Living helices in fluctuating polymer chains: Cooperative nucleation and dynamics

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.