Are the same or different amino acid residues responsible for correct and incorrect protein folding?

It has been shown for 20 proteins that amino acid residues included into the protein folding nucleus, determined experimentally, are often involved in the theoretically determined amyloidogenic fragments. For 18 proteins, Φ-values indicative of the extent of residue involvement into the folding nucleus are on average higher for amino acid residues within amyloidogenic regions. Amyloidogenic fragments were predicted for 20 proteins by two methods chosen from four on the basis of comparison of prediction of amyloidogenic regions known from experimental data. Since theoretical folding nuclei are detected by the protein three-dimensional structure and amyloidogenic regions by the protein chain primary structure, the detected regularity makes possible predictions of folding nucleation sites on the basis of amino acid sequence.     

Is protein unfolding the reverse of protein folding? A lattice simulation analysis.

Simulations and experiments that monitor protein unfolding under denaturing conditions are commonly employed to study the mechanism by which a protein folds to its native state in a physiological environment. Due to the differences in conditions and the complexity of the reaction, unfolding is not necessarily the reverse of folding. To assess the relevance of temperature initiated unfolding studies to the folding problem, we compare the folding and unfolding of a 125-residue protein model by Monte Carlo dynamics at two temperatures; the lower one corresponds to the range used in T -jump experiments and the higher one to the range used in unfolding simulations of all-atom models. The trajectories that lead from the native state to the denatured state at these elevated temperatures are less diverse than those observed in the folding simulations. At the lower temperature, the system unfolds through a mandatory intermediate that corresponds to a local free energy minimum. At the higher temperature, no such intermediate is observed, but a similar pathway is followed. The structures contributing to the unfolding pathways resemble most closely those that make up the "fast track" of folding. The transition state for unfolding at the lower temperature (above Tm) is determined and is found to be more structured than the transition state for folding below the melting temperature. This shift towards the native state is consistent with the Hammond postulate. The implications for unfolding simulations of higher resolution models and for unfolding experiments of proteins are discussed.     

Is protein folding hierarchic? I. Local structure and peptide folding

The folding reactions of some small proteins show clear evidence of a hierarchic process, whereas others, lacking detectable intermediates, do not. Nevertheless, we argue that both classes fold hierarchically and that folding begins locally. If this is the case, then the secondary structure of a protein is determined largely by local sequence information. Experimental data and theoretical considerations support this argument. Part I of this article reviews the relationship between secondary structures in proteins and their counterparts in peptides.     

Who solved the protein folding problem?

For the third time, techniques for the prediction of three-dimensional structures of proteins were critically assessed in a worldwide blind test. Steady progress is undeniable. How did this happen and what are the implications?     

Is protein folding rate dependent on number of folding stages? Modeling of protein folding with ferredoxin-like fold

Statistical analysis of protein folding rates has been done for 84 proteins with available experimental data. A surprising result is that the proteins with multi-state kinetics from the size range of 50–100 amino acid residues (a.a.) fold as fast as proteins with two-state kinetics from the same size range. At the same time, the proteins with two-state kinetics from the size range 101–151 a.a. fold faster than those from the size range 50–100 a.a. Moreover, it turns out unexpectedly that usually in the group of structural homologs from the size range 50–100 a.a., proteins with multi-state kinetics fold faster than those with two-state kinetics. The protein folding for six proteins with a ferredoxin-like fold and with a similar size has been modeled using Monte Carlo simulations and dynamic programming. Good correlation between experimental folding rates, some structural parameters, and the number of Monte Carlo steps has been obtained. It is shown that a protein with multi-state kinetics actually folds three times faster than its structural homologs.     

The posttranslational concept of protein folding: how valid is it?

