The Protein (Free) Energy Landscape. Time and size scales.
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Transcript of The Protein (Free) Energy Landscape. Time and size scales.
![Page 1: The Protein (Free) Energy Landscape. Time and size scales.](https://reader030.fdocuments.net/reader030/viewer/2022032600/56649dbc5503460f94aaea74/html5/thumbnails/1.jpg)
The Protein (Free) Energy Landscape
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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
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A typical protein folding equilibriumconstant K ≈ 1000 means a proteinis unfolded for 100 sec/day!
day
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Folding Coordinate
Levinthal: what the energy landscape cannot look like
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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
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Protein Example
6-mer
2 hydrophobic AA
4 hydrophilic AA
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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
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Rotation Rules
2-D model - no rotations allowed.
Molecules are only al-lowed to change by a single 90˚ “kink” per time step.
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The Journey
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Entropy
WkEntropyS B ln==
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Conformation Analysis
E
ReactionCoordinate
1
0
0.33
0.66Kinetictraps
-0.5 kJ
x
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This is the folding funnel:
E
Entropy
k ln1 = 0
k ln14
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Entropy vs. Energy
-1500 -1000 -500 0Energy (kJ)
Entropy
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Entropy vs. Reaction Coordinate
0 0.33 0.66 0.99
Reaction Coordinate
Entropy
1.0
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Free Energy
(if compressibility is neglected so H ≈ E)
G(x) = H(x) - TS(x) ≈ E(x) - TS(x)
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Free Energy Analysis (200K)0
Reaction Coordinate
Free Energy (G)
1.00.660.330x
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Free Energy Analysis (298K)
0 0.33 0.66 0.99Reaction Coordinate
Free Energy (G)
1.0
Downhill folder
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Free Energy Analysis (360 K)
0 0.33 0.66 0.99Reaction Coordinate
Free Energy (G)
1.0
Two state folder
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Free Energy Analysis (2000K)
0 0.33 0.66 0.99
Reaction Coordinate
Free Energy
1.0
Downhill unfolder
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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