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Abstract 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 “Jequation” differ in the variables used to quantify individual filament behavior, which correspond to different experimental approaches. For example, some variants of theJequation 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 theJequation to each other, (b) determine conditions under which theseJequation forms are and are not equivalent, and (c) identify aspects of the measurements that can affect the accuracy of each form of theJequation. Improved understanding of theJequation and its connections to experimentally measurable quantities will contribute to efforts to build a multiscale understanding of steady‐state polymer behavior. 

Quantification of microtubule (MT) dynamic instability (DI) is essential to mechanistic dissection of MT assembly and the activities of MT binding proteins. Typical methods for quantifying MT dynamics assume that MT behavior consists of growth and shortening phases, with instantaneous transitions (rescues and catastrophes) in between. However, examination of DI data at high temporal and spatial resolution reveals the presence of ambiguous behaviors that cannot easily fit into these categories. Failure to objectively recognize and quantify these behaviors could reduce the reproducibility of DI data and impact attempts to dissect mechanisms. To address these problems, we recently developed STADIA (Statistical Tool for Automated Dynamic Instability Analysis), a MT analysis software package that uses length-history data as input and is (presently) implemented in MATLAB. STADIA uses machine learning methods to objectively analyze and quantify macro-level DI behaviors exhibited by MTs, including variable rates of growth and shortening and a newly quantified DI phase: stutter. Here we overview the process of using STADIA to quantify MT dynamics and provide a set of concrete protocols for using STADIA to process and analyze MT length history data. 

The concept of critical concentration (CC) is central to understanding the behavior of microtubules (MTs) and other cytoskeletal polymers. Traditionally, these polymers are understood to have one CC, measured in multiple ways and assumed to be the subunit concentration necessary for polymer assembly. However, this framework does not incorporate dynamic instability (DI), and there is work indicating that MTs have two CCs. We use our previously established simulations to confirm that MTs have (at least) two experimentally relevant CCs and to clarify the behavior of individuals and populations relative to the CCs. At free subunit concentrations above the lower CC (CC Elongation ), growth phases of individual filaments can occur transiently; above the higher CC (CC NetAssembly ), the population’s polymer mass will increase persistently. Our results demonstrate that most experimental CC measurements correspond to CC NetAssembly , meaning that “typical” DI occurs below the concentration traditionally considered necessary for polymer assembly. We report that [free tubulin] at steady state does not equal CC NetAssembly , but instead approaches CC NetAssembly asymptotically as [total tubulin] increases, and depends on the number of stable MT nucleation sites. We show that the degree of separation between CC Elongation and CC NetAssembly depends on the rate of nucleotide hydrolysis. This clarified framework helps explain and unify many experimental observations.