The nucleated polymerization model is a mathematical framework that has been applied to aggregation and fragmentation processes in both the discrete and continuous settings. In particular, this model has been the canonical framework for analyzing the dynamics of protein aggregates arising in prion and amyloid diseases such as Alzheimer’s and Parkinson’s disease.

We present an explicit steady-state solution to the aggregate size distribution governed by the discrete nucleated polymerization equations. Steady-state solutions have been previously obtained under the assumption of continuous aggregate sizes; however, the discrete solution allows for direct computation and parameter inference, as well as facilitates estimates on the accuracy of the continuous approximation.

成核聚合模型是一个数学框架，已应用于离散和连续设置中的聚集和碎片过程。特别是，该模型已成为分析朊病毒和淀粉样蛋白疾病（例如阿尔茨海默病和帕金森病）中蛋白质聚集体动力学的规范框架。

我们提出了由离散成核聚合方程控制的聚集体尺寸分布的显式稳态解。之前已经在聚集体尺寸连续的假设下获得了稳态解；然而，离散解允许直接计算和参数推断，并且有助于估计连续近似的精度。