the considered temperature.
7.3.2 Lipid-induced protein tilting
The protein tilt angle with respect to the bilayer normal as function of ∆d and protein
size NP is shown in figure 7.5. The snapshots on the right show typical configurations
of the system, for a fixed value of the protein hydrophobic length, for the
three protein sizes, NP=4, 7, and 43, and for the largest (positive) value of mismatch,
∆d=26 ˚A, at the considered temperature, T ∗ =0.7. For ∆d < 0 the tilt angle is very
small, and is within the statistical tilt-fluctuations to which the protein is subject
in the bilayer; as the protein hydrophobic length increases (and the mismatch becomes
positive), the protein undergoes a significant tilting. Also, for equal values of
hydrophobic mismatch, the “thinner” protein (NP=4) is much more tilted than the
“fatter” one (NP=43). These results, combined with the one discussed above, suggest
that in the case of proteins with small surface area, the main mechanism to compensate
for a large hydrophobic mismatch is the tilt, while in the case of proteins
with a large surface area, that cannot accommodate a too large tilt, the mismatch is
mainly compensated for by an increase of the bilayer thickness around the protein,
as is clearly illustrated by the snapshot in figure 7.5 (NP=43).