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Molecular Drug Design The Robotics Way

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Title: Molecular Drug Design The Robotics Way


1
Molecular Drug Design(The Robotics Way)
  • Yogesh A. Girdhar
  • girdhy_at_cs.rpi.edu

2
The story so far
  • The biologists have discovered that HIV-1
    protease (a protein) binds to a molecule produced
    by the HIV virus, hence playing an important role
    in its lifecycle. They however dont know how to
    quickly design a drug to prevent this.
  • It is now up to the Computer Scientist to help
    them out and save the world.

3
Proteins
  • Proteins are the building blocks of life
  • Examples hormones , enzymes, antibodies.
  • The function of proteins depends on their shape.
  • They are a long chain(100-1000s) of amino acids.
  • 20 different kind of amino acids exist.

4
Proteins as Robots
  • You can think of proteins as a BIG serial modular
    robots, where each module is an amino acid.
  • Generally we model a amino acid as a 2 d.o.f.
    robot.
  • There can be 100-1000s of amino acids in a
    protein.
  • C-space qq e (S1)2N, N amino acids.

5
What are Drugs?
  • Most drugs are molecules which bind to a protein
    receptor.
  • More formally called a ligands.
  • They inhibit or enhance the function of a protein
    by blocking the active site.
  • Ligands can also be modeled as a robot!
  • They are typically much smaller molecules with
    3-15 rotatable bonds gt 3-15d.o.f robot.

Example of a ligand.
6
The Problem
  • Given a protein, find a ligand which
    geometrically and energetically binds to it.
  • The site where the drug binds is called binding
    site.
  • The process is called molecular docking.
  • How can we simulate this docking?

Oh boy! What a perfect match
7
Some real Docking
Thermolysin protein with one of its known
inhibitors
8
Models of Docking
  • Rigid Protein Docking
  • Assume the configuration of protein cannot change
    ? its rigid.
  • Most commonly used model at the moment.
  • Partial Protein Flexibility
  • Protein assumed to be flexible only at the
    binding site
  • Can be modeled by adding a few dof in the protein
    binding site to the combined protein/ligand
    C-space.
  • Full Protein Flexibility
  • All dof of the ligand and the protein are taken
    into account
  • We chose a model and then simulate how a ligand
    behaves around a receptor and see if it bind
  • BUT FIRST we need some kind of a guiding/scoring
    function.

9
Scoring Function
  • We would like to have a function which
  • gtgtgt given a configuration of protein and the
    ligand
  • ltltlt returns a number representing "goodness" or
    "energy" of the configuration.
  • Desired properties
  • (Ideally) Lowest value when the ligand is
    naturally docked.
  • Higher value everywhere else
  • Should be able to distinguish between correctly
    and incorrectly docked structures.
  • Should be fast! to compute.

10
No FREE Lunch
  • In generaral More accurate a scoring function,
    more expensive it is
  • Accurate means obeys/simulates all laws of
    physics (known or unknown)
  • Expensive means computationally expensive.

11
Scoring Function Examples
  • Quantum mechanical models
  • Takes 5 days per configuration on a super duper
    computer
  • Van der Waals Electrostatic Potential energy
    (very popular)
  • Hydrogen bonding
  • Surface Area
  • Combination of above

12
Van der Waals Electrostatic Potential
  • E Evan-der-Waals EElectrostatic
  • VDW forces can be used as molecular collision
    detection.
  • VDW forces are only applicable over small
    distances.
  • Electrostatic forces are long range forces.

13
The Docking Process
  • Several algorithms can be used to do the docking
  • Monte Carlo
  • Simulated Annealing
  • Genetic Algorithms
  • PRM

14
Monte Carlo
  • An Analogy
  • A blind man on a mountain trying to come down.
  • Choose a starting configuration
  • Randomly sample around this configuration
  • Take a "step" in the direction which lowers the
    energy (height)

15
Probabilistic Roadmaps
  • We are not interested in just finding a path.
  • We also want the path to be energetically
    favorable.
  • For this first we need energetically possible
    samples.
  • How do we do this?

16
PRM Sample Generation
  • Generate a random configuration
  • Compute its energy
  • Accept the configuration with the
    probabilityP(accepted) 0 if Econfig gt Emax
    (Emax - Econfig)/(Exmax-Emin) if
    EminltEconfigltEmax 1 if Econfig lt
    Emin
  • Notice we do not need to check for collisions
    since VDW energy takes care of that

17
PRM Binding Site Prediction
  • We can bias the sample generation so that
  • More sampling near the low energy areas on the
    surface of the protein.
  • The lowest energy points are possible binding
    sites.

18
PRM Roadmap Construction
  • For each node i Find k-nearest neighbors For
    each neighbor k Connect i,k using a local
    planner (if not already connected)

19
PRM Distance Function
  • One possible distance function
  • Maximum distance between any two corresponding
    atoms .

20
PRM Local Planner
  • One possible local planner- Connect by a
    straight line in C-space- Make sure the line
    path is energetically favorable(No collisions)-
    This can be done by chopping the local path into
    even smaller pieces and computing the weight of
    each smaller part.

21
PRM Local Planner
  • The weight should reflect the "difficulty" of
    traversing the edge.- For i from 1 to n-1 (where
    n is the splittings of the path) - P(i to i1)
    e(- (Ei1 - Ei)/kT)
    ------------------------------------------
    e(- (Ei1 - Ei)/kT) e(- (Ei-1 - Ei)/kT)-
    Basically favors decreasing energy paths
  • Weight of the local path is Weight Si
    (-log(P(i to i1))

22
PRM Docking
  • Run Dijkstra's to compute minimum weight paths
    with the possible docking sites as the source.
  • Compute average path weight for each possible
    docking site
  • The one with the lowest average weight is most
    likely to be the docking site.

23
Conclusion
  • Computational molecular docking is being used
    more and more in pharmaceutical industry for
    designing new drugs
  • At the moment the simplistic rigid protein model
    is being used the most
  • There is a need for more efficient algorithms to
    deal with flexible proteins efficiently.
  • Due to imperfect energy functions the existing
    methods are not perfect.

24
Refrences
  • Molecular Docking A Problem With Thousands of
    Degrees Of Freedom.
  • Teodoro, Philips, Kavaraki
  • A Motion Planning Approach to Flexible Ligand
    Binding
  • Singh, Latombe, Brutlag
  • Computational Approaches to Drug Design
  • Kavraki, Finn

And the computer scientists save the worldagain
THE END
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