La evaluación en el proceso de enseñanza-aprendizaje de los docentes de la escuela

The distribution of local pressure inside the bilayer along the bilayer normal (z-axis) is com- monly referred to as lateral pressure, p(z). The lateral pressure profile is related to many important macroscopic and measurable quantities, such as surface tension, surface free energy, and spontaneous curvature [132]. p(z) arises from local forces acting inside a lipid bilayer in the direction of the membrane plane. The condition for mechanical stability and equilibrium requires that the integrated lateral pressure profile across the membrane vanishes. Neverthe- less, the profile may display different behavior in different regions in the membrane due to a variety of interactions whose relative importance varies across the membrane. Traditionally, three different regimes have been identified: (1) a repulsive contribution in the hydrophilic head group region due to electrostatic and steric interactions and hydration repulsion; (2) an attractive contribution at the membrane-water interface due to the interfacial energy between the water and the hydrocarbon phase, trying to minimize the surface area; and (3) a repulsive contribution inside the membrane due to steric interactions between hydrophobic chains [94]. These forces are assumed to create a non-uniform lateral component of local pressure inside a bilayer [94]. The details may vary considerably from one system to another. The local pressure for a system consisting of particles with many-body potentials can be defined using the local

stress tensor. The lateral pressure profilep(z) is then defined as a difference between the normal (along the membrane normal direction) and the lateral components of the pressure tensor, that is,PN =PzzandPL= (Pxx+Pyy)/2: pz= PL−PN. Qualitatively, this means that a bilayer tends

to expand along the membranexy-plane with positive p(z) and contract with negative p(z). Local pressure is difficult to measure experimentally. In experiments, probes should be employed in different parts of membrane components [146], thus the measured system is not a native one, as is preferred. Computational studies based on atomistic modeling of lipids, however, can shed light on this issue. Here, by means of MD simulations, we analyzed the dependence of lateral pressure profile on the sterol type. The results are presented in Fig. 3.20. The lateral pressure was determined using a customized version of Gromacs, Gromacs 4.0.2. The approach is to re-run the simulations using the customized version of Gromacs while the system is divided into 0.1 nm thick slabs for which the pressure is calculated. Pairwise forces during the pressure calculation are computed from the force field description and MD trajectory. Because pairwise electrostatic forces cannot be obtained using PME method, re-run simulations were carried out by truncating the long-range interactions. As Sonne et al[142] showed that the truncation distance for pressure calculation should bercut > 1.8 nm, we used

rcut= 2.0 nm as for electrostatic cut-offdistance.

As shown in Fig. 3.20, the presence of either sterol affects the qualitative nature of the pressure profile of pure POPC. In CHOL-POPC and DHE-POPC systems the number of peaks and their heights are more than that of pure POPC. To analyze the pressure profile, one should compare it with the density profile presented in Fig. 3.8 and relate the maxima and minima in the lateral pressure profile to the maxima in the density plot. These maxima and minima are in- dicated in Fig. 3.20. The local maximum #1, which is common in pure POPC and sterol-POPC systems, corresponds to the repulsion of head groups of POPC lipids since the density profile of nitrogen and phosphate groups has its maximum at that region. The absolute minimum #2, which is common in pure POPC and sterol-POPC systems, is typical for all membranes and corresponds to the region where the tails start, namely C12, C13and C32(see Fig. 3.8 for com- parison with the density profile). It is an attraction contribution to the pressure profile and is because the membrane tries to minimize its surface area to prevent water from reaching to the hydrophobic region. The next local maximum, #3, which is solely present in sterol-POPC sys- tems is because of the repulsion of OH group of sterols. Its occurs at the same position where the peak of OH density profile does. There is a local maximum, #4, in pure POPC which corresponds to the steric repulsion of POPC acyl chains: the acyl chains repel each other at this region because they are already very close at the parts near the water-membrane interface (peak #2). The next local minimum, which is also not present in the pure POPC system, #5, occurs approximately at z = 4.3 nm and corresponds to the ring structure of sterols. This

3.3. Results 75

means that at this region the membrane components attract each other. In the middle region of the bilayer, where peak #6 occurs, the pressure is almost zero in pure POPC, thus this region can be regarded as a free zone. When sterols are present in the system, however, there are re- pulsive contribution to the pressure profile due to steric repulsion of lipid tails: because lipids are tightly packed at the sterols’ ring area, here, where the ring is no longer present, they try to avoid each other.

Comparison of lateral pressure of CHOL-POPC and DHE-POPC reveals no major differ- ence. However, studies show that the differences due to the sterols in unsaturated bilayers, such as POPC, are considerably smaller than in a saturated ones [110, 109]. Therefore, one should expect more differences to emerge when sterols interact with saturated bilayers. In other words, differences in effects of either sterol on bilayers’ lateral pressure and elasticity are more pronounced when they interact with saturated bilayers such as DPPC.