Quantification of microtubule stutters: dynamic instability behaviors that are strongly associated with catastrophe.

Microtubules (MTs) are cytoskeletal fibers that undergo dynamic instability (DI), a remarkable process involving phases of growth and shortening separated by stochastic transitions called catastrophe and rescue. Dissecting DI mechanism(s) requires first characterizing and quantifying these dynamics, a subjective process that often ignores complexity in MT behavior. We present a Statistical Tool for Automated Dynamic Instability Analysis (STADIA) that identifies and quantifies not only growth and shortening, but also a category of intermediate behaviors that we term "stutters." During stutters, the rate of MT length change tends to be smaller in magnitude than during typical growth or shortening phases. Quantifying stutters and other behaviors with STADIA demonstrates that stutters precede most catastrophes in our in vitro experiments and dimer-scale MT simulations, suggesting that stutters are mechanistically involved in catastrophes. Related to this idea, we show that the anticatastrophe factor CLASP2γ works by promoting the return of stuttering MTs to growth. STADIA enables more comprehensive and data-driven analysis of MT dynamics compared with previous methods. The treatment of stutters as distinct and quantifiable DI behaviors provides new opportunities for analyzing mechanisms of MT dynamics and their regulation by binding proteins.

Behaviors of individual microtubules and microtubule populations relative to critical concentrations: dynamic instability occurs when critical concentrations are driven apart by nucleotide hydrolysis.

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 (CCElongation), growth phases of individual filaments can occur transiently; above the higher CC (CCNetAssembly), the population's polymer mass will increase persistently. Our results demonstrate that most experimental CC measurements correspond to CCNetAssembly, 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 CCNetAssembly, but instead approaches CCNetAssembly asymptotically as [total tubulin] increases, and depends on the number of stable MT nucleation sites. We show that the degree of separation between CCElongation and CCNetAssembly depends on the rate of nucleotide hydrolysis. This clarified framework helps explain and unify many experimental observations.

Investigating the role of gap junctions in seizure wave propagation.

The effect of gap junctions as well as the biological mechanisms behind seizure wave propagation is not completely understood. In this work, we use a simple neural field model to study the possible influence of gap junctions specifically on cortical wave propagation that has been observed in vivo preceding seizure termination. We consider a voltage-based neural field model consisting of an excitatory and an inhibitory population as well as both chemical and gap junction-like synapses. We are able to approximate important properties of cortical wave propagation previously observed in vivo before seizure termination. This model adds support to existing evidence from models and clinical data suggesting a key role of gap junctions in seizure wave propagation. In particular, we found that in this model gap junction-like connectivity determines the propagation of one-bump or two-bump traveling wave solutions with features consistent with the clinical data. For sufficiently increased gap junction connectivity, wave solutions cease to exist. Moreover, gap junction connectivity needs to be sufficiently low or moderate to permit the existence of linearly stable solutions of interest.

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.

Uniform asymptotic approximation of diffusion to a small target: Generalized reaction models.

The diffusion of a reactant to a binding target plays a key role in many biological processes. The reaction radius at which the reactant and target may interact is often a small parameter relative to the diameter of the domain in which the reactant diffuses. We develop uniform in time asymptotic expansions in the reaction radius of the full solution to the corresponding diffusion equations for two separate reactant-target interaction mechanisms: the Doi or volume reactivity model and the Smoluchowski-Collins-Kimball partial-absorption surface reactivity model. In the former, the reactant and target react with a fixed probability per unit time when within a specified separation. In the latter, upon reaching a fixed separation, they probabilistically react or the reactant reflects away from the target. Expansions of the solution to each model are constructed by projecting out the contribution of the first eigenvalue and eigenfunction to the solution of the diffusion equation and then developing matched asymptotic expansions in Laplace-transform space. Our approach offers an equivalent, but alternative, method to the pseudopotential approach we previously employed [Isaacson and Newby, Phys. Rev. E 88, 012820 (2013)PLEEE81539-375510.1103/PhysRevE.88.012820] for the simpler Smoluchowski pure-absorption reaction mechanism. We find that the resulting asymptotic expansions of the diffusion equation solutions are identical with the exception of one parameter: the diffusion-limited reaction rates of the Doi and partial-absorption models. This demonstrates that for biological systems in which the reaction radius is a small parameter, properly calibrated Doi and partial-absorption models may be functionally equivalent.