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Bioinformatics: Practical Application of Simulation and Data Mining Protein Folding I

Bioinformatics: Practical Application of Simulation and Data Mining Protein Folding I. Prof. Corey O’Hern Department of Mechanical Engineering Department of Physics Yale University. Statistical Mechanics. Protein Folding. Biochemistry. What are proteins?. Linear polymer. Folded state.

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Bioinformatics: Practical Application of Simulation and Data Mining Protein Folding I

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  1. Bioinformatics: Practical Application of Simulation and Data MiningProtein Folding I • Prof. Corey O’Hern • Department of Mechanical Engineering • Department of Physics • Yale University

  2. Statistical Mechanics Protein Folding Biochemistry

  3. What are proteins? Linear polymer Folded state • Proteins are important; e.g. for catalyzing and regulating biochemical reactions, • transporting molecules, … • Linear polymer chain composed of tens (peptides) to thousands (proteins) of monomers • Monomers are 20 naturally occurring amino acids • Different proteins have different amino acid sequences • Structureless, extended unfolded state • Compact, ‘unique’ native folded state (with secondary and tertiary structure) required for biological function • Sequence determines protein structure (or lack thereof) • Proteins unfold or denature with increasing temperature or chemical denaturants

  4. Amino Acids I N-terminal C-terminal C peptide bonds R variable side chain • Side chains differentiate amino acid repeat units • Peptide bonds link residues into polypeptides

  5. Amino Acids II

  6. The Protein Folding Problem: What is ‘unique’ folded 3D structure of a protein based on its amino acid sequence? Sequence  Structure Lys-Asn-Val-Arg-Ser-Lys-Val-Gly-Ser-Thr-Glu-Asn-Ile-Lys- His-Gln-Pro- Gly-Gly-Gly-…

  7. Driving Forces • Folding: hydrophobicity, hydrogen bonding, van der Waals interactions, … • Unfolding: increase in conformational entropy, electric charge… Hydrophobicity index inside H (hydrophobic) outside P (polar)

  8. Higher-order Structure

  9. Secondary Structure: Loops, -helices, -strands/sheets -helix -strand -sheet 5Å • Right-handed; three turns • Vertical hydrogen bonds between NH2 (teal/white) backbone group and C=O (grey/red) backbone group four residues earlier in sequence • Side chains (R) on outside; point upwards toward NH2 • Each amino acid corresponds to 100, 1.5Å, 3.6 amino acids per turn • (,)=(-60,-45) • -helix propensities: Met, Ala, Leu, Glu • 5-10 residues; peptide backbones fully extended • NH (blue/white) of one strand hydrogen-bonded to C=O (black/red) of another strand • C ,side chains (yellow) on adjacent strands aligned; side chains along single strand alternate up and down • (,)=(-135,-135) • -strand propensities: Val, Thr, Tyr, Trp, Phe, Ile

  10. Backbonde Dihedral Angles

  11. Ramachandran Plot: Determining Steric Clashes Gly Non-Gly Backbone dihedral angles  theory  4 atoms define dihedral angle:  PDB CCNC =0,180 CN CC  N CCN vdW radii backbone flexibility < vdW radii

  12. How can structures from PDB exist outside Ramachadran bounds? • Studies were performed on alanine dipeptide • Fixed bond angle (=110) [105,115] J. Mol. Biol. (1963) 7, 95-99

  13. Side-Chain Dihedral Angles 4: Lys, Arg 5: Arg Side chain: C-CH2-CH2-CH2-CH2-NH3 Use NCCCCCN to define 1, 2, 3,4

  14. Your model is oversimplified and has nothing to do with biology! Your model is too complicated and has no predictive power! Molecular biologist Biological Physicist

  15. Possible Strategies for Understanding Protein Folding • For all possible conformations, compute free energy from atomic interactions within protein and protein- solvent interactions; find conformation with lowest free energy…e.g using all-atom molecular dynamics simulations Not possible?, limited time resolution • Use coarse-grained models with effective interactions between residues and residues and solvent General, but qualitative

  16. Why do proteins fold (correctly & rapidly)?? Levinthal’s paradox: For a protein with N amino acids, number of backbone conformations/minima  = # allowed dihedral angles How does a protein find the global optimum w/o global search? Proteins fold much faster. Nc~ 3200 ~1095 fold ~ Nc sample ~1083 s fold ~ 10-6-10-3 s vs universe ~ 1017 s

  17. Energy Landscape U, F =U-TS S12 S23 S-1 M2 M3 M1 minimum all atomic coordinates; dihedral angles saddle point maximum

  18. Roughness of Energy Landscape smooth, funneled rough (Wolynes et. al. 1997)

  19. Folding Pathways dead end similarity to native state

  20. Folding Phase Diagram smooth rough

  21. Open Questions • What differentiates the native state from other low-lying energy minima? • How many low-lying energy minima are there? Can we calculate landscape roughness from sequence? • What determines whether protein will fold to the native state or become • trapped in another minimum? • What are the pathways in the energy landscape that a given protein follows to its native state? NP Hard Problem!

  22. Digression---Number of Energy Minima for Sticky Spheres Nm Ns Np 4 1 1 sphere packings 1 5 6 6 2 50 7 5 486 8 13 5500 polymer packings 9 52 49029 10 - - Ns~exp(aNm); Np~exp(bNm) with b>a

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