1. Molecular Mechanics, Molecular Dynamics, and Docking
Michael Strong, PhD
National Jewish Health
University of Colorado, Denver

2. Foldit

3. Proteins are Dynamic Structures
Aquaporin
Water traveling through
Aquaporin pore
Control of the selectivity of the aquaporin water channel family by global orientational tuning. Tajkhorshid E, Nollert P, Jensen MØ, Miercke LJ, O'Connell J, Stroud RM, Schulten K. Science Apr 19;296(5567):

4. Experimental Methods provide clues to less rigid regions
X-ray crystallography
NMR

5. Molecular Mechanics (MM) “The Physics of Proteins”
Describe Proteins in terms of Physiochemical properties of Atoms and Bonds
Calculate the dynamics of a protein, and search for minimum energy, by repeated integration of the forces acting on each atom
Minimum energy conformation in solution assumed to be the native state (relevant to protein folding)

6. Molecular Mechanics •A molecule is described by interacting spheres.
• Different types of spheres describe different types of
atoms.
• The interaction between chemically bound atoms is
described by special bonding interaction terms.
• The interaction of not chemically bound atoms is
described by non-bonding interaction terms.

7. Energy Minimization Many forces act on a protein
- Hydrophobic: inside of protein avoids water
- Packing: Atoms can’t be too close or too far away
- Bond Angle and Length Constraints
- Non-covalent (longer distance)
- Hydrogen Bonds
- Ionic / Salt Bridges
Can calculate all of these forces, and minimize
Computationally intensive

8. Molecular Mechanics Pros/Cons
• detailed stereochemical model that describes certain aspects of biomolecules very well
• conformational flexibility
• dynamic model (time dependence) is possible
• large systems (> 10^4 atoms) can be modeled
Cons:
• computationally demanding
• large scale conformational changes are hard to model
• no electronic (quantum) description, no chemical reaction (bond breaking/forming), no excited states, …
• limited run times

9. Energy Function Target function that MM tries to optimize
Describes the interaction energies of all atoms and molecules in the system
Always an approximation
Closer to real physics --> more realistic, more computation time (I.e. smaller time steps and more interactions increase accuracy)

10. The energy equation Energy = Stretching Energy + Bending Energy +
(in simplistic terms)
Energy =
Stretching Energy +
Bending Energy +
Torsion Energy +
Non-Bonded Interaction Energy (most computationally costly, many)
These equations together with the data (parameters) required to describe the behavior of different kinds of atoms and bonds, is called a force-field. (potential energy)

11. The energy model Proposed by Linus Pauling in the 1930s
Bond angles and lengths are almost always the same
Energy model broken up into two parts:
Covalent terms
Bond distances
Bond angles
Dihedral angles
Non-covalent terms
Forces at a distance between all non-bonded atoms

12. Bond length Spring-like term for energy based on distance
kb is the spring constant of the bond.
r0 is the bond length at equilibrium.
Unique kb and r0 assigned for each bond pair, i.e. C-C, O-H

13. Bond bend k is the spring constant of the bend.
0 is the bond angle at equilibrium.
Unique parameters for angle bending are assigned to each bonded triplet of atoms based on their types (e.g. C-C-C, C-O-C, C-C-H, etc.)

14. Torsion Energy
Energy needed to rotate about bonds. Only relevant to single bonds
The parameters are determined from curve fitting.
Unique parameters for torsional rotation are assigned to each bonded quartet of atoms based on their types (e.g. C-C-C-C, C-O-C-N, H-C-C-H, etc.)
A controls the amplitude of the curve
n controls its periodicity
shifts the entire curve along the rotation angle axis ().

