Molecular Modelling is a significant part of chemistry in drug design which enables the manipulation and or simplification of the structure of a molecule in 3D by the use of computational means. This predicts functional properties of chemicals and other materials which involves specific calculations of quantum. [1]
Examples of the properties that can be calculated include geometries such as bond lengths and bond angles. Energies such as heat of formation and activation energy can also be determined. Electronic properties such as moments, charges, ionization potential and electron affinity can also be obtained as well as spectroscopic properties such as vibrational modes and chemical shifts. It calculates the structure and energy of molecules based on nuclear motions.
A 2 dimensional drawing of the compound of interest is made by the use of a chemical drawing software. This 2D structure has to be transformed into a 3D structure to study the desired chemical properties which involves the use of quantum mechanics and molecular mechanics. [2]
Quantum mechanics is a part of physics that accounts for energy and matter at the atomic level. It states that energy is radiated and absorbed in quanta. It represents the electrons in calculations making it possible to derive properties that are dependent on the electronic distribution. These include chemical reactions such as bond formation and/or bond breaking as wells as thermodynamic properties.
Molecular mechanics calculates the potential energy of all systems in molecular mechanics using force fields. It can be applied to molecules that are small but also to large molecules containing thousands of atoms, like biological systems.
This type of energy is described using the term "force field" which is a function that depends on the atomic positions. It gives an idea of the forces that are present within the molecule and is used to calculate the energy and geometry of a molecule. It takes into account the different types of atoms and parameters for bond lengths, bond angles, torsion angles and equations to calculate the energy of a molecule. [3]
It is assumed that electrons find their optimum distribution as soon as the positions of the nuclei are known and therefore electrons are not considered explicitly. This assumption is based on the Born-Oppenheimer approximation of the Schrödinger equation (H Ψ = E Ψ), where E is energy of the system, Ψ is the wavefunction and H is the Hamiltonian operator which includes terms for both potential and kinetic energy.
According to the Born-Oppenheimer approximation, nuclei are heavier and move slower than electrons; so movement of electrons can be considered independently of the movement of the nuclei. This makes it possible to analyze factors such as nuclear motions, vibration and rotations separately from electrons which are assumed to move fast enough to adjust to any movement of the nuclei.
Molecular modelling treats a molecule as a "collection of weights connected with springs, where the weights represent the nuclei and the springs represent the bonds."
A Force potential equation is obtained by adding up the energies of every component of the equation. These are energy of every bond (ESTRETCH ), angle (EBEND ), van der waal interactions, dipole diopole interactions, torsions and Emiscellaneous for additional terms.
ETOTAL = ESTRETCH + EBEND + EvdW + EDP-DP + ETORSION + Emiscellaneous
It gives the potential surface energy of a molecule, which determines how a particular atom would move due to movements and displacements of all the other atoms in the system of a molecule. [4]
A quadric form of the Hooke's law formula (harmonic potential), is used to obtain bond stretching/bending energies. This is because the Morse potential form isn't suitable as it is accountable for a wide range of behaviour from the strong equilibrium behaviour to dissociation. It is unlikely for bonds to deviate much from their equilibrium so the Hooke's law is used instead. [5]
The following calculations are examples of some force potentials and their parameters such as those discussed above. They calculate ground state "steric" energies of organic molecules.
Bond stretching:
Ks = force constant in mdyn/Ǻ 143.88 converts units to kcal/mol
lo = natural/equilibrium bond length in Ǻ l = actual bond length in Ǻ
If the natural bond length is taken as lo, then any deviation from this value would cause an increase in the potential energy. [6]
If all the terms in the force field are set to zero, the natural bond length lo is the value that the bond adopts. However, the "equilibrium" bond length is only adopted in a minimum energy structure when all other terms in the force field contribute. This may lead to the bond deviating slightly from its natural bond length in order to make up for other contributions to the energy. A lot of energy may be required to cause a bond to deviate significantly from its equilibrium value because the forces between bonded atoms are fairly strong. [7]
Bond bending
kθ = force constant in mdyn/( Ǻrad2)
θo = natural/equilibrium bond angle in degrees
θ = actual bond angle in degrees
0.21914 = conversion factor
As in bond stretching, any deviation from natural bond angle (θo) will cause the potential energy to increase. θo and kθ characterise the contribution of each angle.
Bond bending needs less energy than Bond stretching so the most distortion occurs in the bond angles rather than the bond lengths; therefore the force constants are proportionally smaller.
Energy caused by torsion (intramolecular bond rotations) is described by using the following formula (Fourier series). Many force fields are used for modelling flexible molecules where the major changes in conformation are due to rotations about bonds; in order to simulate it is essential that the force field properly represents the energy profiles of such changes. [8]
ν, ν2, ν3 = force constants in kcal/mol
ν = residual dipole-dipole interactions, van der Waals interactions, or other interactions
ν2 = conjugation/hyper conjugation, related to p orbital's
ν3 = steric, or bonding/antibonding interactions
Torsional potentials are used to mimic the preference for the staggered conformations at the sp3-sp3 bonds and the preference for eclipsed conformations in sp2-sp2. [9]
An example of torsional strain is the conversion of cyclohexane from the chair conformation to the boat conformation which requires Energy.
Van der Waals interactions occur when two non-bonded atoms are bought together which causes an increase in the attraction but decreases the energy. Attraction is at its maximum when atoms approach each other beyond a particular distance and a bond doesn't form. There will be strong van der Waals repulsion causing a sharp increase in energy. This represented using the following equation.
