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A Path Planning Approach for Computing A Path Planning Approach for Computing Large- -Amplitude Motions of Flexible Molecules Amplitude Motions of Flexible Molecules Large Juan Corts & Thierry Simon MOVIE Workshop, Toulouse,

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SLIDE 1

A Path Planning Approach for Computing A Path Planning Approach for Computing Large Large-

  • Amplitude Motions of Flexible Molecules

Amplitude Motions of Flexible Molecules

Juan Cortés & Thierry Siméon

MOVIE Workshop, Toulouse, 7-8/01/2005

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SLIDE 2

MOVIE Workshop, Toulouse, 7-8/01/2005

Context : Computational Biology Context : Computational Biology

( Interaction )

Bio-informatics Molecular modeling Flexibility

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SLIDE 3

MOVIE Workshop, Toulouse, 7-8/01/2005

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Protein Flexibility Protein Flexibility

Local

  • vs. Global

Low

  • vs. Strong

Side chains Plasticity Loop motions Domain motions

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SLIDE 4

MOVIE Workshop, Toulouse, 7-8/01/2005

Difficulty : Complexity of Potential Energy Difficulty : Complexity of Potential Energy

Electrostatic Other Lennard Jones Torsion Bending Stretching

: H bonds, hydrophobic interactions ,…

Bonded terms Non-bonded terms

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SLIDE 5

MOVIE Workshop, Toulouse, 7-8/01/2005

Potential Energy Potential Energy → → Geometric Constraints Geometric Constraints

Electrostatic Other Lennard Jones Torsion Bending Stretching Bonded terms Non-bonded terms

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SLIDE 6

MOVIE Workshop, Toulouse, 7-8/01/2005

A Two A Two-

  • Stage Approach

Stage Approach

  • Exploration under geometric

constraints Motion planning algorithms

Filtering

  • Energy-based exploration

Classical molecular modeling methods New methods ?

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SLIDE 7

MOVIE Workshop, Toulouse, 7-8/01/2005

Geometric Tools : Collision Detection Geometric Tools : Collision Detection

Challenge: Self-collisions of highly articulated mechanisms BioCD

[Robotics’05 (submitted)]

  • Tailored for protein models
  • Dual structure (kd-trees)
  • first level
  • second level
  • Many d.o.f. change simultaneously
  • Performance: Hundreds of tests/second
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SLIDE 8

MOVIE Workshop, Toulouse, 7-8/01/2005

Geometric Tools : Conformational Sampling Geometric Tools : Conformational Sampling

Kinematic loop closure → → → → RLG [ICRA’02]

loop 1 loop 2 loop 3

  • active variables

→ → → → qa

  • passive variables →

→ → → qp active subchain(s) passive subchain non-redundant mechanism

  • planar : 3 d.o.f.
  • spatial : 6 d.o.f.

Mechanical system decomposition

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SLIDE 9

MOVIE Workshop, Toulouse, 7-8/01/2005

Geometric Tools : Conformational Sampling Geometric Tools : Conformational Sampling

Active variables ← ← ← ← guided sampling Passive variables ← ← ← ← inverse kinematics

Kinematic loop closure → → → → RLG [ICRA’02]

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SLIDE 10

MOVIE Workshop, Toulouse, 7-8/01/2005

Geometric Tools : Conformational Sampling Geometric Tools : Conformational Sampling

begin end rigid unit dihedral angle

  • Main chain (backbone)
  • Side chains

Protein loop [J Comput Chem 04]

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SLIDE 11

MOVIE Workshop, Toulouse, 7-8/01/2005

Geometric Tools : Conformational Sampling Geometric Tools : Conformational Sampling

begin end rigid unit dihedral angle

  • passive subchain
  • general 6R IK + BioCD
  • Main chain (backbone)
  • active subchain
  • RLG & BioCD
  • Side chains

Protein loop [J Comput Chem 04]

  • random sampling + BioCD
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SLIDE 12

