Lateral Diffusion of TG and CE is Quite Different Compared to Diffusion of PL and FFA

A Few Words of MARTINI Parameterization

To investigate the effect of surface area change, and the subsequent effects of lipid chain ordering and layer’s conformation changes on lipid diffusion, the diffusion constants in the xy-plane were calculated for each lipid type in the systems. Here we need to note the same limitations as for the previous analyses – the lipid layer does not reside entirely on the xy-plane for higher surface pressures, and thus lipid diffusion in that plane does not fully capture all diffusion in the plane of the lipid layer.

Also we need to note that the diffusion in the coarse grained model is not a target property of the parameterization. MARTINI model is targeted to reproduce primarily only the solubility in different solvents – and that gives justification to our primary finding, which is the separation of TGs to form a separate phase at high surface pressures. The MARTINI model for lipids is also parameterized to reproduce as closely as possible the phase transitions of the lipid tails – i.e. the formation of different liquid-crystalline and fluid phases for the lipid systems [188]. The tail ordering analysis is thus also reliable. However, as not all properties can be targeted at the same time, the diffusion of the particles is more vaguely described. It is known that the lipid molecules in the MARTINI model tend to diffuse approximately four times as fast as lipids in atomistic simulation models. However, the “factor of four” is not entirely true for all particles – the smaller the lipid, the faster it tends to diffuse in MARTINI – the correct correction factor for small lipids may in some cases be more than four [188].

We used a factor of four for all lipids in our system to scale the results to “real diffusion”. That is why one needs to keep in mind when interpreting the data that it may be that the smallest of the lipids (the FFAs) show artificially high diffusion, and maybe the biggest molecules (the TGs) show artificially slow diffusion. The qualitative changes in diffusion rates of the lipid types when altering the surface area of the system can be relied on, however, as the trends of the diffusion mainly follow phase separation boundaries, and mirror the effect of lipid tail ordering. Phase separation in response to different stimuli is one of the target properties of MARTINI, and also lipid tail ordering is reasonably well parameterized. The generation of more or less ordered domains, and different kind of organizational structures and lipid phases within the layer is thus well reproduced. Thus, even when the actual value of diffusion is not expected to be quantitatively correct due to the side effects of the coarse grained

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method chosen for the simulations, the qualitative changes in the diffusion rates of different components, mirroring the phase separation and lipid tail ordering processes, are reliably reproduced.

Results of Diffusion Analysis – PL vs. TFLL

When lipid diffusion in the pure PL system and the TFLL system are compared (Figure 26), the pure PL system is seen to exhibit very high lateral diffusion values for all surface areas simulated. For pure PL the diffusion rate is even increased when the surface area is diminished. In contrast, in the TFLL layer, diffusion is slowed down at low surface areas. Actually, all lipid components of the TFLL system show this trend of slowing down with smaller surface areas.

However, FFA diffusion is very fast in TFLL systems (though slower than PL diffusion in one-component PL systems at a high surface pressure) and is only slightly influenced by surface pressure. This is not only an effect of the MARTINI parameterization, but also partly due to the assembly of FFA molecules to string-like structures along which FFAs can rapidly diffuse short distances (Figure 26).

The qualitative difference in diffusion rates – increasing diffusion rate for PL, and diminished diffusion rate for TFLL – illustrates the unstable nature of the pure PL layer under high surface pressures. Under similar conditions, pure PL systems have been seen to go through the monolayer–bilayer transition, which is possibly related to vesicle formation [52]. This would be drastic for TFLL, as the vesicles detaching from the lipid layer to the aqueous phase are rapidly recycled via lacrimal ducts, which in turn would lead to dramatic depletion of the TFLL [21]. It seems clear that the neutral lipids of tear film are needed to maintain the integrity of the lipid layer by preventing the monolayer–bilayer transition and subsequent vesicle formation.

Results of Diffusion Analysis – TFLL Components

If we take a look at the diffusion of the individual lipid components of the TFLL system (Figure 26), we see that the lipid diffusion in TFLL slows down for increasing surface pressure in a distinctive way, where all lipid components slow down, but the surface lipids FFA and PL do it for different reasons than the non-surfactants TG and CE. The diffusion of the non- surfactants also slows down significantly more than the diffusion of the surfactants.

The surfactants FFAs and PLs diffuse in the vacuum-water interfacial plane for all interfacial areas. Their diffusion is slowed down by the formation of the more ordered lipid layer structure within the surface layer due to increase in surface pressure. This more ordered layer simply does not allow the lipids to diffuse as fast as in more loosely packed layers. The TGs and CEs, in contrast, diffuse along this surface layer only in systems of large interfacial area. For the smaller interfacial areas, they are pushed away from the interface, and form a separate phase to the air side of the interface. Their diffusion is thus efficiently slowed down by the formation of the aggregate structure – the whole TG-CE aggregate can of course diffuse along the lipid layer, and there can be some diffusion within the aggregate itself, but this diffusion is in nature different than the diffusion in the surface plane. The diffusion of the whole aggregate along the surface is very slow. The CE molecules within the aggregate core show more or less three- dimensional diffusion instead of two-dimensional (data not shown), as they are not located at a surface, but rather inside a sphere. The triglycerides show two-dimensional diffusion on the air side of the interface, but this diffusion is restricted to the dimensions of the aggregate, and is also slow, as the TG tails are entangled in between the CE chains inside the aggregate structure. Also the surface lipid tails intertwine the tails of TG and CE tails, which slows down the diffusion of the surface layer.

Due to this effect, for the large lateral pressures, the CE and TG molecules diffuse slowly, and only within their cluster, while PL and FFA molecules are relatively free to diffuse along the whole water–air interface. This type of “fast diffusion on the surface, and slow diffusion in the core” is consistent with diffusion that takes place in lipid droplets and lipoproteins. Recent simulations of spherical lipid droplet particles have shown [216-217] that lipid diffusion is the fastest at the surface, and slows down considerably as one goes toward the core of the particles. Here we see similar behavior, as with increasing surface pressure the diffusion of the CE and TG molecules slows down significantly more than the diffusion of PL and FFA molecules. Comparison of the diffusion constants in two and three dimensions clearly demonstrates that part of this “slowing down” of the neutral lipids is due to the fact that the diffusion in the core is 3-dimensional, instead of 2- dimensional surface diffusion (data not shown). It is however also clear that the neutral lipid aggregate is much more solid and slow than the planar lipid layer – the triglyceride hydrocarbon tails entangle around the cholesterol ester molecules (and somewhat also the phospholipid tails), making the cluster more viscous, and thus hindering the diffusion in the aggregate.

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The present results are consistent with previous simulation results for Langmuir monolayers [228], where one found that the single-particle diffusion coefficient decreases for decreasing area per lipid (increasing surface pressure). Similar trends have also been observed in experiments [229-230].

Figure 26. Lateral diffusion coefficients in the plane of the layer [207]. Results are

given in units of 10−7 _cm2_{/s. Diffusion coefficients reported here have been corrected by}

dividing the values by 4 to compensate for the faster diffusion in the coarse-grained model compared to atomistic descriptions [188]. 1-component PL stands for POPC. Reprinted from Langmuir [207] with co-authors’ and publishers permission, copyright 2012 American Chemical Society.

6.3.6 Studies of Elastic Fluctuations of TFLL Show Protrusions but