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Molecular Drug Design
(The Robotics Way)
Yogesh A. Girdhar
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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 tohelp them out and save the world.
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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.
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Proteins as Robots
You can think of proteinsas a BIG serial modularrobots, where eachmodule is an amino acid.
Generally we model aamino acid as a 2 d.o.f.robot.
There can be 100-1000sof amino acids in a
protein. C-space = {q|q (S1)2N},
N= # amino acids.
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What are Drugs?
Most drugs are moleculeswhich bind to a proteinreceptor.
More formally called a ligands.
They inhibit or enhance the
function of a protein byblocking the active site.
Ligands can also be modeledas a robot!
They are typically much
smaller molecules with 3-15rotatable bonds => 3-15d.o.frobot.
Example of a
ligand.
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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
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Some real Docking
Thermolysin protein with one of its
known inhibitors
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Models of Docking
Rigid Protein Docking Assume the configuration of protein cannot changeits 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 intoaccount
We chose a model and then simulate how a ligandbehaves around a receptor and see if it bind
BUT FIRST we need some kind of a guiding/scoringfunction.
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Scoring Function
We would like to have a function which:>>> given a configuration of protein and the ligand
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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.
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Scoring Function: Examples
Quantum mechanical models
Takes 5 days per configuration on a superduper computer
Van der Waals + Electrostatic Potentialenergy (very popular)
Hydrogen bonding
Surface Area
Combination of above
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Van der Waals + Electrostatic
Potential
E = Evan-der-Waals +EElectrostatic
VDW forces can be
used as molecularcollision detection.
VDW forces are onlyapplicable over small
distances. Electrostatic forcesare long range forces.
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The Docking Process
Several algorithms can be used to do the
docking
Monte Carlo
Simulated Annealing
Genetic Algorithms
PRM
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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)
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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?
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PRM : Sample Generation
Generate a random configuration
Compute its energy
Accept the configuration with the probability:
P(accepted) = 0 if Econfig > Emax= (Emax - Econfig)/(Exmax-Emin) if
Emin
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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.
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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)
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PRM: Distance Function
One possible distance function:
Maximum distance between any two
corresponding atoms .
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PRM: Local Planner
One possible local planner:- Connect by a straight line in C-space- Make sure the line path is energetically favorable(Nocollisions)- This can be done by chopping the local path into even
smaller pieces and computing the weight of each smallerpart.
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PRM: Local Planner
The weight should reflect the "difficulty" oftraversing the edge.- For i from 1 to n-1 (where n is the #
splittings of the path)- P(i to i+1) = e^(- (Ei+1 - Ei)/kT)------------------------------------------
e^(- (Ei+1 - Ei)/kT) + e^(- (Ei-1 -
Ei)/kT)- Basically favors decreasing energy paths
Weight of the local path isWeight = i (-log(P(i to i+1))
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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.
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Conclusion
Computational molecular docking is being used
more and more in pharmaceutical industry for
designing new drugs
At the moment the simplistic rigid protein modelis 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.
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Refrences
Molecular Docking: A Problem WithThousands of Degrees Of Freedom.
Teodoro, Philips, Kavaraki
A Motion Planning Approach to FlexibleLigand Binding
Singh, Latombe, Brutlag
Computational Approaches to DrugDesign
Kavraki, Finn
And the computer scientists save
the world again THE END
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