protein folding kinetics and more chi-lun lee ( 李紀倫 ) department of physics national central...
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Protein folding kinetics and more
Chi-Lun Lee (李紀倫 )
Department of Physics
National Central University
Introduction
Protein (polypeptide chain): chain of amino
acid residues
Primary structure : sequence of amino acid residues
Secondary structure : locally folded three-dimensional structure ( helix, sheet, etc.)
Tertiary structure : fully-folded compact structure
For a single domain globular protein (~100 amid acid residues), its diameter ~ 5nm and molecular mass ~ 10000 daltons (compact structure)
Features of protein folding :
• Volume exclusion and chain connectivity
• Van der Waals interactions
• Hydrogen bond
• Hydrophobic interactions
• …
Peak in specific heat vs. T
c
T
Resemblance with first order transitions
Cooperativity in folding
Concepts from chemical reactions
Transition state theory
F
Reaction coordinate
Unfolded
Transition state
Folded
F*
Arrhenius relation : kAB ~ exp(-F*/T)
foldedunfolded
0 1 (order parameter)
The real world is much more complicated
Energy surface may be rough at times…
• Traps from local minima
• Non-Arrenhius relation
• Non-exponential relaxation
• Glassy dynamics?
• Defining an order parameter
• Specifying a network
• Assigning energy distribution P(E,)
• Projecting the network on the order parameter c
ontinuous time random walk (CTRW)
Statistical Energy Landscape Theory
Generalized master equation
Kinetics : Metropolis dynamics+CTRW
Transition rate between two conformations
( R0 ~ 1 ns )
Results : mean first passage time (MFPT)
Results : second moments
Poisson
long-time relaxation
Results : a dynamic ‘phase diagram’
exponential relaxation
power-law relaxation
A fantasy from the protein folding problem…
A ‘toy’ model : Rubik’s cube
1.E+05
1.E+06
1.E+07
1.E+08
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
1/T
MFPT
Monte Carlo simulations
Summary
• Random walks on a complex energy landscape
• Exponential nonexponential kinetics
• Nonexponential kinetics can happen for a downhi
ll folding process (cf. experimental work by Grue
bele et al., PNAS 96, 6031(1999))