Comment on "Local accumulation times for source, diffusion, and degradation models in two and three dimensions" [J. Chem. Phys. 138, 104121 (2013)]

In a recent paper, Gordon, Muratov, and Shvartsman studied a partial differential equation (PDE) model describing radially symmetric diffusion and degradation in two and three dimensions. They paid particular attention to the local accumulation time (LAT), also known in the literature as the mean action time, which is a spatially dependent timescale that can be used to provide an estimate of the time required for the transient solution to effectively reach steady state. They presented exact results for three-dimensional applications and gave approximate results for the two-dimensional analogue. Here we make two generalizations of Gordon, Muratov, and Shvartsman’s work: (i) we present an exact expression for the LAT in any dimension and (ii) we present an exact expression for the variance of the distribution. The variance provides useful information regarding the spread about the mean that is not captured by the LAT. We conclude by describing further extensions of the model that were not considered by Gordon,Muratov, and Shvartsman. We have found that exact expressions for the LAT can also be derived for these important extensions..

Inhibition of Respiration by Nitric Oxide Induces a Mycobacterium tuberculosis Dormancy Program

An estimated two billion persons are latently infected with Mycobacterium tuberculosis. The host factors that initiate and maintain this latent state and the mechanisms by which M. tuberculosis survives within latent lesions are compelling but unanswered questions. One such host factor may be nitric oxide (NO), a product of activated macrophages that exhibits antimycobacterial properties. Evidence for the possible significance of NO comes from murine models of tuberculosis showing progressive infection in animals unable to produce the inducible isoform of NO synthase and in animals treated with a NO synthase inhibitor. Here, we show that O2 and low, nontoxic concentrations of NO competitively modulate the expression of a 48-gene regulon, which is expressed in vivo and prepares bacilli for survival during long periods of in vitro dormancy. NO was found to reversibly inhibit aerobic respiration and growth. A heme-containing enzyme, possibly the terminal oxidase in the respiratory pathway, likely senses and integrates NO and O2 levels and signals the regulon. These data lead to a model postulating that, within granulomas, inhibition of respiration by NO production and O2 limitation constrains M. tuberculosis replication rates in persons with latent tuberculosis