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

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

6. 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

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

8. 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.

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

10. The Journey

11. Entropy

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

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

14. Entropy vs. Energy

15. Entropy vs. Reaction Coordinate

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

17. Free Energy Analysis (200K) x

18. Free Energy Analysis (298K) Downhill folder

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

20. Free Energy Analysis (2000K) Downhill unfolder

21. Free energy x Enthalpy Config. entropy  S<0  G>0  H<0  G<0 Wolynes Bryngelson Onuchic Luthey-Schulten Dill Thirumalai 0 1 Free energy x Energy Funnel and Free Energy Surface  G =  H - T  S