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