Simple two-state protein folding kinetics requires near-levinthal thermodynamic cooperativity

Detection and structure determination of an equilibrium unfolding intermediate of Rd-apocytochrome b562: native fold with non-native hydrophobic interactions

The absence of detectable kinetic and equilibrium folding intermediates by optical probes is commonly taken to indicate that protein folding is a two-state process. However, for some small proteins with apparent two-state behavior, unfolding intermediates have been identified in native-state hydrogen exchange or kinetic unfolding experiments monitored by nuclear magnetic resonance. Rd-apocytochrome b(562), a four-helix bundle, is one such protein. Here, we found another unfolding intermediate for Rd-apocytochrome b(562). It is based on a cooperative transition of (15)N chemical shifts of amide protons as a function of urea concentrations before the global unfolding. We have solved the high-resolution structure of the protein at 2.8 M urea, which is after this cooperative transition but before the global unfolding. All four helices remained intact, but a number of hydrophobic core residues repacked. This intermediate provides a possible structural interpretation for the kinetic unfolding intermediates observed using nuclear magnetic resonance methods for several proteins and has important implications for theoretical studies of protein folding.

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.

Characterization of the Folding Energy Landscapes of Computer Generated Proteins Suggests High Folding Free Energy Barriers and Cooperativity may be Consequences of Natural Selection

To determine the extent to which protein folding rates and free energy landscapes have been shaped by natural selection, we have examined the folding kinetics of five proteins generated using computational design methods and, hence, never exposed to natural selection. Four of these proteins are complete computer-generated redesigns of naturally occurring structures and the fifth protein, called Top7, has a computer-generated fold not yet observed in nature. We find that three of the four redesigned proteins fold much faster than their naturally occurring counterparts. While natural selection thus does not appear to operate on protein folding rates, the majority of the designed proteins unfold considerably faster than their naturally occurring counterparts, suggesting possible selection for a high free energy barrier to unfolding. In contrast to almost all naturally occurring proteins of less than 100 residues but consistent with simple computational models, the folding energy landscape for Top7 appears to be quite complex, suggesting the smooth energy landscapes and highly cooperative folding transitions observed for small naturally occurring proteins may also reflect the workings of natural selection.

Contact order dependent protein folding rates: kinetic consequences of a cooperative interplay between favorable nonlocal interactions and local conformational preferences

Physical mechanisms underlying the empirical correlation between relative contact order (CO) and folding rate among naturally occurring small single-domain proteins are investigated by evaluating postulated interaction schemes for a set of three-dimensional 27mer lattice protein models with 97 different CO values. Many-body interactions are constructed such that contact energies become more favorable when short chain segments sequentially adjacent to the contacting residues adopt native-like conformations. At a given interaction strength, this scheme leads to folding rates that are logarithmically well correlated with CO (correlation coefficient r = 0.914) and span more than 2.5 orders of magnitude, whereas folding rates of the corresponding Gō models with additive contact energies have much less logarithmic correlation with CO and span only approximately one order of magnitude. The present protein chain models also exhibit calorimetric cooperativity and linear chevron plots similar to that observed experimentally for proteins with apparent simple two-state folding/unfolding kinetics. Thus, our findings suggest that CO-dependent folding rates of real proteins may arise partly from a significant positive coupling between nonlocal contact favorabilities and local conformational preferences.