Cooperativity in two-state protein folding kinetics

The N-terminal to C-terminal motif in protein folding and function

Essentially all proteins known to fold kinetically in a two-state manner have their N- and C-terminal secondary structural elements in contact, and the terminal elements often dock as part of the experimentally measurable initial folding step. Conversely, all N-C no-contact proteins studied so far fold by non-two-state kinetics. By comparison, about half of the single domain proteins in the Protein Data Bank have their N- and C-terminal elements in contact, more than expected on a random probability basis but not nearly enough to account for the bias in protein folding. Possible reasons for this bias relate to the mechanisms for initial protein folding, native state stability, and final turnover.

Monitoring protein folding at atomic resolution

Elucidation of the mechanisms by which proteins fold from disordered conformations to their unique native conformations is one of the most challenging tasks facing structural biologists. Understanding the mechanism(s) of protein folding involves the characterization of all structural species that occur in the protein-folding reaction. Nuclear magnetic resonance (NMR) spectroscopy is a powerful and versatile technique that provides an avenue to investigate the structures of the various conformational states at the residue level along the protein-folding reaction coordinate. In this Account, we provide a comprehensive review of the recent progress on the applications of NMR to monitor equilibrium and kinetic conformational states of the protein-folding reaction.

Explicit-chain model of native-state hydrogen exchange: Implications for event ordering and cooperativity in protein folding

Native-state hydrogen exchange experiments on several proteins have revealed partially unfolded conformations with diverse stabilities. These equilibrium observations have been used to support kinetic arguments that folding proceeds via a sequential "pathway." This interpretative logic is evaluated here by analyzing the relationship between thermodynamic behavior and folding kinetics in a class of simplified lattice protein models. The chain models studied have varying degrees of cooperative interplay (coupling) between local helical conformational preference and favorable nonlocal interactions. When model cooperativity is high, as native conditions are weakened, "isotherms" of free energy of exchange for residues belonging to the same helix merge together before global unfolding. The point of merger depends on the model energetic favorability of the helix. This trend is similar to the corresponding experimental observations. Kinetically, we find that the ordering of helix formation in the very last stage of native core assembly tends to follow the stabilities of their converged isotherms. In a majority (but not all) of folding trajectories, the final assembly of helices that are thermodynamically more stable against exchange precedes that of helices that are less stable against exchange. These model features are in partial agreement with common experimental interpretations. However, the model results also underscore the ensemble nature of the folding process: the kinetics of helix formation is not a discrete, strictly "all-or-none" process as that envisioned by certain non-explicit-chain models. Helices generally undergo many cycles of partial formation and dissolution before their conformations are fixed in the final assembly stage of folding, a kinetic stage that takes up only approximately 2% of the average folding time in the present model; and the ordering of the helices' final assembly in some trajectories can be different from the dominant ordering stipulated by the exchange isotherms.

Phi-value analysis and the nature of protein-folding transition states

Phi values are used to map structures of protein-folding transition states from changes in free energies of denaturation (DeltaDeltaG(D-N)) and activation on mutation. A recent reappraisal proposed that Phi values for DeltaDeltaG(D-N) < 1.7 kcal/mol are artifactual. On discarding such derived Phi values from published studies, the authors concluded that there are no high Phi values in diffuse transition states, which are consequently uniformly diffuse with no evidence for nucleation. However, values of DeltaDeltaG(D-N) > 1.7 kcal/mol are often found for large side chains that make dispersed tertiary interactions, especially in hydrophobic cores that are in the process of being formed in the transition state. Conversely, specific local interactions that probe secondary structure tend to have DeltaDeltaG(D-N) approximately 0.5-2 kcal/mol. Discarding Phi values from lower-energy changes discards the crucial information about local interactions and makes transition states appear uniformly diffuse by overemphasizing the dispersed tertiary interactions. The evidence for the 1.7 kcal/mol cutoff was based on mutations that had been deliberately designed to be unsuitable for Phi-value analysis because they are structurally disruptive. We confirm that reliable Phi values can be derived from the recommended mutations in suitable proteins with 0.6 < DeltaDeltaG(D-N) < 1.7 kcal/mol, and there are many reliable high Phi values. Transition states vary from being rather diffuse to being well formed with islands of near-complete secondary structure. We also confirm that the structures of transition-state ensembles can be perturbed by mutations with DeltaDeltaG(D-N) >> 2 kcal/mol and that protein-folding transition states do move on the energy surface on mutation.