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A Kinematic View of Loop Closure

A Kinematic View of Loop Closure. EVANGELOS A. COUTSIAS, CHAOK SEOK, MATTHEW P. JACOBSON, KEN A. DILL. Presented by Keren Lasker. Agenda. Problem definition The Tripeptide Loop-Closure Problem Generalization Applications. The Loop Closure problem.

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A Kinematic View of Loop Closure

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  1. A Kinematic View of Loop Closure EVANGELOS A. COUTSIAS, CHAOK SEOK, MATTHEW P. JACOBSON, KEN A. DILL Presented by Keren Lasker

  2. Agenda • Problem definition • The Tripeptide Loop-Closure Problem • Generalization • Applications

  3. The Loop Closure problem Finding the ensemble of possible backbone structures of a chain segment of a protein that is geometrically consistent with preceding & following parts of the chain whose structures are given. SER ILE HIS ASP ALA ALA THR SER LEU ASN

  4. R R R Constants : bond lengths, bond angles Variables : backbone torsions

  5. Special case • Six free rotation angles • The angles form three/four rigid pairs

  6. R R R

  7. Moving to a coarser problem

  8. The Tripeptide Loop-Closure Problem Problem definition : Special case six torsion angles at three Ca atoms located consecutively along a peptide backbone. The atoms are fixed in space Output : The exact position of the loop atoms 3 variables 3 constrains

  9. C N Notation

  10. Finding the bonds length

  11. d

  12. Moving to a polynomial equation

  13. r2 r1 Derivation of a 16th Degree Polynomial for the 6-angle Loop Closure

  14. Find the rotation angles Position the atoms

  15. Noncontiguous Ca atoms The problem characteristic do not depend on the Ca atoms continuity

  16. Additional Dihedral Angle

  17. Rigid sampling coverage of the real protein structure space Dataset : Top500

  18. sampling with perturbation 5 degree perturbation of the NCaC angles 10 degree perturbation of the NCaC angles

  19. Application to Loop Modeling • Use PLOP to sample all the torsions except for a three residue gap in the middle of the loop.

  20. Plop - 0.29(459,0.73) 1.66(236,1.6) 3.25(42,106) 0.27(5000,8.5) 1.04 (5000,6.1) 1.89(5000,23)

  21. Thank you !

  22. Moving to a polynomial equation

  23. Moving to a polynomial equation

  24. This extends to the orientation of Cb

  25. A bimodal example

  26. Theta-perturbations are not enough

  27. Biological motivation • Homology modeling • Monte Carlo simulation

  28. TODO • Check that the bond angles are really constant in proteins? • Which angles do we try to find in the coarser proble m? • Why the consec helps , what is the big problem in non consecutive ? • Condtion 3 in the special case?

  29. R N C C N C R

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