Molecular Mechanics, Molecular Dynamics, and Docking
Michael Strong, PhD
National Jewish Health
University of Colorado, Denver
Foldit
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. 2002 Apr 19;296(5567):525-30.
Experimental Methods provide clues
to less rigid regions
X-ray crystallography
NMR
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)
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.
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
Molecular Mechanics Pros/Cons
Pros:
• 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
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)
The energy equation
(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 forcefield. (potential energy)
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
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
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, CC-H, etc.)
Torsion Energy
Energy needed to rotate about bonds. Only relevant to single bonds
A controls the amplitude of the curve
n controls its periodicity
 shifts the entire curve along the
rotation angle axis ().
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-CC, C-O-C-N, H-C-C-H, etc.)
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
A determines the degree the attractiveness
B determines the degree of repulsion
B determines the degree of repulsion
q is the charge
q is the partial atomic charge
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
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. 6002 341-346
Why simulate motion?
•
•
•
•
Predict structure
Understand interactions
Understand properties
Experiment on what cannot be studied
experimentally
• 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).
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)
Anton
massively parallel supercomputer
512-node machine: 17,000 nanoseconds of simulated time per day for a proteinwater 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”
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)
Popular Molecular Dynamics Programs – Linux Based
AMBER (Peter Kollman, UCSF; David Case, Scripps)
CHARMM (Martin Karplus, Harvard)
GROMOS (Van Gunsteren, ETH, Zurich)
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
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
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
Molecular Docking
(Example in TB)
A
B
C
Heme
W107
H108
W321
Isoniazid
KatG Dimer with 2
heme molecules
R104
T314
S315
KatG Heme Binding Site is
also the site of Isoniazid
Activation
D
P136 A139
L205
P232
T314 D282
S315 A281
G316
I317
Isoniazid Docked into the
KatG active site
Steps:
1. Get crystal structure of protein from PDB
2. Get small molecule coordinates (DrugBank)
3. Use AutoDock
4. Add Hydrogens to both structures
5. Identify potential binding site, specify GridBox (center on heme) (dimensions 40x40x40)
6. Dock using Genetic Algorithm, 10 runs, 2,500,000 evaluations
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
Docking example
Biotin docking with Streptavidin, from Olsen lab at Scripps
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
Docking Resources
• AutoDock http://autodoc.scripps.edu/
• Dock
http://www.cmpharm.ucsf.edu/kuntz/dock.html