  It has been difficult to measure efficacy of T cell-based vaccines and to
correlate efficacy of CD8$^+$T cell responses with protection against viral
infections. In part, this difficulty is due to our poor understanding of the in
vivo efficacy of CD8$^+$T 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 CD8$^+$T 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 CD8$^+$T 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 CD8$^+$T cells does not follow the
mass action law because the death rate of targets saturates at high frequencies
of memory CD8$^+$T 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
CD8$^+$T cell frequencies, effector and memory CD8$^+$T 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 CD8$^+$T
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.