Two concepts of protein folding are known. One of them, the cotranslational concept, states that a protein folds during the synthesis of the polypeptide chain on the ribosome. According to the other, the posttranslational concept, the protein starts to fold just after the synthesis of its polypeptide chain. This article attempts to show that the posttranslational concept is hardly suited to solve the problem of protein folding. In our opinion, polypeptide chains cannot be represented as random coils. They are stiff chain-like macromolecules rather than flexible ones: the single bond rotational barriers of a polypeptide substantially exceed the accepted standard values; even in strong denaturing conditions, a protein possesses a considerable amount of residual folded structures. We believe that the popular "hierarchical" models for the protein folding mechanism are not realistic because the formation of secondary and tertiary structures of proteins occurs simultaneously and cooperatively. The time for the elongation of a polypeptide chain by one amino acid residue during biosynthesis exceeds considerably the time of the formation of alpha-helices and beta-sheets in proteins as well as the time supposed for the spatial structure formation of a native protein during renaturation. Thus, we believe that the mechanism of protein folding in vivo cannot be clarified by denaturation-renaturation experiments. In our opinion, the phenomenon of protein renaturation is no more than the restoration of native protein conformation (which initially forms cotranslationally) disrupted during denaturation, and thus denaturation-renaturation experiments cannot serve as a model to clarify the mechanism of protein folding.     

Is the unfolded state the Rosetta Stone of the protein folding problem?

Solving the protein folding problem is one of the most challenging tasks in the post genomic era. Identification of folding-initiation sites is very important in order to understand the protein folding mechanism. Detection of residual structure in unfolded proteins can yield important clues to the initiation sites in protein folding. A substantial number of studied proteins possess residual structure in hydrophobic regions clustered together in the protein core. These stable structures can work as seeds in the folding process. In addition, local preferences for secondary structure in the form of turns for beta-sheet initiation and helical turns for alpha-helix formation can guide the folding reaction. In this respect the unfolded states, studied at increasing structural resolution, can be the Rosetta Stone of the protein folding problem.     

When is now? Perception of simultaneity.

We address the following question: Is there a difference (D) between the amount of time for auditory and visual stimuli to be perceived? On each of 1000 trials, observers were presented with a light-sound pair, separated by a stimulus onset asynchrony (SOA) between -250 ms (sound first) and +250 ms. Observers indicated if the light-sound pair came on simultaneously by pressing one of two (yes or no) keys. The SOA most likely to yield affirmative responses was defined as the point of subjective simultaneity (PSS). PSS values were between -21 ms (i.e. sound 21 ms before light) and +150 ms. Evidence is presented that each PSS is observer specific. In a second experiment, each observer was tested using two observer-stimulus distances. The resultant PSS values are highly correlated (r = 0.954, p = 0.003), suggesting that each observer''s PSS is stable. PSS values were significantly affected by observer-stimulus distance, suggesting that observers do not take account of changes in distance on the resultant difference in arrival times of light and sound. The difference RTd in simple reaction time to single visual and auditory stimuli was also estimated; no evidence that RTd is observer specific or stable was found. The implications of these findings for the perception of multisensory stimuli are discussed.     

What determines protein folding type? An investigation of intrinsic structural properties and its implications for understanding folding mechanisms

Protein folding experiments demonstrate that the folding behaviors of many proteins can be roughly classified into two types: two-state kinetics and multi-state kinetics. Although the two types of protein folding kinetics have been observed for a long time, what determines the folding type of a protein is still largely unclear. The present work performed a comparative study based on a dataset of 43 two-state and 42 multi-state folders at different levels of proteins' intrinsic properties from the simplest sequence length to native structure topology. The results show that protein's amino acids composition and the long-range interaction-based topological complexity rather than secondary structure contents are the major determinants of protein folding type. Furthermore, a sequence-based folding type prediction achieved an accuracy of more than 80%. These findings implicate that there is no clear boundary between secondary and tertiary structure formation during the protein folding process and support the existence of a continuum of folding mechanism between the two ends of hierarchic and nucleation folding scenarios.     

What is the best reference state for designing statistical atomic potentials in protein structure prediction?

