Molecular modelling

The backbone dihedral angles are included in the molecular model of a protein.

Molecular mechanics is one aspect of molecular modelling, as it involves the use of classical mechanics (Newtonian mechanics) to describe the physical basis behind the models. Molecular models typically describe atoms (nucleus and electrons collectively) as point charges with an associated mass. The interactions between neighbouring atoms are described by spring-like interactions (representing chemical bonds) and Van der Waals forces. The Lennard-Jones potential is commonly used to describe the latter. The electrostatic interactions are computed based on Coulomb's law. Atoms are assigned coordinates in Cartesian space or in internal coordinates, and can also be assigned velocities in dynamical simulations. The atomic velocities are related to the temperature of the system, a macroscopic quantity. The collective mathematical expression is termed a potential function and is related to the system internal energy (U), a thermodynamic quantity equal to the sum of potential and kinetic energies. Methods which minimize the potential energy are termed energy minimization methods (e.g., steepest descent and conjugate gradient), while methods that model the behaviour of the system with propagation of time are termed molecular dynamics.

${\displaystyle E=E_{\text{bonds}}+E_{\text{angle}}+E_{\text{dihedral}}+E_{\text{non-bonded}}\,}$

${\displaystyle E_{\text{non-bonded}}=E_{\text{electrostatic}}+E_{\text{van der Waals}}\,}$

This function, referred to as a potential function, computes the molecular potential energy as a sum of energy terms that describe the deviation of bond lengths, bond angles and torsion angles away from equilibrium values, plus terms for non-bonded pairs of atoms describing van der Waals and electrostatic interactions. The set of parameters consisting of equilibrium bond lengths, bond angles, partial charge values, force constants and van der Waals parameters are collectively termed a force field. Different implementations of molecular mechanics use different mathematical expressions and different parameters for the potential function.[2] The common force fields in use today have been developed by using chemical theory, experimental reference data, and high level quantum calculations. The method, termed energy minimization, is used to find positions of zero gradient for all atoms, in other words, a local energy minimum. Lower energy states are more stable and are commonly investigated because of their role in chemical and biological processes. A molecular dynamics simulation, on the other hand, computes the behaviour of a system as a function of time. It involves solving Newton's laws of motion, principally the second law, ${\displaystyle \mathbf {F} =m\mathbf {a} }$. Integration of Newton's laws of motion, using different integration algorithms, leads to atomic trajectories in space and time. The force on an atom is defined as the negative gradient of the potential energy function. The energy minimization method is useful to obtain a static picture for comparing between states of similar systems, while molecular dynamics provides information about the dynamic processes with the intrinsic inclusion of temperature effects.

Molecules can be modelled either in vacuum, or in the presence of a solvent such as water. Simulations of systems in vacuum are referred to as gas-phase simulations, while those that include the presence of solvent molecules are referred to as explicit solvent simulations. In another type of simulation, the effect of solvent is estimated using an empirical mathematical expression; these are termed implicit solvation simulations.

Molecular modelling methods are now used routinely to investigate the structure, dynamics, surface properties, and thermodynamics of inorganic, biological, and polymeric systems. A large number of molecular models of force field are today readily available in databases.[4][5] The types of biological activity that have been investigated using molecular modelling include protein folding, enzyme catalysis, protein stability, conformational changes associated with biomolecular function, and molecular recognition of proteins, DNA, and membrane complexes.[6]