Biology Reference
In-Depth Information
and is called the van der Waals interaction. The short-range repulsive
term results from the Pauli exclusion principle.
The electrostatic term, which is the sixth term in Eq. (4); accounts
for the interaction between point charges located at the atomic nuclei.
This functional form is an approximation, since the molecular electronic
density is sometimes far from being spherical, as in covalent bonds. The
electrostatic potential is the longest-range interaction with a 1
/r
depend-
ence; and its treatment requires specific techniques to lower the compu-
tational cost, like the Ewald summation.
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Several limitations are inherent to the functional form of
V(r)
given in
Eq. (4). First of all, the partial charges of all atoms are fixed at the begin-
ning of the simulation. This approach clearly neglects the electronic polar-
ization, though the conformational polarization is still present, notably in
the water molecules that solvate the system. Polarizable force fields are now
emerging
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and might become the standard in a few years. Second, the
quadratic nature of the bond-stretching energy terms does not allow bond
braking or bond creation. This strongly limits the use of this approach for
the study of enzymatic reactions with covalent bond modifications. To
address this limitation, the most common approach is to use Morse poten-
tials
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or a hybrid quantum mechanics/molecular mechanics (QM/MM)
approach, where the system is divided into a quantum part in which bond
creation takes place
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and a classical part surrounding the quantum one.
Despite their inherent simplicity and evident shortcomings, force
fields have been used successfully over the last few decades and will pro-
vide the basis of molecular modeling for several decades to come. The
improvement of semiempirical methods still represents a very active
domain of research.
3. Molecular Dynamics Simulations
3.1. Integration of the Equation of Motion
Given the potential energy function
V
of Eq. (4); one can compute the
force acting on atom
i
:
=-
d
d
V
r
.
F
(5)
i
i
