fundamental forces towards higher level emergent phenomena, very tangible fields
exist everywhere. For instance, a rope can transduce a tensile force along its length,
and we can describe this using continuum elasticity as the underlying “field
equation.”
Just like ropes, fluid lipid membranes are continuous media at a sufficiently
coarse level of description. But, their rich physical structure equips them with
several properties that can take on the role of a field, for instance:
1. The membrane thickness can be considered as a spatially varying field that
couples to the protein content (see Sect. 2.1.3)
2. The lipids can have a spatially varying orientation or tilt order
3. In mixed membranes, the local lipid concentrations can be viewed as a field
4. The Hamiltonian Eq. (1) associates a characteristic energy to a given shape of a
membrane, thus rendering its entire geometry a field
These fields differ quite substantially in their theoretical description: concentrations are scalar variables, orientations are vectors, and differential geometry is
at heart a tensor theory; but, all of them are known to mediate interactions. For
instance, the fact that proteins might prefer one lipid composition over another
and thus aggregate [217–220] is central to an important mechanism attributed to
lipid rafts. Tilt-mediated protein interactions have also been studied in multiple
contexts [32, 33, 159, 221–223]. It is even possible to describe all these phenomena within a common language [224], using the framework of covariant surface
stresses [154, 155, 157–161]. However, in the present review we will restrict the
discussion to only two examples, both related to membrane elasticity: in Sect. 3.1
we will discuss interactions due to hydrophobic mismatch, and in Sect. 3.2 we will
look at interactions mediated by the large-scale curvature deformation of the
membrane.
3.1 Hydrophobic Mismatch
Proteins distort or disrupt membranes, which in turn act back on proteins. Structural
perturbations contribute to protein function and are among the most important
sources of membrane-induced interactions between proteins. Unfortunately, perturbations or transformations of lipid bilayers due to proteins are very difficult to
probe experimentally [225]. Complementary theoretical and computer simulation
studies can help to elucidate the role of the lipid bilayer in processes such as protein
aggregation and function.
One major source of membrane–protein interactions that has been discussed in
the literature for many decades is hydrophobic mismatch [20–22, 24, 26, 28, 29,
226–233]. If the width of the hydrophobic transmembrane domain of a protein is
larger than the thickness of the lipid bilayer, the system can respond in two ways:
either the protein tilts [234–236] or the membrane deforms [18, 23, 24]. Both
responses have biologically relevant consequences. On the one hand, the
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exist everywhere. For instance, a rope can transduce a tensile force along its length,
and we can describe this using continuum elasticity as the underlying “field
equation.”
Just like ropes, fluid lipid membranes are continuous media at a sufficiently
coarse level of description. But, their rich physical structure equips them with
several properties that can take on the role of a field, for instance:
1. The membrane thickness can be considered as a spatially varying field that
couples to the protein content (see Sect. 2.1.3)
2. The lipids can have a spatially varying orientation or tilt order
3. In mixed membranes, the local lipid concentrations can be viewed as a field
4. The Hamiltonian Eq. (1) associates a characteristic energy to a given shape of a
membrane, thus rendering its entire geometry a field
These fields differ quite substantially in their theoretical description: concentrations are scalar variables, orientations are vectors, and differential geometry is
at heart a tensor theory; but, all of them are known to mediate interactions. For
instance, the fact that proteins might prefer one lipid composition over another
and thus aggregate [217–220] is central to an important mechanism attributed to
lipid rafts. Tilt-mediated protein interactions have also been studied in multiple
contexts [32, 33, 159, 221–223]. It is even possible to describe all these phenomena within a common language [224], using the framework of covariant surface
stresses [154, 155, 157–161]. However, in the present review we will restrict the
discussion to only two examples, both related to membrane elasticity: in Sect. 3.1
we will discuss interactions due to hydrophobic mismatch, and in Sect. 3.2 we will
look at interactions mediated by the large-scale curvature deformation of the
membrane.
3.1 Hydrophobic Mismatch
Proteins distort or disrupt membranes, which in turn act back on proteins. Structural
perturbations contribute to protein function and are among the most important
sources of membrane-induced interactions between proteins. Unfortunately, perturbations or transformations of lipid bilayers due to proteins are very difficult to
probe experimentally [225]. Complementary theoretical and computer simulation
studies can help to elucidate the role of the lipid bilayer in processes such as protein
aggregation and function.
One major source of membrane–protein interactions that has been discussed in
the literature for many decades is hydrophobic mismatch [20–22, 24, 26, 28, 29,
226–233]. If the width of the hydrophobic transmembrane domain of a protein is
larger than the thickness of the lipid bilayer, the system can respond in two ways:
either the protein tilts [234–236] or the membrane deforms [18, 23, 24]. Both
responses have biologically relevant consequences. On the one hand, the
256
M. Deserno et al.