The investigation of protein folding is one of the fundamental issues in the field of molecular biology. In the past several decades, experimental as well as theoretical studies have been carried out incessantly in order to reveal the general mechanism of protein folding.1–4 The short peptides and protein fragments become the ideal model systems for the investigation because of their small size and structural simplicity. Of particular interest are -helices and -hairpins, which are the two fundamental secondary structures in most of the proteins.4–9 Experiments display that the formation of -hairpins is generally more complicated than the formation of -helices. The latter is normally formed within the time scale of several hundreds of nanoseconds whereas the former normally in the time scale of microseconds.8,10 To date, the general mechanisms of individual -helix and -hairpin formation become largely understood but the details still remain elusive.
Despite of its structural simplicity, the -hairpin is believed to fold in a manner which is similar to the folding of small proteins.6,9 The folding process of an individual -hairpin structure generally involves several kinetic events: the hydrophobic cluster packing, the native cross-strand hydrogen bond interaction, and the turn formation.9 However, the occurrence order of these events is still under debate. Among the hairpin systems studied, the GB1 peptide, which is the C-terminal -hairpin residues 41–56 from the B1 domain of protein G its amino acid sequence is GEWTYD- DATKTFTVTE, PDB code: 2GB1 Ref. 11 , is the most attractive.9,12–16 The GB1 peptide has its peculiar characteristics compared to the other -hairpin peptides under studies because it is a segment of a natural protein. The folded structure of the GB1 peptide is normally considered to be the same as that in the integral protein, as shown in Fig. 1. A well packed hydrophobic cluster residues 43 and 54 and 45 and 52 is close to the ends of the turn and six native hydrogen bonds exist which cross the strand. Munoz et al. showed that the GB1 peptide folds in a two-state manner.9 Its folding time measured from experiment is around 6 s.9 Two folding mechanisms have been proposed and each was supported by various experimental and theoretical simulation studies.9,12–16 The divergence of the two mechanisms mainly exists in the contribution of the two structural segments, the hydrophobic core and the turn, on the formation and stabilization of the hairpin structure and on the formation order of two segments during the folding process. Eaton and co-workers first developed a “hydrogen bond zipping” mechanism,9,14 which suggests that -hairpin folding starts from the turn formation and propagates to the terminals. In this mechanism, the hydrophobic core forms in the final stage and plays an important role in stabilizing the hairpin structure. More recently another mechanism, “hydrophobic core centric” mechanism, was proposed.16 In this mechanism the hydrophobic core is packed rapidly after the initial structure collapse and simultaneously a portion of the hydrogen bonds is likely to form. Subsequently the assembly of hydrogen bonds is accomplished and the turn structure is configured. In comparison to the first mechanism, the second one is supported by more recent simulations.17–20
Many different all-atom force fields have been used for the computational simulations of the GB1 peptide, e.g., CHARMM, AMBER, OPLS, and GROMOS96, employed with either explicit or implicit solvent models.16,18,21 The all- atom models with explicit solvent are probably more desirable for elucidating the details of protein folding pathways regardless of requirement of enormous entral processing unit time. At the same time implicit solvent models are developed to economize the computation time, of which a popular model is the generalized Born/surface area GB/SA model.22,23 One question regarding the implicit solvent models is how well the models reproduce or predict the thermodynamics and kinetics of protein folding. For the sake of answering this question, Zhou performed the replica exchange molecular dynamics simulations on the folding of the GB1 peptide with different force fields in combination with different implicit models and compared the results to those from explicit solvent models.24 Of the implicit solvent models studied, only AMBER96/GBSA reproduced reasonable results comparable to the explicit model. More recently Shell et al. tested the stability of several peptides GB1 peptide, trpzip2, C peptide, and EK helix with AMBER force fields and GB/SA models with different generalized Boltzmann models.25 It turned out that the combination of AMBER96 with the GBOBC model igb= 5 is the best choice to balance the -helix and -hairpin tendencies of the peptides tested.25
As the popular implicit models, the GB models approach an approximate numerical solution of the Poisson–Boltzmann equation, which describes the electrostatic energy due to the interaction between solute and solvent as a sum of pairwise interaction terms between atomic charges.23 The effective Born radius of each solute atom becomes the key parameter for the calculation of the solvation free energy, the amount given by the Coulomb field approximation:26 Ri-1 = ρi-1 - I, where i is the intrinsic radius of atom i and I is the integral over the solute volume of atom i. The integral calculation is the main issue in the GB models, with different approaches leading to different versions. In the early GBHCT model igb= 1 ,27 the integral I is estimated over the van der Waals(vdM) sphere of each protein atom, which, as a drawback, creats regions of interstitial high dielectrics where the solvent molecule is to large to enter. To reduce the influence of interstitial high deilectrics, in the GB OBC model (igb=2 or 5), the effective Born RADIUS is given by a well-behaved three-parameter scaling function (α， β，and γ) with the integral first derived from the HCT approach introduced by Hawkins, Cramer, and Truhlar .29 In the GBn model igb= 7 , a correction term is first added to the integral over the vdW surface to make up for the difference between vdW and molecular surfaces; then the scaling function is performed with the new integral and a new set of α，β，and γ values to achieve the accurate effective Born radius.28 As a result, the GBOBC model produces geometry-independent effective Born radius whereas the calculation of the effective Born radius in the GBn model is geometry specific.28
In this article, we used an enhanced sampling method30 to investigate the folding behavior and the relevant free energy surface of the GB1 peptide quantitatively. The two best behaved models from the studies of Shell et al.25 GBOBC and GBn were tested to study quantitatively the influence of implicit models on the folding mechanism of the GB1 peptide. Multiple folding and unfolding transitions between the folded and the extended conformation were observed in several independent molecular dynamics MD trajectories, each running in the time scale of several hundred nanoseconds. It is worth mentioning that the dynamics information in the enhanced sampling simulation is lost due to the exertion of the biased potential energy. Therefore the present studies mainly focus on the thermodynamics of the -hairpin folding.
