TimeEfficient Flexible

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Time-Efficient Flexible
Superposition of
Medium-sized Molecules
(Lemmen Lengauer)
Presented by Tamar Sharir
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Outline

• Definitions
• Goals in superposition of molecules
• Structural-Activity relations
• Problem definition
• Assumptions and simplifications
• Biologic background for the algorithm
• The main algorithm
• Modifications and improvments
• Results
• Summary

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What does it look like ?
Receptor
Ligand
Receptor Pocket
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Definitions

• Receptor- a protein, molecule which give a
  biological response upon uniting with
  chemically complementary molecules.
• Ligand - Small organic molecule, composed of
  atoms that forms a complex compound
• Receptor Pocket - The binding area (site)

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Definitions-Cont.

• Pharmacophore Model-Can be considered as the
  largest common denominator shared by a set of
  active molecules. Represent an abstract concept
  that accounts for the common molecular
  interaction capacities of a group of compounds
  towards their target structure

Receptor
Receptor
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Areas of Interests

• Pharmaceutical Research Area- design molecules
  that interfere with specific biochemical pathways
  in living systems.
• Drug Design Area -develop small organic molecules
  with a high affinity of binding towards a given
  receptor (competition)

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So we have a receptor and we have a ligand, where
is the problem???
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Structural-Activity Relationship

• 3D structure of receptor is enough
• But not always exists!
• In many cases, we only know a set of ligands
  together with their biological activities towards
  a receptor

• Structural activity relationship studies (3D
  QSAR) aim to correlate measured activities
  with structure-based properties of the
  ligands.

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What can we do with the results?

• Extract the relevant chemical features of ligands
• Create a pharmacophore model.
• Search ligands with the same activity
• Provide an estimate of the binding affinity of a
  novel ligand towards a given receptor
• Take the negative imprint of the set of
  superimposed ligands as a crude description of
  the binding pocket. (receptor modeling)

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The Problem in Visual
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Problem Definition

• Input 2 molecules
• The reference ligand - rigid, presented in the
  conformation inside the receptor packet
• The test ligand - flexible, given in an arbitrary
  conformation

Output the best structural alignment of the 2
molecules received in a short given time
besthighest score
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Overall Goal
Drastically reduce run time, while limiting the
inaccuracies of the model and the computation to
a tolerable level
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Existing Approaches

• Some methods need to be given the pharmacophore
  that displays the commonalities of both ligands
• Other methods treat both molecules as rigid
• Methods that handle molecular flexibility
  without extraneous knowledge of commonalities of
  both ligands are rare, but are in high demand

This method takes into account the molecular
flexibility of the test ligand and needs no
predefined information on the pharmacophore
shared by the reference and test ligands
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Assumptions Simplifications

• Reference and test ligands occupy maximally
  overlapping areas in space
• Reference and test ligands usually interact with
  the same functional group of the amino acids in
  the binding pocket
• Only pairs of ligands are considered (no multiple
  superposition of several ligands)
• Number of degrees of freedom is reduced to the
  torsional degree of freedom of the test ligand
• Atoms of the reference ligand are kept fixed in
  space.

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Why do we allow these simplifications?

• Strong binding requires optimal space-filling
  of the binding pocket
• The run time is small enough to perform
  several runs
• with different conformations of the reference
  ligand
• pairwise comparisons among a larger set of
  ligands.
• Runs can be performed independently and in
  parallel
• existing methods that can be used for
  refining the superposition
• The more rigid the molecules, the higher
  their binding affinity

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How do we score?
We will use physicochemical properties of the
ligands not only for scoring, but also for
generating the solutions
van der Waals volume
electrostatic potential
hydrogen-bonding donor and acceptor
potentials
hydrophobicity

• The two main contributions for scoring
• paired inter-molecular interactions
• 2. overlap volumes

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How we score? Cont.

• The contributions to the scoring function
  are divided into two groups called hard and soft
  criteria.
• The hard criteria can be used to generate
  placements and to reject unsatisfactory ones
  (example minimum threshold for the overlap
  volume serves as a criterion to reject
  unlikely placements)
• the soft criteria are used only for
  scoring and not for eliminating unlikely
  solutions (example the scoring terms for the
  paired intermolecular interactions)

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Paired Intermolecular Interactions
Intermolecular interactions with a
potential receptor atom that are plausible for
both ligands are paired and contribute a term to
the overall score.

• interaction surfaces are defined
• They amount to sections of a spherical surface
  surrounding the functional group of interest
• To each such interaction center a particular
  interaction type is attributed

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Paired Intermolecular Interactions
hypothetical receptor side
H
N
interaction surface
H
O
N
Test Ligand
Reference Ligand
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Paired Intermolecular Interactions
L1
Receptor
L2

• sets of paired intermolecular interactions are
  called matches
• To quantify the weight of a match, a scoring
  function is defined
• Summing over the contributions of all matches
  results in the match score

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Overlap volumes of different chemical properties
provide the major contributions to the binding
affinity towards the receptor

• We assume for two ligands, which achieve a
  similar binding affinity, that their chemical
  fingerprints inside the receptor pocket are
  similar
• The scoring scheme also considers the
  physicochemical properties of both ligands

