The free-energy landscape of the alpha-helix of protein G is studied by means of metadynamics coupled with a solute tempering algorithm. Metadynamics allows to overcome large energy barriers, whereas solute tempering improves the sampling with an affordable computational effort. From the sampled free-energy surface we are able to reproduce a number of experimental observations, such as the fact that the lowest minimum corresponds to a globular conformation displaying some degree of beta-structure, that the helical state is metastable and involves only 65% of the chain. The calculations also show that the system populates consistently a pi-helix state and that the hydrophobic staple motif is present only in the free-energy minimum associated with the helices, and contributes to their stabilization. The use of metadynamics coupled with solute tempering results then particularly suitable to provide the thermodynamics of a short peptide, and its computational efficiency is promising to deal with larger proteins.
The B1 domain of streptococcal protein G (Protein G thereafter) is the immunoglobulin binding domain of the protein and comprises 56 residues located at its N-terminus. The folding of this small protein has been studied thoroughly, and accurate structural and thermodynamic characterizations are available for it. The domain is a stable globular folding unit with no disulfide cross-links, and in its native fold a central α-helix is packed against a four-stranded β-sheet, formed by two anti-symmetrically disposed β-hairpins [1]. The folding occurs without detectable intermediates. Differential scanning calorimetry [2] and stopped-flow mixing methods [3] show that the protein exhibits a two-state unfolding behavior over a wide pH range, and that the kinetics of folding and unfolding can be fit to a single, first-order rate constant over a wide temperature range.
Interestingly, the three fragments of secondary structure have different stabilities when isolated from the remainder of the protein; in particular, the second β-hairpin (comprising residues 41 through 56) is the most stable one, while the helix (residue 21 through 40) and the first β-hairpin (residues 1 through 20) are unstructured in water [4]. Moreover, the αhelix fragment has been found to be stabilized by some non-native hydrophobic interactions with its C-and N-terminus residues. [5]. Finally, replacing the helix wild-type sequence at residues 21 through 40 with the second-hairpin sequence, the same native fold is obtained, suggesting that are the non-local interactions due to the β-hairpin that determines the fold of protein G [6].
By studying the effects of point mutations in protein G, McCallister, et al. [7] suggest that its transition state is characterized by a largely structured second β-hairpin forming three stranded β-sheet with the N-terminal β-strand of the first hairpin. In the transition state the helix seems only partially formed towards the C-terminus region.
Although such intense experimental work provides interesting information about the folding dynamics of protein G, the extremely complex nature of the process makes it hard to rationalize its details, making the problem well suited for a computational analysis. While it would be computationally easy to make standard unfolding simulations of a 20-residues peptide, we pursue a more ambitious goal: to calculate its equilibrium free-energy landscape.
With standard molecular dynamics simulations, this is reached only after a large number of folding and unfolding events, corresponding to many crossing of barriers whose height is much larger than k b T .
To overcome this limit and explore the thermodynamic properties of such systems within all-atom, explicit solvent models, several different methods have been proposed. Among them are: a) the parallel tempering method [8,9] that allows the system to diffuse faster along its phase space by stochastically swapping different replicas with different temperature; b) the metadynamics [10,11,12], where the system is allowed to climb over large free-energy barriers by introducing a non-Markovian potential defined as a function of a set of few collective variables (CV) which disfavor the exploration of region already sampled. These two different approaches were combined recently [13] to get the free energy surface (FES) of protein-G second β-hairpin.
The application of such method to larger systems, however, is hampered by the need to use a big number of replicas in order to ensure a proper rate of exchange. The acceptance probability of a swap between two replicas is proportional to exp(∆β∆E), where ∆β is the difference of the inverse of replicas temperatures times the Boltzmann constant, and ∆E is the replicas’ energy difference. The larger the system (and thus the larger ∆E), the smaller the difference in temperature between replicas and thus the larger the number of replicas needed for a fast equilibration. This computational limitation prevents the use of parallel tempering for systems larger than ∼ 10 residues. To overcome this limit Liu, et al. [14], proposed a replica-exchange solute tempering algorithm which reduces the number of replicas needed for an efficient equilibration, thus allowing the study of larger systems.
In this work we combine metadynamics and solute tempering for the first time, and use it to hike the FES of the α-helix of the protein G. We show that the combined action of the two approaches constitutes a powerful method to study the thermodynamic properties of large complex systems at the all-atom level with explicit solvent. Furthermore we demonstrate that metadynamics and solute tempering is computationally more affordable than parallel tempering metadynamics.
From the sampled FES we are able to reproduce and to provide an interpretation of several experimental findings. Our calculations correctly show that the helix is not stable in water, that the metastable helical state is shorter than the helix as it is
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