Understanding Complex Biological Systems with Mathematics by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9783319980836
Publisher: Springer International Publishing

2 Mathematical Model

Our mathematical model consists of a system of ordinary differential equations that describes interactions between MM and the immune system. Specifically, we track the temporal dynamics of the following four populations in the peripheral blood: M protein produced by MM cells, M(t); cytotoxic T lymphocytes (CTLs), T C(t); natural killer (NK) cells, N(t); and regulatory T cells (Tregs), T R(t). The NK population is part of the innate immune system, while CTLs and Tregs are part of the adaptive immune response and are assumed to be specific to myeloma cells. The three immune cell populations included in the model were also chosen for the following additional reasons. First, they are all implicated in the development of MM [25, 41], and have interrelated dynamics [25]. Second, each is affected by a therapy we plan to study in silico with this model: NK cells are targeted by the approved MM therapy elotuzumab [67]; Tregs are affected by the approved MM therapy daratumumab [47]; and the main effect of anti-programmed death 1 (anti-PD-1) therapy is on effector T cells [66]. Third, levels of each of the three immune cell types could be obtained from patient peripheral blood samples in clinical studies, which would allow the estimation of certain parameters in the model. The interactions between populations included in this model are illustrated in Fig. 1 and listed in Table 1. In Sect. 2.1, we discuss in greater detail the biological basis for each interaction pathway used in the model.

Fig. 1Diagram of population interactions. M represents M protein produced by MM cells, T C represents CTLs, N represents NK cells, and T R represents Tregs. The solid curves represent an increase (arrows pointing in) or decrease (arrows only pointing out) in population sizes. The dashed curves represent interactions that either boost (arrows) or inhibit (solid circles) population sizes or rates of change. These interaction pathways (labeled a–k) are described in Table 1 and in Sect. 2.1

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