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

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

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

3. 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

4. Experimental Methods NMR Spectroscopy X-ray Crystallography

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

6. Physical Properties

7. Mathematical Model Initial-Value Problem

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

9. 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

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

11. Alternative Approaches Boundary-Value Formulation Ron Elber 1996

12. 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

13. 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

14. Alternative Approaches Energy Minimization minE (x1, x2, … , xn) Scheraga, et al.

15. Energy Landscape Peter Wolynes, et al.

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

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

18. 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.