Section: New Results

Immune response

Identification of nascent memory CD8 T cells and modeling of their ontogeny

Primary immune responses generate short-term effectors and long-term protective memory cells. The delineation of the genealogy linking naive, effector and memory cells has been complicated by the lack of phenotypes discriminating effector from memory differentiation stages. Using transcriptomics and phenotypic analyses, we identify ( see [17]) a novel marker combination that allows us to track nascent memory cells within the effector phase. We then use a formal approach based on mathematical models describing the dynamics of population-size evolutions to test potential progeny links and demonstrate that most cells follow a linear naive-early effector-late effector-memory pathway. Moreover, our mathematical model allows long-term prediction of memory cell numbers from a few early experimental measurements. Our work thus provides a phenotypic means to identify effector and memory cells, as well as a mathematical framework to investigate the ontology of their generation and to predict the outcome of immunization regimens in terms of memory cell numbers generated.

Modelling the dynamics of virus infection and immune response in space and time

Spreading of viral infection in the tissues such as lymph nodes or spleen depends on virus multiplication in the host cells, their transport and on the immune response. Reaction–diffusion systems of equations with delays in proliferation and death terms of the immune cells represent an appropriate model to study this process. The properties of the immune response and the initial viral load determine the regimes of infection spreading. In the proposed model [13], the proliferation rate of the immune cells is represented by a bell-shaped function of the virus concentration which increases for small concentrations and decreases if the concentration is sufficiently high. We use such a model system to show that an infection can be completely eliminated or it can remain present together with a decreased concentration of immune cells. Finally, immune cells can be completely exhausted leading to a high virus concentration in the tissue. In addition, we predicted two novel regimes of infection dynamics not observed before. Infection propagation in the tissue can occur as a superposition of two travelling waves: first wave propagates as a low level infection front followed by a high level infection front with a smaller speed of propagation. Both of the travelling waves can have a positive or a negative speed corresponding to infection advancement or retreat. These regimes can be accompanied by instabilities and the emergence of complex spatiotemporal patterns.

Estimates and impact of lymphocyte division parameters from CFSE data using mathematical modeling

Carboxyfluorescein diacetate succinimidyl ester (CFSE) labelling has been widely used to track and study cell proliferation. In [23], we use mathematical modeling to describe the kinetics of immune cell proliferation after an in vitro polyclonal stimulation tracked with CFSE. This approach allows us to estimate a set of key parameters, including ones related to cell death and proliferation. We develop a three-phase model that distinguishes a latency phase, accounting for non-divided cell behaviour, a resting phase and the active phase of the division process. Parameter estimates are derived from model results, and numerical simulations are then compared to the dynamics of in vitro experiments, with different biological assumptions tested. Our model allows us to compare the dynamics of CD4+ and CD8+ cells, and to highlight their kinetic differences. Finally we perform a sensitivity analysis to quantify the impact of each parameter on proliferation kinetics. Interestingly, we find that parameter sensitivity varies with time and with cell generation. Our approach can help biologists to understand cell proliferation mechanisms and to identify potential pathological division processes.