ε = energy parameter which sets depth of potential energy well
rv = sum of van der Waals radii of interacting atoms
ro = distance between the interacting centres.
Electrostatic interactions affect the total energy of a system which are represented by dipole moments. This enables the calculation of properties of a wider range of molecules such as the polarisation of a carbonyl group towards the oxygen. The energy of interaction of two carbonyls will be different if they are aligned or opposed. Such effects are quantified by assigning a partial charge to every atom.
The equation below is derived from Coulombs law, whereby the energy is determined by considering all dipole-dipole interactions in a given molecule. [10]
D = dielectric constant of solvent
X = angle between two dipoles (μi and μj)
αi and αj = angles between dipoles and a vector connecting the two dipole
rij = distance between the dipoles
Force fields can be assigned into 3 classes. Class I are harmonic terms such as bond stretching and angle bending and only diagonal elements in the force constant matrix, which is a mechanical force field that gives an idea of what the structure is like (AMBER,CHARMM, MM2).
Class II includes cubic and anharmonic terms and explicit off-diagonal elements (MM3), which is also a mechanical force field and predicts the structure and can give a vibrational spectra. Due to the higher, off-diagonal terms the force field can better predict the properties of highly strained systems and allow it to produce better vibrational spectra. Class III is like class II but includes chemical effects such as electronegativity and hyper conjugation (MM4). [11]
The MM3 force field has the dipole-dipole potential but interactions of formal charges are taken into account (NH3- group), which is possible by using coulombs law of charge-charge potential and a charge-dipole potential [12] .
CHARMM (biological force field) uses more parameters which include the electrostatic interaction potential. It has a columbic term for short range interactions and works by using different hydrogen bond potentials with lower power repulsion, attraction and terms. [13]
In the AMBER force field the non-bonding interactions of hydrogen binding pairs are calculated using Lennard Jones potential (attractive forces decrease with distance) which is parameterized separately. The H-bond potential is replaced with a parameterized vdW potential. [14]
The MM2, MM3 and MM4 force fields are for calculating small molecules but the AMBER and CHARMM force fields are used for larger molecules, such as proteins and nucleic acids. [15]
Molecular modelling plays an important role in industry as it saves time and money, thanks to the use of computers as they are faster than humans; saving money. They are reliable and have good reproducibility. It shows how molecules interact with one another, which is rather difficult by using experiments. An example of this would be when trying to determine how a molecule will interact with another bioactive molecule such as an enzyme binding to a receptor site. This is where molecular modelling calculations would help in determining the 3D structure of a molecule. [16]
A significant application of Molecular Modelling is in the pharmaceutical industry where it supports the development of new drugs. For example: "Mechanism and Extrapolation Technologies (MET) use a wide range of technologies to determine the mechanisms by which drugs are absorbed, distributed, metabolised and eliminated. MET can further capitalise on the information generated by incorporating data into simulation and physiologically based pharmacokinetic models to predict clinical effects resulting from inhibition to induction of clearance pathways (drug interactions). Integrating modelling with safety and efficacy data significantly contributes to the overall knowledge and understanding of new drugs." [17]
Pesticides, veterinary drugs and mycotoxins are low molecular weight food contaminants which have a significant role in food safety. The increasing number of food contaminants requires the application of effective safety programs which needs analytical techniques that are not expensive and fast. Immunoassays depended on antibody-antibody-binding-properties are suitable methods that fulfil the need for an analytical technique to support the assessment of food quality and food safety.
According to Newman and Price the intermolecular forces of the antibody-epitope (antibody binding site) interactions are fundamental to the design of immunoassays.
The immunochemist turns to novel approaches (Computer-assisted molecular modelling) to be able to develop immunoassays which are more specific and economical; providing useful information regarding the physical/chemical properties of analytes.
Molecular Modelling gives an understanding of molecular structure and biological activity, which is normally very difficult or impossible to obtain. Recently, it was shown that CAMM was one of several useful applications helping immunochemists to develop anti-hapten antibodies with desirable properties.
CAMM enabled the development of immunoassays used for detection of low molecular weight food contaminants such as an algaecide, antibiotics, cork taint, herbicides, mycotoxins, pesticides, veterinary drugs and other chemicals. It also assists in hapten design, antibody-antigen recognition in cross-reactivity studies and model antibody binding sites [18] .
Antibody-antigen interactions are fundamental to immunoassay. These interactions are comprised of hydrogen bonds, Vdw forces, hydrophobic interactions and electrostatic bonds. Usually, researchers study antibody-antigen binding properties indirectly through experimental data. However, the use of CAMM in drug discovery and biology enabled the understanding and prediction of molecular recognition, both structurally (3D) by finding likely binding modes, and energetically by predicting binding affinity. [19]
Another example of application of molecular modelling to a rather different area is "The Atmospheric Chemistry group at the University of Leicester who apply molecular modelling to tropospheric chemistry, stratospheric chemistry, atmospheric composition and photochemistry. They investigate by modelling the resultant data to understand the controlling chemical and physical processes." [20] This again is a very good example of one of the wide uses of molecular modelling to atmospheric chemistry where the chemistry of the atmosphere on the earth is studied.
Molecular modelling is a relatively new area of science that assists in the development of new drugs. It gives an insight into 3D molecular structure and biological activity that are difficult or impossible to obtain in other ways. However, the need of high computational input may be a disadvantage also because large scale conformational changes are hard to model. Nevertheless, molecular modelling is a vital tool for scientist in drug discovery which will be more advance in the near future.
