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Protein folding kinetics and more

Protein folding kinetics and more. Chi-Lun Lee ( 李紀倫 ). Department of Physics National Central University. Introduction. Protein (polypeptide chain): chain of amino acid residues. Primary structure : sequence of amino acid residues.

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Protein folding kinetics and more

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  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 (a helix, b 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. Cooperativity in folding Peak in specific heat vs. T c T Resemblance with first order transitions

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

  7. The real world is much more complicated unfolded folded 0 r (order parameter) 1

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

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

  10. Kinetics : Metropolis dynamics+CTRW Transition rate between two conformations ( R0 ~ 1 ns )

  11. Results : mean first passage time (MFPT)

  12. Results : second moments long-time relaxation Poisson

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

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