The helix-coil transition revisited

Exposing the Nucleation Site in α-Helix Folding: A Joint Experimental and Simulation Study

One of the fundamental events in protein folding is α-helix formation, which involves sequential development of a series of helical hydrogen bonds between the backbone C═O group of residues i and the -NH group of residues i + 4. While we now know a great deal about α-helix folding dynamics, a key question that remains to be answered is where the productive helical nucleation event occurs. Statistically, a helical nucleus (or the first helical hydrogen-bond) can form anywhere within the peptide sequence in question; however, the one that leads to productive folding may only form at a preferred location. This consideration is based on the fact that the α-helical structure is inherently asymmetric, due to the specific alignment of the helical hydrogen bonds. While this hypothesis is plausible, validating it is challenging because there is not an experimental observable that can be used to directly pinpoint the location of the productive nucleation process. Therefore, in this study we combine several techniques, including peptide cross-linking, laser-induced temperature-jump infrared spectroscopy, and molecular dynamics simulations, to tackle this challenge. Taken together, our experimental and simulation results support an α-helix folding mechanism wherein the productive nucleus is formed at the N-terminus, which propagates toward the C-terminal end of the peptide to yield the folded structure. In addition, our results show that incorporation of a cross-linker can lead to formation of differently folded conformations, underscoring the need for all-atom simulations to quantitatively assess the proposed cross-linking design.

Unfolding of α-helical 20-residue poly-glutamic acid analyzed by multiple runs of canonical molecular dynamics simulations

Elucidating the molecular mechanism of helix-coil transitions of short peptides is a long-standing conundrum in physical chemistry. Although the helix-coil transitions of poly-glutamic acid (PGA) have been extensively studied, the molecular details of its unfolding process still remain unclear. We performed all-atom canonical molecular dynamics simulations for a 20-residue PGA, over a total of 19 μs, in order to investigate its helix-unfolding processes in atomic resolution. Among the 28 simulations, starting with the α-helical conformation, all showed an unfolding process triggered by the unwinding of terminal residues, rather than by kinking and unwinding of the middle region of the chain. The helix-coil-helix conformation which is speculated by the previous experiments was not observed. Upon comparison between the N- and C-termini, the latter tended to be unstable and easily unfolded. While the probabilities of helix elongation were almost the same among the N-terminal, middle, and C-terminal regions of the chain, unwinding of the helix was enriched at the C-terminal region. The turn and 3₁₀-helix conformations were kinetic intermediates in the formation and deformation of α-helix, consistent with the previous computational studies for Ala-based peptides.

Microscopic nucleation and propagation rates of an alanine-based α-helix

An infrared temperature-jump (T-jump) study by Huang et al. (Proc. Natl. Acad. Sci. U. S. A., 2002, 99, 2788-2793) showed that the conformational relaxation kinetics of an alanine-based α-helical peptide depend not only on the final temperature (Tf) but also on the initial temperature (Ti) when Tf is fixed. Their finding indicates that the folding free energy landscape of this peptide is non-two-state like, allowing for the population of conformational ensembles with different helical lengths and relaxation times in the temperature range of the experiment. Because α-helix folding involves two fundamental events, nucleation and propagation, the results of Huang et al. thus present a unique opportunity to determine their rate constants - a long-sought goal in the study of the helix-coil transition dynamics. Herein, we capitalize on this notion and develop a coarse-grained kinetic model to globally fit the thermal unfolding curve and T-jump kinetic traces of this peptide. Using this strategy, we are able to explicitly determine the microscopic rate constants of the kinetic steps encountered in the nucleation and propagation processes. Our results reveal that the time taken to form one α-helical turn (i.e., an α-helical segment with one helical hydrogen bond) is about 315 ns, whereas the time taken to elongate this nucleus by one residue (or backbone unit) is 5.9 ns, depending on the position of the residue.

Statistical mechanical treatments of protein amyloid formation

Protein aggregation is an important field of investigation because it is closely related to the problem of neurodegenerative diseases, to the development of biomaterials, and to the growth of cellular structures such as cyto-skeleton. Self-aggregation of protein amyloids, for example, is a complicated process involving many species and levels of structures. This complexity, however, can be dealt with using statistical mechanical tools, such as free energies, partition functions, and transfer matrices. In this article, we review general strategies for studying protein aggregation using statistical mechanical approaches and show that canonical and grand canonical ensembles can be used in such approaches. The grand canonical approach is particularly convenient since competing pathways of assembly and dis-assembly can be considered simultaneously. Another advantage of using statistical mechanics is that numerically exact solutions can be obtained for all of the thermodynamic properties of fibrils, such as the amount of fibrils formed, as a function of initial protein concentration. Furthermore, statistical mechanics models can be used to fit experimental data when they are available for comparison.

