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?

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)

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

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

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

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).

Some Example of Protein Structures 1CTF 1CRN 1GB1

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 Folding Solvent

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

Is compactness alone driving secondary structure formation? K.A. Dill & H.S. Chan, Origin of structures in globular proteins, PNAS 87, 6388-6392 (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, 557-573 (1994). N.D. Socci, W.S. Bialek, & J.N. Onuchic, Properties and origins of secondary structure, PRE 49, 3440-3443 (1994) Conclusion: compactness alone (in the absence of hydrogen bonding) does not drive secondary structure formation.

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, 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).

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 Nearly parallel placement of different nearby portions of the tube Optimal helix (pitch/radius=2.512..): generalization of Kepler problem for hard spheres

Ground State Phase Diagram For Short Tubes

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, 214-225 (1994). J.P. Kemp & Z.Y. Chen, Formation of helical structures in wormlike polymers, Phys. Rev. Lett. 81, 3880-3883 (1998). A. Trovato, J. Ferkinghoff-Borg & M.H. Jensen, Compact phases of polymers with hydrogen bonding, Phys. Rev. E67, 028108 (2003). Conclusion: Secondary structures formation is enhanced by hydrogen bonding, but no particular resemblance with native-like tertiary arrangements of secondary motifs.

Formulation of the Model Representa C - a 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 rij binormals at the j-th and i-th residues i i+1 j+1 j j-1

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 !

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

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

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

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

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 T Extended conformation is entropically favored: implication for aggregation in amyloid fibrils? length = 24

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 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!

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)