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

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Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

Protein Structure and Dynamics

Zhijun Wu

Department of Mathematics

Program on Bio-informatics and Computational Biology

Iowa State University

Ames, Iowa


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

. . .


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

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


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

Experimental Methods

NMR Spectroscopy

X-ray Crystallography


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

Holdings in the PDB Protein Data Bank

http://www.rcsb.org


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

Physical Properties


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

Mathematical Model

Initial-Value Problem


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

Numerical Solutions

x

x(t)

xk+1

xk

t

tk

tk+1

Verlet 1967


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

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


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

Folding of Villin Headpiece Subdomain (HP-36)

Duan and Kollman 1998


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

Alternative Approaches

Boundary-Value Formulation

Ron Elber 1996


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

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


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

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


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

Alternative Approaches

Energy Minimization

minE (x1, x2, … , xn)

Scheraga, et al.


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

Energy Landscape

Peter Wolynes, et al.


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

Energy Transformation

Scheraga et al. 1989, Shalloway 1992, Straub 1996


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

Transformation Theory

High frequency components are reduced with increasing λ values.

Wu 1996, More & Wu 1997


Zhijun wu department of mathematics program on bio informatics and computational biology iowa state university ames iowa

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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