Abstract
Cytotoxic T lymphocyte (CTL)-mediated killing involves the formation of a synapse with a target cell, followed by delivery of perforin and granzymes. Previously, we derived a general functional response for CTL killing while considering that CTLs form stable synapses (i.e., single-stage) and that the number of conjugates remains at steady state. However, the killing of target cells sometimes requires multiple engagements (i.e., multistage). To study how multistage killing and a lack of steady state influence the functional response, we here analyze a set of differential equations as well as simulations employing the cellular Potts model, in both cases describing CTLs that kill target cells. We find that at steady state the total killing rate (i.e., the number of target cells killed by all CTLs) is well described by the previously derived double saturation function. Compared to single-stage killing, the total killing rate during multistage killing saturates at higher CTL and target cell densities. Importantly, when the killing is measured before the steady state is approached, a qualitatively different functional response emerges for two reasons: First, the killing signal of each CTL gets diluted over several targets and because this dilution effect is strongest at high target cell densities; this can result in a peak in the dependence of the total killing rate on the target cell density. Second, the total killing rate exhibits a sigmoid dependence on the CTL density when killing is a multistage process, because it takes typically more than one CTL to kill a target. In conclusion, a sigmoid dependence of the killing rate on the CTLs during initial phases of killing may be indicative of a multistage killing process. Observation of a sigmoid functional response may thus arise from a dilution effect and is not necessarily due to cooperative behavior of the CTLs.
Highlights
Cytotoxic T lymphocyte (CTL)-mediated killing of tumor and virus-infected cells generally involves four steps: localization of the target cell; formation of a specialized junction with the target; delivery of effector molecules, such as perforin and granzymes; and detachment from the dying target, followed by resumption of the search for new targets
We have shown that the killing of target cells by the accumulation of several short-lived cytotoxic kinapses at steady state results in a similar functional response as killing by long-lived synapses: a previously defined double saturation function saturating in both CTL and target cell densities (4) describes simulation data from both a CPM and an ordinary differential equations (ODEs) model well
This qualitative similarity no longer holds for simulation data collected during the initial period of killing when fresh targets are mixed with CTLs
Summary
Cytotoxic T lymphocyte (CTL)-mediated killing of tumor and virus-infected cells generally involves four steps: localization of the target cell; formation of a specialized junction with the target (called a ‘‘cytotoxic synapse’’); delivery of effector molecules, such as perforin and granzymes; and detachment from the dying target, followed by resumption of the search for new targets. The functional response of CTL-mediated killing is defined as the rate at which a single CTL kills target cells as a function of the CTL and target cell frequencies, and has been studied using mathematical models that are analogous to enzyme-substrate kinetics (1–4). Recent in vivo experiments using intravital twophoton microscopy revealed that virus-infected cells break their synapses with CTLs, and tend to be killed during subsequent conjugates with other CTLs (5). In these experiments, CTLs rarely formed stable synapses and remained motile after contacting a target cell. Depending on the antigen concentration and the avidity of the interaction, the killing of a target cell may take several short kinapses (hereafter referred to as ‘‘multistage’’ killing), rather than the one long synapse (hereafter referred to as ‘‘single-stage’’ killing) that was assumed in the modeling hitherto (1–4)
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