Molecular Modelling: Explained

Molecular modelling is one of the fastest growing fields in science, but what is it and what does it mean?

“Molecular modelling encompasses all theoretical methods and computational techniques used to model or mimic the behaviour of molecules. The techniques are used in the fields of computational chemistry, drug design, computational biology and materials science for studying molecular systems ranging from small chemical systems to large biological molecules and material assemblies. The simplest calculations can be performed by hand, but inevitably computers are required to perform molecular modelling of any reasonably sized system. The common feature of molecular modelling techniques is the atomistic level description of the molecular systems. This may include treating atoms as the smallest individual unit (the molecular mechanics approach), or explicitly modelling electrons of each atom (the quantum chemistry approach).”^[1]

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As stated, molecular modelling is a way to notice the interaction of a molecule with a molecular system. The best way currently to carry out this process is through computer modelling, but it is still plausible to perform the simplest of studies through the use of molecular mechanics or through the use of a notepad, pen and calculator. However the main concern is that most of the time it may be necessary to carry out molecular modelling through computer modelling as it can be very difficult to work out some of the calculations by hand, whereas the computer can accomplish this for us.

So what is it?

Furthermore to this all, molecular modelling is an expanding topic with more and more developments occurring within the field as the days go on. New scientific papers and methods are being posted as well as an increased amount of journals being published. From this we can see that it’s a topic with a huge variety knowledge and background. This is justified alone from how many issues there are with the problems where molecular modelling can be applied and the abundance of methods that can be used. The journals and papers written about molecular modelling also go into detail of theoretical chemistry and computational chemistry. As a result of this, it is very hard to keep up with molecular modelling techniques and theories due to the fact that there is an increased knowledge of the field as each day goes on. Thanks to the role of the internet, scientists are able to access more journals and papers to find articles on the relevant field they are interested in studying. This in turn also means that there are articles directed for all readers to understand, whether you know nothing at all to someone who is a researcher in the field of theoretical chemistry. The brilliance of this all is that there are documents of research, which keep up to date with only the recent developments, so it’s a quick fix for some scientists to see what they’ve missed out.^[2]

Molecular modelling is alternatively know as molecular mechanics. The basis of the method is to work out the structure and calculate the energy of molecules from their nuclear motion.

The idea of how molecular modelling works is assumed on the Born-Oppenheimer approximation of the Schrödinger equation. This meaning that the approximation states that nuclei, due to their mass being greater than electrons, move more slowly. As a result we can identify the nuclear motion of nuclei separately to that of electrons and therefore the rotations and vibrations can be studied alone assuming that electrons move fast enough to adjust to any movement of its nuclei.

Through the use of force fields, we can calculate the energy and geometry of a molecule. This creates the measure for molecular modelling. A force field is a collection of atom types, parameters and equations.

By looking into further examples, we can show how molecular modelling is used. Looking into the idea of force fields, we can see that certain atoms have several atom types. We can look at compounds like ethylbenzene, which contains hybridised carbon atoms and aromatic carbon atoms.

Through this, we can further explain it to show the parameters of force fields in different bonds as ethylbenzene has different C-C bonds, which are present in the ethyl group and phenyl ring. The total energy of a molecule is separated into different parts named force potentials. These are calculated separately and then added together to give the total energy present within a molecule. These force potentials are what are associated with the equations for the energies with bond stretching, bond bending, torsional strain and van der Waals interactions.

E(total) = E(stretch) + E(bend) + E(s-b) + E(torsion) + E(vdW) + E(dp-dp)

• Energy due to Bond Stretching

If a bond within a compound is stretched or compressed, the energy of the bond increases. The form of calculation for the potential energy for a bond stretching and compressing is a similar calculation to that of Hooke’s law for a spring, except a cubic term is included. As a result of the cubic term, it helps to keep the energy from rising too sharply when the bond is stretched.

• Energy due to Bond Angle Bending

When bonds are bent away from the standard degree, the energy increases. However, there are some exceptions for the calculations of this energy, as cyclic compounds provide special atom types and parameters, which are used in the force field.

• Energy due to Stretch-Bend Interactions

Bonds will stretch to release tension when two bonds have their angle reduced. Through the use of cross term potential functions, we can take into account the terms of bond stretching and bond bending together.

• Energy due to Torsional Strain

intramolecular rotations require energy. The torsional potential is a Fourier series that accounts for all one to four through-bond relationships.

• Energy due to van der Waals Interactions

The van der Waals radius of an atom gives its effective size. As two non-bonded atoms are brought together, the attraction increases causing a decrease in energy. If the distance between the two non-bonded atoms equals the sum of the can der Waals radii the attraction is at a maximum. The closer the atoms are brought together, the greater the energy and the greater the van der Waals repulsion.

• Energy due to Dipole-Dipole Interactions

The calculation for dipole-dipole interactions is similar to that of Coulomb’s law. We can calculate it by considering all the interactions in a molecule. If there is a net charge present in the molecule, calculations must be carried out for charge-charge and charge-dipole.^[3]

To put this all into layman terms, molecular modelling varies from the construction and imaging of simple molecules to creating computer simulations on large protein molecules. Through the use of advanced computer software, we can visualise, rotate, optimise and manipulate molecular models. Some calculations can take up to a few seconds but there are models where it would take months to produce results.^[4]

What is it used for?

