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Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iow

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Protein Structure and Dynamics. Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa. Protein Folding. LEU. ARG. ASN. PRO. ALA. ASN. GLN. GLU. GLU. VAL. GLU. VAL. GLU. ASN. GLN. ALA. ASN. PRO. ARG. LEU.

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slide1
Protein Structure and Dynamics

Zhijun Wu

Department of Mathematics

Program on Bio-informatics and Computational Biology

Iowa State University

Ames, Iowa

slide2
Protein Folding

LEU

ARG

ASN

PRO

ALA

ASN

GLN

GLU

GLU

VAL

GLU

VAL

GLU

ASN

GLN

ALA

ASN

PRO

ARG

LEU

. . .

slide3
Myoglobin, John Kendrew, 1962,

Nobel Prize in Chemistry

Photosynthetic Reaction Center,

Johann Deisenhofer, 1988,

Nobel Prize in Chemistry

Prion, Stanley B. Prusiner, 1997,

Nobel Prize in Physiology and Medicine

slide4
Experimental Methods

NMR Spectroscopy

X-ray Crystallography

slide7
Mathematical Model

Initial-Value Problem

slide8
Numerical Solutions

x

x(t)

xk+1

xk

t

tk

tk+1

Verlet 1967

slide9
Time Scales for Protein Motion

Bond

vibration

Isomeris-

ation

Water

dynamics

Helix

forms

Fastest

folders

Typical

folders

Slow

folders

10-15

femto

10-12

pico

10-9

nano

10-6

micro

10-3

milli

100

seconds

slide11
Alternative Approaches

Boundary-Value Formulation

Ron Elber 1996

slide12
Single Shooting

x1

x

x1 = ψ(v0)

φ(v0)= ψ(v0)-x1

φ(v0)= 0

x1

v0

x0

v0

t=0

t=1

t

Newton’s Method

slide13
Multiple Shooting

x

φj(xj-1, vj-1, xj) = ψj(xj-1, vj-1) - xj

φj(xj-1, vj-1, xj) = 0

j = 1, …, m

ψj

xm

(xj-1,vj-1)

x0

t=0

t=m

t

(Vedell and Wu 2005)

Newton’s Method

slide14
Alternative Approaches

Energy Minimization

minE (x1, x2, … , xn)

Scheraga, et al.

slide15
Energy Landscape

Peter Wolynes, et al.

slide16
Energy Transformation

Scheraga et al. 1989, Shalloway 1992, Straub 1996

slide17
Transformation Theory

High frequency components are reduced with increasing λ values.

Wu 1996, More & Wu 1997

slide18
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.

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