Molecular modelling

Question 1

Molecular modelling - definition

Use of a ………………………….. to study ………….., …………., …………….. and ……………. of molecules.

Answer 1

Use of a theoretical model to study structure, energy, dynamics and reactivity of molecules.

Question 2

Molecular modelling - types (examples)

• …………………….. (………………..)
• …………………… (…………, ………….., …………….)
• …………………….. (……………………………………………).

Answer 2

• Visual/physical (stick model)
• Mathematical (physics, kinetics, reactivity)
• Computational (as mathematical but larger scale)

Question 3

Molecular modelling - uses

• ……………………………………
• …………………………………
• ………………………………………………………….
• ………………….

Answer 3

• Structural determination
• Structure visualisation
• Calculating forces between molecules
• Experimental

Question 4

Potential energy surface

Answer 4

U - energy associated with a configuration of a mechanical system which can be converted to work

Question 5

Potential energy and molecule shape

Most likely shape of a molecule has …………………………………………., ie. exists at …………………… …………… of plot of ………………………………………………

Answer 5

Most likely shape of a molecule has the lowest potential energy, ie. exists at a global energy minimum of plot of potential energy vs geometry.

Question 6

Potential energy functions - most detailed ⇒ least detailed

Answer 6

Required to calculate PES.

Ab initio QM, QM; semi-empirical QM; molecular mechanics/force fields; scoring functions.

Question 7

Ab initio QM - basis set

Answer 7

Fitted functions correlated to orbitals for use in the Schrödinger equation.

Neglects e^–e^– interaction (assumes e^– moves under average influence of all other e^–)

Question 8

Ab initio QM - Limitations

Answer 8

• Takes a long time
• Calculation complexity scales M⁴ for M AOs
• Supercomputers can manage systems ∼1-2k atoms

Question 9

Ab initio QM - Advantages

Answer 9

• Few approximations/parameters
• Accuracy improves systematically
• Can be applied to reactions as well as structure

Question 10

Ab initio QM - Methods

(most accurate ⇒ least)

Answer 10

With electron correlation: Configuration interaction; CASSCF; DFT

With no electron correlation: Unrestricted Hartree Fock; Hartree Fock

Question 11

Semi empirical QM - basis set

Answer 11

Similar to AB but uses modified Hamiltonian operator, neglecting some interactions and replacing others with parameters.

Question 12

Semi empirical QM - Limitations

Answer 12

• Accuracy cannot systematically improve
• Some cases may need correction (common for peptide bonds)
• Reactions can be studied but may lack accuracy

Question 13

Semi empirical QM - Advantages

Answer 13

• Includes some electron correlation
• Much faster than AB
• Systems can be 2-3k atoms
• Using distributed processing systems (eg. fold@home), large structures >10k atoms like proteins can be modelled

Question 14

Semi empirical QM - Methods

(most accurate ⇒ least)

Answer 14

• CNDO (1965)
• MNDO (1977)
• PM3 (1989)
• SAM1 (1993)
• PM6 (2007).

Question 15

Molecular mechanics (“force field”) - basis set

Answer 15

Treats nuclei and electrons as atoms, connected by compressable springs.

Question 16

Molecular mechanics (“force field”) - Bonded terms

Answer 16

• Applies up to 3 covalent bonds apart
• bond length (d), angle stretching (θ)
• Rotations about single bonds/dihedral angle (ϕ)
• U_bond (d) + U_angle (θ) + U_dihedral (ϕ)

Question 17

Molecular mechanics (“force field”) - Nonbonded interactions

Answer 17

• Operates over a longer range, r_ab
• Electrostatic energy (r^-1) – uses Coulomb’s Law. Treats charges as fitted constants (q_a/b)
• U_elec (r_ab) = ^atoms∑_a,b q_aq_b / r_ab
• Van der Waals – close-range attraction (r^-6) & repulsion (r¹²).
• U_vdw (r_ab) = ^atoms∑_a,b (A / r_ab¹² − C / r_ab⁶)

Question 18

Molecular mechanics (“force field”) - Total potential energy

Answer 18

U_total (d, θ, ϕ, r_ab) = U_bond (d) + U_angle (θ) + U_dihedral (ϕ) + U_elec (r_ab) + U_vdw (r_ab)

