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In molecular mechanics, the potential energy of a protein molecule is the sum of a number of components, which relate to the molecule's internal structure and its interaction with nearby molecules.

Internal potential energy of a molecule is described by a system of functions known as force field. The potential energy usually includes several terms:

E_{total} = E_{bond}+ E_{angle}+ E_{torsion} + E_{electro} +E_{vdw}

When two atoms are connected by a chemical bond, they tend to maintain a fixed distance. The fixed distance depends on the atoms that forms the bond. Any variation from this fixed distance which is the equilibrium point adds additional potential energy to the protein. This is similar to the concept of Hooke's Law, so the bond can be envisaged as a spring connecting the atoms together. Total potential energy based on bond length is over set S_{bond} set of pairs of atoms that are connected by chemical bond defined as:

E_{bond} = Σ_{ (i,j) E Sbond} k_{ij}^{b}(α_{ij}-α_{ij0})^{2}

where:

k_{ij}^{b} is the force constant

α_{ij0} is the equilibrium length

α_{ij} is the current length

for the bond between ith and jth atoms.

Just as the potential energy can be written as a quadratic form in the internal coordinates, so it can also be written in terms of generalized forces. The resulting coefficients are termed compliance constants.

Like bond length, when three atoms are connected with two chemical bonds, the two bonds tend to form a fixed angle. Any variation from this fixed equilibrium angle contributes to protein potential energy. Total potential energy based on angle is defined as over set S_{angle} the triplet of atoms that are connected by two chemical bonds:

E_{angle} = Σ_{ (i,j,k) E Sangle}k_{ijk}^{a}(α_{ijk}-α_{ijk0})^{2}

where:

k_{ijk} is the force constant

α_{ijk0} is the equilibrium angle

α_{ijk} is the bond angle

The middle bond of three bonds formed by four atoms maintains a certain angle which is also known as torsion is defined over set S_{torsion} the quartet of atoms that are connected by three chemical bonds, as follows:

E_{torsion} = Σ_{ (i,j,k,l) E Storsion}k_{ijkl}^{t}[1+cos(nα_{ijkl}- α_{ijkl}^{0
})]

where:

k_{ijkl}^{t} is the force constant

α_{ijkl}^{0} is the equilibrium angle

α_{ijkl} is the torsion angle

Interaction between charged atoms adds potential energy to the protein based on the distance between pairs of atoms defined over S_{electro}, the set of pairs of atoms with electrostatic interactions, as follows:

E_{electro} = Σ_{ (i,j) E Selectro} ( q_{i}q_{j})/(e_{ij}r_{ij})

where:

e_{ij} is a constant

q_{i}q_{j} are charges of atoms

r_{ij} is the distance between atoms

Depending on van der Waals radii of atoms every atom of protein interacts with each other that are not far apart. The potential energy contribution of this interaction is defined over S_{vdW}, set of atoms with van der Waals interaction, as:

E_{vdw} = Σ_{ (i,j) E Svdw} ε_{ij}
[ (σ_{ij}/r_{ij})^{12} - 2(σ_{ij}/r_{ij})^{6}]

where:

r_{ij} distance between atoms

σ_{ij} distance at Van der Waals energy is minimum

- Wu, Zhijun. "Lecture notes on computational structural biology", World Scientific Publishing, 2008.