Behaviors of dynamic polymers such as microtubules and actin are frequently assessed at one or both of the following scales: (a) net assembly or disassembly of bulk polymer, (b) growth and shortening of individual filaments. Previous work has derived various forms of an equation to relate the rate of change in bulk polymer mass (i.e., flux of subunits into and out of polymer, often abbreviated as “J”) to individual filament behaviors. However, these versions of the “J equation” differ in the variables used to quantify individual filament behavior, which correspond to different experimental approaches. For example, some variants of the J equation use dynamic instability parameters, obtained by following particular individual filaments for long periods of time. Another form of the equation uses measurements from many individuals followed over short time steps. We use a combination of derivations and computer simulations that mimic experiments to (a) relate the various forms of the J equation to each other, (b) determine conditions under which these J equation forms are and are not equivalent, and (c) identify aspects of the measurements that can affect the accuracy of each form of the J equation. Improved understanding of the J equation and its connections to experimentally measurable quantities will contribute to efforts to build a multiscale understanding of steady‐state polymer behavior.

中文翻译：

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单个微管的动态不稳定性与亚基流入和流出聚合物的通量之间的关系。

经常在以下一种或两种规模下评估动态聚合物（例如微管和肌动蛋白）的行为：（a）散装聚合物的净组装或拆卸，（b）单丝的生长和缩短。先前的工作已经得出方程的各种形式，以将本体聚合物质量的变化率（即，亚基流入和流出聚合物的通量，通常缩写为“ J ”）与单个长丝行为联系起来。但是，“ J方程”的这些版本在用于量化单个细丝行为的变量上有所不同，这些变量对应于不同的实验方法。例如，J的某些变体该方程使用动态不稳定性参数，这些参数是通过长时间跟踪特定的单个细丝而获得的。该方程式的另一种形式是使用许多个人的测量结果，然后进行短时间的测量。我们将推导和计算机模拟相结合，将模拟实验模拟为：（a）将J方程的各种形式相互关联；（b）确定这些J方程形式相等与不相等的条件；（c）确定可能影响J方程每种形式的精度的测量方面。更好地了解J 方程及其与实验可测量量的联系将有助于建立对稳态聚合物行为的多尺度理解。