Alignment of Flexible

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Alignment of Flexible Molecular Structures
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Motivation

• Proteins are flexible. One would like to align
  proteins modulo the flexibility.
• Hinge and shear protein domain motions
  (Gerstein, Lesk , Chotia).
• Conformational flexibility in drugs.

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Motivation
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Flexible protein alignment without prior hinge
knowledge

• FlexProt - algorithm
• detects automatically flexibility regions
• exploits amino acid sequence order

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Examples
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Experimental Results
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• Task largest flexible alignment by decomposing
  the two molecules into a minimal number of rigid
  fragment pairs having similar 3-D structure.

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FlexProt Main Steps
Detection of Congruent Rigid Fragment Pairs
Joining Rigid Fragment Pairs
Rigid Structural Comparison
Clustering (removing ins/dels)
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Structural Similarity Matrix
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Detection of Congruent Rigid Fragment Pairs
i1
i-1
i
j-1
j1
j
vi-1 vi vi1 wj-1 wj wj1
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FlexProt Main Steps
Detection of Congruent Rigid Fragment Pairs
Joining Rigid Fragment Pairs
Rigid Structural Comparison
Clustering (removing ins/dels)
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How to Join Rigid Fragment Pairs ?
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Graph Representation
Graph Node
Graph Edge
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Graph Representation

• The fragments are in ascending order.
• The gaps (ins/dels) are limited.
• Allow some overlapping.

W
a
b
Size of the rigid fragment pair (node b) - Gaps
(ins/dels) - Overlapping
Penalties
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Graph Representation

• DAG (directed acyclic graph)

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W_k
W_m
W_n
W_t
W_i

• Single-source shortest paths
• O(EV)

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FlexProt Main Steps
Detection of Congruent Rigid Fragment Pairs
Joining Rigid Fragment Pairs
Rigid Structural Comparison
Clustering (removing ins/dels)
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Clustering (removing ins/dels)
T1
T2
If joining two fragment pairs gives small RMSD
(T1 T2) then put them into one cluster.
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FlexProt Main Steps
Detection of Congruent Rigid Fragment Pairs
Joining Rigid Fragment Pairs
Rigid Structural Comparison
Clustering (removing ins/dels)
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Rigid Structural Comparison
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Multiple Structural Alignment
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Multiple Structural Alignment Schemes

• Linear progressive. Starts with one object and
  successively compares the other objects to the
  results.

• Tree progressive. The alignment is created
  according to a similarity tree. The alignment
  direction is from the leaves to the tree root.
• Gerstein and Levitt 1998.
• Orengo and Taylor 1994. SSAPm method.
• Sali and Blundell 1990
• Russell and Barton 1992
• Ding et al. 1994

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Multiple Structural Alignment Schemes

• Pivot. Uses one object as the pivot and compares
  it to all other objects. The results are then
  analyzed to find the common similarities.
• Leibowitz, Fligelman, Nussinov, and Wolfson 1999.
  Geometric Hashing technique.
• Escalier, Pothier, Soldano, Viari 1998. Exploits
  all common substructures.

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Multiple Structural Alignment Schemes

• Optimization Techniques.
• Guda, Scheeff, Bourne, Shindyalov. Monte Carlo
  optimization.

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Previous Work Multiple Structural Alignment

• Disadvantages
• Most methods do not detect partial solutions.
• The methods which detect partial solutions are
  not efficient for a large number of molecules.

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Partial Solutions
B

• Detection of local similarities.
• Detection of subset of molecules that share some
  local structural pattern.

A
A
B is harder to detect than A
A
B
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Largest Common Point Set (LCP)
Given two point sets detect the largest common
sub-set. exact congruence or e-congruence
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Solution Space

• The number of solutions, which answer the minimal
  criteria, could be exponential.

a-1
a-2
a-3
323 kM
a-1
a-2
a-1
a-2
a-3
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Partial Multiple-LCP
Detect t largest alignments between exactly k
molecules. We are interested in above solutions
for each k, 2 ? k ? m.
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MultiProt
/home/silly6/mol/demos/MultiProt/

• Non-predefined Pattern detection.
• Partial Solutions.
• Time Efficient
• 5 protein in 14 seconds
• 20 proteins (500 a.a.) in 10 minutes
• 50 proteins (200 a.a.) in 19 minutes
• PentiumII 500MHz 512Mb memory

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Algorithm Features

• Assumption any multiple alignment of proteins
  should align, at least short, contiguous
  fragments (minimum 3 points) of input points.
• Reduction of solution space The aligned
  contiguous fragments are of maximal length.
• All (almost, because of e-congruence) possible
  solutions (transformations) are detected (optimal
  solutions are hard to select).

