Three-helix-bundle protein in a Ramachandran model

Abstract

We study the thermodynamic behavior of a model protein with 54 amino acids that forms a three-helix bundle in its native state. The model contains three types of amino acids and five to six atoms per amino acid and has the Ramachandran torsional angles i, i as its degrees of freedom. The force field is based on hydrogen bonds and effective hydrophobicity forces. For a suitable choice of the relative strength of these interactions, we find that the three-helixbundle protein undergoes an abrupt folding transition from an expanded state to the native state. Also shown is that the corresponding one-and two-helix segments are less stable than the three-helix sequence. It is not yet possible to simulate the formation of proteins' native structures on the computer in a controlled way. This goal has been achieved in the context of simple lattice and off-lattice models, where typically each amino acid is represented by a single interaction site corresponding to the C ␣ atom, and such studies have provided valuable insights into the physical principles of protein folding (1-5) and the statistical properties of functional protein sequences (6, 7). However, these models have their obvious limitations. Therefore, the search for computationally feasible models with a more realistic chain geometry remains a highly relevant task.In this paper, we discuss a model based on the well-known fact that the main degrees of freedom of the protein backbone are the Ramachandran torsional angles i , i (8). Each amino acid is represented by five or six atoms, which makes this model computationally slightly more demanding than C ␣ models. On the other hand, it also makes interactions such as hydrogen bonds easier to define. The formation of native structure is, in this model, driven by hydrogen-bond formation and effective hydrophobicity forces; hydrophobicity is widely held as the most important stability factor in proteins (9, 10), and hydrogen bonds are essential to properly model the formation of secondary structure.In this model, we study in particular a three-helix-bundle protein with 54 amino acids, which represents a truncated and simplified version of the four-helix-bundle protein de novo designed by Regan and DeGrado (11). This example was chosen partly because there have been earlier studies of similar-sized helical proteins using models at comparable levels of resolution (12-18). The behavior of small fast-folding proteins is a current topic in both theoretical and experimental research, and a three-helix-bundle protein that has been extensively studied both experimentally (19,20) and theoretically (14,17,21,22) is fragment B of staphylococcal protein A.In addition to the three-helix protein, to study size dependence, we also look at the behavior of the corresponding oneand two-helix segments. By using the method of simulated tempering (23-25), a careful study of the thermodynamic properties of these different chains is performed.Not unexpectedly, it turns out that the behavior of the model strongly depends on the relative streng...

Folding of a small helical protein using hydrogen bonds and hydrophobicity forces

“…[20] which, as discussed earlier, has a very abrupt collapse transition. It turns out that E hb and R g evolve in a strongly correlated manner in this case.…”

“…[20]. This is not surprising, as that sequence has a hy- drophobicity pattern that fits its native structure perfectly.…”

“…The first two terms E loc and E sa are local φ, ψ and selfavoidance potentials, respectively (see Ref. [20]). The third term is the hydrogenbond energy E hb , which is given by where i and j represent H and O atoms, respectively, and where r ij denotes the HO distance, α ij the NHO angle, and β ij the HOC ′ angle.…”

“…[20] is that alanine forms its own hydrophobicity class, besides the previous two hydrophobic and polar classes. Alanine † Cys, Met, Thr, Trp and Val do not occur in the sequence studied.…”

“…[20] and has three types of amino acids: hydrophobic, polar and glycine. This version was applied to a designed three-helix-bundle protein with 54 amino acids [20]. For a suitable relative strength of the hydrogen bonds and hydrophobicity forces, it was found that this sequence does form a stable three-helix bundle, except for a twofold topological degeneracy, and that its folding transition is first-order-like and coincides with the collapse transition (the parameter σ of Ref.…”