Considerations in Multi-molecular Simulations
One of the powers of molecular mechanics is the ability to approximate the interactions
between a large number of atoms. This can be extended to interactions between multiple
molecules.
In biomolecular systems, the molecules never exist in an isolated gas phase. The ability
to include solvent molecules and counter ions explicitly in a simulation has the potential
to lead to a realistic model for the molecule and its environment.
There are several issues that need to be considered before and during a simulation on
such a complex system. These include:
Initial Configuration
Initial Velocities
Solvent Model
Boundary Conditions
Non-Bonded Interaction Cutoffs
Group-based Cutoffs
Updating Neighbour Lists
Temperature/Pressure/Volume Control
Measuring Equilibration
Initial Configuration
Before beginning a simulation it is necessary to have an initial 3-D structure for the
molecule.
In the case of a protein, the initial conformation may be one for which a
crystalographically determined structure has been reported. In this case it is
straightforward to download the Cartesian coordinates from the Protein Database at the
Brookhaven National Laboratories.
http://www.pdb.bnl.gov/
The coordinates are stored in a "standard" format known as PDB format.
A faster site for local access is maintained in the Department of Biochemistry and
Molecular Biology at UGA:
http://www.uga.edu/~biocryst/
At the PDB web site it is possible to search for and retrieve structures from NMR and
theoretical studies, although by far the majority of structures are from X-ray diffraction.
Alternatively, the initial structure may have been obtained through an earlier
experimental (NMR) or modeling study (homology modeling). For more flexible
molecules, such as carbohydrates, the initial structure may be more hypothetical, since it
will be expected to change and "converge" to a realistic ensemble of structures during the
simulation.
Once the structure is obtained there are still a few details to address, in particular,
1)
Are all of the residues recognized by the force field of choice?
That is, are all of the atom types in the PDB file the same as those that the force
field expects? If not, they may have to be manually corrected.
Does the structure contain structurally important metal ions? Are these
parameterized in the force field? Does the structure contain any counter ions
(SO42-, Ca2+, Na+ etc), and are they treated properly by the force field?
2)
Does the structure contain hydrogen atoms? Most X-ray determined protein
structures do not, and they must be added. This is usually an automated
procedure based on simple valence geometry rules. For example, if the atom is
sp3 hybridized (such as the CA in an amino acid), the hydrogen is tetrahedrally
positioned with respect to the CA atom.
But what about charged groups? Most amino acids that have ionizable side
chains (Asp, Glu, Lys, Arg and the C- and N-terminus) are ionized at
physiological pH (i.e. 6 - 8).
Note, the imidazole side chain of histidine may be neutral or charged (its observed
pKa = 6 - 7), therefore its ionization state must be specified and a hydrogen atom
added as necessary. Further, in the neutral state the side chain must contain a
hydrogen atom at one of the nitrogen atoms (either ND1 or NE2), usually NE2 but it depends on the local pH.

N


N
H

C
+H+
-H



C
O
O
"HIE"
"HIP"

