Modeling of folding and unfolding mechanisms in alanine-based alpha-helical polypeptides

Thermodynamics of protein folding using a modified Wako-Saitô-Muñoz-Eaton model

Herein, we propose a modified version of the Wako-Saitô-Muñoz-Eaton (WSME) model. The proposed model introduces an empirical temperature parameter for the hypothetical structural units (i.e., foldons) in proteins to include site-dependent thermodynamic behavior. The thermodynamics for both our proposed model and the original WSME model were investigated. For a system with beta-hairpin topology, a mathematical treatment (contact-pair treatment) to facilitate the calculation of its partition function was developed. The results show that the proposed model provides better insight into the site-dependent thermodynamic behavior of the system, compared with the original WSME model. From this site-dependent point of view, the relationship between probe-dependent experimental results and model's thermodynamic predictions can be explained. The model allows for suggesting a general principle to identify foldon behavior. We also find that the backbone hydrogen bonds may play a role of structural constraints in modulating the cooperative system. Thus, our study may contribute to the understanding of the fundamental principles for the thermodynamics of protein folding.

Direct assessment of the α-helix nucleation time

The nucleation event in α-helix formation is a fundamental process in protein folding. However, determining how quickly it takes place based on measurements of the relaxation dynamics of helical peptides is difficult because such relaxations invariably contain contributions from various structural transitions such as from helical to nonhelical states and helical to partial-helical conformations. Herein, we measure the temperature-jump (T-jump) relaxation kinetics of three model peptides that fold into a single-turn α-helix, using time-resolved infrared spectroscopy, aiming to provide a direct assessment of the helix nucleation rate. The α-helical structure of these peptides is stabilized by a covalent cross-linker formed between the side chains of two residues at the i and i + 4 positions. If we assume that this cross-linker mimics the structural constraint arising from a strong side chain-side chain interaction (e.g., a salt bridge) in proteins, these peptides would represent good models for studying the nucleation process of an α-helix in a protein environment. Indeed, we find that the T-jump induced relaxation rate of these peptides is approximately (0.6 μs)(-1) at room temperature, which is slower than that of commonly studied alanine-based helical peptides but faster than that of a naturally occurring α-helix whose folded state is stabilized by a series of side chain-side chain interactions. Taken together, our results put an upper limit of about 1 μs for the helix nucleation time at 20 °C and suggest that the subsequent propagation steps occur with a time constant of about 240 ns.

UV resonance Raman investigation of the conformations and lowest energy allowed electronic excited states of tri- and tetraalanine: charge transfer transitions

UV resonance Raman excitation profiles and Raman depolarization ratios were measured for trialanine and tetraalanine between 198 and 210 nm. Excitation within the pi --> pi* electronic transitions of the peptide bond results in UVRR spectra dominated by amide peptide bond vibrations. In addition to the resonance enhancement of the normal amide vibrations, we find enhancement of the symmetric terminal COO(-) vibration. The Ala(3) UVRR AmIII(3) band frequencies indicate that poly-proline II and 2.5(1) helix conformations and type II turns are present in solution. We also find that the conformation of the interior peptide bond of Ala(4) is predominantly poly-proline-II-like. The Raman excitation profiles of both Ala(3) and Ala(4) reveal a charge transfer electronic transition at 202 nm, where electron transfer occurs from the terminal nonbonding carboxylate orbital to the adjacent peptide bond pi* orbital. Raman depolarization ratio measurements support this assignment. An additional electronic transition is found in Ala(4) at 206 nm.

Salt dependence of an alpha-helical peptide folding energy landscapes

We used CD, UV resonance Raman spectroscopy, and molecular dynamics simulation to examine the impact of salts on the conformational equilibria and the Ramachandran Psi angle (un)folding Gibbs free energy landscape coordinate of a mainly polyalanine alpha-helical peptide, AP of sequence AAAAA(AAARA)(3)A. NaClO(4) stabilizes alpha-helical-like conformations more than does NaCl, which stabilizes more than Na(2)SO(4) at identical ionic strengths. This alpha-helix stabilization ordering is the reverse of the Hofmeister series of anions in their ability to disorder water hydrogen bonding. Much of the NaClO(4) alpha-helix stabilization results from ClO(4)(-) association with the AP terminal -NH(3)(+) groups and Arg side chains. ClO(4)(-) stabilizes 3(10)-helix conformations but destabilizes turn conformations. The decreased Cl(-) and SO(4)(2-) AP alpha-helix stabilization probably results from a decreased association with the Arg and terminal -NH(3)(+) groups. Cl(-) is expected to have a smaller binding affinity and thus stabilizes alpha-helical conformations intermediately between NaClO(4) and Na(2)SO(4). Electrostatic screening stabilizes pi-bulge conformations.

Thermodynamics of a conformational change using a random walk in energy-reaction coordinate space: Application to methane dimer hydrophobic interactions

A random walk sampling algorithm allows the extraction of the density of states distribution in energy-reaction coordinate space. As a result, the temperature dependences of thermodynamic quantities such as relative energy, entropy, and heat capacity can be calculated using first-principles statistical mechanics. The strategies for optimal convergence of the algorithm and control of its accuracy are proposed. We show that the saturation of the error [Q. Yan and J. J. de Pablo, Phys. Rev. Lett. 90, 035701 (2003); E. Belardinelli and V. D. Pereyra, J. Chem. Phys. 127, 184105 (2007)] is due to the use of histogram flatness as a criterion of convergence. An application of the algorithm to methane dimer hydrophobic interactions is presented. We obtained a quantitatively accurate energy-entropy decomposition of the methane dimer cavity potential. The presented results confirm the previous results, and they provide new information regarding the thermodynamics of hydrophobic interactions. We show that the finite-difference approximation, which is widely used in molecular dynamic simulations for the energy-entropy decomposition of a free energy potential, can lead to a significant error.

The effect of charge-charge interactions on the kinetics of alpha-helix formation

The formation of the monomeric alpha-helix represents one of the simplest scenarios in protein folding; however, our current understanding of the folding dynamics of the alpha-helix motif is mainly based on studies of alanine-rich model peptides. To examine the effect of peptide sequence on the folding kinetics of alpha-helices, we studied the relaxation kinetics of a 21-residue helical peptide, Conantokin-T (Con-T), using time-resolved infrared spectroscopy in conjunction with a laser-induced temperature jump technique. Con-T is a neuroactive peptide containing a large number of charged residues that is found in the venom of the piscivorous cone snail Conus tulipa . The temperature-jump relaxation kinetics of Con-T is distinctly slower than that of previously studied alanine-based peptides, suggesting that the folding time of alpha-helices is sequence-dependent. Furthermore, it appears that the slower folding of Con-T can be attributed to the fact that its helical conformation is stabilized by charge-charge interactions or salt bridges. Although this finding contradicts an earlier molecular dynamics simulation, it also has implications for existing models of protein folding.

Nonadditive interactions in protein folding: the zipper model of cytochrome C

Hydrogen exchange experiments (Krishna et al. in J. Mol. Biol. 359:1410, 2006) reveal that folding-unfolding of cytochrome c occurs along a defined pathway in a sequential, stepwise manner. The simplified zipper-like model involving nonadditive coupling is proposed to describe the classical "on pathway" folding-unfolding behavior of cytochrome c. Using free energy factors extracted from HX experiments, the model can predict and explain cytochrome c behavior in spectroscopy studies looking at folding equilibria and kinetics. The implications of the proposed model are discussed for such problems as classical pathway vs. energy landscape conceptions, structure and function of a native fold, and interplay of secondary and tertiary interactions.