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 Problem Simple Model

General FeaturesFrom Simple

Models

Physical Interactions

Van der Waals interaction

Electrostatic interaction

Hydrogen bonding

Hydrophobic interaction

A

r12 B

r6

q1q2

r

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}:

EHH EHP EPP

2D 3D

( )i j i j

i j

H E r r

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

Num

ber

of s

truc

ture

s

Most Designable Structures

Helix Strand

Characterizing Highly Designable Structures

What are the geometric properties which make These structures special ?

0 corner1 edge

Surface

2 Bulk

112222221101221122101122110122112210

Tsb N sbNb

0.4

Real Proteins

Implementation of Realistic Geometries

Thermodynamics

F=E-TS=NbbEbb+NwwEww+NwrEwr+NwbEwb--TSchain-TSsolution

Schain is simulated by MD or MCSsolution=NwwSww+NwrSwr+NwbSwb

Nww≈N0-Nwr-Nwb

F-N0(Eww-T Sww) ≈NbbEbb+ Nwr((Ewr- Eww)-T(Swr-Sww))+ Nwb((Ewb- Eww)-T(Swb-Sww))-TSchain

F-F0=NbbEbb+ NwrEwr+ NwbEwb- TSchain

Compact Structures SpaceF-F0=-Nbb|Ebb|+ Nwr|Ewr|- Nwb|E|wb- TSchain

Ebb < 0Ewr > 0Ewb < 0

|Ebb|

|Ewb|

|Ewr|

Spanning the Phase-Space

Globular Helical Strand Globular

“Real” protein like

Coarse-Graining the Structures

110010111110000010100...

1 Bulk0 Surface

Tsb N sbNb

Surface to Bulk Transition Rate

Rsc N sNb

Surface to Core Ratio

Rate of Surface to Bulk Transitions