Structure optimization and potential functions for AB-model proteins

1. Structure optimization and potential functions for AB-model proteins Sang Bub Lee (KNU, KIAS) Seung-Yeon Kim (KIAS)

2. Motivation • AB model with Fibonacci sequences in 2D and 3D exhibited different energy landscape. (In 2D there might be no folding transition.) • AB model in 3D with different energy functions exhibited different conformations. (Are the optimized structures folded or protein-like?) • In 2D lattice model, recent work reported that certain sequences exhibit no folding transition. What about 3D with a particular energy function?

3. AB-Model:off-lattice version of HP model [Stilinger et al., PRE 48, 1469 (1993)]A : hydrophobic, B : hydrophilic Fibonacci sequences: Four sequences:

4. Model I :Hsu, Mehra, and Grassberger (2003) Model II :Irback, Peterson, and Potthast (1997), Liang (2004)

5. 50* random conformations * Arbitrary numbers Energy minimization Copy Update Bank& Reduce First Bank Bank Generate 50* random conformations, minimize their energiesand add them to both Bank and First Bank Yes All used as a seed ? No No Minimum energy found ? Select 20* seeds Stop Yes Generate 3000 conformations (60* for each seed) by modifying seeds Energy minimization Global optimization method : conformational space annealing

6. D c u t D a A B E C a D A Global Minimum • Trial conformation:a • Bank conformations: A, B, C, D & E • The closest conformation A (to a) at a distance DaA. • If DaA < Dcut , a replaces A if a is lower in energy than A. • If DaA > Dcut , a replaces B, the highest energyconformation in thebank, if a, in addition, is lower in energy than B. • If a does not satisfy the “lower in energy” condition in either of the two cases, a is discarded.

7. Energy function: RMSD versus energy for low-lying local minimum energy conformations.

8. Optimized structures for Model I Model II

9. Table I. The lowest energies of Model I and Model II for the 3D AB model by CSA, in comparison with those by nPERMis, ELP, and ACMC, respectively. nPERMis : Hsu, Mehra, and Grassberger, Phys. Rev. E 68, 021113 (2003). ELP : Bachmann, Arkin , and Janke, Phys. Rev. E 71, 031906 (2005). ACMC : Liang, J. Chem. Phys. 120, 6756 (2004).

10. Are those optimized structures all proteinlike? Protein Low temp. RW Theta point SAW High temp. Collapse transition Folding transition Nu = 0.6 (SAW) Nu = 0.5 (RW) Nu < 0.5 (proteins)

11. Gyration radius AB-model proteins with Fibonacci sequences. Proteins of four different classes in the SCOP database

12. Energy components : Circle : bending term Square : LJ AA-interaction Triangle : LJ BB-interaction Diamond : LJ AB-interaction Cross : torsional term Inverted triangle : total energy Optimized structures for E1 Optimized structures for E2

13. Propose simple energy function • Take a bending energy term as simple. • Neglect the torsional energy term. • Vary the LJ attractive term. Green Cn(A,B) = 0 Red Cn(A,B) = 0.5 Gyration radii of the optimized structures for various energy functions

14. Conclusions • • The AB-attractive interaction is crucial for folded structures. • Folding transition need to be examined carefully using, e.g., the • partition-function zero method. (This is on-going project.)