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The Protein (Free) Energy Landscape

The Protein (Free) Energy Landscape. Time and size scales. A typical protein folding equilibrium constant K ≈ 1000 means a protein is unfolded for 100 sec/day!. day. Levinthal: what the energy landscape cannot look like. Folding Coordinate . Energy and Free Energy Landscapes.

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The Protein (Free) Energy Landscape

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  1. The Protein (Free) Energy Landscape

  2. Time and size scales

  3. A typical protein folding equilibrium constant K ≈ 1000 means a protein is unfolded for 100 sec/day! day

  4. Levinthal: what the energy landscape cannot look like Folding Coordinate 

  5. Energy and Free Energy Landscapes • Amino acid represented as beads • Black bead: hydrophobic (H) • White bead: hydrophilic (P) • Bonds represented by straight lines • H-H (= -1000J) and P-P (= -250J) bonds favorable Based on work by N. Go M. Levitt, K. A. Dill, Shakhnovich/Karplus

  6. Protein Example • 6-mer • 2 hydrophobic AA • 4 hydrophilic AA

  7. Chirality • To avoid issues with chirality, all molecules are made so that the first two amino acids go upwards. • Also, the first kink always goes to the right.

  8. Rotation Rules • 2-D model - no rotations allowed. • Molecules are only al-lowed to change by a single 90˚ “kink” per time step.

  9. The Journey

  10. Entropy

  11. Conformation Analysis Reaction Coordinate x E 0 0.33 -0.5 kJ Kinetic traps 0.66 1

  12. This is the folding funnel: Entropy E k ln14 k ln1 = 0

  13. Entropy vs. Energy

  14. Entropy vs. Reaction Coordinate

  15. Free Energy G(x) = H(x) - TS(x) ≈ E(x) - TS(x) (if compressibility is neglected so H ≈ E)

  16. Free Energy Analysis (200K) x

  17. Free Energy Analysis (298K) Downhill folder

  18. Free Energy Analysis (360 K) Two state folder

  19. Free Energy Analysis (2000K) Downhill unfolder

  20. DG>0 DG<0 Free energy DS<0 DH<0 x Energy Funnel and Free Energy Surface Wolynes Bryngelson Onuchic Luthey-Schulten Dill Thirumalai Enthalpy Config. entropy Free energy DG = DH - T DS -1 0 1 x

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