N


+
N
H
H


N


H

N
H
-H
+
+H
+
HN

N



N

C
H
O
"HID"
HIS = histidine
pKa = 6.5
3)
Does the structure contain any "waters of crystallization" if so they should be
retained in the structure if they appear to be filling any surface or interior
cavities. Otherwise they may be deleted. Note, the names for the waters (atomic
and residue) must agree with the water model used in the simulation, and, these
individual waters must be treated the same as the rest of the solvent waters. That
is they must be treated as part of the solvent, not part of the solute.
Initial Velocities
To begin a MD simulation initial velocities must be assigned to each of the atoms. Since
the initial temperature of the simulation is very low, the initial velocities are very small.
The velocities are usually assigned randomly from a Maxwell-Boltzman probability
distribution at the initial temperature (typically 5 K).
 (vix)  (
1
2
mi
) e
2 k B T
(
mi vix
)
2 kb T
That is,
1) select the temperature (T)
2) for each atom (i) choose a random number ρ between 0 - 1 (from a generator that
produces a value that is distributed according to a Boltzman probability), and
calculate the velocity component (vx, vy, vz) for that atom, remember velocity is
vector property.
3) Repeat for each component and each atom.
Water Model
The choice of solvent model depends on which properties are important in the simulation.
Generally, the more sophisticated the water model, the slower the calculation. Therefore
you must decide on a suitable level of accuracy. Are you more interested in the solute or
the solvent? Does a rigid water model that displays the correct bulk water behavior
(density, radial distribution) suffice? Or, is a relaxed model that allows the O–H bonds to
stretch and the valence angle to bend necessary?
Water Model: General considerations
Regardless of the geometry of the model, the electrostatic interactions between the
solvent and the solute will be important.
It is good practice to model the electrostatic interactions between the water and the solute
in the same way that the way that the water was designed for.
For example, a poor approach is to employ a protein model with partial atomic charges
on each atom derived from one approximation with a water model in which the partial
atomic charges were derived from a different approximation.
As an extreme example, an unbalanced model would be expected to result from
employing MM3 (which does not use partial atomic charges) to model a solute, with a
model for water (TIP3P) that incorporates partial atomic charges.
This sort of apples and oranges mixture of models is sometimes the result when an
investigator creates a new force field for a particular class of solute. The solute force
field may be (indeed should be!) internally consistent, but it may not have been derived
with attention to applying it with a given water model.
Water Model: Validation
How is a water (or any solvent) model judged? One obvious criteria is density of the
simulated solvent. But that doesn't say anything about the dynamics of the model. Other
experimentally observable properties include the diffusion coefficient and the viscosity.
The diffusion coefficient (D) can be calculated in a straightforward way from a
simulation by knowing the initial and final position (r) of a molecule after a time t, during
which the molecule has diffused through the solvent.
D
1
| ri (t )  ri (0)|2 
6t
Information about the detailed "structure" of a liquid may be obtained from a study of the
radial distribution function (rdf) also known as the g(r). The rdf is a measure of the
number of molecules at a given distance from a central molecule. Since liquids are
dynamic, the rdf gives a characteristic average structure. X-ray diffraction can be used to
measure the rdf of liquids.
The rdf of a molecule give the probability of finding a molecule
a distance r from another molecule. In practice, the environment
of the molecule is divided up into thin shells of thickness dr.
The number of molecules in each shell is then counted and
averaged over the course of the simulation.
For short distances (r < the molecular radius) the
rdf is zero since there can be no other molecules
within the molecular surface. Thereafter, the rdf
exhibits ripples corresponding to solvation
shells. The first peak it the largest indicating a
high probability of finding another molecule at
that intermolecular separation. As the
separation increases, there is less order and the
peak intensities decrease. The area under the
curve defines the number of molecules in the
solvation shell. For water, there is a high
probability of finding another water molecule
~3Å away corresponding to a water-water
hydrogen bond.
Boundary Conditions: Molecular Clusters or Droplets
If a molecule is simply surrounded by a droplet of other molecules (perhaps solvent),
there will exist a boundary between the droplet and the vacuum around it. It then
becomes difficult to prevent the molecules from diffusing into the vacuum. An artificial
restraint may be applied to force the molecules to stay within the boundary, but this does
not correspond to a traditional thermodynamic ensemble.
Variable Density
Vacuum
Boundary
Periodic Boundary Conditions (PBC)
An alternative to the droplet model is to arrange the molecules into a regular lattice
structure. By mirroring the contents (positions and velocities) of the central "box" a
periodic system is generated. This periodic boundary system avoids edge effects. When
a molecule diffuses out of one side of the box, it reenters on the other. Thus a constant
density can be maintained.
If the box dimensions are allowed to
change with temperature, it is
possible to maintain a constant
internal pressure (NPT ensemble),
alternatively, if the box dimensions
are kept frozen, the internal pressure
will fluctuate with temperature (NVT
ensemble).