Question 19

Molecular mechanics (“force field”) - Approximations/parameters

Answer 19

• MM treats as atoms, not independent electrons/nuclei
• Inputs: d, θ, ϕ, r_ab
• Paramaters: A/C/q. Accuracy of calculation depends on accuracy of paramaters

Question 20

Molecular mechanics (“force field”) - Limitations

Answer 20

• Needs new parameters for each molecule ID
• Cannot treat chemical reactions

Question 21

Molecular mechanics (“force field”) - Advantages

Answer 21

• Can treat v large systems (up to 1m)
• Can be accurate if used correctly (ie. accurate paramaters)

Question 22

Scoring functions - types

Answer 22

• First Principles
• Empirical
• Knowledge-based

Question 23

Scoring: first principles

Answer 23

Physics based approach, considering molecular mechanics force field (VdW, electrostatic effects).

U_total (r_ab) = ^atoms∑_a,b q_aq_b / r_ab + ^atoms∑_a,b (A / r_ab¹² − C / r_ab⁶)

Question 24

Scoring: first principles - Limitations

Answer 24

• Can be slow to calculate
• Depends on reliable paramaters
• Force fields provide potential energy, not free energy

Question 25

Scoring: empirical

Answer 25

Computes binding free energy ΔG

C are constants, f are functions of distance ΔR & angle Δα between interacting groups on protein & ligand.

Question 26

Scoring: empirical - Parametrising functions

Answer 26

• Training set: LR complexes with crystal structures and experimentally measured binding affinities ΔG_bind
• Structures from training set are used to predict ΔG_bind using a scoring function and constants C are modified until this matches experimental values
• Performance can be tested using other sets of known data (test sets)

Question 27

Scoring: empirical - Advantages

Answer 27

• Fast
• Calculates free energy

Question 28

Scoring: knowledge-based potentials

Answer 28

• Generates a free energy function ΔG_bind for each X-Y pair of protein-ligand atom IDs X/Y
• Extracted from set of known protein-ligand X-ray structures from PDB
• Assumes a Boltzmann distribution of protein atoms around ligands
• Averaged over all structures in database, eg. N,O pairs can be expected to be distance r apart:
• Δ^N-OG_bind (r_N-O) = - RT ln g(r_N-O) where g = distribution/variance in database
• Total ΔG_bind is sum of all pairs of ΔG_bind energies

Question 29

Scoring: knowledge-based - Limitations

Answer 29

• Boltzmann statistics for distribution of atom pairs not realistic
• Difficult to define reference state

Question 30

Scoring: knowledge-based - Advantages

Answer 30

• Fast
• Calculates free energy
• More general than empirical approaches

Question 31

Computational docking

Answer 31

• Predicts how ligand L binds to a given 3D structure of receptor R.
• Geometry of bound ligand = binding mode/docked pose.

Question 32

Computational docking - conformational search methods

Answer 32

• Systematic/grid based
• Genetic algorithm
• Graph theory
• Extant knowledge can provide a starting point/bias predictions.

Question 33

Computational docking - search process

Answer 33

1. Characterise active site (where, shape etc)
2. Conformational search of ligand in active site (= one generation)
3. Score ligand poses using scoring functions

Question 34

Computational docking - genetic algorithm

Answer 34

1. Conformation data stored on “chromosome” (eg. side-chain dihedral angles, coordinates in active site)
2. Initial population ranked using scoring function. Lowest energy conformations retained, highest removed.
3. Conformations not removed share information by cross-over (AA/BB → AB/BA swap) or mutation (random data point change).
4. New conformations scored.

(eg. pop = 7. 1,2 retained. 6,7 removed. 3-5 share information with 1,2 producing new 3-7. Pop = old 1,2, new 3-7.)

Conformations will get progressively lower in energy and so more accurate to experimental data.

Question 35

Computational docking - testing docking

Answer 35

1. RL complex with experimentally known 3D structure selected from database
2. L removed from R and redocked
3. Root-mean-square-distance determines if geometry reproduced:

rmsd = √ [(^Natoms∑_i=1 d_i²)/N_atoms]

• where d_i = distance between equivalent atoms i between superimposed structures
• rmsd < 2Å acceptable for small ligands

Question 36

Computational docking - limitations

Answer 36

• Proteins are flexible and often induce fit upon binding - cannot be accounted for
• Water in/around binding site may change entropy/enthalpy values