Molecular modelling

Question 1

Goals of structure-based drug design

Answer 1

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

Question 2

What do the goals of structure-based drug design require?

Answer 2

Computer graphics for visualising X-ray crystal structures
Quantitative modelling of drug-receptor interactions - quantitative relationships between structure and energy are required for this

Question 3

Modelling methods

Answer 3

Quantum mechanics
Molecular mechanics
Quantum mechanics/molecular mechanics

Question 4

Quantum mechanical model

Answer 4

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

Question 5

Molecular mechanical model

Answer 5

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

Question 6

Quantum mechanics/molecular mechanics

Answer 6

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

Question 7

Equation for QM/MM system

Answer 7

Etotal = Eqm + Emm + Eqm/mm

Where Eqm/mm = interaction

Question 8

Description of molecular mechanics

Answer 8

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)

Question 9

Internal energy

Answer 9

Associated with bonds, valence angles and dihedral angles

Question 10

External energy

Answer 10

Associated with non-bonded interactions such as van der Waals and electrostatic forces

Question 11

Change in bond length

Answer 11

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

Question 12

Kb

Answer 12

Force constant

i.e. how ‘difficult’ is it to stretch the bond?

Question 13

(b-b0)

Answer 13

Displacement away from equilibrium bond length

Question 14

Differences between single, double and triple bonds

Answer 14

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)

Question 15

Change in bond angle

Answer 15

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

Question 16

Change in dihedral/torsion angle

Answer 16

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

Question 17

Graph for bond-length/3-atom angle

Answer 17

Draw

Question 18

Graph for torsion angle

Answer 18

Draw

Question 19

Lennard Jones graph

Answer 19

Approximates the interaction between a pair of neutral atoms/molecules
A graph of strength vs distance
Draw

Question 20

Equation for external energy

Answer 20

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

Question 21

When is the electrostatic energy negative?

Answer 21

If opposite charges are attracted to each other

But the potential only varies slowly as 1/r

Question 22

van der Waals portion of external energy function

Answer 22

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

Question 23

Hydrogen bonding

Answer 23

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)

Question 24

Example of when electrostatic energy and dihedral angle may be opposed to one another

Answer 24

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

Question 25

Equation for overall total potential energy of a molecular system

Answer 25

Vtotal = Vbonds + Vangles + Vdihedral + Vexternal

Question 26

Examples of popular force fields for molecular mechanics

Answer 26

AMBER
CHARMM
GROMOS
MMFF
OPLS
UFF

Question 27

Molecular mechanics can be used to…

Answer 27

…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)

Question 28

How is the overall minimum in total potential energy obtained?

Answer 28

By energy minimisation

Question 29

Energy minimisation

Answer 29

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)

Question 30

Why do proteins have many local energy minima?

Answer 30

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)

Question 31

How can conformational space be explored?

Answer 31

Using molecular dynamics simulations

Question 32

Molecular dynamics

Answer 32

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

Question 33

GRID program

Answer 33

A computational procedure for determining energetically favourable binding sites on molecules of known structure

Question 34

GRID program procedure

Answer 34

1. Prepare a 3D lattice of grid points encompassing the binding site
2. 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
3. Select the most favourable interaction sites
4. 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

Question 35

Probe molecules in GRID program

Answer 35

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

Question 36

Example of a drug designed from the GRID program

Answer 36

Zanamivir

Question 37

Why is theoretical modelling an important tool?

Answer 37

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

Question 38

What are molecular mechanics methods primarily used for?

Answer 38

Systems built from organic molecules

Question 39

Advantages of classical methods

Answer 39

Energy can be easily evaluated

Large systems can be studied

Question 40

Drawbacks of classical methods

Answer 40

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

Question 41

Advantages of quantum chemical methods

Answer 41

Can be used for the study of chemical reactions where molecules are formed and destroyed

Question 42

Disadvantages of quantum chemical methods

Answer 42

Very demanding in terms of computing time and storage

Only smaller systems can be handled