Two-state folding over a weak free-energy barrier

Stitched α-helical peptides via bis ring-closing metathesis

Conformationally stabilized α-helical peptides are capable of inhibiting disease-relevant intracellular or extracellular protein-protein interactions in vivo. We have previously reported that the employment of ring-closing metathesis to introduce a single all-hydrocarbon staple along one face of an α-helical peptide greatly increases α-helical content, binding affinity to a target protein, cell penetration through active transport, and resistance to proteolytic degradation. In an effort to improve upon this technology for stabilizing a peptide in a bioactive α-helical conformation, we report the discovery of an efficient and selective bis ring-closing metathesis reaction leading to peptides bearing multiple contiguous staples connected by a central spiro ring junction. Circular dichroism spectroscopy, NMR, and computational analyses have been used to investigate the conformation of these "stitched" peptides, which are shown to exhibit remarkable thermal stabilities. Likewise, trypsin proteolysis assays confirm the achievement of a structural rigidity unmatched by peptides bearing a single staple. Furthermore, fluorescence-activated cell sorting (FACS) and confocal microscopy assays demonstrate that stitched peptides display superior cell penetrating ability compared to their stapled counterparts, suggesting that this technology may be useful not only in the context of enhancing the drug-like properties of α-helical peptides but also in producing potent agents for the intracellular delivery of proteins and oligonucleotides.

Polymer uncrossing and knotting in protein folding, and their role in minimal folding pathways

We introduce a method for calculating the extent to which chain non-crossing is important in the most efficient, optimal trajectories or pathways for a protein to fold. This involves recording all unphysical crossing events of a ghost chain, and calculating the minimal uncrossing cost that would have been required to avoid such events. A depth-first tree search algorithm is applied to find minimal transformations to fold [Formula: see text], [Formula: see text], [Formula: see text], and knotted proteins. In all cases, the extra uncrossing/non-crossing distance is a small fraction of the total distance travelled by a ghost chain. Different structural classes may be distinguished by the amount of extra uncrossing distance, and the effectiveness of such discrimination is compared with other order parameters. It was seen that non-crossing distance over chain length provided the best discrimination between structural and kinetic classes. The scaling of non-crossing distance with chain length implies an inevitable crossover to entanglement-dominated folding mechanisms for sufficiently long chains. We further quantify the minimal folding pathways by collecting the sequence of uncrossing moves, which generally involve leg, loop, and elbow-like uncrossing moves, and rendering the collection of these moves over the unfolded ensemble as a multiple-transformation "alignment". The consensus minimal pathway is constructed and shown schematically for representative cases of an [Formula: see text], [Formula: see text], and knotted protein. An overlap parameter is defined between pathways; we find that [Formula: see text] proteins have minimal overlap indicating diverse folding pathways, knotted proteins are highly constrained to follow a dominant pathway, and [Formula: see text] proteins are somewhere in between. Thus we have shown how topological chain constraints can induce dominant pathway mechanisms in protein folding.

Evaluation of coarse grained models for hydrogen bonds in proteins

Backbone hydrogen bonds contribute very importantly to the stability of proteins and therefore they must be appropriately represented in protein folding simulations. Simple models are frequently used in theoretical approaches to this process, but their simplifications are often confronted with the need to be true to the physics of the interactions. Here we study the effects of different levels of coarse graining in the modeling of backbone hydrogen bonds. We study three different models taken from the bibliography in a twofold fashion. First, we calculate the hydrogen bonds in 2gb1, an (alpha + beta)-protein, and see how different backbone representations and potentials can mimic the effects of real hydrogen bonds both in helices and sheets. Second, we use an evolutionary method for protein fragment assembly to locate the global energy minimum for a set of small beta-proteins with these models. This way, we assess the effects of coarse graining in hydrogen bonding models and show what can be expected from them when used in simulation experiments.

