Transition States in Protein Folding Thomas Weikl Max Planck Institute of Colloids and Interfaces Department of Theory and Bio-Systems

Mutational  -value analysis of the folding kinetics Modeling  -values for  -helices Modeling  -values for small  -sheet proteins Overview

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 ”old view”: Metastable folding intermediates guide a protein into its native structure The Levinthal paradox: How does a protein find its folded conformation as ”needle in the haystack“? 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 Schuler et al., Nature 2002 State-dependent transfer efficiency

2-state folding: Protein ensemble rapid mixing to initiate folding N protein + den. H20H20 denatured state D native state N single-exponential relaxa- tion for 2-state process: time (ms) spectroscopic signal

Mutational analysis of 2-state folding G D T N Transition state theory: k  exp(-G T–D ) D T N N’ T’ G Mutations change the folding rate k and stability G N–D Central quantities:  -values     G T–D  G N–D

 = 1: mutated residue is native-like structured in T Traditional interpretation of  D T N N’ T’ G G  = 0: mutated residue is unstructured in T D T N N’ T’

 : degree of structure formation of a residue in T Inconsistencies: - some  ’s are 1 - different mutations of the same residue can have different  -values  -values Goldenberg, NSB 1999 Traditional interpretation of 

Example:  -helix of CI2 S12G S12A E15D E15N A16G K17G K18G I20V L21A L21G D23A K24G mutation  Itzhaki, Otzen, Fersht,1995  -values for mutations in the helix range from to 1.06 Our finding: 

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 transition- state conformation T i we have two structural parameters per helix: - the degree of secondary structure   in T - the degree of tertiary structure  t in T

we split up mutation-induced free energy changes into secondary and tertiary components: general form of  -values for mutations in an  -helix: Splitting up free energies G D T N

 -values for  -helix of CI2 general formula:     1.0  t  0.15 mutational data for CI2 helix: D23A

 -values for helix 2 of protein A general formula: mutational data for helix 2:    1.0  t  0.45  11 33 22

Summary C Merlo, KA Dill, TR Weikl, PNAS 2005 TR Weikl, KA Dill, JMB 2007 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

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 folding- unfolding MD simulations result: either hairpin 1 or hairpin 2 structured in T Rao, Settanni, Guarnera, Caflisch, JCP 2005

A simple model for WW domains we have two transition- state conformations with a single hairpin formed  -values have the general form: the folding rate is:

 -values for FBP WW domain a first test:  ’s for mutations affecting only hairpin 1 should have value  1 general formula:  exp

 theo  exp single-parameter fit:  1  0.77  2 = 1-  1  0.23  -values for FBP WW domain general formula:

Summary C Merlo, KA Dill, TR Weikl, PNAS 2005 TR Weikl, KA Dill, J Mol Biol 2007 TR Weikl, Biophys J 2008 Reconstruction of transition states from mutational  -values based on: substructural cooperativity of helices and hairpins splitting up mutation-induced free energy changes