An impulsive differential equation model for Marek's disease

Many dynamical processes are subject to abrupt changes in state. Often these perturbations can be periodic and of short duration relative to the evolving process. These types of phenomena are described well by what are referred to as impulsive differential equations, systems of differential equations coupled with discrete mappings in state space. In this thesis we employ impulsive differential equations to model disease transmission within an industrial livestock barn. In particular we focus on the poultry industry and a viral disease of poultry called Marek's disease. This system lends itself well to impulsive differential equations. Entire cohorts of poultry are introduced and removed from a barn concurrently. Additionally, Marek's disease is transmitted indirectly and the viral particles can survive outside the host for weeks. Therefore, depopulating, cleaning, and restocking of the barn are integral factors in modelling disease transmission and can be completely captured by the impulsive component of the model. Our model allows us to investigate how modern broiler farm practices can make disease elimination difficult or impossible to achieve. It also enables us to investigate factors that may contribute to virulence evolution. Our model suggests that by decrease the cohort duration or by decreasing the flock density, Marek's disease can be eliminated from a barn with no increase in cleaning effort. Unfortunately our model also suggests that these practices will lead to disease evolution towards greater virulence. Additionally, our model suggests that if intensive cleaning between cohorts does not rid the barn of disease, it may drive evolution and cause the disease to become more virulent.

INVESTIGATING THE MECHANISM OF AUTOIMMUNE DISEASE ASSOCIATED-LQTS

The human ether-a-go-go-related gene (hERG) protein passes the rapidly activating delayed rectifier potassium channel (IKr), and malfunction of hERG protein/IKr is the primary cause of acquired long QT syndrome (LQTS). Autoimmune diseases are significantly correlated with prolonged QT intervals, for which autoantibodies have been implicated. The anti-Ro52 autoantibody is the most frequently evaluated, and importantly has been correlated with prolonged QT intervals. Pathological anti-Ro52-hERG interactions have been discussed as a mechanism for autoimmune disease-related LQTS. However, the mechanism is unclear, and it does not explain LQTS in autoimmune diseases which do not commonly express anti-Ro52. In this thesis, I investigated the effects of anti-Ro52 on hERG/IKr function. Through Western blot analysis, whole-cell patch-clamp, and immunofluorescence, I show that anti-Ro52 chronically (12 h) reduced hERG protein expression and hERG current by over 50%, but did not acutely block the channel. My work revealed a novel mechanism in which the Fc portion of anti-Ro52 interacts with the extracellular S5-pore linker of the channel to induce internalization through a tyrosine phosphorylation dependent pathway. This phenomenon extends beyond anti-Ro52 IgG, as other IgG, regardless of their antigen binding specificity, have the potential to reduce hERG expression/current. Rather, the ability of IgG to reduce hERG expression and current is dependent on the IgG subclass, as we show mouse IgG2A was the only mouse IgG subclass which reduced hERG expression. These results provide a novel explanation for autoimmune disease associated LQTS. It also has implications in the development of safe monoclonal antibody drugs.