[81], in agreement with the so-called “raft hypothesis” [82]. As a generic model that
reproduces nanoscale structures in lipid membranes (ripple states and rafts), simulations of the Lenz model can provide insight into the physics of nanostructure
formation in lipid bilayers. This will be discussed in more detail in Sect. 2.5.
2.2.3 MARTINI Model
The MARTINI model for lipids [83, 84] is a hybrid between a top-down and a
bottom-up model: approximately four heavy atoms are mapped to a single CG bead,
and these CG beads come in a variety of types, depending on their polarity, net
charge, and the ability to form hydrogen bonds. The systematic aspect of MARTINI
largely derives from the fact that the nonbonded interactions between these building
blocks (shifted Lennard–Jones and possibly shifted Coulomb potentials) have been
parameterized to reproduced most of the thermodynamics correctly, especially the
partitioning free energy between different environments, such as between aqueous
solution and oil. Given a particular molecule, a judicious choice of assignments
from groups of heavy atoms to MARTINI beads, together with standard bonded
interactions (harmonic, angular, and dihedral potentials), leads to the CG version of
a molecule.
The complete MARTINI force field encompasses more than lipids and sterols
[83, 84]; it is currently also available for proteins [85], carbohydrates [86], and
glycolipids [87]. The far-reaching possibilities for looking at multicomponent
systems without the need to explicitly cross-parametrize new interactions have
substantially contributed to the attractiveness of this force field. Of course, care
must still be taken that one’s mapping onto the CG level is consistent overall and
chemically meaningful: Even though the nonbonded interactions are derived from a
single guiding principle, which is both conceptually attractive and computationally
powerful, there is no guarantee that it will work under all circumstances for one’s
particular choice of system and observable, so it is up to the user to perform
judicious sanity checks. After all, with great power there must also come great
responsibility [88].
2.3 Obtaining Material Parameters
The Hamiltonian in Eq. (1) is an excellent phenomenological description of fluid
membranes, but it does not predict the material parameters entering it, which must
instead come from experiment or simulation. Let us briefly list a number of ways in
which this is achieved, both in experiment and in simulation.
The bending modulus κ is measured by techniques such as monitoring the
thermal undulations of membranes [89–94], probing the low-tension stress–strain
relation [95], X-ray scattering [96–99], neutron spin echo measurements [100–102]
(note however the caveats raised by Watson and Brown [103]), or pulling thin
Computational Studies of Biomembrane Systems: Theoretical Considerations. . .
243
reproduces nanoscale structures in lipid membranes (ripple states and rafts), simulations of the Lenz model can provide insight into the physics of nanostructure
formation in lipid bilayers. This will be discussed in more detail in Sect. 2.5.
2.2.3 MARTINI Model
The MARTINI model for lipids [83, 84] is a hybrid between a top-down and a
bottom-up model: approximately four heavy atoms are mapped to a single CG bead,
and these CG beads come in a variety of types, depending on their polarity, net
charge, and the ability to form hydrogen bonds. The systematic aspect of MARTINI
largely derives from the fact that the nonbonded interactions between these building
blocks (shifted Lennard–Jones and possibly shifted Coulomb potentials) have been
parameterized to reproduced most of the thermodynamics correctly, especially the
partitioning free energy between different environments, such as between aqueous
solution and oil. Given a particular molecule, a judicious choice of assignments
from groups of heavy atoms to MARTINI beads, together with standard bonded
interactions (harmonic, angular, and dihedral potentials), leads to the CG version of
a molecule.
The complete MARTINI force field encompasses more than lipids and sterols
[83, 84]; it is currently also available for proteins [85], carbohydrates [86], and
glycolipids [87]. The far-reaching possibilities for looking at multicomponent
systems without the need to explicitly cross-parametrize new interactions have
substantially contributed to the attractiveness of this force field. Of course, care
must still be taken that one’s mapping onto the CG level is consistent overall and
chemically meaningful: Even though the nonbonded interactions are derived from a
single guiding principle, which is both conceptually attractive and computationally
powerful, there is no guarantee that it will work under all circumstances for one’s
particular choice of system and observable, so it is up to the user to perform
judicious sanity checks. After all, with great power there must also come great
responsibility [88].
2.3 Obtaining Material Parameters
The Hamiltonian in Eq. (1) is an excellent phenomenological description of fluid
membranes, but it does not predict the material parameters entering it, which must
instead come from experiment or simulation. Let us briefly list a number of ways in
which this is achieved, both in experiment and in simulation.
The bending modulus κ is measured by techniques such as monitoring the
thermal undulations of membranes [89–94], probing the low-tension stress–strain
relation [95], X-ray scattering [96–99], neutron spin echo measurements [100–102]
(note however the caveats raised by Watson and Brown [103]), or pulling thin
Computational Studies of Biomembrane Systems: Theoretical Considerations. . .
243