What determines the structure of
the native folds of proteins?
Antonio Trovato
INFM
Università 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
• Levinthal paradox: how to
reconcile the uniqueness of
the native state with its
kinetic accessibility?
Energy
(from cubic lattice models)
• Principle of minimal frustration
Energy-entropy relationship is
carving a funnel for designed
sequences in the energy
landscape
Energy
Conformations
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 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?
Compactness-Hydrophobicity
H
P
Solvent
Secondary structures
Linus Pauling: Hydrogen bond is consistent with
a and b motifs.
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.
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).
Degrees of freedom
b
i
i i
i-th
a
All bond length and bond angles are kept fixed
 to180
 5o slightly.
except that NCaC’ bond angle is allowed
pertubed
Torsional angle about the peptide bond
Strong Hint
Both hydrogen bonding
and
steric interaction
encourage secondary structure
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).
Optimal packing of short tubes leads to
the emergence of secondary structures
Optimal helix (pitch/radius=2.512..):
generalization of Kepler problem
for hard spheres
Nearly parallel placement of
different nearby portions of
the tube
Formulation of the Model
Ca  Representation
• Tube Constraint (three-body constraint)
• Hydrogen bonding geometric constraint
• Hydrophobic interaction: e
• Local bending penalty: e
R
W
Formulation of the Model: Rules.
H-Bond
From 600 proteins in the PDB
Ca  Representa tion

bi
i
rij
j
j+1

bj
i+1
j-1

binormals at the j-th and i-th residues


b i  r ij


b j  bbj j 1 r ij
How Many Parameters?
Local i – i+3 eH = -1
Hydrogen bonding
Non-Local i – i+5, i+6,… eH = -0.7
Remark: no H-bond between i – i+4 !
Cooperativity ecoop = -0.3
Ground State Phase Diagram
eR = bending penalty
ew = water mediated hydrophobic interaction
No sequence specificity: HOMOPOLYMER
4
3
eR
2
Structureless
1
Swollen
Compact
?
0
-5 -4 -3 -2
-1
0
eW
+1 +2 +3 +4
bending energy
Ground State Phase Diagram
4
3
eR
2
1
Structureless
Compact
Swollen
0
-5 -4
-3 -2
-1
0
eW
+1 +2 +3 +4
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!
length = 24
Free Energy Landscape At Non Zero T
Extended conformation
is entropically favored:
implication for aggregation
in amyloid fibrils?
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
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
Alessandro Flammini
Trinh Xuan Hoang
Davide Marenduzzo
Amos Maritan
Cristian Micheletti
Flavio Seno
(Penn State)
(SISSA Trieste)
(Hanoi)
(Oxford)
(INFM Padova)
(SISSA Trieste)
(INFM Padova)