Potential Energy of Protein =
A protein

Protein

Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

 folds into the state of lowest potential energy

Potential energy

In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...

. Potential energy of a protein can be evaluated with quantum chemistry

Quantum chemistry

Quantum chemistry is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems...

. However required computation

Computation

Computation is defined as any type of calculation. Also defined as use of computer technology in Information processing.Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc...

 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 atom

Atom

The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s are connected by a chemical bond

Chemical bond

A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...

, 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

Angle

In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

. 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;

Etorsion/sub> = Σ _{(i,j,k,l) E Storsion}k_ijkl^t[1+cos(nα_ijkl- α_ijkl⁰
)]

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

Van der Waals radius

The van der Waals radius, r, of an atom is the radius of an imaginary hard sphere which can be used to model the atom for many purposes. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics, as he was the first to recognise that atoms had a finite size and to...

 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

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