Hybrid approach to model the spatial regulation of T cell responses

Abstract

BackgroundMoving from the molecular and cellular level to a multi-scale systems understanding of immune responses requires the development of novel approaches to integrate knowledge and data from different biological levels into mechanism-based integrative mathematical models. The aim of our study is to present a methodology for a hybrid modelling of immunological processes in their spatial context.MethodsA two-level hybrid mathematical model of immune cell migration and interaction integrating cellular and organ levels of regulation for a 2D spatial consideration of idealized secondary lymphoid organs is developed. It considers the population dynamics of antigen-presenting cells, CD4 + and CD8 + T lymphocytes in naive-, proliferation- and differentiated states. Cell division is assumed to be asymmetric and regulated by the extracellular concentration of interleukin-2 (IL-2) and type I interferon (IFN), together controlling the balance between proliferation and differentiation. The cytokine dynamics is described by reaction-diffusion PDEs whereas the intracellular regulation is modelled with a system of ODEs.ResultsThe mathematical model has been developed, calibrated and numerically implemented to study various scenarios in the regulation of T cell immune responses to infection, in particular the change in the diffusion coefficient of type I IFN as compared to IL-2. We have shown that a hybrid modelling approach provides an efficient tool to describe and analyze the interplay between spatio-temporal processes in the emergence of abnormal immune response dynamics.DiscussionVirus persistence in humans is often associated with an exhaustion of T lymphocytes. Many factors can contribute to the development of exhaustion. One of them is associated with a shift from a normal clonal expansion pathway to an altered one characterized by an early terminal differentiation of T cells. We propose that an altered T cell differentiation and proliferation sequence can naturally result from a spatial separation of the signaling events delivered via TCR, IL-2 and type I IFN receptors. Indeed, the spatial overlap of the concentration fields of extracellular IL-2 and IFN in lymph nodes changes dynamically due to different migration patterns of APCs and CD4 + T cells secreting them.ConclusionsThe proposed hybrid mathematical model of the immune response represents a novel analytical tool to examine challenging issues in the spatio-temporal regulation of cell growth and differentiation, in particular the effect of timing and location of activation signals.Electronic supplementary materialThe online version of this article (doi:10.1186/s12865-017-0205-0) contains supplementary material, which is available to authorized users.

Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics

“…The dynamics of infectious diseases in humans is subject to many random effects resulting from stochastic fluctuations in biochemical and cellular processes underlying the infection of target cells, within-thecell replication and effect of the immune responses. The potential of the stochastic models has been appreciated in recent studies based on single scale models formulated with SDEs [21], discrete stochastic models [24,27], genetic algorithms [4] as well as multi-scale hybrid models [6,7,23,30].…”

Towards a Multiscale Model of Acute HIV Infection

“…The characteristic units of the model are the minute for time and the domain length for space. Further details of the numerical methods are described in the Appendix to [50]. The numerical code implementing the model is available upon request to the first author or can be directly assessed at https://github.com/MPS7/MultiScale-HIV.…”

Towards multiscale modeling of the CD8+T cell response to viral infections

“…Model predictions qualitatively reproduced the CD8 + T cell counts observed in mice lymph nodes early in infection. Bouchnita, Bocharov, Meyerhans, and Volpert () have constructed a more detailed model incorporating, additionally, signaling via the interferon receptors, as well as help from CD4+ T cells. Further, cell division was assumed to be asymmetric (J. T. Chang et al, ; J. T. Chang et al, ).…”