Transition States in Protein Folding

Thomas Weikl

Max Planck Institute of Colloids and InterfacesDepartment 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 foldingN

protein + den.

H20

denatured state D

native state N

• single-exponential relaxa-tion for 2-state process:

time (ms)0 100 200 300

spec

tros

copi

c si

gnal

Mutational analysis of 2-state folding

G

D

T

N

• Transition state theory:

k exp(-GT–D)

D

T

N

N’

T’G

• Mutations change the folding

rate k and stability GN–D

• Central quantities: -values

GT–D

GN–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 < 0 or > 1

- different mutations of

the same residue can

have different -values

-values

G

old

en

be

rg,

NS

B 1

99

9

Traditional interpretation of

Example: -helix of CI2

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

mutation

Itzhaki, Otzen, Fersht,1995

• -values for mutations in the helix range from -0.25 to 1.06

• Our finding:

€

Gα ΔGN

• 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 Ti

• 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:

€

≡GT

ΔGN

= χ t + χ α − χ t( )ΔGα

ΔGN

Splitting up free energies

€

GT = χ α ΔGα + χ tΔGt

€

GN = ΔGα + ΔGt G

D

T

N

-values for -helix of CI2

general formula:

€

=t + χα − χt( )ΔGα

ΔGN

1.0t 0.15

mutational data for CI2 helix:

€

Gα ΔGN

D23A

-values for helix 2 of protein A

general formula:

€

=t + χα − χt( )ΔGα

ΔGN

mutational data for helix 2:

1.0t 0.45

1

3

2

€

Gα ΔGN

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

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 transition-state conformations with a single hairpin formed

€

≡−RT Δlogk

ΔGN

=χ1ΔG1 + χ 2ΔG2

ΔGN

• -values have the general form:

• the folding rate is:

€

k ≈ 12 e −G1 R T + e −G 2 R T( )

-values for FBP WW domain

• a first test: ’s for mutations affecting only hairpin 1 should have value 1

• general formula:

€

theo =χ 1ΔG1 + χ2ΔG2

ΔGN

exp

theo

exp

• single-parameter fit:

1 0.772 = 1- 1 0.23

-values for FBP WW domain

• general formula:

€

theo =χ 1ΔG1 + χ2ΔG2

ΔGN

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