Kein Folientitel

1
In order to predict binding constants ...
...all we have to do is to calculate ?G of the
protein-ligand complex formation!
2
Enthalpic (?H) contributions to ?G

• Bonded interactions

3
Enthalpic (?H) contributions to ?G

• Non-bonded interactions

Hydrogen bonds (? 5-10 kJ/mol)
Ionic interactions (? 40 kJ/mol)
Metal complexes
Hydrophobic interactions (? 3 kJ/mol)
Cation-? interactions
4
How can we calculate these enthalpic
contributions?

• by Quantum Mechanics (QM)
• atomic forces are treated as wave functions
• approximation of the Schrödinger equation
• by Molecular Mechanics/Force field calculations
  (MM)
• atomic forces are treated as separate components
  of an analytical function
• bonded interactions are treated by Newton's laws
  of classical mechanics

5
Molecular Mechanics calculations
Etot (?H) Ebond Eangle Etorsion
Eout-of-plane Enon-covalent
6
Enthalpic (?H) components to ?G
Etot (?H) Ebond Eangle Etorsion
Eout-of-plane Enon-covalent

• Bonded interactions

7
Enthalpic (?H) components to ?G
Etot (?H) Ebond Eangle Etorsion
Eout-of-plane Enon-covalent

• Non-covalent interactions

8
(No Transcript)
9
Energy function for a simple Molecular Mechanics
force field
10
Example for bond stretching potential
Parameters for C-C bond b0 1.52 Å k 322
E k(b - b0)2
11
Example for Lennard-Jones potential
Parameters for C-C bond Aij 1981049 Bij
1126
12
Aim of Molecular Mechanics calculations

• Finding energetically favourable conformations
• of ligand
• of protein
• of protein-ligand complex
• Estimating (relative) interaction energies
  (?H!!!)

Problems

• Many local energy minima
• Treatment of solvation (?S)

13
Energy minimization calculations
14
The local minima problem

• Optimization of energy function ("energy
  minimization") moves towards "nearest" local
  minimum
• Energy barriers cannot be overcome by MM
  calculations!
• Conformational analysis is required

15
Conformational analysis

• Goal of conformational analysis Determination of
  physiologically possible energy minima
• Under physiological conditions, many
  conformations of a molecule can exist
• Relative population of different conformations
  can be calculated by Boltzmann distribution
• Receptor-bound conformation in most cases is not
  the global minimum conformation of free ligand!

16
Boltzmann distribution
Ph Probability of existence for high-energy
conformation h Pl Probability of existence for
low-energy conformation l ? E Energy difference
of h and l k Boltzmann factor T Absolute
temperature
17
Boltzmann distribution
18
Conformational analysis methods

• Systematic search
• Monte-Carlo search (MC)
• Knowledge-based search
• Molecular Dynamics/Simulated Annealing (MD/SA)

19
Conformational analysis methods

• Systematic search
• Systematically twist rotatable bonds by some
  increment (e.g. by 10) gt about 300000 different
  conformations!
• Discard conformations with overlapping VDW radii
• Energy minimize remaining conformations
• Check for identical conformations

20
Conformational analysis methods

• Monte-Carlo (MC) search
• Generate many random conformations
• Discard conformations with overlapping VDW radii
• Energy minimize remaining conformations
• Check for identical conformations

21
Conformational analysis methods

• Knowledge-based search
• Generate only torsion angles which exist in
  experimental structures (e.g. crystal structures)
• Discard conformations with overlapping VDW radii
• Energy minimize remaining conformations
• Check for identical conformations

22
Knowledge-based search
23
Systematic Search
24
Monte-Carlo Search
25
Knowledge-based Search
26
Molecular Dynamics (MD)

• Simulation of atomic motions over time
• Numerical solution of Newtons equation of
  motion
• F m a
• Initialize random velocities
• Calculate accelerations, using molecular
  mechanics force field
• Move atoms forward by a small amount of time
  (typically 1 fs)
• Calculate new accelerations

27
(No Transcript)
28
Molecular Dynamics
29
Molecular Dynamics
30
MD/Simulated Annealing

• Run MD simulation at high temperature(e.g.
  1200K) to sample conformational space
• Save high-temperature structures at fixed time
  intervals
• Slowly cool down high-temperature
  structures(e.g. to 300K)
• Minimize cooled structures to next local minimum
• Cluster resulting conformations

31
MD/Simulated Annealing
32
MD/Simulated Annealing
Conformational space (local minima) for Ketanserin
33
MD/Simulated Annealing
Conformational space (local minima) for Meloxicam