Using Rate-EquilibriumUsing Rate-EquilibriumFree Energy Relationships to Free Energy Relationships to Characterize Protein Folding Characterize Protein Folding

Transition StatesTransition States

I. E. Sánchez and T. KiefhaberI. E. Sánchez and T. Kiefhaber

Rate-EquilibriumRate-EquilibriumFree Energy RelationshipsFree Energy Relationships

in Protein Foldingin Protein Folding

Part 1Part 1

Experimental Characterization of Reaction KineticsExperimental Characterization of Reaction Kinetics

Leffler’s Rate-Equilibrium Free Energy RelationshipsLeffler’s Rate-Equilibrium Free Energy Relationships

x G0‡ x

G0 x

The relative effect of a perturbation x on the free energy of the transition state of a reaction (compared to the effect on the free energy of the ground states) allows a structural characterization of the transition state for the reaction coordinate probed by x (Leffler, 1953)

(≠ Brønsted: relationship between the rate constant of an acid- or base-catalyzed reaction and the dissociation constant of the catalyst)

Medium-Induced Rate-EquilibriumMedium-Induced Rate-EquilibriumFree Energy RelationshipsFree Energy Relationships

dG0 V 0dp S0dT i0dn i

dG0‡ V 0‡dp S0‡dT i0‡dni

v G0‡ /pG 0 /p

V 0‡

V 0

C Cp

0‡

Cp0

T G0‡ /TG 0 /T

S0‡

S0

D G f

0‡ / D G0 / D

m f

meq

Structure-Induced Rate-EquilibriumStructure-Induced Rate-EquilibriumFree Energy RelationshipsFree Energy Relationships

S f G f

0‡ /StructureG0 /Structure

Measures the normalized energetic role of side chains in the transition state (Matthews, Fersht & co-workers)

Can be defined for single residues, secondary structure elements or the whole protein

Analysis of Changes in Analysis of Changes in xx with Changes in with Changes in

Stability (Hammond Behavior)Stability (Hammond Behavior)

• Shifts in D with increasing denaturant concentration are generally due to a change in the rate-limiting step for folding between consecutive transition states on a linear pathway (Sánchez and Kiefhaber, 2003a)

• Genuine Hammond behavior is rare (1 of 21 proteins), apparent changes in the position of the transition state are mostly due to ground state effects (commonly, disruption of residual structure in the unfolded state) (Sánchez and Kiefhaber 2003b, c)

ff-Values -Values Vs.Vs. Solvent-Induced Solvent-Induced xx-Values-Values

Solvent-induced x-values:Large number of data points over a broad range of G0

f-values:Two-point analysis

folding: f

unfolding: f-1

Two-Point Two-Point Vs.Vs. Many-Point Many-Point ff-Values-Values

Multiple mutations at position 24 of the fyn SH3 domain(data from Northey et al., 2002)

Drastic mutations do not affect transition state structure

f = 0.33

f = 0.33

(f-1)

Artificially high and low f-values for |G0|<7 kJ/mol

Two-Point Two-Point Vs.Vs. Many-Point Many-Point ff-Values-Values

(Data from Mok et al., 2001 and Northey et al., 2002)

Two-point f-values match the true f-values for |G0|>7 kJ/mol

Update: Two-Point Update: Two-Point Vs.Vs. Many-Point Many-Point ff-Values-Values

for Position 53 of RNase HIfor Position 53 of RNase HI

(Data from Spudich et al., 2004)

Drastic mutations do not affect transition state structure

Artificially high and low f-values for |G0|<7 kJ/mol

f = 1.12

(f-1)

Two-Point Two-Point Vs.Vs. Many-Point Many-Point ff-Values in the -Values in the

Gating Reaction of the Acetylcholine ReceptorGating Reaction of the Acetylcholine Receptor

A many-point f-value analysis by Cymes et al., 2002

ln(Keq)

ln

(kop

)

Artificially high and low f-values for |G0|<6 kJ/molTwo-point f-values match the true f-value for |G0|>6 kJ/mol

Factors Affecting Two-point Factors Affecting Two-point f-Value Analysis of -Value Analysis of

Protein Folding Protein Folding (S(Sánchez and Kiefhaber, 2003d)ánchez and Kiefhaber, 2003d)

• A two-point f-value is inaccurate if |G0|<7 kJ/mol

• “|G0|-independent noise” in the rate-equilibrium free energy relationship may be due to small changes in transition state structure or in the pre-exponential factor k0

