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 presculpted by 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. Protein folding is complex
20 type of amino acids with distinct side chains
huge number of degrees of freedom
polymer chain constraint
steric constraints (excluded volume)
crucial role of the aqueous solvent
quantum chemistry (hydrogen bond)

5. How to tackle the problem?
All atom models: remarkable results for short peptides
but problems for longer proteins:
time constraint, stability of force fields
Knowledge-based models: learn parameters from PDB;
ok for structure prediction,
but general or selected properties?
Coarse-grained models: how to learn correctly the main
rules in the game?
In all cases: sequence by sequence approach

6. Energy landscape paradygm (from cubic lattice models)
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
Energy
Conformations
Energy
Conformations

7. Funnel determined by native topology?
Practical recipe (for off-lattice models): use Go model
- a priori knowledge of the native conformation
- folding mechanism (to some extent) depends only
on the topology of the native state

8. 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).

9. Some Example of Protein Structures
1CTF
1CRN
1GB1

10. Most common superfolds
the same fold can house many different sequences and perform several biological functions
can the emergence of a rich yet limited number of folds
be explained by means of simple physical arguments?

11. Compactness-Hydrophobicity
Folding
Solvent

12. Compact Phases of Standard Polymers:
String and beads model r
all pairs
Compact disordered phase
Crystalline phase: Hamiltonian walks T
Swollen

13. Is compactness alone driving secondary structure formation?
K.A. Dill & H.S. Chan, Origin of structures in globular proteins, PNAS 87, (1990).
D.P. Yee, H.S. Chan, T.F. Havel & K.A. Dill, Does compactness induce secondary structure in proteins? – A study of poly-alanine chains computed by distance geometry, JMB 241, (1994).
N.D. Socci, W.S. Bialek, & J.N. Onuchic, Properties and origins of secondary structure, PRE 49, (1994)
Conclusion: compactness alone (in the absence
of hydrogen bonding) does not drive
secondary structure formation.

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

15. 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, (1968).

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

17. Thick Homopolymers Features & 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).

18. 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= ):
generalization of Kepler problem
for hard spheres

19. Ground State Phase Diagram For Short Tubes

20. Previous Attempts with H-bonds
N.G. Hunt, L.M. Gregoret & F.E. Cohen, The origin of protein secondary structure: Effects of packing density and hydrogen bonding studied by a fast conformational search, J. Mol. Biol. 241, (1994).
J.P. Kemp & Z.Y. Chen, Formation of helical structures in wormlike polymers, Phys. Rev. Lett. 81, (1998).
A. Trovato, J. Ferkinghoff-Borg & M.H. Jensen, Compact phases of polymers with hydrogen bonding, Phys. Rev. E67, (2003).
Conclusion: Secondary structures formation is
enhanced by hydrogen bonding, but no particular
resemblance with native-like tertiary arrangements
of secondary motifs.

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

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

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

24. Formulation of the Model: Rules. Thickness - Steric
Curvature-Steric
Ramachandran R Vc R eR

25. Formulation of the Model: Rules
Formulation of the Model: Rules. Hydrophobicity From 600 proteins in the PDB k l V ew

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

27. Ground State Phase Diagram
bending energy
attraction energy eW 4 3 2 1 eR
Swollen
Structureless
Compact

28. Ground State Phase Diagram

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

30. Similar structures for longer chains (48 residues)

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

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

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

34. CONCLUSIONS Homopolymer with:
hydrogen bonding
hydrophobic interaction
thickness + steric interaction + curvature
Phase diagram where in the vicinity of the swollen
phase marginally compact structures emerges:
Huge reduction in the ground state degeneracy  few folds (menu)!
Marginally compact tertiary structures  biological function (disordered proteins)
Pre-sculpted free energy landscape  Specific protein sequence chooses the native state from a fixed menu of possible folds
Large basin of attraction  mutation stability & easier folding
evolution of protein-protein interactions!

35. 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 presculpted by 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

36. 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)