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

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

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116 Mesoscopic model for lipid bilayers with embedded proteins A somehow different scenario arises when a protein is subjected to a negative mismatch, as illustrated in the snapshot in figure 7.8(b), which shows a typical configuration obtained from the simulations on a bilayer with embedded a protein with ˜dP=14 ˚A, thus subjected to negative mismatch ∆d=-23 ˚A. In this case the protein orients antiparallel to the orientation of the lipids; also, the lipids in the vicinity of the protein interdigitate to decrease the bilayer hydrophobic thickness and thus fulfill the matching condition. To better illustrate this phenomenon, we have depicted the end-bead of of the lipid chains in darker color. From the snapshot in figure 7.8(b) it can be seen that, in the vicinity of the protein, the end-tail of the lipids in one monolayer are close to the headgroups of the lipids in the opposite monolayer. As described in section 5.3 of Chapter 5, by increasing the temperature above T∗ =0.35, the pure lipid bilayer undergoes a transition from the Lβ ′ phase to a ‘striated’ phase that resembles the Pβ ′ phase of phospholipid bilayers. Interestingly, upon incorporation of a protein, and depending on the mismatch condition, the protein segregates into the striated region whose hydrophobic thickness better matches the protein hydrophobic length. This is clearly shown in the snapshots in figure 7.9, which depict two typical configurations of the systems at a reduced temperature T∗ =0.4, and in the case of proteins with ˜dP=41 ˚A and 18 ˚A, respectively. The calculated value of the pure lipid bilayer hydrophobic thickness is do L =(30.0±0.3) ˚A. Both cases refer to a protein of size NP=7. For positive values of hydrophobic mismatch (see fig- (a) ∆d > 0 (b) ∆d < 0 Figure 7.9: Snapshots of two typical configurations of lipid-protein bilayers at a reduced tem- perature T ∗ =0.4, in the ‘striated’ gel phase, which resembles the Pβ ′ phase in phospholipid bilayers. The calculated value of the pure lipid bilayer hydrophobic thickness is d o L =(30.0±0.3) ˚A. In (a) is shown the case of a protein of size NP=7 and ˜dP=41 ˚A, thus subjected to a positive mismatch ∆d=11 ˚A, while in (b) is shown the case of a NP=7 size protein, but with ˜dP=18 ˚A, thus subjected to negative mismatch ∆d=-12 ˚A. ure 7.9(a)), the protein prefers to segregate in the striated region formed by lipids in the gel-like state. Instead, in the case of negative mismatch, the protein prefers the region where the chains are fluid-like (see figure 7.9(b)). The interplay between the underlying structure of the striated phase and the mismatch-induced perturbation could provide a mean to tune the lateral organization of membrane proteins, and thus control their segregation in the two-dimensional ordered structure. To understand how ordered structures might form is important because scattering methods

7.4 Conclusion 117 make use of ordered structure as a matrix to determine the three-dimensional structure of proteins [187, 188]. 7.4 Conclusion We have presented a mesoscopic model for lipid bilayers with embedded proteins, which we have studied with the Dissipative Particle Dynamics simulation method. One of our aims was to point out the advantages of the DPD-simulation-CG-model approach by addressing some simple issues related to the collective nature of a threedimensional membrane system, a lipid bilayer containing just one lipid species and an embedded protein. More specifically, we have investigated the effect due to mismatch and protein size on the perturbation induced by the protein on the surrounding lipid bilayer. The perturbation around the protein was quantified in terms of the bilayer hydrophobic thickness profile. We found that the profile may have an exponential form, decays to the value of the thickness of the unperturbed system (i.e. without protein), and can be characterized by the coherence length, ξP, of the spatial fluctuation around the protein. We found that, under well defined thermodynamic conditions, the value of ξP may depend on mismatch and protein size, the larger the mismatch/size the larger ξP. Also, we found that to adapt to a too thin bilayer the protein may tilt (or even bend) in a manner which is mismatch and protein-size dependent. We have found that the model predictions are in qualitative agreement with previous theoretical and experimental findings. We want to stress that the phenomena that we have investigated with the DPD simulation method involve molecular rearrangements in the membrane plane via, among others, diffusion of molecules whose time scale might be outside the range of investigation of more ‘traditional’ simulation techniques, such as MD. The results discussed above refer to a model for DMPC bilayers. The trend shown by these results can also be applied to lipid bilayers with other types of phospholipids, i.e. with longer or shorter hydrocarbon chains then the ones of DMPC. We would like to conclude by saying that the predictions that arise from numerical simulation studies of model systems, such as the one presented here, may be used as a complementary tool to experimental studies to reveal information not otherwise accessible; also, results from numerical studies can provide a framework for the interpretation of experimental data, as well as serve as a source of inspiration for future experiments.

