Potential energy of protein

Contents 1 Potential Energy of Protein 1.1 Ebond, Bond Length Potential Energy Contribution 1.2 E angle, Bond Angle Potential Energy Contribution 1.3 Etorsion, Torsion Angle Potential Energy Contribution 1.4 E electro , Electrostatic Potential Energy Contribution 1.5 EvdW, van der Waals Potential Energy Contribution 1.6 References

Potential Energy of Protein

A protein folds into the state of lowest potential energy. Potential energy of a protein can be evaluated with quantum chemistry. However required computation is too much. Another approach is to evaluate major terms that contribute to potential energy and sum them up to find an approximate potential energy.

E_total = E_bond+ E_angle+ E_torsion + E_electro +E_vdw

E_bond, Bond Length Potential Energy Contribution

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. 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_ijk-α_ijk⁰)²

where

k_ij^b is the force constant

r_ij⁰ is the equilibrium length

r_ij is the current length

for the bond between ith and jth atoms.

E _angle, Bond Angle Potential Energy Contribution

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

k_ijk is the force constant

α_ijk⁰ is the equilibrium angle

α_ijk is the bond angle

E_torsion, Torsion Angle Potential Energy Contribution

The middle bond of three bonds formed by four atom 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/sub> = Σ (i,j,k,l) E Storsionkijkl^t[1+cos(nαijkl- αijkl⁰ )]}

where

k_ijkl^t is the force constant

α_ijkl⁰ is the equilibrium angle

α_ijkl is the torsion angle

E _electro , Electrostatic Potential Energy Contribution

Interaction between charged atoms adds potential energy to the protein based on distance of 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_iq_j)/(e_ijr_ij)

where

e_ij is a constant

q_iq_j are charges of atoms

r_ij is the distance between atoms

E_vdW, van der Waals Potential Energy Contribution

Depending on van der Waals radii of atoms every atom of protein interacts with each others 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]

r_ij distance between atoms

σ_ij distance at van der Waals energy is minimum

References