98 <strong>Mesoscopic</strong> model for <strong>lipid</strong> <strong>bilayers</strong> <strong>with</strong> <strong>embedded</strong> proteins they do not take into full account the three dimensional structure <strong>of</strong> the bilayer), <strong>and</strong>, for example, they can not be used to investigate the <strong>lipid</strong>-induced protein tilting. Simulations on more realistic <strong>models</strong>, such as all-atom <strong>models</strong> for <strong>lipid</strong> <strong>bilayers</strong> <strong>with</strong> <strong>embedded</strong> proteins, have anyway confirmed that, at least <strong>with</strong>in a time <strong>of</strong> the order <strong>of</strong> the nanoseconds, a mismatched protein may induce a deformation <strong>of</strong> the <strong>lipid</strong> bilayer structure [10, 63, 170], <strong>and</strong> that the deformation is <strong>of</strong> the exponential type [11]. The same type <strong>of</strong> studies have also shown that—although to reduce a possible hydrophobic mismatch synthetic peptides may prefer to deform the <strong>lipid</strong> bilayer, rather than undergo tilting [171]—tilting may also occur for membrane peptides [7,8]. Incidentally, the results from these studies indicated that the helical-peptides experience a slight bend in the middle <strong>of</strong> the helix. No matter the huge body <strong>of</strong> experimental <strong>and</strong> theoretical studies on <strong>lipid</strong> <strong>bilayers</strong> <strong>with</strong> <strong>embedded</strong> proteins, issues such as the range <strong>of</strong> the protein-induced <strong>lipid</strong> bilayer perturbation, its dependence on protein size, <strong>and</strong> the occurrence <strong>of</strong> protein tilting (or even bending) to adjust for hydrophobic mismatch, are still a matter <strong>of</strong> debate. Here we want to focus on these issues by adopting the DPD simulation method to study the behavior <strong>of</strong> a mesoscopic model for <strong>lipid</strong> <strong>bilayers</strong> <strong>with</strong> <strong>embedded</strong> proteins. We have focused our attention on the perturbation caused by a membrane protein on the surrounding <strong>lipid</strong>s, its possible dependence on hydrophobic mismatch, protein size, <strong>and</strong> on temperature. We have investigated whether <strong>and</strong> to which extent—due to hydrophobic mismatch <strong>and</strong> via the cooperative nature <strong>of</strong> the system—a protein may prefer to tilt (<strong>with</strong> respect to the normal to the bilayer plane), rather than to induce a bilayer deformation <strong>with</strong>out (or even <strong>with</strong>) tilting. 7.2 Computational details 7.2.1 Lipid <strong>and</strong> protein <strong>models</strong> Within the mesoscopic approach, each molecule <strong>of</strong> the system (or groups <strong>of</strong> molecules) is coarse-grained by a set <strong>of</strong> beads. In particular, to model the bilayer <strong>and</strong> the <strong>embedded</strong> proteins, we consider three types <strong>of</strong> beads: a water-like bead, labeled ’w’; a hydrophilic bead, labeled ’h’, which <strong>models</strong> a part <strong>of</strong> the headgroup <strong>of</strong> either the <strong>lipid</strong> or the protein; <strong>and</strong> a hydrophobic bead, labeled either ’tL’ or ’tP’, depending on whether it refers to a portion <strong>of</strong> the <strong>lipid</strong> hydrocarbon chain or a portion <strong>of</strong> the hydrophobic region <strong>of</strong> protein, respectively. The systems that we have simulated are made <strong>of</strong> model <strong>lipid</strong>s having three headgroup beads <strong>and</strong> two tails <strong>of</strong> five beads each; this corresponds to the case <strong>of</strong> acyl chains <strong>with</strong> fourteen carbon atoms, namely to a model for a dimyristoylphosphatidylcholine (DMPC) phospho<strong>lipid</strong>, as illustrated in figure 2.2 <strong>of</strong> Chapter 2, <strong>and</strong> in figure 7.1(a). Within the model formulation, a protein is considered as a rod-like object, <strong>with</strong> no appreciable internal flexibility, <strong>and</strong> characterized by a hydrophobic length dP. The model for the transmembrane protein is
7.2 Computational details 99 dL o (a) (b) (c) eff dL (r) dP (d) φ tilt Figure 7.1: Schematic representation <strong>of</strong> a model-<strong>lipid</strong> (a), <strong>and</strong> a model protein (NP=43 <strong>and</strong> ˜dP=41˚A) (b). A typical configuration <strong>of</strong> the assembled bilayer <strong>with</strong> <strong>embedded</strong> a model-protein (as results from the simulations) is shown in the snapshot (c). The drawing in (d) shows to which part <strong>of</strong> the system the following quantities refer to: the pure <strong>lipid</strong> bilayer hydrophobic thickness, d o L, the perturbed <strong>lipid</strong> bilayer hydrophobic thickness, dL(r), the protein hydrophobic length, dP, the tilted-protein hydrophobic length, d eff P , <strong>and</strong> the tilt-angle, φ tilt . dP