Criteria for downhill protein folding: Calorimetry, chevron plot, kinetic relaxation, and single-molecule radius of gyration in chain models with subdued degrees of cooperativity

Recent investigations of possible downhill folding of small proteins such as BBL have focused on the thermodynamics of non-two-state, "barrierless" folding/denaturation transitions. Downhill folding is noncooperative and thermodynamically "one-state," a phenomenon underpinned by a unimodal conformational distribution over chain properties such as enthalpy, hydrophobic exposure, and conformational dimension. In contrast, corresponding distributions for cooperative two-state folding are bimodal with well-separated population peaks. Using simplified atomic modeling of a three-helix bundle-in a scheme that accounts for hydrophobic interactions and hydrogen bonding-and coarse-grained C(alpha) models of four real proteins with various degrees of cooperativity, we evaluate the effectiveness of several observables at defining the underlying distribution. Bimodal distributions generally lead to sharper transitions, with a higher heat capacity peak at the transition midpoint, compared with unimodal distributions. However, the observation of a sigmoidal transition is not a reliable criterion for two-state behavior, and the heat capacity baselines, used to determine the van't Hoff and calorimetric enthalpies of the transition, can introduce ambiguity. Interestingly we find that, if the distribution of the single-molecule radius of gyration were available, it would permit discrimination between unimodal and bimodal underlying distributions. We investigate kinetic implications of thermodynamic noncooperativity using Langevin dynamics. Despite substantial chevron rollovers, the relaxation of the models considered is essentially single-exponential over an extended range of native stabilities. Consistent with experiments, significant deviations from single-exponential behavior occur only under strongly folding conditions.

Theoretical Characterization of α-Helix and β-Hairpin Folding Kinetics

By means of the conformational free energy surface and corresponding diffusion coefficients, as obtained by long time scale atomistic molecular dynamics simulations (mus time scale), we model the folding kinetics of alpha-helix and beta-hairpin peptides as a diffusive process over the free energy surface. The two model systems studied in this paper (the alpha-helical temporin L and the beta-hairpin prion protein H1 peptide) exhibit a funnel-like almost barrierless free energy profile, leading to nonexponential folding kinetics matching rather well the available experimental data. Moreover, using the free energy profile provided by Muñoz et al. [Muñoz et al. Nature 1997, 390: 196-199], this model was also applied to reproduce the two-state folding kinetics of the C-terminal beta-hairpin of protein GB1, yielding an exponential folding kinetics with a time constant (approximately 5 micros) in excellent agreement with the experimentally observed one (approximately 6 micros). Finally, the folding kinetics obtained by solving the diffusion equation, considering either a one-dimensional or a two-dimensional free energy surface, are also compared in order to understand the relevance of the possible kinetic coupling between conformational degrees of freedom in the folding process.

Folding thermodynamics of peptides

A simplified interaction potential for protein folding studies at the atomic level is discussed and tested on a set of peptides with approximately 20 residues each. The test set contains both alpha-helical (Trp cage, F(s)) and beta-sheet (GB1p, GB1m2, GB1m3, Betanova, LLM) peptides. The model, which is entirely sequence-based, is able to fold these different peptides for one and the same choice of model parameters. Furthermore, the melting behavior of the peptides is in good quantitative agreement with experimental data. Apparent folded populations obtained using different observables are compared, and are found to be very different for some of the peptides (e.g., Betanova). In other cases (in particular, GB1m2 and GB1m3), the different estimates agree reasonably well, indicating a more two-state-like melting behavior.

Folding thermodynamics of three beta-sheet peptides: a model study

We study the folding thermodynamics of a beta-hairpin and two three-stranded beta-sheet peptides using a simplified sequence-based all-atom model, in which folding is driven mainly by backbone hydrogen bonding and effective hydrophobic attraction. The native populations obtained for these three sequences are in good agreement with experimental data. We also show that the apparent native population depends on which observable is studied; the hydrophobicity energy and the number of native hydrogen bonds give different results. The magnitude of this dependence matches well with the results obtained in two different experiments on the beta-hairpin.

Sequence-based study of two related proteins with different folding behaviors

Z(SPA-1) is an engineered protein that binds to its parent, the three-helix-bundle Z domain of staphylococcal protein A. Uncomplexed Z(SPA-1) shows a reduced helix content and a melting behavior that is less cooperative, compared with the wild-type Z domain. Here we show that the difference in folding behavior between these two sequences can be partly understood in terms of an off-lattice model with 5-6 atoms per amino acid and a minimalistic potential, in which folding is driven by backbone hydrogen bonding and effective hydrophobic attraction.