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The Algorithm

• Fragmentation and determination
• of a base fragment

• Placement of the base fragment
• (onto the reference ligand)

• iterative Incremental construction of
• the entire test ligand

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1.Placing the Base Fragment

• approximate the interaction surfaces by sets of
  points
• search for nearly congruent triangles of such
  interaction points in both ligands.
• Each pair of nearly congruent triangles
  determines a unique transformation that
  superimposes one triangle in the first molecule
  onto the other triangle in the second molecule

Through this operation a possible placement
of the fragment under consideration is
defined
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1.Placing the Base Fragment-Cont.
(Data Structures) The triangles for the
reference ligand are stored in a triangle hash
table (RL-table) in a preprocessing step. A
query to this table, given a triangle from the
test ligand (query triangle), results in a list
of all triangles in the reference ligand that are
nearly congruent to
Pair consisting of the query triangle and a
triangle in this list defines one placement
of the base fragment over the reference ligand
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2. Clustering the query triangles

• we label each query triangle by the types of its
  corners (t(p1), t(p2) and t(p3), corresponding
  to the type of interaction points p1, p2 and
  p3) and the lengths of its sides (l(p1,p2),
  l(p2,p3) and l(p3,p1 ))
• 2. To make this label unique, the entries of the
  label t(pi), t(pj), t(pk), l(pi,pj),
  l(pj,pk), l(pk,pi) are ordered such that
  t(pi) lt t(pj) and t(pj) lt t(pk) hold

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Example
lt
Rule
p1
5.0
5.6
t(p1)t(p2)
p3
p2
t(p3)
8.1
Two possible orderings by type
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2. Clustering the query triangles-Cont.

• All query triangles are compiled in a list
  (called TL-list), which is sorted
  lexicographically by the triangle labels (The
  reason for doing so is to obtain contiguous
  segments of triangles with identical labels
  (called L-segments)
• query each triangle in the TL-list against the
  RL-table (In fact, we perform such queries only
  for the first triangle in each L-segment)
• The triangles which we retrieve from the RL-
  table are mapped onto each triangle in the L-
  segment.

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2. Clustering the query triangles-Cont.
Normally, we produce between several hundred
thousand up to millions of matches of triangles
and, consequently, as many possible
placements for the base fragment.
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2. Clustering the query triangles-Cont.
So how we reduce the number of query triangles??
1. Reject matches for which the additional
criterion for pairing interactions is missing
2. Van der Waals overlap volumes are computed
to filter out unsatisfactory solutions 3. Run an
efficient on-line procedure in order to
cluster similar placements
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3. On-Line Clustering of placements

• The first computed placement p0 is
• taken as a reference from now on.

• For every new placement pnew, the
• RMS deviation dnew from p0 is determined.
  

• Check if there is a cluster represented by a
• placement p that is similar to pnew

YES
NO
we merge p and pnew.

• pnew is retained as the
• representative of a new cluster.

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3. On-Line Clustering of placements-Cont.

• the search for p is restricted to clusters
  that have an RMS distance d to the reference p0
  which falls in the range of dnew -delta,dnew
  delta
• we sort all placements by their RMS distance d
  to p0.
• The sorted list is maintained as a leaf-
  chained search tree.
• In this tree, placements within the range
  dnew -delta,dnew delta form a continuous
  segment inside the leaf-chain

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So how do we know we received a good result of
the alignment???
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Evaluation Method
Data Sets

• How do we use the data sets?
• Lets say we take a receptor R and Ligands L1 and
  L2. According to the data set we know connections
  between some receptors and ligands. Lets assume
  we know the connection between receptor R and
  ligand L1 and the connection between receptor R
  and ligand L2.
• We wish to find connection between L1 and L2
• By matching the connections of R-L1 and R-L2 we
  get a connection between L1 and L2

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Evaluation Method-Cont.
The real Alignment derived from the Data-Sets
L2
L1
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Evaluation Method-Cont.
L2
L1
Our Result
RMS Deviation
The accuracy of the result
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RMS Results

• The quality of our results is measured in
  terms of the RMS deviation of the
  predicted from the measured orientation and
  conformation of the test ligand

• The mean RMS deviation is below 2 Å, and
  about 1 Å.

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Run time Results

• The mean run time over all test cases is
  below 4 minutes per instance

• The run time spent parts on the base placement
  and on the complex construction is about equal
• Only a minor fraction of the run time is spent on
  I/O and preprocessing

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Result Example
Black- Reference Ligand White-Test Ligand
(computed by our algorithm) Gray-The real result
(from the data set)
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Result Example
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Disadvantages of Method

• Inaccuracy of the solutions

• Prevent to produce better results for large
  ligands

• The requirement of the rigid reference ligand
  (not always known)

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Advantages of Method

• Quick superimposing

• Reasonable accurancy

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Method Summary

• Structural alignment of medium-sized organic
  molecules
• For applications in 3D QSAR and in
  receptor modeling
• Ligand flexibility is modeled by decomposing the
  test ligand into molecular fragments
• Superimposes a base fragment of the test ligand
  onto the reference ligand and then attaches the
  remaining fragments of the test ligand in
  a step-by-step fashion
• The run time on a single problem instance is a
  few minutes on a common-day workstation