Molecular modelling allows us to create a greater visual aspect to show the shapes of molecules and show how they interact. It is used vastly in certain fields, such as, Biology. An example of this would be through enzymes. Their substrates, receptors and their signalling. As of this we can see how useful and how certain molecules interact with one another forming complex molecules where we can then evaluate how strong the binding affinity is and how it would visually be seen.

The biological activity of a drug molecule is supposed to depend on just one unique shape amongst all low energy structures. Through the use of molecular modelling, we can search and target these bioactive conformations. Molecular modelling allows us to identify the atomic and molecular interactions that control the behaviour of a physical system. The molecular interactions that would be identified would be those mentioned above to work out the energy of the force potentials.

One of the first approaches to calculating molecule-molecule binding free energy differences was through the use of comparative molecular field analysis (CoMFA) [Cramer et al., 1988], which allowed us to understand and interpret the active sites of enzymes without a crystal structure being present.

Molecular mechanics allows us to find the best viable solution in which we can model large and non-symmetrical chemical systems. This can be for molecules such as proteins and polymers. Through the use of the classical laws of physics, molecular mechanics allows us to predict the chemical properties of molecules. The issue with this is that we cannot calculate or deal with bond breakage or formation where the treatment of electrons dominate the effects. We tend to turn to molecular mechanics for comparative results rather than absolute quantities. For example, a force field is an empirical approximation for structure-energy relationships in molecules, which allows us to show a comparison between speed and accuracy.

We can produce a better, or even, a more realistic geometry value for the vast majority of organic molecules, due to the fact they are highly parameterised thanks to molecular mechanics.

Molecular dynamics is highly dependent on Newtonian mechanics. this is a conformation space search where atoms are given an initial velocity and are then allowed to evolve in the time. [van Gunsteren & Berendsen, 1977]. The issue with molecular dynamics is that we have to use minimisation schemes, but if we take a look at the effects of temperature, some molecules can overcome the potential energy at the surface. Through the use of simulated annealing, we can control these issues at present [Kirkpatrick et al, 1983, Cerny, 1985]. This allows us to use molecular dynamic calculation in which the system temperature is raised to a large value to allow a spread of exploration of the available conformational space. With an increase in dynamics, the system temperature would be decreased. The last phase would be to use minimisation to select a minimum energy molecular conformation.^[5]

Molecular Modelling Challenges

There are numerous challenges that pose in the way of molecular modelling. They range from the lack of knowledge about certain species of molecules to the free energy calculations that are taken place.

There has been vast development in knowledge within areas such as in gene databases. The issue is, there is a lack of information in the laws of protein folding for example. There is only so much we know about sequence information but with the little intelligence we have about protein folding, it restricts the inference of structure from sequence.

A novel approach scans a pathological vector victimisation the tools of molecular biology; of the various relevant proteins made, a couple of are often isolated, crystallised, and structurally elucidated. The structures of traditional and pathological molecules are often compared and compounds designed to inhibit pathogenic enzymes or receptors by selection. distinguishing the targets is that the initial downside we tend to encounter.

So with the structure of even one target protein, and therefore the information of function of its receptor or active site, it’s currently doable to use computer tools to make and dock a ligand or inhibitor before investing time and resources for synthesis and testing. Conversely, large-scale screening might detect “new leads” that then should be modelled so as to explore later synthetic analogs. In either case, molecular modelling is crucial for understanding and exploring the structure-function relationship. attractive and repulsive forces are often summed and therefore the work quantified. Ideally, one seeks a correlative listing of experimental and computational values to offer assurance that novel compounds are often evaluated before being synthesised. However, there still are exceptions and sudden surprises (Meyer et al., 1995) that has to temper the passion of the molecular modeller.

Based on Fischer’s “lock and key” simile, the mechanical view of molecular interactions are often understood and applied to biomolecules. However, even “rigid” molecules have local flexibility and fluxional water molecules are typically a structural appendage of each the “lock” and therefore the “key,” which implies the in vivo structure might disagree considerably from that on the display screen. Therefore, modelling code must have a choice to simulate the presence of pervasive water molecules.

Molecular mechanics calculations will solely seek the local energy minimum, however are unable to climb the pass into the next energy level. Molecular dynamics simulations are a strong tool for inclusion of the fluxional nature of biomolecules and in best circumstances, will explore the energetic landscape in search of the energy minimum. Atomic parameters are approximate and based on a generic, classical atom, whereas these parameters change modify in a fluxional structure, thus quantum molecular dynamics is required. This field has however to mature, and necessary computational resources greatly exceed today’s supercomputers, to not mention the PC. Again, however does one treat water rigorously (dielectric constant, ionisation state, fluxional H-bond- ing; bulk vs. microscopic quantities)? Challenge #3 could be a rigorous computational simulation of a biochemical reaction in an exceedingly in a accessible to the synthetic chemist, as mentioned by professor Ursula Roethlisberger (ETH Zentrum, Zürich, Switzerland) at this symposium.^[6]

Another big issue is the topi that there is extreme difficulty in calculation free energies by computer. Free energy is often considered to be the most important value when looking into thermodynamics. It can be expressed in two ways, Helmholtz function or Gibbs function. Both work similarly in the sense that they both work with only a constant number of particles and a constant temperature, but Gibbs free energy works with also a constant pressure (NPT) and Helmholtz works with a constant volume (NVT). Most experiments that are carried out, it is best suited to use the Gibbs function as most conditions are kept under constant temperature and pressure.

