1. Protein Folding, Bridging Lattice Models and Reality Skorobogatiy Maksim, Ned Wingreen, Chao Tang NEC, Princeton, NJ

2. The Protein Folding Problem

3. A Reductionist’s Approach Real ProblemSimple Model General Features From Simple Models

4. Physical Interactions Van der Waals interaction Electrostatic interaction Hydrogen bonding Hydrophobic interaction

5. Essentials for a “Minimal” Model of Protein Folding Self-avoiding polymer At least two different types of monomers Short range contact interaction

6. HP Model on a Lattice (Lau, Chan, Dill) Sequence {  }: Structure {r}: 2D3D

7. Designability of Structures A structure S is designable by a sequence {  } if S is the unique ground state of {  }

8. Designability Histogram Number of sequences designing a structure Number of structures

9. Most Designable Structures  Helix  Strand

10. Characterizing Highly Designable Structures What are the geometric properties which make These structures special ? 112222221101221122101122110122112210

11. Real Proteins

12. Implementation of Realistic Geometries

13. Thermodynamics F=E-TS= N bb E bb +N ww E ww +N wr E wr +N wb E wb - -TS chain -TS solution S chain is simulated by MD or MC S solution =N ww S ww +N wr S wr +N wb S wb N ww ≈N 0 -N wr -N wb F-N 0 (E ww -T S ww ) ≈ N bb E bb + N wr ((E wr - E ww )-T(S wr -S ww )) + N wb ((E wb - E ww )-T(S wb -S ww ))-TS chain F-F 0 = N bb E bb + N wr E wr + N wb E wb - TS chain

14. Compact Structures Space F-F 0 = -N bb |E bb |+ N wr |E wr |- N wb |E| wb - TS chain E bb < 0 E wr > 0 E wb < 0 |E bb | |E wb | |E wr |

15. Spanning the Phase-Space Globular  Helical  Strand Globular “Real” protein like

16. Coarse-Graining the Structures 110010111110000010100... Surface to Bulk Transition Rate Surface to Core Ratio

17. Rate of Surface to Bulk Transitions