168
H. Sun et al.
The mapping rules are determined by a tradeoff between the gain in computational efficiency and the fidelity of representation. Understanding any level of coarse
graining will lose some details, we design the mapping rules with the capability of
predicting physical properties in mind. For polymers, a rigid body such as a small
ring or multiple-bond fragment is represented by one bead; 2–3 heavy atoms in the
backbone are defined as a bead so that the chain conformations can be modeled;
and beads of symmetric representation are defined by splitting atoms on boundaries
in order to keep the charge-neutrality and consistence of bead-bead interactions.
For small molecules up to 4–6 heavy atoms are represented by one bead seems
acceptable. For hydrated ions and water, several molecules are grouped to one bead,
as commonly used by other researchers. These rules can be programmed so that
consistent definitions of bead types can be obtained.
Using the bead types, analytic functions are used to represent the CGFFs. This
is similar to that analytic functions coupled with atom types are used in AAFFs.
Common force field functions are used to present the bonded energy terms: bond,
angle, and dihedral-angle. Since CGFF is essentially describing potential of mean
forces, the parameters are temperature dependent. The dependency is minimal for the
bonded parameters, but cannot be ignored for the nonbonded interactions. Another
important feature is about the combination rules of nonbonded interactions. We found
the modified LB combination rules with the energy parameters scaled by one generic
parameter are acceptable for nonpolar and weak-polar molecules.
The hybrid method consisting of the bottom-up and top-down approaches is at
the center of our parametrization strategy. Simulations using AAFFs can provide
essentially unlimited number of data for fitting CGFF parameters, which avoids the
common overfitting problem in empirical parameterization. However, the bottom-up
approach is limited by the ability to predict physical properties at the upper level
based on the data obtained at lower level. For example, the distribution functions
obtained from AAFF are not adequate for representing the thermodynamic states
that the resulting CGFF is intended to describe. The top-down approach, which fits
a few physical properties by adjusting the most sensitive (nonbonded) parameters, is
an effective way to correct the problem. The data used for top-down are not limited
to the experimental data, as some physical properties such as density, internal energy
and surface tension can be well predicted by using AAFF.
Appendix
On the Temperature Dependency of CGFF
The development of coarse-grained model from an all-atom (AA) representation is
to reduce the degrees of freedom (DoFs) in atomistic representation of molecule by
effectively incorporating fast dynamics in AA model into the CG DoFs. Considering
an AA model of natoms in the configuration r
n
= (r 1 , · · · r n ), momenta p
n
=
H. Sun et al.
The mapping rules are determined by a tradeoff between the gain in computational efficiency and the fidelity of representation. Understanding any level of coarse
graining will lose some details, we design the mapping rules with the capability of
predicting physical properties in mind. For polymers, a rigid body such as a small
ring or multiple-bond fragment is represented by one bead; 2–3 heavy atoms in the
backbone are defined as a bead so that the chain conformations can be modeled;
and beads of symmetric representation are defined by splitting atoms on boundaries
in order to keep the charge-neutrality and consistence of bead-bead interactions.
For small molecules up to 4–6 heavy atoms are represented by one bead seems
acceptable. For hydrated ions and water, several molecules are grouped to one bead,
as commonly used by other researchers. These rules can be programmed so that
consistent definitions of bead types can be obtained.
Using the bead types, analytic functions are used to represent the CGFFs. This
is similar to that analytic functions coupled with atom types are used in AAFFs.
Common force field functions are used to present the bonded energy terms: bond,
angle, and dihedral-angle. Since CGFF is essentially describing potential of mean
forces, the parameters are temperature dependent. The dependency is minimal for the
bonded parameters, but cannot be ignored for the nonbonded interactions. Another
important feature is about the combination rules of nonbonded interactions. We found
the modified LB combination rules with the energy parameters scaled by one generic
parameter are acceptable for nonpolar and weak-polar molecules.
The hybrid method consisting of the bottom-up and top-down approaches is at
the center of our parametrization strategy. Simulations using AAFFs can provide
essentially unlimited number of data for fitting CGFF parameters, which avoids the
common overfitting problem in empirical parameterization. However, the bottom-up
approach is limited by the ability to predict physical properties at the upper level
based on the data obtained at lower level. For example, the distribution functions
obtained from AAFF are not adequate for representing the thermodynamic states
that the resulting CGFF is intended to describe. The top-down approach, which fits
a few physical properties by adjusting the most sensitive (nonbonded) parameters, is
an effective way to correct the problem. The data used for top-down are not limited
to the experimental data, as some physical properties such as density, internal energy
and surface tension can be well predicted by using AAFF.
Appendix
On the Temperature Dependency of CGFF
The development of coarse-grained model from an all-atom (AA) representation is
to reduce the degrees of freedom (DoFs) in atomistic representation of molecule by
effectively incorporating fast dynamics in AA model into the CG DoFs. Considering
an AA model of natoms in the configuration r
n
= (r 1 , · · · r n ), momenta p
n
=