What determines the structure of the native folds of proteins?

Antonio Trovato

INFMUniversità di Padova

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

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?

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

Conformations

Ener

gy

Ener

gy

Conformations

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).

Most commonsuperfolds

the same fold can housemany different sequencesand perform severalbiological functions

can the emergence of a rich yet limited number of foldsbe explained by means of simple physical arguments?

Compactness-Hydrophobicity

HH PP

SolventSolvent

Secondary structures

Linus Pauling:

L. Pauling & R.B. Corey, Conformations of polypeptides chains with favored orientations around single bonds: two new plated sheets, PNAS 37, 729-740 (1951); ibid with H.R. Branson 205-211.

motifs. and with consistent is bondHydrogen

Steric constraints

D e g r e e s o f f r e e d o m

i i

i

i - t h

A l l b o n d l e n g t h a n d b o n d a n g l e s a r e k e p t f i x e de x c e p t t h a t N C C ’ b o n d a n g l e i s a l l o w e d t o p e r t u b e d s l i g h t l y .T o r s i o n a l a n g l e a b o u t t h e p e p t i d e b o n d o5180

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).

Strong Hint

encourage secondary structure

Both hydrogen bonding and steric interaction

Thick HomopolymersFeatures & 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).

Optimal packing of short tubes leads to the emergence of secondary structures

Optimal helix (pitch/radius=2.512..):generalization of Kepler problemfor hard spheres

Nearly parallel placement ofdifferent nearby portions ofthe tube

Formulation of the Model

tionRepresenta C

• Tube Constraint (three-body constraint)

• Hydrogen bonding geometric constraint

• Hydrophobic interaction: eW

• Local bending penalty: eR

Formulation of the Model: Rules. H-Bond

From 600 proteins in the PDB

tionRepresenta C

i

i+1

j+1

j

j-1

ib

jb

binormals at the j-th and i-th residues1

jj bb ij

rb jiji rb

rij

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 !

-5 -4 -3 -2 -1 0 +1 +2 +3 +4

eW

4

3

2

1

0

eR

Ground State Phase Diagram

ew = water mediated hydrophobic interaction

No sequence specificity: HOMOPOLYMER

eR = bending penalty

Structureless Compact Swollen

?

Ground State Phase Diagram

-5 -4 -3 -2 -1 0 +1 +2 +3 +4

eW

4

3

2

1

0

eR

SwollenStructureless Compact

bend

ing

ener

gy

attraction energy

Ground State Phase Diagram

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

Similar structures for longer chains(48 residues)

Pre-sculpted energy landscape

Sequence selection is easy!

Free Energy Landscape At Non Zero Tle

ngth

= 2

4

Extended conformationis entropically favored:

implication for aggregationin amyloid fibrils?

Aggregation of short peptides

Aggregation in amyloid fibrils is a universalfeature of the polypeptide backbone chain

Jimenez et al., EMBO J. 18, 815-821 (1999)

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

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)