What determines the structure of the native folds of proteins?

1. What determines the structure of the native folds of proteins? Antonio Trovato INFM Università di Padova

2. Outline • Protein folding problem: native sequences vs. structures - sequences are many and selected by evolution - folds are few and conserved • Simple physical model capturing of main folding driving forces: hydrophobicity, sterics, hydrogen bonds • Protein energy landscape is presculptedby the general physical-chemical properties of the polypeptide backbone

3. Protein Folding Problem • Central Dogma of Molecular Biology: DNA  RNA  Amino Acid Sequence (primary structure)  Native conformation (tertiary structure)  Biological Function • Anfinsen experiment: small globular proteins fold reversibly in vitro to a unique native state  free energy minimum • Which Hamiltonian? • Which structure? • Levinthal paradox: how does a protein always find its native state in ms-s time?

4. Energy landscape paradygm(from cubic lattice models) Energy • Levinthal paradox: how to reconcile the uniqueness of the native state with its kinetic accessibility? • Principle of minimal frustration Energy-entropy relationship is carving a funnel for designed sequences in the energy landscape Conformations Energy Conformations

5. However Only a Limited Number of Fold Topology Exists Protein sequences have undergone evolution but folds have not…. they seem immutable • - M. Denton &C. Marshall, Nature 410, 417 (2001). • - C. Chotia & A.V. Finkelstein, Annu. Rev. Biochem. 59, 1007 (1990). • C. Chotia, Nature 357, 543 (1992). • C. P. Pointing & R.R. Russel, Annu. Rev. Biophys. Biomol. Struct. 31, 45 (2002). • A.V. Finkelstein, A.M. Gutun & A.Y. Badretdinov, FEBS Lett. 325, 23 (1993).

6. Most commonsuperfolds the same fold can housemany different sequencesand perform severalbiological functions can the emergence of a rich yet limited number of folds be explained by means of simple physical arguments?

7. Folding Compactness-Hydrophobicity H P Solvent

8. Hydrogen bond is consistent with a b and motifs. Secondary structures Linus Pauling: L. Pauling & R.B. Corey,Conformations of polypeptides chains with favoredorientations around single bonds: two new plated sheets, PNAS 37, 729-740 (1951); ibid with H.R. Branson 205-211.

9. Steric constraints Ramachandran plot: Only certain regions in the phi-psi plane are allowed for most of the a.a.; constraints are specific G.N. Ramachandran & Sasisekharan, Conformations of polypeptides and proteins, Adv. Protein. Chem. 23, 283-438 (1968).

10. Strong Hint Both hydrogen bonding and steric interaction encourage secondary structure

11. ThickHomopolymersFeatures &Motivations • Chain directionality breaks rotational symmetry of the tethered objects. • Need for a three body interaction. • Continuum limit without singular interaction potentials  2-body interaction must be discarded. • Nearby objects due to chain constraint do not necessarily interact. • Compact phase of relatively short thick polymers are different from the compact phase of the standard string and beads model. O. Gonzalez & J.H. Maddocks,PNAS 96, 4769 (1999). J.R. Banavar, O. Gonzalez, J.H. Maddocks & A. Maritan,J. Stat. Phys.110,35(2003). A. Maritan, C.Micheletti, A. Trovato & J.R. Banavar, Nature 406, 287 (2000) . J.R. Banavar, A. Maritan, C. Micheletti & A. Trovato, Proteins. 47, 315 (2002). J.R. Banavar, A. Flammini, D. Marenduzzo, A. Maritan & A. Trovato, ComPlexUs 1, 8 (2003).

12. Optimal packing of short tubes leads to the emergence of secondary structures Nearly parallel placement of different nearby portions of the tube Optimal helix (pitch/radius=2.512..): generalization of Kepler problem for hard spheres

13. - C Representa tion a Formulation of the Model • Tube Constraint (three-body constraint) • Hydrogen bonding geometric constraint • Hydrophobic interaction: eW • Local bending penalty: eR

14. j rij i j+1 i+1 j-1 binormals at the j-th and i-th residues Formulation of the Model: Rules. H-BondFrom 600 proteins in the PDB

15. Local i – i+3 eH = -1 Non-Local i – i+5, i+6,… eH = -0.7 Cooperativityecoop = -0.3 How Many Parameters? Hydrogen bonding Remark: no H-bond between i – i+4 !

16. 4 3 2 1 0 eR Structureless Compact Swollen -5 -4 -3 -2 -1 0 +1 +2 +3 +4 eW Ground State Phase Diagram eR = bending penalty ew = water mediated hydrophobic interaction No sequence specificity: HOMOPOLYMER ?

17. bending energy 4 3 2 1 0 eR Structureless Compact Swollen -5 -4 -3 -2 -1 0 +1 +2 +3 +4 eW attraction energy Ground State Phase Diagram

18. Ground State Phase Diagram

19. All Minima In The Vicinity Of the Swollen Phase (Marginally Compact)

20. Similar structures for longer chains(48 residues)

21. Pre-sculpted energy landscape Sequence selection is easy!

22. Free Energy Landscape At Non Zero T Extended conformation is entropically favored: implication for aggregation in amyloid fibrils? length = 24

23. Aggregation of short peptides Jimenez et al., EMBO J. 18, 815-821 (1999) Aggregation in amyloid fibrils is a universal feature of the polypeptide backbone chain

24. Conclusions • Simple physical model capturing geometry and symmetry of main folding driving forces: hydrophobicity, sterics, hydrogen bonds • Proteinlike conformations emerge as coexisting energy minima for an isolated homopolymer in a marginally compact phase flexibility ; aggregation in amyloid fibrils is promoted increasing chain concentration • The energy landscape is presculptedby the physical-chemical properties of the polypeptide backbone; - design for folding is “easy”:  neutral evolution - evolutionary pressure for optimizing protein-protein interaction (active sites, binding sites) and against aggregation

25. Acknowledgments Jayanth R. Banavar (Penn State) Alessandro Flammini (SISSA Trieste) Trinh Xuan Hoang (Hanoi) Davide Marenduzzo (Oxford) Amos Maritan (INFM Padova) Cristian Micheletti (SISSA Trieste) Flavio Seno (INFM Padova)