Interplay between Secondary and Tertiary Structure Formation in Protein Folding Cooperativity

Protein folding cooperativity is defined by the nature of the finite-size thermodynamic transition exhibited upon folding: two-state transitions show a free energy barrier between the folded and unfolded ensembles, while downhill folding is barrierless. A microcanonical analysis, where the energy is the natural variable, has shown better suited to unambiguously characterize the nature of the transition compared to its canonical counterpart. Replica exchange molecular dynamics simulations of a high resolution coarse-grained model allow for the accurate evaluation of the density of states, in order to extract precise thermodynamic information, and measure its impact on structural features. The method is applied to three helical peptides: a short helix shows sharp features of a two-state folder, while a longer helix and a three-helix bundle exhibit downhill and two-state transitions, respectively. Extending the results of lattice simulations and theoretical models, we find that it is the interplay between secondary structure and the loss of non-native tertiary contacts which determines the nature of the transition.

💡 Research Summary

This paper investigates the thermodynamic nature of protein‑folding cooperativity by employing a high‑resolution coarse‑grained model combined with replica‑exchange molecular dynamics (REMD) and a microcanonical analysis. The authors argue that the microcanonical ensemble, where energy is the natural variable, provides a clearer distinction between two‑state (first‑order‑like) and downhill (continuous) folding transitions than canonical analyses based on heat‑capacity curves. By accurately estimating the density of states Ω(E) with the Weighted Histogram Analysis Method (WHAM), they compute the entropy S(E)=k_B ln Ω(E) and its derivative, the inverse microcanonical temperature β(E)=∂S/∂E. The curvature ΔS(E)=H(E)−S(E), where H(E) is the tangent to S(E) in the transition region, serves as a quantitative marker of convexity (two‑state) versus concavity (downhill).

Three peptide systems are examined: a short α‑helix (AAQAA)_3, a longer α‑helix (AAQAA)_15, and a 73‑residue three‑helix bundle (α3D, PDB 2A3D). For each system, structural observables—radius of gyration R_g(E), hydrogen‑bond energy E_hb (proxy for secondary structure), and side‑chain interaction energy E_sc (proxy for tertiary contacts)—are plotted as functions of the total energy. Their energy derivatives dE_hb/dE and dE_sc/dE reveal the rates at which secondary and tertiary structures form or dissolve across the transition.

The short helix displays a pronounced ΔS peak, a non‑zero latent heat ΔQ, and a back‑bending region in the microcanonical inverse temperature, all hallmarks of a two‑state transition. In this case dE_hb/dE shows a sharp positive spike within the coexistence region, while dE_sc/dE remains essentially flat, indicating that folding is driven almost exclusively by secondary‑structure formation.

In contrast, the longer helix exhibits a smooth ΔS curve with ΔQ≈0, characteristic of downhill folding. R_g reaches a minimum slightly above the transition point, reflecting a maximally compact non‑native ensemble that later reorganizes into the native helix. Here dE_sc/dE becomes negative over a finite energy interval, signifying an energetic penalty for forming tertiary contacts, whereas dE_hb/dE displays a broad maximum, showing that hydrogen‑bond formation is spread over a wide energy range.

The three‑helix bundle again shows a clear ΔS peak and finite latent heat, confirming a two‑state transition. Both dE_hb/dE and dE_sc/dE are sharply localized within the same narrow energy window, indicating that secondary‑structure formation and the loss of non‑native tertiary contacts occur cooperatively. The strong side‑chain‑side‑chain interactions drive chain compaction, and the inter‑helical cooperativity encoded in the sequence ensures that all three helices form simultaneously.

From these observations the authors conclude that folding cooperativity is governed by the interplay between secondary‑structure acquisition and the dissolution of non‑native tertiary contacts. When the loss of tertiary contacts (identified by dE_sc/dE < 0) coincides with rapid secondary‑structure formation (large dE_hb/dE), the transition is highly cooperative and manifests as a two‑state process. When secondary‑structure formation is distributed over a broader energy range while tertiary contacts are only weakly perturbed, the transition becomes downhill and less cooperative. This mechanistic picture extends earlier lattice‑model and theoretical studies (e.g., Zimm‑Bragg, heteropolymer collapse) by providing atomistic‑level, energy‑resolved evidence.

Overall, the work demonstrates that microcanonical analysis, combined with accurate density‑of‑states estimation from REMD, offers a powerful framework for dissecting the thermodynamic and structural determinants of protein‑folding cooperativity, bridging the gap between calorimetric criteria and microscopic folding pathways.