The Smoluchowski equation in population dynamics and the spread of infection

This dissertation is a report on an interdisciplinary investigation consisting of an application of random walk techniques to problems in ecology, particularly to the spread of Hantavirus epidemic among rodents that live on an open terrain. The population of mice that we consider is made up of infectious disease-carrying mice and susceptible mice that are disease-free, and each mouse has its own home range around which it executes a random walk. We describe an event of infection transmission in such a population via reaction-diffusion theory. Our simple model consists of two mice, one infected and the other susceptible, the disease being passed upon encounter as the two mice move on the terrain. The existence of home ranges of the mice is included in the model by representing each mouse to be a Smoluchowski random walker. Such a simple model is appropriate for a dilute population where only one infected-susceptible mice pair is considered to meet at a time. However the calculation helps the understanding of underlying microscopic processes of an epidemic outbreak in an arbitrary population density. The two-mice model is formulated in an arbitrary number of dimensions and explicit calculation in 1-dimension is performed first. We uncover an interesting effect of the home ranges on the characteristics of infection-transmission event. We find that there is an optimal configuration of the home ranges for which infection-transmission occurs most efficiently. Furthermore, the practical application of our model to higher dimensions requires an extension of the theory to circumvent a seemingly well-known problem in reaction-diffusion theory that the `reaction\u27 site cannot be a 0-dimensional object for problems considered in higher dimension than 1. We develop a detailed resolution and present a practical extension with an explicit calculation demonstrated in 2-dimensions. Our work is, thus, useful in two ways. One is the further development of reaction-diffusion theory to tethered random walkers and dimensions higher than 1. The other is to gain insights into the practical problem of the spread of the Hantavirus epidemic

Emerging roles of ARHGAP33 in intracellular trafficking of TrkB and pathophysiology of neuropsychiatric disorders

Intracellular trafficking of receptor proteins is essential for neurons to detect various extracellular factors during the formation and refinement of neural circuits. However, the precise mechanisms underlying the trafficking of neurotrophin receptors to synapses remain elusive. Here, we demonstrate that a brain-enriched sorting nexin, ARHGAP33, is a new type of regulator for the intracellular trafficking of TrkB, a high-affinity receptor for brain-derived neurotrophic factor. ARHGAP33 knockout (KO) mice exhibit reduced expression of synaptic TrkB, impaired spine development and neuropsychiatric disorder-related behavioural abnormalities. These deficits are rescued by specific pharmacological enhancement of TrkB signalling in ARHGAP33 KO mice. Mechanistically, ARHGAP33 interacts with SORT1 to cooperatively regulate TrkB trafficking. Human ARHGAP33 is associated with brain phenotypes and reduced SORT1 expression is found in patients with schizophrenia. We propose that ARHGAP33/SORT1-mediated TrkB trafficking is essential for synapse development and that the dysfunction of this mechanism may be a new molecular pathology of neuropsychiatric disorders

Site-level progression of periodontal disease during a follow-up period

<div><p>Periodontal disease is assessed and its progression is determined via observations on a site-by-site basis. Periodontal data are complex and structured in multiple levels; thus, applying a summary statistical approach (i.e., the mean) for site-level evaluations results in loss of information. Previous studies have shown the availability of mixed effects modeling. However, clinically beneficial information on the progression of periodontal disease during the follow-up period is not available.</p><p>We conducted a multicenter prospective cohort study. Using mixed effects modeling, we analyzed 18,834 sites distributed on 3,139 teeth in 124 patients, and data were collected 5 times over a 24-month follow-up period. The change in the clinical attachment level (CAL) was used as the outcome variable. The CAL at baseline was an important determinant of the CAL changes, which varied widely according to the tooth surface. The salivary levels of periodontal pathogens, such as <i>Porphyromonas gingivalis</i> and <i>Aggregatibacter actinomycetemcomitans</i>, were affected by CAL progression. “Linear”- and “burst”-type patterns of CAL progression occurred simultaneously within the same patient. More than half of the teeth that presented burst-type progression sites also presented linear-type progression sites, and most of the progressions were of the linear type. Maxillary premolars and anterior teeth tended to show burst-type progression. The parameters identified in this study may guide practitioners in determining the type and extent of treatment needed at the site and patient levels. In addition, these results show that prior hypotheses concerning "burst" and "linear" theories are not valid.</p></div

Multilevel logistic regression model with repeated measures to distinguish “linear” and “burst” progression during the 24-month follow-up period.

