Dead-End Elimination for Protein Design with Flexible Rotamers

1. Dead-End Eliminationfor Protein Designwith Flexible Rotamers Ivelin Georgiev Donald Lab 02/19/2008

3. Computational Design wildtype energy function input structure rotamer library protein design algorithm stability specificity novel function drug design mutant …

4. C MinDEE provable energy minimization ensembles partition function ε-approximation algorithm q q* Contributions redesign for Leu

5. Desmet et al., 1992 Traditional-DEE it ir E upper bound E lower bound fixed backbone/side-chains rotamer pruning ir O(q2n2) E it conformations Enumerate GMEC

6. Conformations Traditional-DEE with Rigid Rotamers/Backbone Energy it

7. Conformations Traditional-DEE with Side-chain Dihedral Flexibility min Energy max it

8. C C C Traditional-DEE MinDEE Traditional-DEE E minimization E minimization rigid energies X √ √ not provably-correct provably-correct provably-correct

9. C MinDEE E minimization √ provably-correct

10. continuous side-chain dihedral space MinDEE voxels bound rotamer movement

11. lower/ upper energy bounds ir MinDEE it js ir Energy E(ir , js) js χir ir js χjs

12. pruning candidate lower/ upper energy bounds ir it competitor js witness MinDEE: - - > 0 lowerbound on ir conformation energies upperbound on it conformation energies possible energy changes due to rotamer movement not in trad-DEE

13. MinDEE: Side-chain Dihedral Flexibility traditional-DEE MinDEE

14. MinDEE Applications

15. min K*: provably-accurate approximation to the binding constant via conformational ensembles ∫ a 1 Z GMEC-based MinDEE Applications single lowest-energy conformation Ensemble-based JCB’05 weighted average

16. MinDEE/A*: GMEC-based Method

17. C’ MinDEE/A*: GMEC-based Method C MinDEE pruning O(n2r2) A* search (E lower bounds) full E minimization

18. C’ MinDEE/A*: GMEC-based Method C MinDEE pruning O(n2r2) A* search (E lower bounds) full E minimization

19. C’ MinDEE/A*: GMEC-based Method C MinDEE pruning O(n2r2) A* search (E lower bounds) … full E minimization …

20. C’ … … MinDEE/A*: GMEC-based Method C MinDEE pruning O(n2r2) A* search (E lower bounds) … … full E minimization minGMEC B(c) > E(best)

21. Hybrid-K*: Ensembles Method

22. C’ Hybrid-K*: Ensembles Method Volume filter seq1 C DEE pruning A* search (E lower bounds) … … full E minimization p’ q*

23. C’ Hybrid-K*: Ensembles Method Volume filter seq1 C DEE pruning A* search (E lower bounds) … … full E minimization p’ q*

24. C’ Hybrid-K*: Ensembles Method C DEE pruning A* search (E lower bounds) … full E minimization p’ q* q* < (1-ε)q

25. C’ Hybrid-K*: Ensembles Method repeat search C C DEE pruning DEE pruning C’ A* search (E lower bounds) A* search (E lower bounds) … … … full E minimization full E minimization p’ p’ q* q* q* < (1-ε)q q* ≥ (1-ε)q

26. C’ C’ Hybrid-K*: Ensembles Method Volume filter seq1 seqn … C C DEE pruning DEE pruning A* search (E lower bounds) A* search (E lower bounds) … … … full E minimization full E minimization p’ q* q* q* ≥ (1-ε)q q* ≥ (1-ε)q

27. C’ Hybrid-K*: Inter-mutation Pruning Volume filter seq1 seqn C C DEE pruning A* search (E lower bounds) … full E minimization p’ q* q* ≥ (1-ε)q

28. C’ C’ Hybrid-K*: Inter-mutation Pruning Volume filter seq1 seqn … C C DEE pruning DEE pruning A* search (E lower bounds) A* search (E lower bounds) … … full E minimization full E minimization p’ p’ q* q* Ķ*n K*i <

29. C’ C’ Hybrid-K*: Inter-mutation Pruning Volume filter seq1 seqn … C C DEE pruning DEE pruning A* search (E lower bounds) A* search (E lower bounds) … … … full E minimization p’ full E minimization p’ q* q* q* < (1-ε)q K*i >>> Ķ*n

30. C’ C’ Hybrid-K*: Intra-mutation Pruning Volume filter seq1 seqn … C C DEE pruning DEE pruning A* search (E lower bounds) A* search (E lower bounds) … … … full E minimization full E minimization p’ q* q* q* ≥ (1-ε)q q* ≥ (1-ε)q

31. this work previous Results Traditional-DEE single structure rigid energies MinDEE: GMEC-based K* (RECOMB’04) E minimization ensembles MinDEE: Ensembles

32. Structural Model • 1AMU (Conti et al., 1997) • Residues: 39 • flexible: 9 • steric shell: 30 • Flexible ligand • AMP • Richardsons’ rotamer library • AMBER (vdW,elect,dihed) + EEF1 • 2-point mutation search for Leu • GAVLIFYWM allowed GrsA-PheA Active Site

33. trad-GMEC  minGMEC Comparison to Traditional-DEE • trad-GMEC ranked 397th • E(minGMEC) < E(rigid-GMEC) by ≈ 6 kcal/mol minGMEC: * minGMEC rotamer pruned by traditional-DEE

34. Top 40 Mutations – Hybrid-K* Hybrid-K* • Computational • 9 hrs. on 24 processors • Original K* fully-evaluated 30% more conformations • K* w/o filters: ≈ 3,263 days • Predictions • T278M/A301G (Stachelhaus et al., 1999) ranked 3rd • G301 in all known natural Leu adenylation domains • Experimental verification

35. MinDEE/A* Top 40 Mutations – MinDEE/A* • Ew = 12.5 kcal/mol • 4 days on a single processor • 206 of 421 rotamers pruned • over 60,000 extracted conformations • 7,261 conformations (221 unique sequences) within Ew • minGMEC: A236M/A322M Rotamer Diversity for A236M/A322M Conf Energies vs. RMSD for A236M/A322M 

36. Top 40 Mutations – Hybrid-K* Conclusions and Future Work • Traditional-DEE not correct with energy minimization • MinDEE provably-correct and efficient • MinDEE capable of returning lower-energy conformations • Ensemble-based and GMEC-based redesign predictions are substantially different • MinDEE: Ensembles Method successfully predicts both known and novel redesigns • Improve MinDEE pruning efficiency • Improve model accuracy • Marriage of MinDEE and BD

37. Acknowledgments • Bruce Donald • Ryan Lilien • Amy Anderson • Serkan Apaydin • John MacMaster • Tony Yan • All members of Donald Lab Funding: • NIH • NSF