Zhijun WuDepartment of Mathematics
Program on Bio-informatics and Computational Biology
Iowa State UniversityAmes, Iowa
Protein Structure and Dynamics
Protein Folding
GLU GLU ASNVAL LEUARGPROASNALAGLN . . .
GLU VAL
GLU
ASN GLN
ALA
ASN PRO
ARG
LEU
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
Experimental Methods
X-ray Crystallography
NMR Spectroscopy
Holdings in the PDB Protein Data Bank
http://www.rcsb.org
Physical Properties
),...,(: 1 nxxEEnergy
),...,(),...,(: 11 nn xxExxFFieldForce
nixxxExxf inni ,,1,/),,(),,( 11
inni
iiiinii
i
xxxExxf
nivvxxxxfdtxdm
/),,(),,(
,...,1,)0(,)0(),,...,(
11
0012
2
Initial-Value Problem
Mathematical Model
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
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
Folding of Villin Headpiece Subdomain (HP-36)
Duan and Kollman 1998
Boundary-Value Formulation
inni
iiiinii
i
xxxExxf
nixxxxxxfdtxdm
/),,(),,(
,...,1,)1(,)0(),,...,(
11
1012
2
Alternative Approaches
Ron Elber 1996
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
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)
Alternative Approaches
min E (x1, x2, … , xn)
Energy Minimization
Scheraga, et al.
Energy Landscape
Peter Wolynes, et al.
Energy Transformation
nRnn dxxxxfxf ')/||'||exp()'(1)( 22
2/
Scheraga et al. 1989, Shalloway 1992, Straub 1996
)()4/||||(exp)( 22 ff
,||||,/,0 c
.|)(|
|)(|
ff
Transformation Theory
Wu 1996, More & Wu 1997
High frequency components are reduced with increasing λ values.
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.