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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

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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. - PowerPoint PPT Presentation

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Page 1: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

Zhijun WuDepartment of Mathematics

Program on Bio-informatics and Computational Biology

Iowa State UniversityAmes, Iowa

Protein Structure and Dynamics

Page 2: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

Protein Folding

GLU GLU ASNVAL LEUARGPROASNALAGLN . . .

GLU VAL

GLU

ASN GLN

ALA

ASN PRO

ARG

LEU

Page 3: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

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

Page 4: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

Experimental Methods

X-ray Crystallography

NMR Spectroscopy

Page 5: 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

Page 6: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

Physical Properties

),...,(: 1 nxxEEnergy

),...,(),...,(: 11 nn xxExxFFieldForce

nixxxExxf inni ,,1,/),,(),,( 11

Page 7: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

inni

iiiinii

i

xxxExxf

nivvxxxxfdtxdm

/),,(),,(

,...,1,)0(,)0(),,...,(

11

0012

2

Initial-Value Problem

Mathematical Model

Page 8: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

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

Page 9: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

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

Page 10: 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

Page 11: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

Boundary-Value Formulation

inni

iiiinii

i

xxxExxf

nixxxxxxfdtxdm

/),,(),,(

,...,1,)1(,)0(),,...,(

11

1012

2

Alternative Approaches

Ron Elber 1996

Page 12: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

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

Page 13: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

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)

Page 14: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

Alternative Approaches

min E (x1, x2, … , xn)

Energy Minimization

Scheraga, et al.

Page 15: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

Energy Landscape

Peter Wolynes, et al.

Page 16: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

Energy Transformation

nRnn dxxxxfxf ')/||'||exp()'(1)( 22

2/

Scheraga et al. 1989, Shalloway 1992, Straub 1996

Page 17: Zhijun Wu Department of Mathematics Program on Bio-informatics and Computational Biology Iowa State University Ames, Iowa

)()4/||||(exp)( 22 ff

,||||,/,0 c

.|)(|

|)(|

ff

Transformation Theory

Wu 1996, More & Wu 1997

High frequency components are reduced with increasing λ values.

Page 18: 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.