Download Protein folding kinetics and more

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 threedimensional structure (a helix, b 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
• …
Cooperativity in folding
Peak in specific heat vs. T
c
T
Resemblance with first order transitions
Concepts from chemical reactions
Transition state theory
Transition state
F
DF*
Unfolded
Folded
Reaction coordinate
Arrhenius relation : kAB ~ exp(-DF*/T)
The real world is much more complicated
unfolded
0
folded
r (order parameter)
1
Energy surface may be rough at times…
• Traps from local minima
• Non-Arrenhius relation
• Non-exponential
relaxation
• Glassy dynamics?
Statistical Energy Landscape Theory
• Defining an order parameter r
• Specifying a network
• Assigning energy distribution P(E,r)
• Projecting the network on the order parameter
continuous time random walk (CTRW)
Generalized master equation
Kinetics : Metropolis dynamics+CTRW
Transition rate between two conformations
( R0 ~ 1 ns )
Results : mean first passage time (MFPT)
Results : second moments
long-time
relaxation
Poisson
Results : a dynamic ‘phase diagram’
power-law relaxation
exponential relaxation
A fantasy from the protein folding problem…
A ‘toy’ model : Rubik’s cube
Monte Carlo simulations
1.E+08
MFPT
1.E+07
1.E+06
1.E+05
0
0.2
0.4
0.6
0.8
1/T
1
1.2
1.4
1.6
Summary
• Random walks on a complex energy landscape
• Exponential
nonexponential kinetics
• Nonexponential kinetics can happen for a
downhill folding process (cf. experimental work
by Gruebele et al., PNAS 96, 6031(1999))