116 <strong>Mesoscopic</strong> model for <strong>lipid</strong> <strong>bilayers</strong> <strong>with</strong> <strong>embedded</strong> proteins<br />

A somehow different scenario arises when a protein is subjected to a negative<br />

mismatch, as illustrated in the snapshot in figure 7.8(b), which shows a typical configuration<br />

obtained from the simulations on a bilayer <strong>with</strong> <strong>embedded</strong> a protein <strong>with</strong><br />

˜dP=14 ˚A, thus subjected to negative mismatch ∆d=-23 ˚A. In this case the protein orients<br />

antiparallel to the orientation <strong>of</strong> the <strong>lipid</strong>s; also, the <strong>lipid</strong>s in the vicinity <strong>of</strong> the<br />

protein interdigitate to decrease the bilayer hydrophobic thickness <strong>and</strong> thus fulfill<br />

the matching condition. To better illustrate this phenomenon, we have depicted the<br />

end-bead <strong>of</strong> <strong>of</strong> the <strong>lipid</strong> chains in darker color. From the snapshot in figure 7.8(b) it<br />

can be seen that, in the vicinity <strong>of</strong> the protein, the end-tail <strong>of</strong> the <strong>lipid</strong>s in one monolayer<br />

are close to the headgroups <strong>of</strong> the <strong>lipid</strong>s in the opposite monolayer.<br />

As described in section 5.3 <strong>of</strong> Chapter 5, by increasing the temperature above<br />

T∗ =0.35, the pure <strong>lipid</strong> bilayer undergoes a transition from the Lβ ′ phase to a ‘striated’<br />

phase that resembles the Pβ ′ phase <strong>of</strong> phospho<strong>lipid</strong> <strong>bilayers</strong>. Interestingly,<br />

upon incorporation <strong>of</strong> a protein, <strong>and</strong> depending on the mismatch condition, the protein<br />

segregates into the striated region whose hydrophobic thickness better matches<br />

the protein hydrophobic length. This is clearly shown in the snapshots in figure<br />

7.9, which depict two typical configurations <strong>of</strong> the systems at a reduced temperature<br />

T∗ =0.4, <strong>and</strong> in the case <strong>of</strong> proteins <strong>with</strong> ˜dP=41 ˚A <strong>and</strong> 18 ˚A, respectively. The calculated<br />

value <strong>of</strong> the pure <strong>lipid</strong> bilayer hydrophobic thickness is do L =(30.0±0.3) ˚A. Both cases<br />

refer to a protein <strong>of</strong> size NP=7. For positive values <strong>of</strong> hydrophobic mismatch (see fig-<br />

(a) ∆d > 0 (b) ∆d < 0<br />

Figure 7.9: Snapshots <strong>of</strong> two typical configurations <strong>of</strong> <strong>lipid</strong>-protein <strong>bilayers</strong> at a reduced tem-<br />

perature T ∗ =0.4, in the ‘striated’ gel phase, which resembles the Pβ ′ phase in phospho<strong>lipid</strong><br />

<strong>bilayers</strong>. The calculated value <strong>of</strong> the pure <strong>lipid</strong> bilayer hydrophobic thickness is d o L =(30.0±0.3)<br />

˚A. In (a) is shown the case <strong>of</strong> a protein <strong>of</strong> size NP=7 <strong>and</strong> ˜dP=41 ˚A, thus subjected to a positive<br />

mismatch ∆d=11 ˚A, while in (b) is shown the case <strong>of</strong> a NP=7 size protein, but <strong>with</strong> ˜dP=18 ˚A,<br />

thus subjected to negative mismatch ∆d=-12 ˚A.<br />

ure 7.9(a)), the protein prefers to segregate in the striated region formed by <strong>lipid</strong>s in<br />

the gel-like state. Instead, in the case <strong>of</strong> negative mismatch, the protein prefers the<br />

region where the chains are fluid-like (see figure 7.9(b)). The interplay between the<br />

underlying structure <strong>of</strong> the striated phase <strong>and</strong> the mismatch-induced perturbation<br />

could provide a mean to tune the lateral organization <strong>of</strong> membrane proteins, <strong>and</strong><br />

thus control their segregation in the two-dimensional ordered structure. To underst<strong>and</strong><br />

how ordered structures might form is important because scattering methods

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