Structural Basis of Folding Cooperativity in Model Proteins: Insights from a Microcanonical Perspective

Two-state cooperativity is an important characteristic in protein folding. It is defined by a depletion of states lying energetically between folded and unfolded conformations. While there are different ways to test for two-state cooperativity, most of them probe indirect proxies of this depletion. Yet, generalized-ensemble computer simulations allow to unambiguously identify this transition by a microcanonical analysis on the basis of the density of states. Here we perform a detailed characterization of several helical peptides using coarse-grained simulations. The level of resolution of the coarse-grained model allows to study realistic structures ranging from small alpha-helices to a de novo three-helix bundle - without biasing the force field toward the native state of the protein. Linking thermodynamic and structural features shows that while short alpha-helices exhibit two-state cooperativity, the type of transition changes for longer chain lengths because the chain forms multiple helix nucleation sites, stabilizing a significant population of intermediate states. The helix bundle exhibits the signs of two-state cooperativity owing to favorable helix-helix interactions, as predicted from theoretical models. The detailed analysis of secondary and tertiary structure formation fits well into the framework of several folding mechanisms and confirms features observed so far only in lattice models.

💡 Research Summary

This paper presents a comprehensive microcanonical analysis of folding cooperativity in a set of model helical peptides, using a high‑resolution implicit‑solvent coarse‑grained (CG) force field. The authors argue that traditional calorimetric or canonical observables (heat‑capacity peaks, van’t Hoff analysis, CD curves) only indirectly probe the depletion of intermediate states that defines two‑state (cooperative) folding. By directly estimating the density of states Ω(E) from replica‑exchange molecular dynamics combined with WHAM, they reconstruct the entropy S(E)=k_B ln Ω(E) and examine its curvature. A convex intruder in S(E) signals a suppression of intermediate energies, which manifests as a back‑bending in the inverse microcanonical temperature T_μ⁻¹(E)=∂S/∂E and a non‑zero microcanonical latent heat ΔQ. The presence of ΔQ>0 therefore provides an unambiguous criterion for a true two‑state transition, while ΔQ=0 indicates a continuous downhill folding process.

Four variants of the repeat peptide (AAQAA)_n with n = 3, 7, 10, 15 were studied, together with a de novo three‑helix bundle (α3D) of comparable length. For the shortest peptide (n = 3) the entropy curve displays a clear convex intruder, ΔQ>0, a sharp rise in helicity θ(E) and a jump from 0 to 1 in the number of helices H(E). This is the textbook two‑state folder: the system switches abruptly between a disordered coil and a single, fully formed α‑helix. The n = 7 peptide still shows a modest barrier and a finite ΔQ, suggesting a weakened but still cooperative transition. In contrast, the n = 10 and n = 15 chains lose the convex intruder; ΔQ vanishes and T_μ⁻¹(E) becomes monotonic. Structural analysis reveals that, in the transition region, H(E) exceeds one, indicating the simultaneous presence of multiple helix nucleation sites. Residue‑wise helicity maps show that for n = 15 two distinct helical segments nucleate near the chain centre and fold independently before merging into a single long helix at lower energies. This multiplicity of nucleation sites creates a broad ensemble of intermediate conformations, turning the folding into a downhill process.

The three‑helix bundle α3D, despite having the same number of residues as (AAQAA)_15, behaves differently. Its entropy still contains a convex intruder and a finite ΔQ, and the helicity and H(E) increase sharply but monotonically across the transition. The cooperative interaction between the three helices stabilizes the transition state, preserving a genuine two‑state character.

Beyond secondary structure, the authors examine tertiary‑level observables. The radius of gyration R_g(E) and the normalized acylindricity c(E) both display non‑monotonic behavior for the longer chains and α3D: a compact, nearly spherical “globular” state appears at energies just above the transition, followed by elongation as the helices form. Contact analysis shows that the total number of non‑local contacts peaks within the transition region, while the number of native contacts rises monotonically. Thus, to reach the native state the peptide must first break many non‑native contacts, a hallmark of a cooperative collapse‑then‑fold mechanism reminiscent of molten‑globule models.

Overall, the study demonstrates that microcanonical analysis of Ω(E) provides a direct, quantitative probe of folding cooperativity, capable of distinguishing true two‑state behavior from downhill folding even when canonical signatures are ambiguous. By coupling entropy analysis with detailed secondary‑ and tertiary‑structure metrics, the work links microscopic structural events (multiple nucleation sites, helix‑helix interactions, chain collapse) to macroscopic thermodynamic signatures. The findings corroborate theoretical predictions that short helices fold cooperatively, whereas longer helices become downhill due to the emergence of multiple independent nucleation sites, and that favorable inter‑helix contacts can restore two‑state behavior in multi‑helix bundles. This methodology offers a powerful framework for future studies of protein folding landscapes, rational protein design, and the interpretation of experimental calorimetry data.