Abstract
During the primary CD8 T cell immune response, CD8 T cells undergo proliferation and continuous differentiation, acquiring cytotoxic abilities to address the infection and generate an immune memory. At the end of the response, the remaining CD8 T cells are antigen-specific memory cells that will respond stronger and faster in case they are presented this very same antigen again. We propose a nonlinear multiscale mathematical model of the CD8 T cell immune response describing dynamics of two inter-connected physical scales. At the intracellular scale, the level of expression of key proteins involved in proliferation, death, and differentiation of CD8 T cells is modeled by a delay differential system whose dynamics define maturation velocities of CD8 T cells. At the population scale, the amount of CD8 T cells is represented by a discrete density and cell fate depends on their intracellular content. We introduce the model, then show essential mathematical properties (existence, uniqueness, positivity) of solutions and analyse their asymptotic behavior based on the behavior of the intracellular regulatory network. We numerically illustrate the model's ability to qualitatively reproduce both primary and secondary responses, providing a preliminary tool for investigating the generation of long-lived CD8 memory T cells and vaccine design.
Highlights
We aim, in this paper, at providing a novel continuous multiscale model of the primary and secondary CD8 T cell immune responses, able to describe the kinetics of a classical response against an intracellular pathogen[1] at both molecular and cellular scales, and able to run fast and efficiently while accurately describing the various processes involved in the immune response
The generation of an efficient immune memory strongly depends on molecular signaling during the early stages of the response, it is necessary to couple molecular and cellular dynamics within a model of the CD8 T cell immune response in order to investigate the development of memory cells and eventually optimize vaccine design
We introduced a multiscale model of the CD8 T cell immune response to an acute infection, accounting for both intracellular dynamics and CD8 T
Summary
In this paper, at providing a novel continuous multiscale model of the primary and secondary CD8 T cell immune responses, able to describe the kinetics of a classical response against an intracellular pathogen[1] at both molecular and cellular scales, and able to run fast and efficiently while accurately describing the various processes involved in the immune response. Prokopiou et al [47] and Gao et al [26] recently developed a hybrid multiscale model of the CD8 T cell immune response, coupling descriptions of both molecular regulatory mechanisms (through a minimal molecular regulatory network) and cellular dynamics These latter are based on a description of the activation and differentiation processes in the early stages of the immune response (with an explicit description of spatial interactions). Except for the naive CD8 T cell population, the other four CD8 T cell subpopulations (activated, early effector, late effector, memory) mainly distinguish themselves by their ability to survive and proliferate, characterized by the expressions of two relevant biological markers, identified in Crauste et al [16]: Ki67 that is a proliferation marker [50] and Bcl that is a survival marker [21].
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