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Protein folding kinetics and more Chi-Lun Lee ( 李紀倫 ) Department of Physics National Central University
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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
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For a single domain globular protein (~100 amid acid residues), its diameter ~ 5nm and molecular mass ~ 10000 daltons (compact structure)
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Features of protein folding : Volume exclusion and chain connectivity Van der Waals interactions Hydrogen bond Hydrophobic interactions …
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Peak in specific heat vs. T c T Resemblance with first order transitions Cooperativity in folding
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Concepts from chemical reactions Transition state theory F Reaction coordinate Unfolded Transition state Folded F* Arrhenius relation : k AB ~ exp(- F*/T)
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foldedunfolded 01 (order parameter) The real world is much more complicated
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Energy surface may be rough at times… Traps from local minima Non-Arrenhius relation Non-exponential relaxation Glassy dynamics?
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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
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Kinetics : Metropolis dynamics+CTRW Transition rate between two conformations ( R 0 ~ 1 ns )
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Results : mean first passage time (MFPT)
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Results : second moments Poisson long-time relaxation
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Results : a dynamic ‘phase diagram’ exponential relaxation power-law relaxation
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A fantasy from the protein folding problem…
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A ‘toy’ model : Rubik’s cube
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Monte Carlo simulations
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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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