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Multiple Alignment with Pivot
Input Pivot Molecule Mp
(participates in all solutions) Set of Molecules
SS\Mp Error Threshold e

• Detect all possibly aligned fragments of maximal
  length between the input molecules (chance to
  detect subtle similarities).
• Select solutions that give high scoring global
  structural similarity.
• Iterate over all possible pivots, Mp M1 Mm

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Bio-Core Detection

• Geom. Bio. Constraints
• Classification
• hydrophobic (Ala, Val, Ile, Leu, Met, Cys)
• polar/charged (Ser, Thr, Pro, Asn, Gln, Lys,
  Arg, His, Asp, Glu)
• aromatic (Phe, Tyr, Trp)
• glycine (Gly)

Or any other scoring matrix!
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Experimental Results
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Superhelix, 5 molecules.
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Concavalin, 6 molecules.
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Partial Solution Detection
B
1adj 1hc7 1qf6 1ati
A
Task to detect A and B
x
B
A
z
A
y
B
A
B
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• Domain A ranked first (142 matched atoms)
• Domain B ranked eightth (85 matched atoms)

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4 proteins aligned based on detected domain A
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Multiple Alignment of domain A
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Multiple Alignment of domain A (enlarged)
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4 proteins aligned based on domain B
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Multiple Alignment of domain B
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Multiple Alignment of domain B (enlarged)
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Application to G proteins
A
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Substrate assisted catalysis application to G
proteins
Substrate assisted catalysis application to G
proteins. Mickey Kosloff and Zvi Selinger, TRENDS
in Biochemical Sciences Vol.26 No.3 March 2001
161
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Aspects of Structural Comparison

• A large number of structures (hundreds)
  Molecular Dynamics.
• Structural flexibility proteins are not rigid
  structures.
• Structure representation
• C-alpha atoms are suitable for comparisons of
  folds.
• Detection of similar function requires different
  representation. This brings another problem
  side chain flexibility.
• Sequence order in structural alignment.
• Detection of active sites might require different
  approach. Proteins with different folds might
  provide the same function.
• Statistical Significance
• Measure of geometrical similarity (RMSD,
  bottleneck, ), biological scoring function.

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Molecular Surface Representation

• Applications to docking

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Motivation

• Prediction of biomolecular recognition.
• Detection of drug binding cavities.
• Molecular Graphics.

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Rasmol Spacefill display
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1. Solvent Accessible Surface SAS2.
Connolly Surface
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Connollys MS algorithm

• A water probe ball (1.4-1.8 A diameter) is
  rolled over the van der Waals surface.
• Smoothes the surface and bridges narrow
  inaccessible crevices.

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Connollys MS algorithm - cont.

• Convex, concave and saddle patches according to
  the no. of contact points between the surface
  atoms and the probe ball.

• Outputs pointsnormals according to the
• required sampling density (e.g. 10 pts/A2).

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Example - the surface of crambin
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Critical points based on Connolly rep. (Lin,
Wolfson, Nussinov)

• Define a single pointnormal for each patch.
• Convex-caps, concave-pits, saddle - belt.

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Critical point definition
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Connolly gt Shou Lin
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Solid Angle local extrema
hole
knob
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Chymotrypsin surface colored by solid angle
(yellow-convex, blue-concave)
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Protein-protein and Protein-ligand Docking

• The geometric filtering

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Shape Complementarity
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Geometric Docking Algorithms

• Based on the assumption of shape complementarity
  between the participating molecules.
• Molecular surface complementarity -
  protein-protein, protein-ligand, (protein -
  drug).
• Hydrogen donor/acceptor complementarity -
  protein-drug.
• Remark usually protein here can be replaced
  by DNA or RNA as well.

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Issues to be examined when evaluating docking
methods

• Rigid docking vs Flexible docking
• If the method allows flexibility
• Is flexibility allowed for ligand only, receptor
  only or both ?
• No. of flexible bonds allowed and the cost of
  adding additional flexibility.
• Does the method require prior knowledge of the
  
• active site ?
• Performance in unbound docking experiments.
• Speed - ability to explore large libraries.

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General Algorithm outline

• Calculate the molecular surface of the receptor
  and the ligands and their interest points (
  normals).
• Match the interest points and recover candidate
  transformations.
• Check for inter-molecule and intra-molecule
  penetrations and score the amount of contact.
• Rank by geom-score/energies.

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Shape feature and signature (Norel et al.)
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Unbound docking examples
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GGH based flexible docking
Applies either to flexible ligands or to flexible
receptors.
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Flexible DockingCalmodulin with M13 ligand
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Flexible Docking HIV Protease Inhibitor