![]() The evaluations of the long-range electrostatic interactions can be difficult and was often ignored beyond a specific cut-off distance resulting in approximations in a calculation. ![]() The LJ and Coulomb potentials describe the short-range non-bonded interactions. q i is the partial atomic charge, ε 0 is the vacuum permittivity, and r ij is the distance between atom i and atom j. The parameter ε ij is related to the well-depth of Lennard-Jones (LJ) potential, r 0 ij is the distance at which the LJ potential has its minimum. The non-bonded energy is the sum of repulsion, attraction and electrostatics between non-bonded atoms. The torsion term represents a periodic rotation of a dihedral angle with periodicity n and phase γ. Three force constants: k l, k θ and V n characterise the energetic cost relative to the equilibrium value, needed to increase the value of a bond length ( l 0), angle ( θ 0) or rotation around a torsion angle. The bonded terms represent the stretching of bonds ( l), bending of valence angles ( θ) and rotation of torsional angles ( ω) cf. The potential energy is calculated by adding up the energy terms that describe interactions between bonded atoms (bonds, angles and torsions) and terms that describe the non-bonded interactions, such as van der Waals and electrostatic interactions ( eqn (1.1)). The giant leap in system size is possible due to reasonable simplicity of the MM potential energy functional. The surrounding environment could take up to 90% of all atoms in a model system, and its presence is crucial for the correct representation of living matter. Thus, the latter class of methods has become popular among researchers dealing with bio-macromolecular systems, which exist and function in aqueous solutions or lipid environments. molecular mechanics (MM), can easily handle several hundred thousand atoms, and in case of a coarse-grained approach-several million atoms. For comparison, a feasible size of a system treated by quantum chemistry calculations, even today, does not exceed a few hundred atoms, whereas the empirical methods, e.g. Starting from quantum chemistry, where molecular orbitals and electrons occupying these are described, allows us to calculate any physical or chemical property that directly depends on the electron distribution reaching all the way to coarse-grained molecular dynamics simulations, where groups of atoms described as beads interacting by laws of Newtonian mechanics, providing valuable insights into the complexity of biological processes on a bigger, cellular level scale. The palette of computational chemistry methods has become increasingly versatile. In order for the chapter to be ‘readable’ to interested researchers and PhD students in the biochemical and biomolecular fields our aim has been to do so without weighing down the text with too much detailed mathematics-yet at the same time providing a sufficient level of theory so as to give an understanding of what is implied when talking about molecular dynamic simulations, docking or homology modelling. In this introductory chapter, the basics of biomolecular modelling are outlined, to help set the foundation for the subsequent, more specialised chapters. Today, we readily screen virtual libraries of several million compounds searching for potential new inhibitors, run simulations of large biomolecular complexes in micro or even millisecond timescales, or predict protein structures with similar accuracy to high-resolution X-ray crystallography. This is related to significant developments in terms of methodology and software, as well as the amazing technological advances in computational hardware, and fruitful connections across different disciplines. Computational modelling has gained an increasingly important role in biochemical and biomolecular sciences over the past decades.
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