The issue with all of this, is that free energy calculations are difficult to carry out then working with liquids or flexible macromolecules as they have far too many minimum energy configurations separated by low-energy barriers. Other calculations that are difficult to carry out are those such as entropy and chemical potentials. Through the use of the Monte Carlo simulation or ‘standard’ molecular dynamics, it is still very difficult to calculate free energy because said simulations do not sufficiently sample the regions of phase space, which contribute greatly to free energy.

The two simulations, molecular dynamics sampling and Monte Carlo, are used to find the lower-energy reasons of phase space. as a result, the sampling data will not show reflection of the high-energy regions, so calculating free energy through simulation tends to give inaccurate values.

Another problem is the calculation of free energy differences of two states. We can approach these issues mentioning the simulations above. Three methods have been proposed; thermodynamic perturbation, thermodynamic integration and slow growth. From these we can calculate the free energy differences.

New methods for calculating free energy changes can be worked out with errors no more than 1 kcal / mol in certain cases. Through the use of the two different simulations, one of the initial system and one of the final system. The energies calculated from the two systems are large numbers, with a great error. The difference would be comparable in magnitude to the error in the energy of each system. We determine what the free energy is in terms of interactions involving the solute, which in turn allows us to give a more accurate reading in energy calculations. The two energy systems calculated, are large numbers with a great deal of error, but from this we can take the enthalpy difference and error difference then compare them in magnitude. From this, free energy is calculated based on the interactions involving the solute, therefore we can calculate free energy much more accurately.

When looking at the major sources of error with free energy calculations in computer simulations, they can result from inaccuracies in potential model choice or its implementation. Our other source of error comes from the phase space, by collection insufficient sampling.

The main issue is the fact that we cannot find a method that guarantees adequate coverage of phase space, meaning it is hard to calculate free energy values. We can identify the inadequate sampling through two methods, we can run the simulation for an increased duration, so using the molecular dynamics simulation, or for an increased amount of repetitions, so the Monte Carlo simulation. We can perform this in both the forward and reverse directions, so a different scheme can be use to calculate the free energy difference. Most of the time, the simulation is run in both directions, and from this, we can calculate the lower-bound estimate of the error in calculation from the different in free energy values.

One thing we have to be cautious of is the fact that we need to be careful when carrying out these simulations, because when we cary out more than necessary amounts of simulation over a short simulation, estimating errors is a lot more difficult because the results give a near zero difference between the forward and reverse directions. If the time of simulation exceeds that of the relaxation time of the system, then it is possible to carry it out reversibly. However, if the time of simulation is that of the same order of magnitude as the relaxation time then approximately zero hysteresis may result. This would be due to the incapability of the system to adjust to the changes. Within this, free energies in both directions could appear to be the same and as a result, quite likely to be wrong.^[7]

^[1] Molecular modelling – Wikipedia, the free encyclopedia. 2014. Molecular modelling – Wikipedia, the free encyclopedia. [ONLINE] Available at: http://en.wikipedia.org/wiki/Molecular_modelling. [Accessed 22 March 2014].

^[2] Leach, Andrew R., 2001. Molecular Modelling: Principles and Applications. 2nd ed. London: Harlow : Prentice Hall.

^[3] Introduction to Molecular Modeling. 2014. Introduction to Molecular Modeling. [ONLINE] Available at: http://chemistry.gsu.edu/Glactone/modeling/MMintro.html. [Accessed 22 March 2014].

^[4] What is Molecular Modeling?. 2014. What is Molecular Modeling?. [ONLINE] Available at: http://www.worldofmolecules.com/txtbk2/topic1.htm. [Accessed 22 March 2014].

^[5] Using Molecular Modelling to Study Interactions Between Molecules with Biological Activity | InTechOpen. 2014. Using Molecular Modelling to Study Interactions Between Molecules with Biological Activity | InTechOpen. [ONLINE] Available at: http://www.intechopen.com/books/bioinformatics/using-molecular-modelling-to-study-interactions-between-molecules-with-biological-activity. [Accessed 22 March 2014].

^[6] Edgar F. Meyer, Stanley M. Swanson, Jocylin A. Williams, 2000. Molecular Modelling and Drug Design. Pharmacology & Therapeutics, [Online]. 85, 113–121.

^[7] Leach, Andrew R., 2001. Molecular Modelling: Principles and Applications. 2nd ed. London: Harlow : Prentice Hall.