Macrophage response to Mycobacteriumtuberculosis infection

Abstract

The immune response to Mycobacterium tuberculosis (Mtb) infection is the formation of multicellular lesions, or granolomas, in the lung of the individual. However, the structure of the granulomas and the spatial distribution of the immune cells within is not well understood. In this paper we develop a mathematical model investigating the early and initial immune response to Mtb. The model consists of coupled reaction-diffusion-advection partial differential equations governing the dynamics of the relevant macrophage and bacteria populations and a bacteria-produced chemokine. Our novel application of mathematical concepts of internal states and internal velocity allows us to begin to study this unique immunological structure. Volume changes resulting from proliferation and death terms generate a velocity field by which all cells are transported within the forming granuloma. We present numerical results for two distinct infection outcomes: controlled and uncontrolled granuloma growth. Using a simplified model we are able to analytically determine conditions under which the bacteria population decreases, representing early clearance of infection, or grows, representing the initial stages of granuloma formation.

Understanding the Immune Response in Tuberculosis Using Different Mathematical Models and Biological Scales

“…Therefore, as discussed in Gammack, Doering, and Kirschner [21], only two outcomes are possible: continued granuloma growth (granuloma radius, R(t), grows unbounded) or control of infection (granuloma radius, R(t), decays to zero). We would expect that, with the addition of other immune cell populations, this growth would either be stopped (leading to a solid granuloma) or continue, leading to a necrotic granuloma.…”

“…For example, the models of Keller and Segel [39,40] were developed to examine how cells move via directed cell movement (chemotaxis). Before discussing our model [21], we briefly discuss the mathematical techniques used to model processes in general biological systems that will be utilized here. In this section we discuss spatio-temporal modeling of Mtb infection using PDEs.…”

“…We now give an overview of our model of the innate immune response to Mtb (for a full account of this model see [21]). There are five dependent variable types in our model: extracellular bacteria, B(t, x), macrophages (uninfected and infected),…”

“…A full list of parameter values can be found in Gammack, Doering, and Kirschner [21]. Parameters were mostly taken from [76] with the estimates for cellular movement and flux taken from various sources [53,54,74,75].…”

“…We have applied these approaches over a range of biological scales. The processes described above can be studied at a single-cell scale [8,62] to a scale of populations of cells [21,45,76]. Further, some of our studies focus on host-bacterial interactions at the local site of infection (cf.…”