Aug 2026· Journal of Chemical Physics· Vol 165 6· 1 citation· 58 references
Medicine
Abstract
Macromolecular coil-to-helix transitions simultaneously modify local geometry and persistence length, driving complex changes in overall chain size. Here, we apply the wormlike (persistent) chain model to both coil and helical fragments to examine how the degree of helicity, θ, and average helical fragment length, kh, dictate global chain dimensions. Using scaling arguments, we construct a conformational diagram comprising six distinct regimes for the end-to-end distance. We then employ a minimal coarse-grained molecular dynamics model to verify the theory. Mapping structural properties extracted from these simulations onto the proposed regime diagram enables direct quantitative comparison. This, alongside microscopic conformational analysis, corroborates our theoretical framework. We highlight that the competition between local chain compactization and increased stiffness upon helix formation produces a non-monotonic behavior of the end-to-end distance. Furthermore, to demonstrate the generality of our approach, we systematically vary the hydrogen-bonding monomer spacing m for pairs {i, i + m}. Spacings of m = 4, 5, and 6 are used as coarse-grained representations of α-, π-, and 1-7 helices, respectively. As m increases, the helix becomes locally more compact while its persistence length grows. The regime diagrams constructed for these distinct configurations, combined with robust quantitative agreement between theory and simulation, demonstrate that our framework effectively captures how variations in helix geometry and stiffness control macromolecular dimensions across the transition.
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
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
The structural feasibility of chain folding within an accepted cellulose-II structure is investigated in this study. We incorporate 3-residue and 5-residue folded glucosyl turns into a cellulose-II fibril crystal model to assess if the dominant structure can be retained. Ten candidate turn models were generated by metadynamics simulations and ranked by semiempirical quantum mechanical energies. Across >30 independent 300 ns molecular dynamics trajectories, the crystalline core retains its unit cell parameters, X-ray diffraction pattern, hydrogen bonding network, and canonical 4C1 ring conformation. This suggests that, should such folds be present, they need not compromise bulk crystalline integrity. No significant fibril twisting was observed in either the unfolded or chain-fold models. At the chain-folding ends of the fibril, high-energy boat and skew-boat conformations drive hydroxymethyl rotamer redistribution and noncanonical hydrogen bonding contacts. The greater structural flexibility of the 5-residue folded turns allows the chain-fold ends to access a broader conformational space, yet the structural perturbation remains localized within the same 3-residue region as the 3-residue folded turns. The 3-residue turn is therefore considered the more plausible chain-fold structure for cellulose-II, should such a structure actually exist in reality.
Linghan Kong, Stephen J. Eichhorn, Richard A. Bryce· Biomacromolecules· 0 citations
The mechanical and structural properties of dsDNA have been successfully described by models with varying levels of complexity and coarse-graining schemes. Prior work has characterized local stacking/twist effects and force-torque phase diagrams under external constraints. However, the role of base-pairing and torsional elasticity in global morphological transitions remain poorly characterized in the absence of external constraints. Here we investigate the delicate balance required for the strength of base-pairing interactions and the twisting energy to preserve the double-helix structure in a model made up of two semiflexible chains. We found that the model exhibits several distinct morphological phases: flat, random coil, double-helix, and the unwound double-helix. We calculate the Gauss linking number to characterize transitions between these phases.
Farisan Dary, Donn Liew, Haiyi Liang et al.· 0 citations
Coiled coils are structural motifs in proteins that play diverse functions. In MRE11-RAD50 (MR) complexes, ATP-driven changes in coiled coils are essential for DNA break sensing. However, coiled coil dynamics and its modulation by protein conformational changes remain unclear, partly due to the lack of quantitative tools. Here, we used high-speed atomic force microscopy (HS-AFM) for real-time visualization of the coiled coil conformational dynamics of individual MR complexes from bacteria and human homologs, and a biomedically relevant variant. The mean square deviation of the end-to-end distance of the coiled coils revealed a power-law scaling with time, conserved across conformational states, homologs, and variants, suggesting a universal dynamic scaling. Coiled coils behave as semi-flexible filaments with strong internal friction, leading to relaxation times that were seconds-long and varied among conformational states and variants. Molecular dynamics simulations indicated that strong friction arose from long-lifetime contacts between coils. Our results suggest that MR complexes modulate the coiled coil dynamics to mediate long-range allosteric and allodynamic communication during DNA repair.
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