wuzj05 05 26

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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 Folding GLU GLU ASN VAL LEU ARG PRO ASN ALA GLN . . . GLU VAL GLU ASN GLN ALA ASN PRO ARG LEU

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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

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Experimental Methods X-ray Crystallography NMR Spectroscopy

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Holdings in the PDB Protein Data Bank http://www.rcsb.org

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Physical Properties

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Initial-Value Problem Mathematical Model

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Numerical Solutions t x tk tk+1 xk xk+1 x(t) Verlet 1967

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10-15 femto 10-12 pico 10-9 nano 10-6 micro 10-3 milli 100 seconds Bond vibration Isomeris- ation Water dynamics Helix forms Fastest folders Typical folders Slow folders Time Scales for Protein Motion

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Folding of Villin Headpiece Subdomain (HP-36) Duan and Kollman 1998

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Boundary-Value Formulation Alternative Approaches Ron Elber 1996

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Single Shooting t x t=0 t=1 x0 x1 x1 v0 v0 x1 = ψ(v0) φ(v0)= ψ(v0)-x1 φ(v0)= 0 Newton’s Method

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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 Newton’s Method ψj (Vedell and Wu 2005)

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Alternative Approaches min E (x1, x2, … , xn) Energy Minimization Scheraga, et al.

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Energy Landscape Peter Wolynes, et al.

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Energy Transformation Scheraga et al. 1989, Shalloway 1992, Straub 1996

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Transformation Theory Wu 1996, More & Wu 1997 High frequency components are reduced with increasing λ values.

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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.