Molecular modelling Flashcards
Goals of structure-based drug design
To understand the atomic details of drug binding strength and specificity
To identify or create novel molecules that will bind to the selected target and elicit a biological response, either by de novo drug design or database-searching techniques
To optimise the therapeutic index of an already available drug or lead compound
What do the goals of structure-based drug design require?
Computer graphics for visualising X-ray crystal structures
Quantitative modelling of drug-receptor interactions - quantitative relationships between structure and energy are required for this
Modelling methods
Quantum mechanics
Molecular mechanics
Quantum mechanics/molecular mechanics
Quantum mechanical model
Best approach for chemical reactivity
Electrons and atomic nuclei are the particles of interest
Treats electrons explicitly so is therefore limited to ~100-200 atoms, due to the time required for the complex computations (can take anywhere from 6h to 2 days)
Offers a very accurate description of chemical reactions and interactions
Molecular mechanical model
In the classic model (Newtonian model), atoms/groups of atoms are the particles considered (i.e. electrons are ignored)
This method attempts to describe chemical systems using mathematical models for the forces between classical objects (e.g. Hooke’s law, Coulomb’s law)
Every atom interacts with every other atom, but this interaction is described by very simple physics such that very large systems (10^4 to 10^6 atoms) can be studied with much shorter computation times
Less accurate than quantum mechanical methods
Quantum mechanics/molecular mechanics
Hybrid methodology
Combines a quantum mechanical ‘core’ for chemical accuracy with a molecular mechanical ‘environment’ for computational speed
Scientists involved in the development of this methodology awarded the Nobel Prize in 2013
Equation for QM/MM system
Etotal = Eqm + Emm + Eqm/mm
Where Eqm/mm = interaction
Description of molecular mechanics
Molecular mechanics uses an empirical energy function, in which the total potential energy of a system is the sum of both the internal and external energy
The interactions between spherical atoms are described by simple mathematical forms (“balls and springs”) that contain empirical parameters pre-assigned to specific sets of atoms
This method sums up the changes in energy for all individual components due to distortions away from ‘ideal’ values of bond lengths/angles etc (see equations)
Internal energy
Associated with bonds, valence angles and dihedral angles
External energy
Associated with non-bonded interactions such as van der Waals and electrostatic forces
Change in bond length
Related to the potential energy by means of a harmonic function (Hooke’s law) (draw)
Vbonds = sum(0.5Kb(b-b0)^2)
(summing over all the bonds in the molecule)
Both the force constant, Kb, and the equilibrium bond length, b0, are entirely empirical parameters whose values are determined by the best fit to some experimental data
Kb
Force constant
i.e. how ‘difficult’ is it to stretch the bond?
(b-b0)
Displacement away from equilibrium bond length
Differences between single, double and triple bonds
Can also be described using the same functional form, but with different values for Kb and b0
Unique Kb and b0 parameters are assigned to each pair of bonded atoms based on their types (i.e. C-C, C-H, C-O etc)
Change in bond angle
Related to the potential energy by means of a harmonic function (Hooke’s law) (draw)
Vangles = sum(0.5Ktheta(theta-theta0)^2
(summing over all bond angles)
Ktheta = force constant Theta = bond angle Theta0 = equilibrium bond angle
Change in dihedral/torsion angle
The potential energy associated with a dihedral/torsion angle is commonly given by a cosine function of the angle phi, which also involves a periodicity n and phase angle delta
Vdihedral = sum(Kphi[1+cos(nphi - delta)])
Kphi = constant defining the "stiffness" of the system towards rotation around the central bond defining the dihedral angle n = 3 for a 3-fold rotor or = 2 for internal rotation about a double bond delta = phase angle, depends on whether phi = 0 is a maximum or minimum in the potential
Graph for bond-length/3-atom angle
Draw
Graph for torsion angle
Draw
Lennard Jones graph
Approximates the interaction between a pair of neutral atoms/molecules
A graph of strength vs distance
Draw
Equation for external energy
The variation with interatomic distance r of the potential energy V associated with the non-bonded interactions is commonly given by the function:
(see flashcard)
This is the sum of a ‘12-6’/’Lennard-Jones’ potential for the van der Waals interactions and an electrostatic (Coulomb) term involving the atomic charge q on each of the atoms i and j
Rmin = distance at which the potential reaches its minimum 3wd = constant, describes the strength of the interaction between the 2 atoms being considered
When is the electrostatic energy negative?
