Mathematical Modelling of Venom Immunotherapy

Abstract

Allergic hypersensitivity of type I for hymenoptera venoms is the most frequent reason for acute IgEmediated anaphylactic reactions. The subcutaneous injection of increasing doses of purified allergen followed by long-term administration of an adequate maintenance dose over a period of 3-5 years called venom immunotherapy (VIT) has been proven to be a very effective treatment achieving protection in about 96% of allergic patients. Even though the principle of hyposensitisation has been introduced already 90 years ago, the underlying immunoregulatory mechanisms of VIT remain poorly understood. Recent studies suggest a shift in cytokine production from a Th2 to a Th1 cytokine profile during therapy. In this paper, a mathematical model for T-cell regulation and a model for mast cell/basophil desensitisation are presented and analysed to explain the mechanism of conventional rush and ultra-rush VIT.

Cellular and population plasticity of helper CD4+ T cell responses

“…The first subgroup of studies developed and analyzed mathematical models of differentiation of naïve CD4 + (Th0) cells into Th1 and Th2 subsets by including the dynamics of Th1/Th2 cytokines, intracellular molecules, and gene regulatory networks (Biedermann and Röcken, 1999; Fishman and Perelson, 1999; Yates et al, 2000, 2004; Bergmann et al, 2001, 2002; Richter et al, 2002; Bettelli et al, 2006; Callard, 2007; Fenton et al, 2008; Eftimie et al, 2010; Naldi et al, 2010; Vicente et al, 2010; Groß et al, 2011; Hong et al, 2011, 2012; Liao et al, 2011). Some of these models described differentiation of naïve CD4 + T cells into different effector T cell subsets via upregulation of the phenotype-specific TF (master regulators) such as T-bet, GATA-3, FoxP3, and ROR-γt (Höfer et al, 2002; Mariani et al, 2004; Yates et al, 2004; Callard, 2007; Van Den Ham and De Boer, 2008; Hong et al, 2011, 2012).…”

Mathematical modeling of allergy and specific immunotherapy: Th1–Th2–Treg interactions

“…The previous model, as discussed for example in Richter et al (2002), was able to explain the therapeutic effect of immunotherapy solely in terms of Th1-Th2 interaction. However, successful therapy was only possible for a very small set of initial conditions and depended crucially on the asymmetry in the cross-regulation of Th1 and Th2 cells.…”

“…The strength of suppression is regulated by the parameters m 1 , m 2 , and m r , respectively. In Richter et al (2002) it was argued that the parameters f, m 1 , and m 2 , which already occur in the old version of the model, have to satisfy the conditions f\1 and m 1 4 m 2 . This was based on empirical findings on the dependency of the type of immune response on the allergen dose (Secrist et al, 1995;Ruedl et al, 2000).…”

“…For numerical simulations, we will always use w ¼ 0:8 and m r ¼ 0:25. From Richter et al (2002) we adopt the choice of the remaining parameters:…”

“…Such a model using nonlinear differential equations describing the dynamics of Th1-Th2-interactions was introduced in Behn et al (2001) and further investigated in Richter et al (2002) and Vogel and Behn (2007). On the following pages we will present an extended version of this model that takes into account the influence of a population of allergen-specific regulatory T cells.…”