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

The Protein Folding Problem

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

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

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

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

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

Designability Histogram Number of sequences designing a structure Number of structures

Most Designable Structures  Helix  Strand

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

Real Proteins

Implementation of Realistic Geometries

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

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 |

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

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

Rate of Surface to Bulk Transitions