zhijun wu department of mathematics program on bio-informatics and computational biology iowa state...

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.