Energy Function

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 ( $i=1,2, \ldots N$) are assumed to hold  $$m_i \ddot{\vec r}_i \;=\; - \nabla_i E(\vec r_1, \vec r_2,\ldots , \vec r_N)$$
where $\vec r_i$ denotes the position of the i-th atom. Here we have used the notation $\nabla_i = \partial / \partial \vec r_i$. The function E $$E \;=\; E_B\,+\,E_\theta\,+\,E_\phi\,+\,E_{El}\,+\,E_{vdW}\,+\,E_H\,+\,E_I\$$
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, $E_{\theta}$, the bending vibrations between two adjacent bonds and the third contribution, $E_{\phi}$, 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.