be highly quantitative and experimentally testable. One always needs to know what
went into a given model to be able to judge the reliability of its predictions.
In Sects. 2.2.1–2.2.3, we will review the basics of three particular CG models
that will feature in the remainder of this paper. The choice of models is not meant to
imply a quality statement but merely reflects our own experience and work.
2.2.1 Cooke Model
The Cooke model [73, 74] is a strongly coarse-grained top-down lipid model in
which every single lipid is represented by three linearly connected beads (one for
the head group, two for the tail) and solvent is implicitly accounted for through
effective interactions. It is purely based on pair interactions and therefore very
easy to handle. Its main tuning parameters are the temperature and the range w c
of the effective cohesion that drives the aggregation of the hydrophobic tail beads.
One might also change the relative size between head and tail beads to control
the lipids’ spontaneous curvature [75]. The bead size σ serves as the unit of length
and the potential depth E as the unit of energy. For the common choice k B T/E ¼ 1.1
and w c /σ ¼ 1.6, lipids spontaneously assemble into fluid membranes with an
area per lipid of about 1.2 σ
2 , a bending rigidity of κ % 12.8 k B T (but rigidities
between 3 k B T and 30 k B T can be achieved without difficulty), and an elastic ratio of
κ =κ % À0:92 [76].
2.2.2 Lenz Model
Like the Cooke model, the Lenz model [77] is a generic model for membranes, but
it has been designed for studying internal phase transitions. Therefore, it puts a
slightly higher emphasis on conformational degrees of freedom than the Cooke
model. Lipids are represented by semiflexible linear chains of seven beads (one for
the head group, six for the tail), which interact with truncated Lennard–Jones
potentials. Model parameters such as the chain stiffness are inspired by the properties of hydrocarbon tails [78]. The model includes an explicit solvent, which is,
however, modeled such that it is simulated very efficiently: it interacts only with
lipid beads and not with itself (“phantom solvent” [79]).
The model reproduces the most prominent phase transitions of phospholipid
monolayers [78] and bilayers [80]. In particular, it reproduces a main transition
from a fluid membrane phase (L α ) to a tilted gel phase (L β 0 ) with an intermediate
ripple phase (P β 0 ), in agreement with experiments. The elastic parameters have been
studied in the fluid phase and are in reasonable agreement with those of saturated
DPPC (dipalmitoyl-phosphatidylcholine) bilayers. Recently, the Lenz model has
been supplemented with a simple cholesterol model [81]. Cholesterol molecules are
taken to be shorter and stiffer than lipids, and they have a slight affinity to lipids.
Mixtures of lipids and cholesterol were found to develop nanoscale raft domains
242
M. Deserno et al.
went into a given model to be able to judge the reliability of its predictions.
In Sects. 2.2.1–2.2.3, we will review the basics of three particular CG models
that will feature in the remainder of this paper. The choice of models is not meant to
imply a quality statement but merely reflects our own experience and work.
2.2.1 Cooke Model
The Cooke model [73, 74] is a strongly coarse-grained top-down lipid model in
which every single lipid is represented by three linearly connected beads (one for
the head group, two for the tail) and solvent is implicitly accounted for through
effective interactions. It is purely based on pair interactions and therefore very
easy to handle. Its main tuning parameters are the temperature and the range w c
of the effective cohesion that drives the aggregation of the hydrophobic tail beads.
One might also change the relative size between head and tail beads to control
the lipids’ spontaneous curvature [75]. The bead size σ serves as the unit of length
and the potential depth E as the unit of energy. For the common choice k B T/E ¼ 1.1
and w c /σ ¼ 1.6, lipids spontaneously assemble into fluid membranes with an
area per lipid of about 1.2 σ
2 , a bending rigidity of κ % 12.8 k B T (but rigidities
between 3 k B T and 30 k B T can be achieved without difficulty), and an elastic ratio of
κ =κ % À0:92 [76].
2.2.2 Lenz Model
Like the Cooke model, the Lenz model [77] is a generic model for membranes, but
it has been designed for studying internal phase transitions. Therefore, it puts a
slightly higher emphasis on conformational degrees of freedom than the Cooke
model. Lipids are represented by semiflexible linear chains of seven beads (one for
the head group, six for the tail), which interact with truncated Lennard–Jones
potentials. Model parameters such as the chain stiffness are inspired by the properties of hydrocarbon tails [78]. The model includes an explicit solvent, which is,
however, modeled such that it is simulated very efficiently: it interacts only with
lipid beads and not with itself (“phantom solvent” [79]).
The model reproduces the most prominent phase transitions of phospholipid
monolayers [78] and bilayers [80]. In particular, it reproduces a main transition
from a fluid membrane phase (L α ) to a tilted gel phase (L β 0 ) with an intermediate
ripple phase (P β 0 ), in agreement with experiments. The elastic parameters have been
studied in the fluid phase and are in reasonable agreement with those of saturated
DPPC (dipalmitoyl-phosphatidylcholine) bilayers. Recently, the Lenz model has
been supplemented with a simple cholesterol model [81]. Cholesterol molecules are
taken to be shorter and stiffer than lipids, and they have a slight affinity to lipids.
Mixtures of lipids and cholesterol were found to develop nanoscale raft domains
242
M. Deserno et al.