Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State...
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Zhijun WuDepartment of Mathematics
Program on Bio-informatics and Computational Biology
Iowa State UniversityAmes, Iowa
Protein Structure and Dynamics
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Protein Folding
GLU GLU ASNVAL LEUARGPROASNALAGLN . . .
GLU VAL
GLU
ASN GLN
ALA
ASN PRO
ARG
LEU
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Prion, Stanley B. Prusiner, 1997, Nobel Prize in Physiology and Medicine
Myoglobin, John Kendrew, 1962, Nobel Prize in Chemistry
Photosynthetic Reaction Center, Johann Deisenhofer, 1988, Nobel Prize in Chemistry
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Experimental Methods
X-ray Crystallography
NMR Spectroscopy
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Holdings in the PDB Protein Data Bank
http://www.rcsb.org
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Physical Properties
),...,(: 1 nxxEEnergy
),...,(),...,(: 11 nn xxExxFFieldForce
nixxxExxf inni ,,1,/),,(),,( 11
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inni
iiiinii
i
xxxExxf
nivvxxxxfdtxdm
/),,(),,(
,...,1,)0(,)0(),,...,(
11
0012
2
Initial-Value Problem
Mathematical Model
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nimxxf
txxx
i
kn
ki
ki
ki
ki ,...,1,),...(2 1
2
11
Numerical Solutions
t
x
tk tk+1
xk
xk+1
x(t)ni
mxxf
dtxd
i
nii ,...,1,),...,( 12
2
nitmxxfxxx
i
kn
kik
iki
ki ,...,1,),...(2 2111
Verlet 1967
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10-15
femto10-12
pico10-9
nano10-6
micro10-3
milli100
seconds
Bond vibration
Isomeris-ation
Waterdynamics
Helixforms
Fastestfolders
Typicalfolders
Slowfolders
Time Scales for Protein Motion
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Folding of Villin Headpiece Subdomain (HP-36)
Duan and Kollman 1998
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Boundary-Value Formulation
inni
iiiinii
i
xxxExxf
nixxxxxxfdtxdm
/),,(),,(
,...,1,)1(,)0(),,...,(
11
1012
2
Alternative Approaches
Ron Elber 1996
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Single Shooting
t
x
t=0 t=1
x0
x1
x1
v0
v0
x1 = ψ(v0)
φ(v0)= ψ(v0)-x1
φ(v0)= 0
)(v)](v'[vv 01000
Newton’s Method
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Multiple Shooting
t
x
t=0 t=m
x0
xm
(xj-1,vj-1)
φj(xj-1, vj-1, xj) = ψj(xj-1, vj-1) - xj
φj( xj-1, vj-1, xj) = 0
j = 1, …, m
),...,(),v,...,(vv),x,...,(xx
v)(x,v)](x,'[v)x,(v)(x,
11-m01-m0
1
m
Newton’s Method
ψj
(Vedell and Wu 2005)
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Alternative Approaches
min E (x1, x2, … , xn)
Energy Minimization
Scheraga, et al.
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Energy Landscape
Peter Wolynes, et al.
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Energy Transformation
nRnn dxxxxfxf ')/||'||exp()'(1)( 22
2/
Scheraga et al. 1989, Shalloway 1992, Straub 1996
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)()4/||||(exp)( 22 ff
,||||,/,0 c
.|)(|
|)(|
ff
Transformation Theory
Wu 1996, More & Wu 1997
High frequency components are reduced with increasing λ values.
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Having puzzled the scientists for decades, the protein folding problem remains a grand challenge of modern science.
The protein folding problem may be studied through MD simulation under certain boundary conditions.
An efficient optimization algorithm may be developed to obtain a fast fold by exploiting the special structure of protein energy landscape.
The successful simulation of protein folding requires correct physics, efficient and accurate algorithms, and sufficient computing power.