Coarse-Grained Modeling for Macromolecular Chemistry - Multiscale Molecular Methods in Applied Chemistry - page 304

the degree of coarse-graining, various models and methods have been proposed in
the literature [ 15 , 17 , 27 - 44 ].
3.1 Structure-Based CG Model
One way to develop a CG model is using a structure-based coarse-graining
approach, where the direct link to the chemistry is achieved through structurally
defined bonded and non-bonded effective CG potentials derived from the atom-
istic model. In this class of methods, the determination of interaction potentials
for the CG model is based on the assumption that the total potential energy can
be separated into bonded and non-bonded contributions. The bonded interactions
are derived such that the conformational statistics of a single molecule is
represented correctly in the CG model. A very important criterion for a mapping
scheme, as mentioned in Sect. 2 , is its ability to decouple internal degrees of
freedom so that the intramolecular (bonded) potentials can be separated into
bond, angle, and torsion terms. One option for deriving the CG bonded potentials
is to use a simple Boltzmann inversion to convert the distributions of interparti-
cle distances or angles into potentials. Another option is to determine analytical
potentials that reproduce the probability distributions for the bonded part, for
example by fitting the (multipeaked) bonded distributions by a series of Gaussian
functions that can then be inverted analytically, resulting in smooth potentials
and forces [ 45 ].
Similar to the bonded interaction functions, there are two options for deriving
the non-bonded potentials: either using analytical potentials or using numerically
derived tabulated potentials. In the first case, analytical potentials of various types
can be used. The “normal” Lennard-Jones 12-6 potential is frequently used, which
is sometimes too repulsive for the CG soft beads [ 44 , 46 ], and for softer cases the
Lennard-Jones-type (e.g., 9-6 or 7-6) [ 21 , 47 ], Buckingham, or Morse potentials
[ 48 ] have been employed. The potential parameters are chosen in such a way that
the CG model reproduces satisfactorily the physical properties of the atomistic
simulation or available experimental data. This task can be done automatically by a
computer in a more efficient way than the usual manual trial and error method by
using, e.g., the simplex algorithm [ 49 , 50 ]. In this algorithm, a penalty function that
compares the calculated values of selected properties with their target values from
atomistic simulations or experiment is minimized by adjusting the force field
parameters. In a parameter space of dimension N , N +1 preliminary molecular
dynamics simulations with slightly different starting parameter sets are performed.
Then, the physical properties of interest and the penalty function for each parame-
ter combination are calculated. If for one of these sets the value of the penalty
function is below a certain user-defined threshold, the corresponding force field
is supposed to be satisfactory. Otherwise, a new molecular dynamics simulation
is run with a new parameter set provided by a simplex move, and this process is
repeated until the penalty function converges. However, slow convergence of the