Nucleated polymerisation in the presence of pre-formed seed filaments

We revisit the classical problem of nucleated polymerisation and derive a range of exact results describing polymerisation in systems intermediate between the well-known limiting cases of a reaction starting from purely soluble material and for a reaction where no new growth nuclei are formed.

💡 Research Summary

This paper revisits the classical Oosawa theory of nucleated polymerisation and extends it to cover the experimentally relevant situation where an arbitrary amount of pre‑formed seed filaments is present at the start of the reaction. Starting from the master equation for the concentration f(j,t) of filaments of size j, the authors assume irreversible growth (depolymerisation is negligible) and growth from both filament ends. Under these conditions the rate equations for the number concentration of filaments P(t) and the free monomer concentration m(t) reduce to the familiar Oosawa forms (Eqs. 2 and 3).

The key methodological step is the substitution z(t)=log m(t), which converts the coupled nonlinear equations into a separable form. By integrating with the appropriate initial conditions (initial monomer concentration m(0) and initial seed concentration P(0)), the authors obtain a closed‑form expression for the polymer mass concentration M(t) (Eq. 9). This expression depends only on two composite parameters:

• λ = √