Microscopic Reversibility of Protein Folding in Molecular Dynamics Simulations of the Engrailed Homeodomain

In 1925, Richard C. Tolman coined the term “microscopic reversibility” in reference to chemical reactions: In recent years increasing use has been made of a new postulate which perhaps cannot yet be stated in its final form, but which requires in a general way in the case of a system in thermodynamic equilibrium not only that the total number of molecules leaving a given state in unit time shall on the average equal the number arriving in that state in unit time, but also that the number leaving by any particular path shall on the average be equal to the number arriving by the reverse of that particular path, thus excluding any cyclical maintenance of the equilibrium state. The writer has ventured to name this postulate the principle of microscopic reversibility (1). This description was recast into structural terms in 1967 by Frank H. Westheimer (2) and was adopted by the IUPAC in 1999: In the case of SN2 reactions at tetrahedral centers implying a formation of the trigonal bipyramid transition state (or intermediate) structure, the original formulation of the principle was extended in the following way: if a molecule or reactant enters a trigonal bipyramid at an apical position, this (or another) molecule or reactant must likewise leave the trigonal bipyramid from an apical position (3). The hypothesis that protein folding may, like chemical reactions, be microscopically reversible has since been offered. If this hypothesis is true, one would expect to observe identical transition states for folding and unfolding, and major events on the folding pathway would occur in reverse order in the unfolding pathway. Supporting evidence has been presented by Jackson et al. who showed through Φ-value analysis on chymotrypsin inhibitor 2 (CI21) that folding and unfolding transition states are the same, suggesting that the pathways are also the same (4). Additionally, molecular dynamics (MD) generated unfolding transition states (TS) of CI2 are in quantitative agreement with experimental data collected for both unfolding and refolding (5, 6). Furthermore, the unfolding and direct refolding pathways of CI2 were shown to be the same in a single continuous MD trajectory (7). The latter MD study was done at the melting temperature (Tm) of the protein, at which point the folding and unfolding rates are equal and ΔG = 0. For these reasons, exchange between the folded and unfolded states is dependent on the energy barrier, ΔG‡ ≈ 2.3 kcal/mol (8), and unfolding and refolding may occur in a single trajectory on time scales tractable by MD. The protein, CI2, passed through three different states, native (N), nearly native (N′), and denatured (D), then returned to N′ over a time period of about 60 ns. When moving from N′ to D and back, unfolding and refolding transition states were identified, and they were the same. The Cα root mean square deviation (RMSD) to the native structure and internal contacts were analyzed to differentiate between the three different states. Day and Daggett (7) defined N′, an alternate, stable state for CI2 at elevated temperature. The protein passed through N′ before it moved through its TS to D. N′ was characterized by many near-native interactions but elongated contact distances. In particular, Trp 5, a fluorescence unfolding probe, was buried in both N and N′, but not in D, as would be expected if both N and N′ were native but D was not. D had a disrupted hydrophobic core and loss of secondary structure. This CI2 study showed direct unfolding and refolding in a single continuous trajectory by the same structural pathways for the first time. Consequently, this behavior needs to be demonstrated in another system to ensure it is reproducible, which we describe here. The engrailed homeodomain (En-HD) of Drosophila melanogaster is a 61-residue three-helix bundle. It is ultra-fast folding (kF = 37,500 s-1 at 25°C and 51,000 s-1 around 42°C) and unfolding (kU = 1,100 s-1 at 25°C and 205,000 s-1 at 63°C), and its folding and unfolding pathways have been extensively characterized through combined experimental and MD studies (9-12). Folding for En-HD follows the framework model involving the docking of HI (residues 10-22), HII (28-38), and HIII (42-55) (13). These properties make En-HD especially well-suited for MD folding studies. In this study, we performed MD simulations of En-HD near its Tm (52°C = 325K (12)) to compare unfolding and refolding under identical conditions. We analyzed 5 simulations, 3 at 323K and 2 at 330K. We compared them to 4 previously described thermal denaturation simulations, 2 each at 373K and 498K, and one native simulation at 298K. The first of the 373K simulations was found to contain a region of particular interest that had not been previously reported, so that simulation was also analyzed in detail. We identified and characterized 3 different states populated during unfolding and refolding: N, N′, and D. We also found 6 transient denaturing events in which En-HD partially unfolded and refolded in 3 of the 5 Tm simulations; from this 12 unfolding and refolding transition state ensembles (TSE) were identified. En-HD unfolded in the 373K/1 simulation, and a TSE in agreement with experiment was reported previously (9, 12, 13). Further investigation of this simulation showed that En-HD later refolded, so we also describe this high temperature refolding TSE. These 13 TSEs agree well with the 4 previously identified unfolding TSEs from the 4 high-temperature simulations. Besides defining TSEs, we analyzed the entire pathway En-HD followed as it unfolded and refolded. Five of the 7 refolding pathways were nearly identical to the unfolding pathways that preceded them. These 5 examples are further evidence that the ensembles of folding and unfolding pathways are one and the same, and that protein folding is a microscopically reversible process. However, in the other 2 cases, En-HD passed through remarkably similar unfolding and refolding transition states, but only a portion of the actual refolding pathway was similar to the unfolding pathway.