Killing of targets by effector CD8$^+$T cells in the mouse spleen follows the law of mass action

It has been difficult to measure efficacy of T cell-based vaccines and to correlate efficacy of CD8T cell responses with protection against viral infections. In part, this difficulty is due to our poor understanding of the in vivo efficacy of CD8T cells. Using a recently developed experimental method of in vivo cytotoxicity we investigated quantitative aspects of killing of peptide-pulsed targets by effector and memory CD8T cells, specific to three epitopes of lymphocytic choriomeningitis virus (LCMV), in the mouse spleen. By analyzing data on killing of targets with varying number of epitope-specific effector and memory CD8T cells, we find that killing of targets by effectors follows the law of mass-action, that is the death rate of peptide-pulsed targets is proportional to the frequency of CTLs in the spleen. In contrast, killing of targets by memory CD8T cells does not follow the mass action law because the death rate of targets saturates at high frequencies of memory CD8T cells. For both effector and memory cells, we also find no support for a killing term that includes the decrease of the death rate of targets with increasing target cell density. Importantly, we find that at low CD8T cell frequencies, effector and memory CD8T cells on the per capita basis are equally efficient at killing peptide-pulsed targets. Our framework provides the guideline for the calculation of the level of memory CD8T cells required to provide sterilizing protection against viral infection. Our results thus form a basis for quantitative understanding of the process of killing of virus-infected cells by T cell responses in tissues and can be used to correlate the phenotype of vaccine-induced memory CD8 T cells with their killing efficacy in vivo . Short running title: Killing by CD8T cells in tissues Abbreviations: LCMV, lymphocytic choriomeningitis virus, CTLs, cytotoxic T lymphocytes, CIs, confidence intervals, RSS, residual sum of squares