orientation of proteins is believed to have a significant influence on their functionality, e.g., in pore formation [237]. Coarse-grained simulations by Benjamini and
Smit have suggested that the cross-angle distributions of packed helix complexes
are mostly determined by the tilt angle of individual helices [211]. Membrane
deformation, on the other hand, induces effective protein–protein interactions and
provides one way to control protein aggregation [229, 230, 238]. In experimental
tilt measurements, hydrophobically mismatched proteins were sometimes found to
tilt; in other cases, the reported tilt angles were surprisingly small compared to
theoretical expectations [239–241]. This was partly attributed to problems with the
analysis of experimental NMR (nuclear magnetic resonance) data [233] and partly
to the presence of anchoring residues flanking the hydrophobic transmembrane
domains, which might prevent tilting through a variety of mechanisms [236, 240,
242, 243].
However, coarse-grained simulations show that the propensity to tilt is also
influenced by more generic factors. Venturoli et al. have reported that cylindrical
inclusions with larger radius tilt less than inclusions with small radius [234]. Neder
et al. have identified hydrophobicity as another crucial factor determining tilt
[244]. In systematic studies of a variety of simple inclusions with cylindrical
shape and similar radii, embedded in a model bilayer of the Lenz type, they
found that the behavior of different proteins mainly depended on their free energy
of insertion, i.e., their binding free energy. Weakly hydrophobic inclusions with
negative binding free energies (which stayed inside the membrane due to kinetic
free energy barriers) react to hydrophobic mismatch by tilting. Strongly hydrophobic inclusions with binding energies in excess of 100 k B T deform the membrane. For the probably most common weakly bound inclusions with binding
energies of around 10 k B T, the situation is more complicated: upon increasing
hydrophobic mismatch, inclusions first distort the bilayer and then switch to a
tilted state once a critical mismatch parameter is reached. Tilting thus competes
with the formation of dynamic complexes consisting of proteins and a shell of
surrounding, stretched lipids, and the transition between these two states was found
to be discontinuous.
In the case where the membrane is deformed, the deformation profiles can be
compared to a variety of theories [16, 17, 27, 33, 245–247]. Both in coarse-grained
[30, 234] and atomistic [248] simulations, it was reported that membrane thickness
profiles as a function of the distance to the protein are not strictly monotonic, but
exhibit a weakly oscillatory behavior. This feature is not compatible with membrane models that predict an exponential decay [16, 17, 27], but it is nicely captured
by the coupled elastic monolayer models discussed earlier [22, 28, 30]. Coarsegrained simulations of the Lenz model showed that the coupled monolayer models
describe the profile data at a quantitative level, with almost no fit parameters except
the boundary conditions [30, 244].
In membranes containing several inclusions, the membrane thickness deformations induce effective interactions between inclusions. These have also been studied
within the Lenz model [30, 249] and other coarse-grained models [250, 251].
The comparison with the elastic theory is less convincing, due to the fact that
Computational Studies of Biomembrane Systems: Theoretical Considerations. . .
257
Smit have suggested that the cross-angle distributions of packed helix complexes
are mostly determined by the tilt angle of individual helices [211]. Membrane
deformation, on the other hand, induces effective protein–protein interactions and
provides one way to control protein aggregation [229, 230, 238]. In experimental
tilt measurements, hydrophobically mismatched proteins were sometimes found to
tilt; in other cases, the reported tilt angles were surprisingly small compared to
theoretical expectations [239–241]. This was partly attributed to problems with the
analysis of experimental NMR (nuclear magnetic resonance) data [233] and partly
to the presence of anchoring residues flanking the hydrophobic transmembrane
domains, which might prevent tilting through a variety of mechanisms [236, 240,
242, 243].
However, coarse-grained simulations show that the propensity to tilt is also
influenced by more generic factors. Venturoli et al. have reported that cylindrical
inclusions with larger radius tilt less than inclusions with small radius [234]. Neder
et al. have identified hydrophobicity as another crucial factor determining tilt
[244]. In systematic studies of a variety of simple inclusions with cylindrical
shape and similar radii, embedded in a model bilayer of the Lenz type, they
found that the behavior of different proteins mainly depended on their free energy
of insertion, i.e., their binding free energy. Weakly hydrophobic inclusions with
negative binding free energies (which stayed inside the membrane due to kinetic
free energy barriers) react to hydrophobic mismatch by tilting. Strongly hydrophobic inclusions with binding energies in excess of 100 k B T deform the membrane. For the probably most common weakly bound inclusions with binding
energies of around 10 k B T, the situation is more complicated: upon increasing
hydrophobic mismatch, inclusions first distort the bilayer and then switch to a
tilted state once a critical mismatch parameter is reached. Tilting thus competes
with the formation of dynamic complexes consisting of proteins and a shell of
surrounding, stretched lipids, and the transition between these two states was found
to be discontinuous.
In the case where the membrane is deformed, the deformation profiles can be
compared to a variety of theories [16, 17, 27, 33, 245–247]. Both in coarse-grained
[30, 234] and atomistic [248] simulations, it was reported that membrane thickness
profiles as a function of the distance to the protein are not strictly monotonic, but
exhibit a weakly oscillatory behavior. This feature is not compatible with membrane models that predict an exponential decay [16, 17, 27], but it is nicely captured
by the coupled elastic monolayer models discussed earlier [22, 28, 30]. Coarsegrained simulations of the Lenz model showed that the coupled monolayer models
describe the profile data at a quantitative level, with almost no fit parameters except
the boundary conditions [30, 244].
In membranes containing several inclusions, the membrane thickness deformations induce effective interactions between inclusions. These have also been studied
within the Lenz model [30, 249] and other coarse-grained models [250, 251].
The comparison with the elastic theory is less convincing, due to the fact that
Computational Studies of Biomembrane Systems: Theoretical Considerations. . .
257