Protein folding is the process by which a polypeptide chain organizes into its three-dimensional structure through a balance of stabilizing and destabilizing interactions encoded by the sequence. A central question in protein biophysics is how thermodynamic factors guide a polypeptide toward its native folded state despite the rugged energy landscape and the competing influence of nonnative interactions. In many biomolecular processes, cooperativity provides a mechanism by which multiple weak interactions act collectively to generate a robust response. In the context of protein folding, such cooperative effects may arise when the formation of one native contact enhances the stability or likelihood of nearby native contacts, thereby promoting collective organization toward the folded state. At the same time, folding is opposed by the much larger number of non-native interactions, whose heterogeneity can introduce frustration and destabilize folding even when the average native bias favors the folded phase. The interplay of these competing effects in determining foldability remains unclear in statistical-mechanical models. Here, we address this problem using a one-dimensional spin-glass model of protein folding with explicit shared-residue cooperative interactions encoded through wedge-based motifs. We show that modest cooperative bias can stabilize folding even where the noncooperative system remains unfolded, whereas non-native energetic fluctuation suppresses folding and shifts the transition to higher cooperative strengths. We further find that partial cooperative coverage is sufficient to lower the folding threshold. Therefore, the model provides a mean-field framework for incorporating cooperative interaction strength into the native one-dimensional model of protein folding and for describing how local cooperativity reshapes the folding transition.
Together, these results show that designed repeat-protein folding is governed by seed formation, interface propagation, and terminal boundary conditions, and establish intramolecular crosslinking as a strategy for rationally reshaping folding landscapes in designed proteins.
Melanie Weiß, Anna Lisa Heit, L. Milles et al.· bioRxiv· 0 citations
This work investigates how protein folding landscapes are altered inside condensates, using the protein α-helix as a model folded domain and develops a chemically specific, residue-resolution model for quantification of α-helical folding and applies it to characterize diverse helices within condensates of varying physicochemical properties.
Nathaniel Hess, Jerelle A. Joseph· Journal of the American Chem...· 0 citations
This work presents a minimal coarse-grained molecular dynamics model for the coil-helix transition in polymers. We demonstrate that the addition of a Morse potential to a freely jointed chain with volume and bond potentials is sufficient to reproduce the essential thermodynamic features of the transition. From the simulations performed, the Zimm-Bragg propagation parameter s and nucleation parameter σ are extracted, providing quantitative measures of helical propensity and cooperativity, respectively. To illustrate the versatility of the model, this study systematically varies the spacing between hydrogen-bonding monomers using an i → i + m motif, with m = 4, 5, and 6 corresponding to coarse-grained representations of α-, π-, and 1-7 helices. This approach is used to evaluate how hydrogen-bond spacing influences the transition behavior and the resulting cooperativity. As the monomer spacing m between hydrogen-bonding pairs increases, the number of monomers that must be confined for the first hydrogen bond to form also increases, leading to increased cooperativity (lower nucleation parameter σ) and a sharper transition, as reflected in the simulation results. This behavior is consistent with that observed in natural helices of different types, underscoring the model's ability to capture how molecular architecture governs helix formation.
Karthik C Sinha, Alexey A. Gavrilov, A. Rumyantsev· Journal of Chemical Physics· 1 citation
How the earliest structure within the unfolded state is formed during biosynthesis on the ribosome and whether it has any consequences for downstream folding remain open questions. Here, we combine 15N paramagnetic relaxation enhancement NMR with all-atom molecular dynamics simulations to characterise the unfolded state of a folding-competent immunoglobulin-like domain on the ribosome at the cusp of folding initiation. We identify three structurally distinct sub-ensembles that differ in compaction and ribosome interactions. Non-native contacts, together with ribosome interactions, likely delay folding, yet their persistence alongside early native-like contacts within a sparsely populated compact sub-ensemble suggests they may also facilitate the formation of a co-translational folding nucleus, whose contacts overlap with those of the downstream intermediates. From these findings we infer a mechanistic model of de novo folding initiation during biosynthesis and, by linking the folding nucleus to downstream partially structured intermediates and the native state, provide a complete atomistic description of a co-translational folding pathway.
Ivana V. Bukvin, Julian O. Streit, Tomasz Włodarski et al.· bioRxiv· 0 citations
Helical segments in polymer chains are often transient, finite, and dynamically evolving, yet their origin and stability remain incompletely understood. Here, we develop a minimal coarse-grained statistical-mechanical theory that explains how such "living helices" emerge in fluctuating polymer systems. Using a three-state model with cooperative interactions, we show that helix formation proceeds through a multistep nucleation mechanism. An initial constrained pre-nucleus forms first, followed by cooperative stabilization that promotes the growth of finite helical segments. The resulting free-energy landscape naturally favors marginally stable helices whose size is determined by a competition between cooperative gains and nonlinear penalties arising from stiffness, torsional strain, and solvent fluctuations. By formulating the dynamics as a stochastic process in segment size, we derive analytical expressions for both formation times and lifetimes within a mean first-passage framework. For representative parameters relevant to flexible polymers and peptide segments, the theory predicts characteristic timescales in the nanosecond to sub-microsecond range. These results provide a unified physical picture of "living helices" as finite, mobile, and fluctuating excitations and identify cooperativity and fluctuations as the key determinants of transient secondary structure in polymeric systems.
Biman Bagchi· Journal of Chemical Physics· 0 citations
Mesoscale self-assembly provides a route toward the design of programmable microsystems. Here, we construct flexible chains of floating monomers whose curved branches impose upward or downward deformations of the liquid interface, corresponding to effective positive or negative capillary charges. These geometrically encoded deformations generate local attractive or repulsive interactions along the chain. By tuning the capillary sequence, we obtain distinct folded configurations, including straight lines, zigzag patterns, and loops. For short chains, folding is largely governed by nearest-neighbor interactions and leads to well-defined structures. As the chain length increases and non-neighboring segments come into proximity and interact, however, the folding landscape becomes increasingly complex, with multiple metastable states whose number grows exponentially with chain length. We map these landscapes numerically and demonstrate experimentally that mechanical agitation allows the chains to transition between metastable configurations. Beyond encoding a target geometry, the capillary sequence therefore controls the complexity of the folding landscape as well as the degeneracy and mutational robustness of folded structures. These results establish capillary chains as a controllable mesoscale platform for investigating how local interaction rules give rise to collective folding and complex sequence-to-structure relationships reminiscent of those encountered in biomolecular systems.
M. Delens, Axel Franckart, M. Poty et al.· 1 citation