On distributions of functionals of anomalous diffusion paths

Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger equation in imaginary time. In recent years there is a growing interest in particular functionals of non-Brownian motion, or anomalous diffusion, but no equation existed for their PDF. Here, we derive a fractional generalization of the Feynman-Kac equation for functionals of anomalous paths based on sub-diffusive continuous-time random walk. We also derive a backward equation and a generalization to Levy flights. Solutions are presented for a wide number of applications including the occupation time in half space and in an interval, the first passage time, the maximal displacement, and the hitting probability. We briefly discuss other fractional Schrodinger equations that recently appeared in the literature.Comment: 25 pages, 4 figure

CHD8 regulates gut epithelial cell function and affects autism-related behaviors through the gut-brain axis

Abstract Autism is a neurodevelopmental disorder characterized by early-onset social behavioral deficits and repetitive behaviors. Chromodomain helicase DNA-binding protein (CHD8) is among the genes most strongly associated with autism. In addition to the core behavioral symptoms of autism, affected individuals frequently present with gastrointestinal symptoms that are also common among individuals harboring mutations in the gene encoding CHD8. However, little is known regarding the mechanisms whereby CHD8 affects gut function. In addition, it remains unknown whether gastrointestinal manifestations contribute to the behavioral phenotypes of autism. The current study found that mice haploinsufficient for the large isoform of Chd8 (Chd8L) exhibited increased intestinal permeability, transcriptomic dysregulation in gut epithelial cells, reduced tuft cell and goblet cell counts in the gut, and an overall increase in microbial load. Gut epithelial cell-specific Chd8 haploinsufficiency was associated with increased anxiety-related behaviors together with a decrease in tuft cell numbers. Antibiotic treatment of Chd8L haploinsufficient mice attenuated social behavioral deficits. Together, these results suggest Chd8 as a key determinant of autism-related gastrointestinal deficits, while also laying the ground for future studies on the link between GI deficits and autism-related behaviors

TMF/ARA160 Governs the Dynamic Spatial Orientation of the Golgi Apparatus during Sperm Development.

TMF/ARA160 is known to be a TATA element Modulatory Factor (TMF). It was initially identified as a DNA-binding factor and a coactivator of the Androgen receptor. It was also characterized as a Golgi-associated protein, which is essential for acrosome formation during functional sperm development. However, the molecular roles of TMF in this intricate process have not been revealed. Here, we show that during spermiogenesis, TMF undergoes a dynamic change of localization throughout the Golgi apparatus. Specifically, TMF translocates from the cis-Golgi to the trans-Golgi network and to the emerging vesicles surface, as the round spermatids develop. Notably, lack of TMF led to an abnormal spatial orientation of the Golgi and to the deviation of the trans-Golgi surface away from the nucleus of the developing round spermatids. Concomitantly, pro-acrosomal vesicles derived from the TMF-/- Golgi lacked targeting properties and did not tether to the spermatid nuclear membrane thereby failing to form the acrosome anchoring scaffold, the acroplaxome, around the cell-nucleus. Absence of TMF also perturbed the positioning of microtubules, which normally lie in proximity to the Golgi and are important for maintaining Golgi spatial orientation and dynamics and for chromatoid body formation, which is impaired in TMF-/- spermatids. In-silico evaluation combined with molecular and electron microscopic analyses revealed the presence of a microtubule interacting domain (MIT) in TMF, and confirmed the association of TMF with microtubules in spermatogenic cells. Furthermore, the MIT domain in TMF, along with microtubules integrity, are required for stable association of TMF with the Golgi apparatus. Collectively, we show here for the first time that a Golgi and microtubules associated protein is crucial for maintaining proper Golgi orientation during a cell developmental process

Paneth cells secrete lysozyme via secretory autophagy during bacterial infection of the intestine

Intestinal Paneth cells limit bacterial invasion by secreting antimicrobial proteins, including lysozyme. However, invasive pathogens can disrupt the Golgi apparatus, interfering with secretion and compromising intestinal antimicrobial defense. Here we show that during bacterial infection, lysozyme is rerouted via secretory autophagy, an autophagy-based alternative secretion pathway. Secretory autophagy was triggered in Paneth cells by bacteria-induced endoplasmic reticulum (ER) stress, required extrinsic signals from innate lymphoid cells, and limited bacterial dissemination. Secretory autophagy was disrupted in Paneth cells of mice harboring a mutation in autophagy gene Atg16L1 that confers increased risk for Crohn's disease in humans. Our findings identify a role for secretory autophagy in intestinal defense and suggest why Crohn's disease is associated with genetic mutations that affect both the ER stress response and autophagy

TMF^-/- spermatids lack an acroplaxome.

<p>Testicular sections from wt (A-D) and TMF^-/- mice (E-F) were subjected to EM analyses. (A) Stage 2/early 3 wt spermatid. (B) Boxed area in <b>A</b> under higher magnification. The acroplaxome is marked by arrows. (C) Stage 4 wt spermatid. (D) The boxed area in <b>C</b> under higher magnification. The acroplaxome is marked by arrows. (E) Stage 4 TMF^-/- spermatid. (F) The boxed area in <b>E</b> under higher magnification. The supposed localization of the acroplaxome is marked by arrows. Ac = acrosome, Nu = Nucleus. Bars represent 2μm (A, C and E) and 1μm (B, D and F). Each image represents one out of twenty different cells selected from three different sections which gave similar results. Immunocytochemical staining of F-actin (red) and acrosome (green) in round spermatids from wt (G-I) and TMF^-/- (J-L) mice, which were exposed to hypotonic shock.DIC images of the stained spermatids are shown in <b>I</b> and <b>L</b>. Acroplaxome margins are marked by arrows in <b>G</b>. (M) Immunocytochemical staining of F-actin (red) in wt round spermatid. (N) Immunocytochemical staining of F-actin (red) in TMF^-/- round spermatid. (O) Immunocytochemical staining of F-actin (red) and TMF (Green) in wt round spermatid. (P) Immunocytochemical staining of F-actin (red) in wt elongated spermatid. (Q) Immunocytochemical staining of F-actin (red) in TMF^-/- elongated spermatid. DIC images of the spermatids are also shown in <b>P</b> and <b>Q</b>. Nuclei were visualized with Hoechst solution (blue). Bars represent 10μm. Images represent one out of five independently prepared cell suspensions that gave similar staining profiles.</p