Transition States in Protein Folding Thomas Weikl Max Planck Institute of Colloids and Interfaces Department of Theory and Bio-Systems.
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Transition States in Protein Folding Thomas Weikl Max Planck Institute of Colloids and Interfaces Department of Theory and Bio-Systems Overview • Mutational -value analysis of the folding kinetics • Modeling -values for -helices • Modeling -values for small -sheet proteins Protein folding problems • The structure problem: In which native structure does a given sequence fold? • The kinetics problem: How does a protein fold into its structure? How does a protein fold? • The Levinthal paradox: How does a protein find its folded conformation as ”needle in the haystack“? • The ”old view”: Metastable folding intermediates guide a protein into its native structure • The ”new view”: Many small proteins fold without detectable intermediates (2-state proteins) 2-state folding: Single molecules • Donor and acceptor dyes at chain ends • State-dependent transfer efficiency 2-state folding: Protein ensemble • rapid mixing to initiate folding N protein + den. • single-exponential relaxation for 2-state process: denatured state D native state N spectroscopic signal H20 0 100 200 300 time (ms) Mutational analysis of 2-state folding • Transition state theory: T G k exp(-GT–D) D N • Mutations change the folding rate k and stability GN–D T’ G • Central quantities: -values GT–D GN–D T D N’ N Traditional interpretation of T’ G T’ T G T D N’ N = 1: mutated residue is native-like structured in T D N’ N = 0: mutated residue is unstructured in T Traditional interpretation of • : degree of structure formation of a residue in T Goldenberg, NSB 1999 • Inconsistencies: - some ’s are < 0 or > 1 - different mutations of the same residue can have different -values -values Example: -helix of CI2 mutation S12G S12A E15D E15N A16G K17G K18G I20V L21A L21G D23A K24G 0.29 0.43 0.22 0.53 1.06 0.38 0.70 0.40 0.25 0.35 -0.25 0.10 • -values for mutations in the helix range from -0.25 to 1.06 • Our finding: G GN • Mutational -value analysis of the folding kinetics • Modeling -values for -helices • Modeling -values for small -sheet proteins Helix cooperativity • we assume that a helix is either fully formed or not formed in transitionstate conformation Ti • we have two structural parameters per helix: - the degree of secondary structure in T - the degree of tertiary structure t in T Splitting up free energies • we split up mutation-induced free energy changes into secondary and tertiary components: GN G Gt GT G t Gt T G D N • general form of -values for mutations in an -helix: GT G t t GN GN -values for -helix of CI2 general formula: t t G GN mutational data for CI2 helix: 1.0 t 0.15 D23A G GN -values for helix 2 of protein A general formula: t t G GN mutational data for helix 2: 3 1 1.0 t 0.45 2 G GN Summary Consistent interpretation of -values for helices: • with two structural parameters: the degrees of secondary and tertiary structure formation in T • by splitting up mutation-induced free energy changes into secondary and tertiary components C Merlo, KA Dill, TR Weikl, PNAS 2005 TR Weikl, KA Dill, JMB 2007 • Mutational -value analysis of the folding kinetics • Modeling -values for -helices • Modeling -values for small -sheet proteins Modeling 3-stranded -proteins • WW domains are 3-stranded -proteins with two -hairpins • we assume that each hairpin is fully formed or not formed in the transition state Evidence for hairpin cooperativity • 3s is a designed 3-stranded -protein with 20 residues • transition state rigorously determined from foldingunfolding MD simulations • result: either hairpin 1 or hairpin 2 structured in T QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. A simple model for WW domains • we have two transitionstate conformations with a single hairpin formed • the folding rate is: k 12 eG1 RT eG2 RT • -values have the general form: RT logk 1G1 2G2 GN GN -values for FBP WW domain 1G1 2G2 • general formula: theo • a first test: ’s for mutations affecting only hairpin 1 should have value 1 exp GN -values for FBP WW domain • general formula: theo • single-parameter fit: exp 1G1 2G2 GN 1 0.77 2 = 1- 1 0.23 theo Summary Reconstruction of transition states from mutational -values based on: • substructural cooperativity of helices and hairpins • splitting up mutation-induced free energy changes C Merlo, KA Dill, TR Weikl, PNAS 2005 TR Weikl, KA Dill, J Mol Biol 2007 TR Weikl, Biophys J 2008