Mathematical and computational approaches can complement experimental studies of host-pathogen interactions

Abstract

In addition to traditional and novel experimental approaches to study host-pathogen interactions, mathematical and computer modelling have recently been applied to address open questions in this area. These modelling tools not only offer an additional avenue for exploring disease dynamics at multiple biological scales, but also complement and extend knowledge gained via experimental tools. In this review, we outline four examples where modelling has complemented current experimental techniques in a way that can or has already pushed our knowledge of host-pathogen dynamics forward. Two of the modelling approaches presented go hand in hand with articles in this issue exploring fluorescence resonance energy transfer and two-photon intravital microscopy. Two others explore virtual or 'in silico' deletion and depletion as well as a new method to understand and guide studies in genetic epidemiology. In each of these examples, the complementary nature of modelling and experiment is discussed. We further note that multi-scale modelling may allow us to integrate information across length (molecular, cellular, tissue, organism, population) and time (e.g. seconds to lifetimes). In sum, when combined, these compatible approaches offer new opportunities for understanding host-pathogen interactions.

Figure 1

Shown is a grid that represents the paracortoid region of a lymph node (or T-cell zone). The grid is subdivided into 20 micron by 20 micron compartments that can hold up to one DC (MDC- mature , LDC-licensed) or up to two T cells (either CD4+ or CD8 + T cells, that are r- resting, a- activated or e- effector). While DCs exist within one compartment, their influence represents a sweep area that extends to the surrounding compartments around the DC allowing any T cell that comes into those spaces to interact with a DC. T cells enter the LN through the afferent lymphatic ducts (AL) and leave via the efferent lymphatic (EF). DCs enter via high endothelial venules (HEV). Shown are enlargements of regions indicating the existence of these complexities on the grid. A computer model solves the rules described for cells interacting on this grid and the output can be visualized as a time-lapse simulation (see http://malthus.micro.med.umich.edu/lab/movies/LNtzone/).

Figure 2

(a) Schematic of a cell that has been loaded with acceptor (yellow)- and donor (blue)-labeled proteins to achieve FRET. Analysis of FRET images can be used to obtain values of the equilibrium dissociation constant (K_d). Note that one obtains a probability distribution rather than a whole-cell averaged value, potentially allowing identification of multiple distinct values of K_d in different cellular regions. (b) Trade-offs during antigen presentation. In the top plot, we show the values of peptide-MHCII affinity and IFN-γ concentration that give the same response, i.e. T cell receptor internalization or T cell cytokine secretion. Within the middle portion of the curve, a deficiency in one parameter can compensate for a change in the other parameter; at the ends of the curve peptide-MHC affinity is dominant. In the lower plot, we show values of the number of peptide-MHCII complexes on a DC and the number of DCs in the LN that give the same number of activated CD4+ T cells leaving the LN. Again, changes in one parameter are observed to compensate for changes in the other. (c) Virtual manipulation of CD8+ T cells during infection with M. tuberculosis. Solid curves show the wild-type response similar to that observed in experiments, dashed curves show an alternative simulation. Top panel: CD8+ CTL T numbers grows slowly, peaking after day 150, and then decay (solid curve), while the CD8+ IFN-γ producing T cells don’t appear until day 200 (not shown). In our in silico alternative simulation, we switch the order of the differential expression: CD8+ IFN-g producing T cells emerge first and slowly decay over time (not shown) while the CD8+ CTL T cells do not appear until day 200 and then slowly decay (dashed curve). Bottom panel: In the wild-type scenario, bacterial load is large, and even oscillating (solid curve) but in the artificial scenario the bacterial load is cleared (dashed curve).