If opposite charges are attracted to each other
But the potential only varies slowly as 1/r
van der Waals portion of external energy function
Has an attractive and repulsive part
Attractive part: varies with distance as 1/r^6, negligible in magnitude due to the values of the parameters Rmin and 3wd
Repulsive part: varies with distance as 1/r^12, rises very steeply at short range and gives rise to the overall minimum in the external potential
Hydrogen bonding
Often treated as an electrostatic interaction by means of appropriate partial charges on the atoms involved to give suitable H-bonding energies (approx. -4 to 20 kJ/mol)
Example of when electrostatic energy and dihedral angle may be opposed to one another
O=C-O-H angle in a carboxyl group equally favours 0 or 180 for the dihedral angle term, but the electrostatic term disfavours the antiperiplanar 180 arrangement
The net result is a 2-fold rotor with unequal energy minima
Equation for overall total potential energy of a molecular system
Vtotal = Vbonds + Vangles + Vdihedral + Vexternal
Examples of popular force fields for molecular mechanics
AMBER CHARMM GROMOS MMFF OPLS UFF
Molecular mechanics can be used to…
…calculate the energy of a molecular system (see all equations)
However, this structure may not necessarily be stable (an energy minimum on the potential energy surface)
How is the overall minimum in total potential energy obtained?
By energy minimisation
Energy minimisation
The process that locates the geometry that reduces the net force in each coordinate/the gradient of the energy to zero
The system is relaxed
(The forces in the individual coordinates e.g. bond lengths/angles etc are generally all in tension against each other)
Why do proteins have many local energy minima?
For a protein with n amino acids, each of which has 10 conformations, the total number of conformations for the whole protein is 10^n
i.e. there is. vast conformational space
Therefore there are lots and lots of local energy minima, but only one of these is the global minimum (lowest energy overall)
How can conformational space be explored?
Using molecular dynamics simulations
Molecular dynamics
Computational technique where the time evolution of a set of atoms is followed
Simulates the natural motion of the molecular system
The energy provided in a molecular dynamics procedure allows the atoms to move and collide with neighbouring atoms
This is a form of ‘conformational searching’ - if enough energy is provided, the molecule will be able to cross the energy barriers that separate the local minima
GRID program
A computational procedure for determining energetically favourable binding sites on molecules of known structure
GRID program procedure
- Prepare a 3D lattice of grid points encompassing the binding site
- Determine the interaction energy (using molecular mechanics) of different types of functional group with the binding site at each individual grid point by moving a small probe molecule from point to point
- Select the most favourable interaction sites
- Determine the relative spatial orientations of the selected interaction sites
(draw)
This information can then guide drug design - it allows a pharmacophore to be constructed, but also allows interaction energies to be estimated
Probe molecules in GRID program
Small species with different properties
e.g.
NH4+ to probe for locations of negative charge in the active site
HCO2- to probe for locations of positive charge
H2C=O to probe for H-bond donor positions
CH4 to prove for hydrophobic locations
Example of a drug designed from the GRID program
Zanamivir
Why is theoretical modelling an important tool?
It serves as a complement to the experimental techniques
e.g. a transition state is not experimentally accessible but there are theoretical methods of obtaining this structure
What are molecular mechanics methods primarily used for?
Systems built from organic molecules
Advantages of classical methods
Energy can be easily evaluated
Large systems can be studied
Drawbacks of classical methods
Can only be used for structures where the interacting molecules are only weakly perturbed
i.e. cannot be used for the study of chemical reactions where new molecules are formed
Advantages of quantum chemical methods
Can be used for the study of chemical reactions where molecules are formed and destroyed
Disadvantages of quantum chemical methods
Very demanding in terms of computing time and storage
Only smaller systems can be handled
