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The Protein (Free) Energy Landscape
aa
1012 cells, 1 m (organism)1010 cells, 0.1 m (organ)
1 cell, 10-5 m(1011 molecules)RNARborganelle, 10-8 m(10-107 molecules)
protein,10 -9 m(1 macromolecule,104 - 107 atoms)covalent and noncovalentinteractions and their dynamics
108 cells, 0.01 m (tissue)
Coulomb interactions,10 -10 mWeak and stronginteractions,10 -15 m
0.1 s - 107 s10-3 s10-12 - 1 s10-15 - 10-12 s
Time and size scales
A typical protein folding equilibriumconstant K ≈ 1000 means a proteinis unfolded for 100 sec/day!
day
Folding Coordinate
Levinthal: what the energy landscape cannot look like
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
a
Core and surface(shown: a configuration with favorable E = <H>)
solventsolventsolventsolventsolventsolventsolventsolventsolventsolventsolvent
Protein Example
6-mer
2 hydrophobic AA
4 hydrophilic AA
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.
a
PPPChiral
Rotation Rules
2-D model - no rotations allowed.
Molecules are only al-lowed to change by a single 90˚ “kink” per time step.
The Journey
Entropy
WkEntropyS B ln==
Conformation Analysis
E
ReactionCoordinate
1
0
0.33
0.66Kinetictraps
-0.5 kJ
x
This is the folding funnel:
E
Entropy
k ln1 = 0
k ln14
Entropy vs. Energy
-1500 -1000 -500 0Energy (kJ)
Entropy
Entropy vs. Reaction Coordinate
0 0.33 0.66 0.99
Reaction Coordinate
Entropy
1.0
Free Energy
(if compressibility is neglected so H ≈ E)
G(x) = H(x) - TS(x) ≈ E(x) - TS(x)
Free Energy Analysis (200K)0
Reaction Coordinate
Free Energy (G)
1.00.660.330x
Free Energy Analysis (298K)
0 0.33 0.66 0.99Reaction Coordinate
Free Energy (G)
1.0
Downhill folder
Free Energy Analysis (360 K)
0 0.33 0.66 0.99Reaction Coordinate
Free Energy (G)
1.0
Two state folder
Free Energy Analysis (2000K)
0 0.33 0.66 0.99
Reaction Coordinate
Free Energy
1.0
Downhill unfolder
aa
0-11Free
ene
rgy
x
EnthalpyConfig.entropy
S<0
G>0
H<0
G<0
Wolynes BryngelsonOnuchicLuthey-SchultenDillThirumalai
0-1 1
Free
ene
rgy
x
Energy Funnel and Free Energy Surface
G = H - T S
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