Explanation of Molecular Modelling

The molecular dynamics method.

By analysing a molecular system using physics, specifically the laws of motion and energy, one can model the movements of atoms within a 3d space or medium. By treating all atoms as ‘balls’ the motions can be calculated based on their interactions with other atoms. These interactions are derived using four main atomic interactions which can be expressed as a ‘spring model’. So we can simulate each state from beginning to the end of the interaction. All interactions are assigned a spring constant (k) which is the energy required to push them past equilibrium. The spring constant is denoted as the equilibrium as two atoms join at rest.

• Bond stretchingThe energy required to pull them apart or push them together can be expressed with the equation
  
• Angle bondingEnergy required to bend a bond
  
• Torsion bondingThe energy required to twist a bond
  
• Non covalent bondsDescribes how atoms behave when no bond is present using electrostatic and Van Der Waal equations
  

This is an ab-initio (from the start) method, which uses only calculations and no previous information, as opposed to using existing databases and knowledge.

By mapping these movements using chemical bond attraction values, using covalent, ionic or electrostatic, we can simulate the movements of atoms as a group and hence predict the movements of a compound. These values are generally known as a ‘forcefield’ and are developed using both experimental and empirical quantum mechanics. In the case of protein structure predication the amino acid compounds are modelled in this way and the aim is to predict where they will end up based on a primary sequence derived from DNA.

Using the energetic interactions between atoms sequential states of protein development can be found over a given time period.

Rugged energy landscape

The amount of states a sequence can take while forming from 150 amino acids is approximately 10^300 but proteins do it, on average, parsing only 10^8 states, so some other force is a play. Something drives the amino acid chain to achieve its native state i.e. a desired protein. This can be modelled as a ‘rugged energy landscape’ based on the observation that the states seem to close in on the native state. The “way” or “path” can be defined as the states the protein takes while moving towards its native state. In reality there are many paths a protein can take but all are guided by achieving a lower energy state. So if we envisage this energy landscape as a mountain range the protein creation process always tries to get to lower ground. Obviously if there is a valley the process will need more energy to get out of it and continue on its way. The entire process (around 10^8 states) is achieved in around 2-3 seconds in biology, but would take many years using modern computational methods.

The problem of simulation time exists due to restrictions in computing power; various methods have been developed to speed up a simulation.

• Energy FloodingWhen using computer methods we can speed them up by adding energy to the process whenever a state is “stuck” in a valley. We must ensure we monitor the amount of energy we add and when we add it, so we can reconstruct the energy landscape.
• Removal of solventIn reality all reactions will take place in a solvent, by incorporating this into the simulation this will increase the amount of interactions between atoms, and hence increase time and calculations necessary. Removing this will increase the speed but decrease the accuracy of the simulation.
• Periodic boundary conditionsThe largest cost of the solvent in a simulation is the edge water i.e. calculating interactions of the water molecules on the edge. By modelling the reaction in a cube we can create an infinite space. If a water molecule gets to the edge it appears on the other side, thus removing edge water and minimising the amount of solvent reactions.

• Granular methodsInstead of calculating the movements of each atom we can group atoms into larger structures thus reducing the amount of calculations. So a group of 9 could be shown and treated as just one or two molecules.

• Steered molecular dynamicsA force is applied to an atom or system and the force required to “steer it” or achieve desired results is noted. E.g. when simulating membrane permeation an atom is held in the membrane and the requiring force is noted. The higher the force required the less it wants to be there and hence the less it is likely to go there on its own.

Even using these methods and with improving computing powers we cannot find the tertiary structure of an average size protein we can only simulate a fraction of the process, around 1-2 Nano-seconds.

Molecular dynamics can be used in drug development by simulating ligand docking and cellular membrane permeation

Because cell membranes, proteins and drugs are all atomic compounds we can use the above methods to simulate the interactions between these compounds. We can model how a drug will dock to a protein or enzyme as well as whether a drug will penetrate a cell membrane.

Click here to see it in action……..