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In this section we review the computational aspects of molecular
dynamics simulations and discuss the relationship between the energy
function used by EGO and that used by the programs
CHARMM [3,4] and
X-PLOR [6], to which it is closely related.
Computer simulations of biological macromolecules are based on a
classical mechanical model of biomolecules. For the nuclei of the *N* atoms
of a molecule the Newtonian equations of motion
(
) are assumed to hold

where denotes the position of the *i*-th atom.
Here we have used the notation
. The
function *E*

defines the total energy of the molecule. It is comprised of several
contributions which correspond to the different types of forces acting
in the molecule.
The first contribution, *E*_{B}, describes the high frequency
vibrations along covalent bonds,
the second contribution,
, the bending
vibrations between two adjacent bonds and
the third contribution, , the torsional
motions around bonds.
The fourth contribution, *E*_{El}, describes electrostatic
interactions between partial atomic charges, the charges being centered at
the positions of the atomic nuclei.
The next term, *E*_{vdW}, accounts for the
van der Waals-interactions between non-bonded atoms in the molecule,
*E*_{H} stands for the energy of hydrogen bonds,
and the last term, *E*_{I}, describes so-called
improper motions of one atom relative to a plane described by three other
atoms. Various research groups have developed functional representations and
corresponding force constants which attempt to faithfully represent atomic
interactions and dynamic properties of
biomolecules [39,3,42,43].
The program which we have developed is based on the energy representation
of CHARMM [3,4]. Actually, our program can
read^{}
a file of force parameters which has a format identical to that used by
X-PLOR [6], a simulation program closely related to CHARMM.
As a result, any adaptation of force constants suggested in the framework of
CHARMM or X-PLOR can be readily transferred to our program.

** Next:** Integration Methods
**Up:** Numerical Tasks in Molecular
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*Helmut Heller *

2000-04-19