Construction of an intermediate-resolution lattice model and re-examination of the helix-coil transition: a dynamic Monte Carlo simulation

In protein modeling, spatial resolution and computational efficiency are always incompatible. As a compromise, an intermediate-resolution lattice model has been constructed in the present work. Each residue is decomposed into four basic units, i.e. the α-carbon group, the carboxyl group, the imino group, and the side-chain group, and each basic coarse-grained unit is represented by a minimum cubic box with eight lattice sites. The spacing of the lattice is about 0.56 Å, holding the highest spatial resolution for the present lattice protein models. As the first report of this new model, the helix-coil transition of a polyalanine chain was examined via dynamic Monte Carlo simulation. The period of formed α-helix was about 3.68 residues, close to that of a natural α-helix. The resultant backbone motion was found to be in the realistic regions of the conformational space in the Ramachandran plot. Helix propagation constant and nucleation constant were further determined through the dynamic hydrogen bonding process and torsional angle variation, and the results were used to make comparison between classical Zimm-Bragg theory and Lifson-Roig theory based on the Qian-Schellman relationship. The simulation results confirmed that our lattice model can reproduce the helix-coil transition of polypeptide and construct a moderately fine α-helix conformation without significantly weakening the priority in efficiency for a lattice model.

Roles of non-native hydrogen-bonding interaction in helix-coil transition of a single polypeptide as revealed by comparison between Gō-like and non-Gō models

To explore the role of non-native interactions in the helix-coil transition, a detailed comparison between a Gō-like model and a non-Gō model has been performed via lattice Monte Carlo simulations. Only native hydrogen bonding interactions occur in the Gō-like model, and the non-native ones with sequence interval more than 4 is also included into the non-Gō model. Some significant differences between the results from those two models have been found. The non-native hydrogen bonds were found most populated at temperature around the helix-coil transition. The rearrangement of non-native hydrogen bonds into native ones in the formation of alpha-helix leads to the increase of susceptibility of chain conformation, and even two peaks of susceptibility of radius of gyration versus temperature exist in the case of non-Gō model for a non-short peptide, while just a single peak exists in the case of Gō model for a single polypeptide chain with various chain lengths. The non-native hydrogen bonds have complicated the temperature-dependence of Zimm-Bragg nucleation constant. The increase of relative probability of non-native hydrogen bonding for long polypeptide chains leads to non-monotonous chain length effect on the transition temperature.

Microscopic formulation of the Zimm-Bragg model for the helix-coil transition

A microscopic spin model is proposed for the phenomenological Zimm-Bragg model for the helix-coil transition in biopolymers. This model is shown to provide the same thermophysical properties of the original Zimm-Bragg model and it allows a very convenient framework to compute statistical quantities. Physical origins of this spin model are made transparent by an exact mapping into a one-dimensional Ising model with an external field. However, the dependence on temperature of the reduced external field turns out to differ from the standard one-dimensional Ising model and hence it gives rise to different thermophysical properties, despite the exact mapping connecting them. We discuss how this point has been frequently overlooked in the recent literature.

Construction of an implicit membrane environment for the lattice Monte Carlo simulation of transmembrane protein

Due to the complexity of biological membrane, computer simulation of transmembrane protein's folding is challenging. In this paper, an implicit biological membrane environment has been constructed in lattice space, in which the lipid chains and water molecules were represented by the unoccupied lattice sites. The biological membrane was characterized with three features: stronger hydrogen bonding interaction, membrane lateral pressure, and lipophobicity index for the amino acid residues. In addition to the hydrocarbon core spanning region and the water solution, the lipid interface has also been represented in this implicit membrane environment, which was proved to be effective for the transmembrane protein's folding. The associated Monte Carlo simulations have been performed for SARS-CoV E protein and M2 protein segment (residues 18–60) of influenza A virus. It was found that the coil–helix transition of the transmembrane segment occurred earlier than the coil–globule transition of the two terminal domains. The folding process and final orientation of the amphipathic helical block in water solution are obviously influenced by its corresponding hydrophobicity/lipophobicity. Therefore, this implicit membrane environment, though in lattice space, can make an elaborate balance between different driving forces for the membrane protein's folding, thus offering a potential means for the simulation of transmembrane protein oligomers in feasible time.