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..

DM influences the abundance of major histocompatibility complex class II alleles with low affinity for class II-associated invariant chain peptides via multiple mechanisms

DM catalyses class II-associated invariant chain peptide (CLIP) release, edits the repertoire of peptides bound to major histocompatibility complex (MHC) class II molecules, affects class II structure, and thereby modulates binding of conformation-sensitive anti-class II antibodies. Here, we investigate the ability of DM to enhance the cell surface binding of monomorphic antibodies. We show that this enhancement reflects increases in cell surface class II expression and total cellular abundance, but notably these effects are selective for particular alleles. Evidence from analysis of cellular class II levels after cycloheximide treatment and from pulse-chase experiments indicates that DM increases the half-life of affected alleles. Unexpectedly, the pulse-chase experiments also revealed an early effect of DM on assembly of these alleles. The allelically variant feature that correlates with susceptibility to these DM effects is low affinity for CLIP; DM-dependent changes in abundance are reduced by invariant chain (CLIP) mutants that enhance CLIP binding to class II. We found evidence that DM mediates rescue of peptide-receptive DR0404 molecules from inactive forms in vitro and evidence suggesting that a similar process occurs in cells. Thus, multiple mechanisms, operating along the biosynthetic pathway of class II molecules, contribute to DM-mediated increases in the abundance of low-CLIP-affinity alleles