1. Protein folding kinetics and more Chi-Lun Lee ( 李紀倫 ) Department of Physics National Central University

2. Introduction Protein (polypeptide chain): chain of amino acid residues Primary structure : sequence of amino acid residues Secondary structure : locally folded three- dimensional structure (  helix,  sheet, etc.) Tertiary structure : fully-folded compact structure

3. For a single domain globular protein (~100 amid acid residues), its diameter ~ 5nm and molecular mass ~ 10000 daltons (compact structure)

4. Features of protein folding : Volume exclusion and chain connectivity Van der Waals interactions Hydrogen bond Hydrophobic interactions …

5. Peak in specific heat vs. T c T Resemblance with first order transitions Cooperativity in folding

6. Concepts from chemical reactions Transition state theory F Reaction coordinate Unfolded Transition state Folded  F* Arrhenius relation : k AB ~ exp(-  F*/T)

7. foldedunfolded 01  (order parameter) The real world is much more complicated

8. Energy surface may be rough at times… Traps from local minima Non-Arrenhius relation Non-exponential relaxation Glassy dynamics?

9. Defining an order parameter  Specifying a network Assigning energy distribution P(E,  ) Projecting the network on the order parameter continuous time random walk (CTRW) Statistical Energy Landscape Theory Generalized master equation

10. Kinetics : Metropolis dynamics+CTRW Transition rate between two conformations ( R 0 ~ 1 ns )

11. Results : mean first passage time (MFPT)

12. Results : second moments Poisson long-time relaxation

13. Results : a dynamic ‘phase diagram’ exponential relaxation power-law relaxation

14. A fantasy from the protein folding problem…

15. A ‘toy’ model : Rubik’s cube

16. Monte Carlo simulations

17. Summary Random walks on a complex energy landscape Exponential nonexponential kinetics Nonexponential kinetics can happen for a downhill folding process (cf. experimental work by Gruebele et al., PNAS 96, 6031(1999))