Bishop M F, Ferrone F A
Biophys J. 1984 Nov;46(5):631-44. doi: 10.1016/S0006-3495(84)84062-X.
We present a perturbation method for analyzing nucleation-controlled polymerization augmented by a secondary pathway for polymer growth. With this method, the solution to the kinetic equations assumes a simple analytic closed form that can easily be used in fitting data. So long as the formation of polymers by the secondary pathway depends linearly on the concentration of monomers polymerized, the form of the solutions is the same. This permits the analysis of augmented growth models with a minimum number of modeling assumptions, and thus makes it readily possible to distinguish between a variety of secondary processes (heterogeneous nucleation, lateral growth, and fragmentation). In addition, the parameters of the homogeneous process, such as the homogeneous nucleus size, can be determined independent of the nature of the secondary mechanism. We describe applications of this method to the polymerization of actin, collagen, and sickle hemoglobin. We present an extensive analysis of data on actin polymerization (Wegner, A., and P. Savko, 1982, Biochemistry, 21:1909-1913) to illustrate the use of the method. Although our conclusions generally agree with theirs, we find that lateral growth describes the secondary pathway better than the fragmentation model originally proposed. We also show how this method can be used to study the degree of polymerization, the parentage of polymers, and the behavior of polymers in cycling experiments.
我们提出了一种微扰方法，用于分析由聚合物生长的二级途径增强的成核控制聚合。通过这种方法，动力学方程的解具有简单的解析封闭形式，可轻松用于拟合数据。只要通过二级途径形成的聚合物线性依赖于聚合单体的浓度，解的形式就是相同的。这允许在最少的建模假设下分析增强生长模型，从而能够轻易区分各种二级过程（异相成核、横向生长和碎片化）。此外，均相过程的参数，如均相核尺寸，可以独立于二级机制的性质来确定。我们描述了该方法在肌动蛋白、胶原蛋白和镰状血红蛋白聚合中的应用。我们对肌动蛋白聚合数据（Wegner, A., and P. Savko, 1982, Biochemistry, 21:1909 - 1913）进行了广泛分析，以说明该方法的使用。尽管我们的结论总体上与他们的一致，但我们发现横向生长比最初提出的碎片化模型能更好地描述二级途径。我们还展示了该方法如何用于研究聚合度、聚合物的谱系以及聚合物在循环实验中的行为。