• Drastic mutations instead of small deletions are recommended

• High-throughput mutagenesis and expression methods may be useful

Implications for the MechanismImplications for the Mechanismof Protein Foldingof Protein Folding

Part 2Part 2

ff-value Studies of Protein Folding Transition States-value Studies of Protein Folding Transition States

There are “polarized”

(Riddle et al., 1999)

and “diffuse” transition states

(Itzhaki et al., 1995)

ff-value Studies of Protein Folding Transition States-value Studies of Protein Folding Transition States

Most f-values are low (Goldenberg, 1999)

“Nucleus”

“Kinetic”

“Kinetic”

The unusual “nucleus” and “kinetic” f-values are considered most important (nucleation-condensation model)

Selection and Analysis of Selection and Analysis of ff-Value Studies-Value Studies

• Large number of variants evenly distributed in the structure

G0 determined from kinetic measurements• Rate and equilibrium constants were

extrapolated to 0M denaturant• Mutants inducing a change in the rate-limiting

step for folding (as seen from D) or in the structure on one of the ground states (as seen from m-values) were kept out

Unusual Unusual ff-values-values in Diffuse Transition Statesin Diffuse Transition States

For all “nucleus” and “kinetic” f-values |G0|<7 kJ/mol

Data for CI2 (Itzhaki et al., 1995)

Unusual Unusual ff-values-values in Diffuse Transition Statesin Diffuse Transition States

For all “nucleus” and “kinetic” f-values |G0|<7 kJ/molTwo-point f-values match the average f for |G0|>7 kJ/mol

Data for CI2, Im9, Cyt b562, ADA2h, Sso7d SH3 and protein G

Update: Transition State for Folding of c-MybUpdate: Transition State for Folding of c-Myb

Data from Gianni et al., 2003

For all “nucleus” and “kinetic” f-values |G0|<7 kJ/molTwo-point f-values match the average f for |G0|>7 kJ/mol

Update: Transition State for Folding of BdpAUpdate: Transition State for Folding of BdpA

Data at 2M denaturant from Sato et al., 2004

For most “nucleus” and “kinetic” f-values |G0|<7 kJ/molTwo-point f-values match the average f for |G0|>7 kJ/mol

Update: Transition State for Folding of Update: Transition State for Folding of Engrailed HomeodomainEngrailed Homeodomain

For most “nucleus” and “kinetic” f-values |G0|<7 kJ/mol

Data from Gianni et al., 2003

Unusual Unusual ff-values-values in Polarized Transition Statesin Polarized Transition States

Data for ACBP, fyn SH3, Im7, protein L and src SH3

For 70% of all “nucleus” and “kinetic” f-values |G0|<7 kJ/mol Larger scattering for |G0|>7 kJ/mol compared to diffuse transition states

Update: Transition State for Folding of CspBUpdate: Transition State for Folding of CspB

For most “nucleus” f-values |G0|<7 kJ/mol

Data from García-Mira et al., 2004

Update: Transition State for Folding of L23Update: Transition State for Folding of L23

No “nucleus” or “kinetic” f-values for |G0|>7 kJ/mol

Data from Hedberg and Oliveberg, 2004

Testing for “Kinetic” Testing for “Kinetic” ff-values in Protein Folding-values in Protein Folding

Only 3 sites of 438 may have a strong kinetic role during folding

For kinetic “sites” G0 should be small -> error in f would be large ->Kinetic sites are better detected in a G0‡ vs. G0 plot

Diffuse TS Polarized TS

The Properties of Protein Folding Transition States The Properties of Protein Folding Transition States (S(Sánchez and Kiefhaber, 2003d)ánchez and Kiefhaber, 2003d)

• Reliable f-values for structured regions of transition states do not point at a folding nucleus formed by a small number of residues -> all side chains have a similar energetic role (distorted native-like structure)

f-values in structured regions of polarized transition states tend to be higher and more diverse than in diffuse transition states

• Side chains with a “kinetic” role in the folding reaction are rare -> only few transient non-native interactions

AcknowledgementsAcknowledgements

Thomas Kiefhaber

Luis Serrano, EMBL Heidelberg

Organizing Committee

Testing for “Kinetic” Testing for “Kinetic” ff-values in Enzyme Catalysis-values in Enzyme Catalysis

(Fersht et al., 1987)