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... Show moreCytotoxic 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. Show less
Cytotoxic T lymphocyte (CTL)-mediated killing of virus infections and tumors occurs over a wide range of conditions. The spatial environments in which CTLs encounter target cells vary from narrow... Show moreCytotoxic T lymphocyte (CTL)-mediated killing of virus infections and tumors occurs over a wide range of conditions. The spatial environments in which CTLs encounter target cells vary from narrow vessels, to two-dimensional epithelial tissues, to densely populated 3-dimensional (3D) T cell areas within lymphoid tissues. How such spatial environments alter the functional response of CTL-mediated killing, i.e., how the killing efficiency depends on cell densities, is unclear. In this study, we perform cellular Potts model simulations in different spatial configurations to investigate how the dimensionality of the space affects the functional response of CTL-mediated killing. Irrespective of the spatial configuration, the function with separate saturation constants for CTL and for target cell densities that we previously proposed can in all cases describe the response, demonstrating its generality. However, the tissue dimensionality determines at which cell densities the killing rate starts to saturate. We show that saturation in a fully 3D environment is stronger than in a “flat” 3D environment, which is largely due to accompanying differences in the CTL–target encounter rates. Show less
Gadhamsetty, S.; Beltman, J.B.; Boer, R.J. de 2015
