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