Many statistical potentials were developed in last two decades for protein folding and protein structure recognition. The major difference of these potentials is on the selection of reference states to offset sampling bias. However, since these potentials used different databases and parameter cutoffs, it is difficult to judge what the best reference states are by examining the original programs. In this study, we aim to address this issue and evaluate the reference states by a unified database and programming environment. We constructed distance-specific atomic potentials using six widely-used reference states based on 1022 high-resolution protein structures, which are applied to rank modeling in six sets of structure decoys. The reference state on random-walk chain outperforms others in three decoy sets while those using ideal-gas, quasi-chemical approximation and averaging sample stand out in one set separately. Nevertheless, the performance of the potentials relies on the origin of decoy generations and no reference state can clearly outperform others in all decoy sets. Further analysis reveals that the statistical potentials have a contradiction between the universality and pertinence, and optimal reference states should be extracted based on specific application environments and decoy spaces.     

Are synthetic proteins relevant to the problem of protein folding?

The possibility to derive the analogs of native proteins by the chemical synthesis is considered to be a serious argument for the concept of posttranslational protein folding. The present paper analyzes for the first time chemically synthesized proteins to reveal whether they are relevant to the problem of protein folding. The results enable the following conclusions to be drawn. The acquisition of the peculiar conformations by the chemically synthesized proteins to exhibit the specific functions is conditioned by the highly marked features of the secondary and tertiary structures of the corresponding native proteins. These features will make themselves evident only if favorable conditions are carefully chosen during the experiments for each individual protein. Thus, in our opinion, the possibility to derive a synthetic protein is hardly evidence for the posttranslational folding of proteins.     

When the feasibility of an ecosystem is sufficient for global stability?

We show via a Liapunov function that in every model ecosystem governed by generalized Lotka-Volterra equations, a feasible steady state is globally asymptotically stable if the number of interaction branches equals n-1, where n is the number of species. This means that the representative graph for which the theorem holds is a 'tree' and not only an alimentary chain. Our result is valid also in the case of non-homogeneous systems, which model situations in which input fluxes are present.     

Is protein folding hierarchic? II. Folding intermediates and transition states

The folding reactions of some small proteins show clear evidence of a hierarchic process, whereas others, lacking detectable intermediates, do not. Evidence from folding intermediates and transition states suggests that folding begins locally, and that the formation of native secondary structure precedes the formation of tertiary interactions, not the reverse. Some notable examples in the literature have been interpreted to the contrary. For these examples, we have simulated the local structures that form when folding begins by using the LINUS program with nonlocal interactions turned off. Our results support a hierarchic model of protein folding.     

Is there a unifying mechanism for protein folding?

Proteins appear to fold by diverse pathways, but variations of a simple mechanism - nucleation-condensation - describe the overall features of folding of most domains. In general, secondary structure is inherently unstable and its stability is enhanced by tertiary interactions. Consequently, an extensive interplay of secondary and tertiary interactions determines the transition-state for folding, which is structurally similar to the native state, being formed in a general collapse (condensation) around a diffuse nucleus. As the propensity for stable secondary structure increases, folding becomes more hierarchical and eventually follows a framework mechanism where the transition state is assembled from pre-formed secondary structural elements.     

Native topology or specific interactions: what is more important for protein folding?

Fifty-five molecular dynamics runs of two three-stranded antiparallel beta-sheet peptides were performed to investigate the relative importance of amino acid sequence and native topology. The two peptides consist of 20 residues each and have a sequence identity of 15 %. One peptide has Gly-Ser (GS) at both turns, while the other has d-Pro-Gly ((D)PG). The simulations successfully reproduce the NMR solution conformations, irrespective of the starting structure. The large number of folding events sampled along the trajectories at 360 K (total simulation time of about 5 micros) yield a projection of the free-energy landscape onto two significant progress variables. The two peptides have compact denatured states, similar free-energy surfaces, and folding pathways that involve the formation of a beta-hairpin followed by consolidation of the unstructured strand. For the GS peptide, there are 33 folding events that start by the formation of the 2-3 beta-hairpin and 17 with first the 1-2 beta-hairpin. For the (D)PG peptide, the statistical predominance is opposite, 16 and 47 folding events start from the 2-3 beta-hairpin and the 1-2 beta-hairpin, respectively. These simulation results indicate that the overall shape of the free-energy surface is defined primarily by the native-state topology, in agreement with an ever-increasing amount of experimental and theoretical evidence, while the amino acid sequence determines the statistically predominant order of the events.