MOVIE Workshop, Toulouse, 7-8/01/2005

Geometric Tools : Conformational Exploration Geometric Tools : Conformational Exploration

Incremental search → → → → RRT [LaValle and Kuffner, 2001] DD-RRT [ICRA’05]

Good performance in very constrained search space

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SLIDE 13

MOVIE Workshop, Toulouse, 7-8/01/2005

Applications : Analysis of Protein Loop Mobility Applications : Analysis of Protein Loop Mobility

Xylanase

from Thermobacillus xylanilyticus

Flexible loop : 69 d.o.f.

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SLIDE 14

MOVIE Workshop, Toulouse, 7-8/01/2005

Applications : Analysis of Protein Loop Mobility Applications : Analysis of Protein Loop Mobility

Conformational sampling

Two-step simulated annealing → Several days of work Geometric approach → Up to few minutes Energetically feasible conformation from geometrically feasible one → RMSD = 0.65 Å

Hydrogen bond network

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SLIDE 15

MOVIE Workshop, Toulouse, 7-8/01/2005

Applications : Analysis of Protein Loop Mobility Applications : Analysis of Protein Loop Mobility

Xylanase

from Thermobacillus xylanilyticus

Exploration with RRT

  • 5000 nodes
  • < 1 hour

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Mutated Xylanase

(deletion 111, 121)

Prediction for directed mutagenesis

Conformational exploration

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SLIDE 16

MOVIE Workshop, Toulouse, 7-8/01/2005

Deep active site (17Å)

Applications : Applications : Ligand Ligand-

  • Protein

Protein Accessibility Pathways Accessibility Pathways

Bulkholderia cepacia Lipase Ligand and side-chain flexibility : 45 d.o.f.

Prediction of enzymatic enantioselectivity

R enantiomer S enantiomer

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SLIDE 17

MOVIE Workshop, Toulouse, 7-8/01/2005

Applications : Applications : Ligand Ligand-

  • Protein

Protein Accessibility Pathways Accessibility Pathways

Ligand: (R)-ph(Br)Et Ligand: (S)-ph(Br)Et

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Prediction of enzymatic enantioselectivity

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SLIDE 18

MOVIE Workshop, Toulouse, 7-8/01/2005

Applications : Applications : Ligand Ligand-

  • Protein

Protein Accessibility Pathways Accessibility Pathways

Similar trajectories and energetic profiles

Correlation of results

Computing time = 3 days Computing time = 30 minutes (including energy minimization) Pseudo-molecular dynamics Two-stage approach

energy-based approach

  • 40
  • 35
  • 30
  • 25
  • 20
  • 15
  • 10

4,5 5,5 6,5 7,5 8,5 9,5 10,5

distance ()

R S

two-stage approach

  • 40
  • 35
  • 30
  • 25
  • 20
  • 15
  • 10

4,5 5,5 6,5 7,5 8,5 9,5 10,5

distance ()

R S

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SLIDE 19

MOVIE Workshop, Toulouse, 7-8/01/2005

Applications : Applications : Ligand Ligand-

  • Protein

Protein Accessibility Pathways Accessibility Pathways

Computing time ratio ~ enantioselectivity

Correlation of results

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SLIDE 20

MOVIE Workshop, Toulouse, 7-8/01/2005

Future Work Future Work

  • Automatic identification of flexible regions

→ Normal mode analysis

Ligand-protein Protein-protein

  • Integrating loop motions in the analysis of interactions
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SLIDE 21

MOVIE Workshop, Toulouse, 7-8/01/2005

A Path Planning Approach for Computing A Path Planning Approach for Computing Large Large-

  • Amplitude Motions of Flexible Molecules

Amplitude Motions of Flexible Molecules

Juan Cortés Thierry Siméon jcortes@laas.fr nic@laas.fr

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SLIDE 22

MOVIE Workshop, Toulouse, 7-8/01/2005