The Protein (Free)
Energy Landscape
108 cells, 0.01 m (tissue)
0.1 s - 10 7 s
1012 cells, 1 m (organism)
10 10 cells , 0.1 m (or gan)
RNA
organelle, 10 -8 m
(10-10 7 molecules)
10-3 s
Rb
1 cell, 10 -5 m
(10 11 molecules)
10-15 - 10-12 s
10-12 - 1 s
protein,10-9 m
(1 macromolecule, 104 - 107 atoms)
covalent and noncovalent
interactions and their dynamics
Coulomb interactions ,10 -10 m
Time and size scales
Weak and strong
interactions ,10 -15 m
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
Core and surface

solvent
solvent
solvent
solvent
Amino acid represented as beads
 Black
bead: hydrophobic (H)
 White bead: hydrophilic (P)
solvent
solvent
solvent
solvent
solvent
solvent
solvent
(shown: a configuration
with favorable E = <H>)

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
Protein Example

6-mer

2 hydrophobic AA

4 hydrophilic AA
Chirality
P
P
P
Chiral

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.
Rotation Rules

2-D model - no
rotations allowed.

Molecules are only allowed to change by a
single 90˚ “kink” per
time step.
The Journey
Entropy
S  Entropy  kB ln W
Conformation Analysis
E
Reaction
Coordinate
x
0
0.33
-0.5 kJ
Kinetic
traps
0.66
1
This is the folding funnel:
Entropy
E
k ln14
k ln1 = 0
Entropy
Entropy vs. Energy
-1500
-1000
Energy (kJ)
-500
0
Entropy
Entropy vs. Reaction
Coordinate
0
0.33
0.66
Reaction Coordinate
1.0
0.99
Free Energy
G(x) = H(x) - TS(x) ≈ E(x) - TS(x)
(if compressibility is neglected so H ≈ E)
Free Energy Analysis (200K)
Free Energy (G)
0
0
0.33
Reaction Coordinate
x
0.66
1.0
Free Energy (G)
Free Energy Analysis (298K)
Downhill folder
0
0.33
0.66
Reaction Coordinate
1.0
0.99
Free Energy Analysis (360 K)
Free Energy (G)
Two state folder
0
0.33
0.66
Reaction Coordinate
1.0
0.99
Free Energy Analysis (2000K)
Free Energy
Downhill unfolder
0
0.33
0.66
Reaction Coordinate
1.0
0.99
Energy Funnel and Free Energy Surface
Wolynes
Bryngelson
Onuchic
Luthey-Schulten
Dill
Thirumalai
Enthalpy
Config.
entropy
Free energy
DG>0
DS<0
-1
DG = DH - T DS
0
x
1
Free energy
DH<0
DG<0
-1
0
x
1