15. Non-bonded Energy Van der Waals – preferred distance between atoms
If atoms are polar, some will have partial electrostatic charges (attract if opposite, repel if same)
A and B constants depending on atom type.
A determines the degree the attractiveness
B determines the degree of repulsion
q is the partial atomic charge
A determines the degree the attractiveness
B determines the degree of repulsion
q is the charge

16. Energy minimization
Given some energy function and initial conditions, we want to find the minimum energy conformation. (steepest decent algorithm)
Various programs: CHARMM, AMBER are two most widely used (and packaged), DE Shaw’s Desmond

17. Molecular Dynamics can be used to predict protein folding (based on the physical properties of the protein)
villin
FiP35
Folding proteins at x-ray resolution, showing comparison of x-ray structures (blue) and last frame of MD simulation (red): (A) simulation of villin RMSD 1A (B) simulation of FiP35
Atomic-Level Characterization of the Structural Dynamics of Proteins
Science 15 October 2010: vol. 330 no

18. Why simulate motion? Predict structure Understand interactions
Understand properties
Experiment on what cannot be studied experimentally

19. Solvation models: water & salt are very important to molecular behavior. Must model as many water atoms as protein atoms (often more than molecule, explicit model).

20. Molecular Dynamics Molecules, especially proteins, are not static.
Dynamics can be important to function
Molecules allowed to interact for a period of time (fs steps)
Consider number of particles, timestep, total time duration, nanoseconds to microseconds (several CPU days to CPU years) (nanosecond simulation -> millions of calculations)
10usec simulation -> 3 months
Trajectories, not just minimum energy state.
MM ignores kinetic energy, does only potential energy
MD takes same force model, but calculates F=ma and calculates velocities of all atoms (as well as positions)

21. Anton massively parallel supercomputer
512-node machine: 17,000 nanoseconds of simulated time per day for a protein-water system consisting of 23,558 atoms. In comparison, MD codes running on general-purpose parallel computers with hundreds or thousands of processor cores achieve simulation rates of up to a few hundred nanoseconds per day on the same chemical system. (enabled first microsecond MD simulation, Science 2010) (modified Amber force field)
named after Anton van Leeuwenhoek : “the father of microscopy”

22. Folding@home : Distributed Computing Project
Stanford University (Vijay S Pande)
As of April 9, 2009 the peak speed of the project overall has reached over 5.0 native PFLOPS (8.1 x86 PFLOPS[18]) from around 400,000 active machines, including PS3. (Record)

23. Popular Molecular Dynamics Programs – Linux Based
AMBER (Peter Kollman, UCSF; David Case, Scripps)
CHARMM (Martin Karplus, Harvard)
GROMOS (Van Gunsteren, ETH, Zurich)

24. Docking Computation to assess binding affinity
Looks for conformational and electrostatic "fit" between proteins and other molecules
Optimization again: what position and orientation of the two molecules minimizes energy?
Large computations, since there are many possible positions to check, and the energy for each position may involve many atoms

25. Docking Similar equation A and B constants depending on atom type.
A determines the degree the attractiveness
B determines the degree of repulsion
q is the partial atomic charge

26. Molecular Docking Start with PDB file, homology model, etc
Add Hydrogens
Select Grid Box
Identify molecule to be docked
>10 runs, > 1 million evaluations
Genetic Algorithm

27. Molecular Docking (Example in TB) A B C D Isoniazid Steps:
H108
A139
P136
Heme
R104
W107
T314
L205
T314
D282
S315
W321
P232
S315
A281
G316
Isoniazid
I317
KatG Heme Binding Site is also the site of Isoniazid Activation
KatG Dimer with 2 heme molecules
Isoniazid Docked into the KatG active site
Steps:
Get crystal structure of protein from PDB
Get small molecule coordinates (DrugBank)
Use AutoDock
Add Hydrogens to both structures
Identify potential binding site, specify GridBox (center on heme) (dimensions 40x40x40)
Dock using Genetic Algorithm, 10 runs, 2,500,000 evaluations

28. Virtual Screening
Docking small ligands to proteins is a way to find potential drugs. Libraries
A small region of interest (pharmacophore) can be identified, reducing computation
Empirical scoring functions are not universal
Various search methods:
Rigid provides score for whole ligand (accurate)
Flexible breaks ligands into pieces and docks them individually

29. Docking example
Biotin docking with Streptavidin, from Olsen lab at Scripps

30. Macromolecular docking
Docking of proteins to proteins or to DNA
Important to understanding macromolecular recognition, genetic regulation, etc.
Conceptually similar to small molecule docking, but practically much more difficult
Score function can't realistically compute energies
Use either shape complementarity alone or some kind of mean field approximation

31. Docking Resources AutoDock http://autodoc.scripps.edu/