<p>Multilevel logistic regression model with repeated measures to distinguish “linear” and “burst” progression during the 24-month follow-up period.</p

Mean values of the CAL changes during the 24-month follow-up period.

<p>CAL changes during the 24-month follow-up period are separately illustrated by the CAL at baseline and by the type of tooth surface. Baseline CAL values are divided into three groups: (A) <3mm; (B) 3 mm; and (C) > 3 mm.</p> <p>─●─: Maxillary molar, ---■---: Maxillary premolar, ···▲···: Maxillary anterior,</p> <p>─○─: Maxillary molar, ---□---: Maxillary premolar, ···△···: Maxillary anterior</p> <p>Baseline CAL values of < 3mm gradually deteriorated, while baseline CAL values of > 3 mm improved. Molars with a baseline CAL of 3 mm progressed, whereas premolars and anterior teeth were stable or improved.</p> <p>CAL: clinical attachment level.</p

CAL change patterns during the 24-month follow-up period.

<p></p><p></p><p></p><p>(A) Changes of the improved, slightly improved, stable, slightly progressed, progressed and fluctuated categories.</p><p>···▲···: Improved, ··△···: Slightly improved, ─●─: Stable.</p><p>---□---: Slightly progressed, ---■---: progressed, ─■─: Fluctuated</p><p>Differences in the CAL changes over 24 months were classified into six categories: ≤ -3 mm, improved; between -3 mm and -2 mm, slightly improved; between -1 mm to 1 mm, stable; between 1 mm and 2 mm, slightly progressed; 3mm, progressed. In addition, cases with both ≤ -3 mm and ≥ 3mm were classified as fluctuated.</p><p></p><p></p><p>(B) CAL progression patterns of the progressed category</p><p>···▲···: Cluster 1, ···△···: Cluster 2, ─●─: Cluster 3.</p><p>─□─: Cluster 4, —■—: Cluster 5</p><p>A hierarchical cluster analysis was performed for the progressed type portrayed in Fig. 2(A), and 5 clusters were generated. The slope of cluster 1 was moderate, and the slopes of the other clusters were steep. Cluster 1 may correspond to the linear-type progressed sites, and the other clusters may correspond to the burst-type progressed sites.</p><p></p><p></p><p></p> <p>(A) Changes of the improved, slightly improved, stable, slightly progressed, progressed and fluctuated categories.</p> <p>···▲···: Improved, ··△···: Slightly improved, ─●─: Stable.</p> <p>---□---: Slightly progressed, ---■---: progressed, ─■─: Fluctuated</p> <p>Differences in the CAL changes over 24 months were classified into six categories: ≤ -3 mm, improved; between -3 mm and -2 mm, slightly improved; between -1 mm to 1 mm, stable; between 1 mm and 2 mm, slightly progressed; 3mm, progressed. In addition, cases with both ≤ -3 mm and ≥ 3mm were classified as fluctuated.</p> <p>(B) CAL progression patterns of the progressed category</p> <p>···▲···: Cluster 1, ···△···: Cluster 2, ─●─: Cluster 3.</p> <p>─□─: Cluster 4, —■—: Cluster 5</p> <p>A hierarchical cluster analysis was performed for the progressed type portrayed in Fig. 2(A), and 5 clusters were generated. The slope of cluster 1 was moderate, and the slopes of the other clusters were steep. Cluster 1 may correspond to the linear-type progressed sites, and the other clusters may correspond to the burst-type progressed sites.</p