Molecular Drug Design

7/29/2019 Molecular Drug Design

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Molecular Drug Design

(The Robotics Way)

Yogesh A. Girdhar

[[email protected]]


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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

Molecular Drug Design

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