Investigating CTL Mediated Killing with a 3D Cellular Automaton

Cytotoxic T lymphocytes (CTLs) are important immune effectors against intra-cellular pathogens. These cells search for infected cells and kill them. Recently developed experimental methods in combination with mathematical models allow for the quantification of the efficacy of CTL killing in vivo and, hence, for the estimation of parameters that characterize the effect of CTL killing on the target cell populations. It is not known how these population-level parameters relate to single-cell properties. To address this question, we developed a three-dimensional cellular automaton model of the region of the spleen where CTL killing takes place. The cellular automaton model describes the movement of different cell populations and their interactions. Cell movement patterns in our cellular automaton model agree with observations from two-photon microscopy. We find that, despite the strong spatial nature of the kinetics in our cellular automaton model, the killing of target cells by CTLs can be described by a term which is linear in the target cell frequency and saturates with respect to the CTL levels. Further, we find that the parameters describing CTL killing on the population level are most strongly impacted by the time a CTL needs to kill a target cell. This suggests that the killing of target cells, rather than their localization, is the limiting step in CTL killing dynamics given reasonable frequencies of CTL. Our analysis identifies additional experimental directions which are of particular importance to interpret estimates of killing rates and could advance our quantitative understanding of CTL killing.Author Summary: The immune response mediated by cytotoxic T lymphocytes (CTLs), which kill infected cells, is thought to be essential to control viral infections. Experiments offer data which allow one to address the efficacy of this cell population in vivo and to estimate characterizing parameters. However, it is unclear which mathematical description reflects the experimental situation best and leads to reliable parameter estimates that quantify CTL efficacy. We simulate the spatial interaction of CTLs and infected cells in a 3-dimensional computer model to examine different mathematical descriptions of the experimental situation, independently of experimental data. Thereby we find an appropriate mathematical term to describe the killing process. Estimates obtained so far describe CTL efficacy on a population level. By varying the individual properties of simulated CTLs, such as the velocity, we find that the time a CTL needs to kill an infected cell is probably the key factor limiting CTL killing efficacy. Our analysis identifies additional experimental directions which could advance our quantitative understanding of CTL killing for different diseases.