The transition state ensemble during the folding process of globular proteins occurs when a sufficient number of intrachain contacts are formed, mainly, but not exclusively, due to hydrophobic interactions. These contacts are related to the folding nucleus, and they contribute to the stability of the native structure, although they may disappear after the energetic barrier of transition states has been passed. A number of structure and sequence analyses, as well as protein engineering studies, have shown that the signature of the folding nucleus is surprisingly present in the native three-dimensional structure, in the form of closed loops, and also in the early folding events. These findings support the idea that the residues of the folding nucleus become buried in the very first folding events, therefore helping the formation of closed loops that act as anchor structures, speed up the process, and overcome the Levinthal paradox. We present here a review of an algorithm intended to simulate in a discrete space the early steps of the folding process. It is based on a Monte Carlo simulation where perturbations, or moves, are randomly applied to residues within a sequence. In contrast with many technically similar approaches, this model does not intend to fold the protein but to calculate the number of non-covalent neighbors of each residue, during the early steps of the folding process. Amino acids along the sequence are categorized as most interacting residues (MIRs) or least interacting residues. The MIR method can be applied under a variety of circumstances. In the cases tested thus far, MIR has successfully identified the exact residue whose mutation causes a switch in conformation. This follows with the idea that MIR identifies residues that are important in the folding process. Most MIR positions correspond to hydrophobic residues; correspondingly, MIRs have zero or very low accessible surface area. Alongside the review of the MIR method, we present a new postprocessing method called smoothed MIR (SMIR), which refines the original MIR method by exploiting the knowledge of residue hydrophobicity. We review known results and present new ones, focusing on the ability of MIR to predict structural changes, secondary structure, and the improved precision with the SMIR method.
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The protein folding problem would be considered “solved” when it will be possible to “read genes”, i.e., to predict the native fold of proteins, their dynamics, and the mechanism of fast folding based solely on sequence data. The long-term goal should be the creation of an algorithm that would simulate the stepwise mechanism of folding, which constrains the conformational space and in which random search for stable interactions is possible. Here, we focus attention on the initial phases of the folding transition starting with the compact disordered collapsed ensemble, in search of the initial sub-domain structural biases that direct the otherwise stochastic dynamics of the backbone. Our studies are designed to test the “loop hypothesis”, which suggests that fast closure of long loop structures by non-local interactions between clusters of mainly non-polar residues is an essential conformational step at the initiation of the folding transition of globular proteins. We developed and applied experimental methods based on time-resolved resonance excitation energy transfer (trFRET) measurements combined with fast mixing methods and studied the initial phases of the folding of Escherichia coli adenylate kinase (AK). A series of AK mutants were prepared, in which the ends of selected backbone segments that form long closed loops or secondary structure elements were labeled by donors and acceptors of excitation energy. The end-to-end distance distributions of such segments were determined under equilibrium and during the fast folding transitions. These experiments show that three out of seven long loops that were labeled in the AK molecule are closed very early in the transition. The N terminal 26-residue loop (loop I) is closed in <200 μs after the initiation of folding, while the β strand included in loop I is still disordered. The closure of the second 44-residue loop (loop II, which starts at the end of loop I) is also complete within <300 μs. Four other loops as well as five secondary structures of the CORE domain of AK (an α helix and four β strands) are formed at a late step, at a rate of 0.5±0.3 s–1, the rate of the cooperative folding of the molecule. These experiments reveal a hierarchically ordered pathway of folding of the AK molecule, ranging from microseconds to seconds. The results reviewed here, obtained mainly from studying a small number of model proteins, support the counterintuitive mechanism whereby non-local interactions are effective in the initiation of the folding pathways. The experiments presented demonstrate the importance of mapping the rates of sub-domain structural transitions along the folding transition, in situ, in the context of the other sections of the chain, whether folded or disordered. These experiments also show the power of the time-resolved FRET measurements in achieving this goal. A large body of data obtained by theoretical and experimental studies that support, or can accommodate, the loop hypothesis is reviewed. We suggest that mapping multiple sub-domain structural transitions during the refolding transition of many proteins using the approach presented here will refine the conclusions and help reveal some common principles of the initiation of the folding. To achieve this goal, the trFRET measurements should be combined with mutagenesis experiments where the role of selected residue clusters will be tested by perturbation mutations. Nevertheless, the solution of the protein folding problem depends on the application of many additional approaches, both experimental and theoretical, while the approach presented here is only a small section of the big puzzle.
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