Relationship between dynamic instability of individual microtubules and flux of subunits into and out of polymer

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.