boundary conditions that mimic the presence of other surrounding particles. They
prove that within this approximation the lateral pressure between colloids is always
repulsive, even in the nonlinear regime;
6 however, how well the cell model actually
captures a multiparticle assembly is difficult to say. Auth and Gompper have also
used a cell model approach [287], but they specifically apply it to a curved
background membrane. They argue that even if the forces are repulsive, they
might be less repulsive, and thus the free energy per colloid smaller, if the
background membrane is curved because this background curvature screens the
repulsion between the colloids. This could provide a driving force for creating
curved vesicle buds from flat membranes studded with isotropic membrane-curving
colloids, provided the average area density of colloids remains fixed. The latter is
usually the case in simulations, and Auth and Gompper show that the sizes of the
vesicles that detach from the parent membrane for differently curved colloids are
compatible with the observations of Reynwar et al. [282]. What would fix this
density in real systems is less clear, but it is conceivable that this is yet another
situation where rafts come into play. If the membrane-curving particles have to stay
within a finite raft, their mutual repulsion can, by virtue of the mechanism discussed
by Auth and Gompper, lead to a budding of that raft domain.
In conclusion, we see that the situation is substantially more tricky than the
seemingly simple question “do membrane-curving particles attract or repel?” leads
one to expect. Nonlinearities, multibody interactions, fluctuations, background
curvature, boundary conditions, and anisotropies are only some of the “details”
that affect the answer to this question. At the moment, the situation remains not
completely solved, but the results outlined in this section should provide a reliable
guide for future work.
4 Multiscale Modeling of Lipid and Membrane Protein
Systems
4.1 Multiscale Modeling: Approaches and Challenges
As we have seen in the previous sections, coarse-grained lipid models have been
enormously successful for investigating phenomena in lipid bilayers and lipid
bilayer/protein systems. In particular, rather coarse, generic models that reduce
the lipids to their most essential features and shed almost all chemical specificity
have contributed enormously to our understanding of effective interactions, generalized processes, and their driving forces. A different branch of coarse-grained
models, the bottom-up models, has also progressed quite dramatically in the past
6 They used the same techniques that also led to the exact Eq. (14), only that in the cell model case
the sign is evident from the expression.
Computational Studies of Biomembrane Systems: Theoretical Considerations. . .
265
prove that within this approximation the lateral pressure between colloids is always
repulsive, even in the nonlinear regime;
6 however, how well the cell model actually
captures a multiparticle assembly is difficult to say. Auth and Gompper have also
used a cell model approach [287], but they specifically apply it to a curved
background membrane. They argue that even if the forces are repulsive, they
might be less repulsive, and thus the free energy per colloid smaller, if the
background membrane is curved because this background curvature screens the
repulsion between the colloids. This could provide a driving force for creating
curved vesicle buds from flat membranes studded with isotropic membrane-curving
colloids, provided the average area density of colloids remains fixed. The latter is
usually the case in simulations, and Auth and Gompper show that the sizes of the
vesicles that detach from the parent membrane for differently curved colloids are
compatible with the observations of Reynwar et al. [282]. What would fix this
density in real systems is less clear, but it is conceivable that this is yet another
situation where rafts come into play. If the membrane-curving particles have to stay
within a finite raft, their mutual repulsion can, by virtue of the mechanism discussed
by Auth and Gompper, lead to a budding of that raft domain.
In conclusion, we see that the situation is substantially more tricky than the
seemingly simple question “do membrane-curving particles attract or repel?” leads
one to expect. Nonlinearities, multibody interactions, fluctuations, background
curvature, boundary conditions, and anisotropies are only some of the “details”
that affect the answer to this question. At the moment, the situation remains not
completely solved, but the results outlined in this section should provide a reliable
guide for future work.
4 Multiscale Modeling of Lipid and Membrane Protein
Systems
4.1 Multiscale Modeling: Approaches and Challenges
As we have seen in the previous sections, coarse-grained lipid models have been
enormously successful for investigating phenomena in lipid bilayers and lipid
bilayer/protein systems. In particular, rather coarse, generic models that reduce
the lipids to their most essential features and shed almost all chemical specificity
have contributed enormously to our understanding of effective interactions, generalized processes, and their driving forces. A different branch of coarse-grained
models, the bottom-up models, has also progressed quite dramatically in the past
6 They used the same techniques that also led to the exact Eq. (14), only that in the cell model case
the sign is evident from the expression.
Computational Studies of Biomembrane Systems: Theoretical Considerations. . .
265