Using Rate-Equilibrium Free Energy Relationships to Characterize Protein Folding Transition States I. E. Sánchez and T. Kiefhaber

Rate-Equilibrium Free Energy Relationships in Protein Folding Part 1

Experimental Characterization of Reaction Kinetics

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

Structure-Induced Rate-Equilibrium Free Energy Relationships 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  x with Changes in 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)

 f -Values Vs. Solvent-Induced  x -Values Solvent-induced  x -values: Large number of data points over a broad range of  G 0  f -values: Two-point analysis folding:  f unfolding:  f -1

Two-Point Vs. Many-Point  f -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 -1) Artificially high and low  f -values for |  G 0 |<7 kJ/mol

Two-Point Vs. Many-Point  f -Values (Data from Mok et al., 2001 and Northey et al., 2002) Two-point  f -values match the true  f -values for |  G 0 |>7 kJ/mol

Update: Two-Point Vs. Many-Point  f -Values for 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 |  G 0 |<7 kJ/mol  f = 1.12 (  f -1)

Two-Point Vs. Many-Point  f -Values in the Gating Reaction of the Acetylcholine Receptor A many-point  f -value analysis by Cymes et al., 2002 ln(K eq ) ln(k op ) Artificially high and low  f -values for |  G 0 |<6 kJ/mol Two-point  f -values match the true  f -value for |  G 0 |>6 kJ/mol

Factors Affecting Two-point  -Value Analysis of Protein Folding (Sánchez and Kiefhaber, 2003d) Factors Affecting Two-point  f -Value Analysis of Protein Folding (Sánchez and Kiefhaber, 2003d) A two-point  f -value is inaccurate if |  G 0 |<7 kJ/mol “|  G 0 |-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 k 0 Drastic mutations instead of small deletions are recommended High-throughput mutagenesis and expression methods may be useful

Implications for the Mechanism of Protein Folding Part 2

 f -value Studies of Protein Folding Transition States There are “polarized” (Riddle et al., 1999) and “diffuse” transition states (Itzhaki et al., 1995)

 f -value Studies of Protein Folding Transition States Most  f -values are low (Goldenberg, 1999) “Nucleus” “Kinetic” The unusual “nucleus” and “kinetic”  f -values are considered most important (nucleation-condensation model)

Selection and Analysis of  f -Value Studies Large number of variants evenly distributed in the structure  G 0 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  f -values in Diffuse Transition States For all “nucleus” and “kinetic”  f -values |  G 0 |<7 kJ/mol Data for CI2 (Itzhaki et al., 1995)

Unusual  f -values in Diffuse Transition States For all “nucleus” and “kinetic”  f -values |  G 0 |<7 kJ/mol Two-point  f -values match the average  f for |  G 0 |>7 kJ/mol Data for CI2, Im9, Cyt b562, ADA2h, Sso7d SH3 and protein G

Update: Transition State for Folding of c-Myb Data from Gianni et al., 2003 For all “nucleus” and “kinetic”  f -values |  G 0 |<7 kJ/mol Two-point  f -values match the average  f for |  G 0 |>7 kJ/mol

Update: Transition State for Folding of BdpA Data at 2M denaturant from Sato et al., 2004 For most “nucleus” and “kinetic”  f -values |  G 0 |<7 kJ/mol Two-point  f -values match the average  f for |  G 0 |>7 kJ/mol

Update: Transition State for Folding of Engrailed Homeodomain For most “nucleus” and “kinetic”  f -values |  G 0 |<7 kJ/mol Data from Gianni et al., 2003

Unusual  f -values in Polarized Transition States Data for ACBP, fyn SH3, Im7, protein L and src SH3 For 70% of all “nucleus” and “kinetic”  f -values |  G 0 | 7 kJ/mol compared to diffuse transition states

Update: Transition State for Folding of CspB For most “nucleus”  f -values |  G 0 |<7 kJ/mol Data from García-Mira et al., 2004

Update: Transition State for Folding of L23 No “nucleus” or “kinetic”  f -values for |  G 0 |>7 kJ/mol Data from Hedberg and Oliveberg, 2004

Testing for “Kinetic”  f -values in Protein Folding Only 3 sites of 438 may have a strong kinetic role during folding For kinetic “sites”  G 0 should be small -> error in  f would be large -> Kinetic sites are better detected in a  G 0‡ vs.  G 0 plot Diffuse TSPolarized TS

The Properties of Protein Folding Transition States (Sánchez 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

Acknowledgements Thomas Kiefhaber Luis Serrano, EMBL Heidelberg Organizing Committee

Testing for “Kinetic”  f -values in Enzyme Catalysis (Fersht et al., 1987)