Spatial Heterogeneity and Peptide Availability Determine CTL Killing Efficiency In Vivo

The rate at which a cytotoxic T lymphocyte (CTL) can survey for infected cells is a key ingredient of models of vertebrate immune responses to intracellular pathogens. Estimates have been obtained using in vivo cytotoxicity assays in which peptide-pulsed splenocytes are killed by CTL in the spleens of immunised mice. However the spleen is a heterogeneous environment and splenocytes comprise multiple cell types. Are some cell types intrinsically more susceptible to lysis than others? Quantitatively, what impacts are made by the spatial distribution of targets and effectors, and the level of peptide-MHC on the target cell surface? To address these questions we revisited the splenocyte killing assay, using CTL specific for an epitope of influenza virus. We found that at the cell population level T cell targets were killed more rapidly than B cells. Using modeling, quantitative imaging and in vitro killing assays we conclude that this difference in vivo likely reflects different migratory patterns of targets within the spleen and a heterogeneous distribution of CTL, with no detectable difference in the intrinsic susceptibilities of the two populations to lysis. Modeling of the stages involved in the detection and killing of peptide-pulsed targets in vitro revealed that peptide dose influenced the ability of CTL to form conjugates with targets but had no detectable effect on the probability that conjugation resulted in lysis, and that T cell targets took longer to lyse than B cells. We also infer that incomplete killing in vivo of cells pulsed with low doses of peptide may be due to a combination of heterogeneity in peptide uptake and the dissociation, but not internalisation, of peptide-MHC complexes. Our analyses demonstrate how population-averaged parameters in models of immune responses can be dissected to account for both spatial and cellular heterogeneity.

Mice were sacri ced seven days later, and cells from the spleen were analysed by ow cytometry. Representative FACS plots (A) were rst gated on CD8+ cells, and the proportion of cells expressing a TCR speci c for the NP68 dextramer was determined (le panels). Within this NP68-speci c population (right panels), donor F5 cells were identi ed by expression of Ly5.2, and activation status was determined by expression of CD44. Numbers indicate the percentage of cells within each gate. Graphs in (B) show the mean plus standard error of the percentage of all CD8+ cells that were labelled by the NP68 dextramer (le panel; at least four mice per group), and the total number of NP68-speci c cells that were either F5 donor or host derived in the spleen of each mouse (right panel).

C Quantifying enrichment for unpulsed cells in blood, and non-speci c loss or egress of transferred cells from the spleen
Ratios of pulsed to unpulsed cells in the blood were measured between 30 and 240 minutes post-transfer. e upper panels in the gure below show the ts of a linear model to the logarithm of the pulsed/unpulsed ratio, such that P/U ∼ exp(−εt). Enrichment for unpulsed cells in both populations was signi cant (p < .) and more rapid for T cells (half-life log()/ε = 260 min, 95% CI (200,360)) than for B cells (log()/ε = 680 (430, 1700)). e lower panels show the kinetics of unpulsed cells in the spleen, as they ingress rapidly and are lost more slowly either due to egress or death in the spleen. is kinetic was modeled with Equation (3) in the main text: where λ = σ + δ, the total rate of loss of transferred unpulsed cells from the blood. We estimate λ and φ by tting the above to the timecourse of the frequencies of unpulsed cells in the spleen. e half-lives of loss of unpulsed T and B cells from the blood were not signi cantly different (T cells, log()/λ = 67 ( 42, 110) mins; B cells, 77 ( 52, 120) mins). e non-speci c loss/egress from the spleen was much slower, with half-life 15 (11, 21) hours for T cells and 25 (17, 41) hours for B cells. is difference is at least qualitatively in line with reports that T cells recirculate through the spleen more rapidly than B cells [2].

Decay model
Peptide pulsed targets P are assumed to progressively lose susceptibility; where σ is the per capita rate of ow from blood into spleen, δ is the rate of loss of unpulsed cells from the blood into other organs, ε is the excess rate at which pulsed targets are lost from blood into other organs, φ is the rate of non-speci c loss or egress of both unpulsed and pulsed cells, K(t) is the (time-dependent) per capita rate of killing of pulsed targets in the spleen, f is the initial ratio of pulsed to unpulsed cells in the inoculum, and N is an unspeci ed scaling constant that relates the units of measurement of cells in the blood to those in the spleen. Susceptibility falls exponentially once killing commences, e fractional killing corrected for the inoculum ratio e populations U spleen and P spleen are each governed by a rst order differential equation of the form dy/dt = σN g(t) − h(t) y(t) (eqns. 2 and 3), which has solution y(t) proportional to the unknown constant σN. is constant therefore disappears when forming the ratio P spleen /U spleen . e fractional killing is then a function of three unknowns K  , T and q and can be identi ed from the (analytic) solutions to Equations 2 and 3. Solutions were generated in Mathematica [3] and parameters were estimated using the nls function in R [4].

Hidden-target Model
Only a proportion q of peptide-pulsed cells are susceptible. Susceptible cells (S) and cells that are either refractory to killing or who will migrate to areas of the spleen inaccessible to CTL (H) ow in from the blood at rates proportional to qP blood and ( − q)P blood respectively. Surviving cells remain in their respective states for the duration of the assay.

Hybrid Model
Here peptide-pulsed cells S transition into a non-susceptible state H at rate ν. Since this transition can occur both in the blood and the spleen, we write the equations for both compartments in full: where in eqn. 14 we have used the solution of eqns. 10 and 11 for H blood (t). Again, K  is zero for t < T, and the fractional killing is  No detectable positive correlation between CTL abundance and the extent of target cell killing. For each target cell type, dose (labels 6-9, indicating -log  (peptide dose)) and timepoint (coloured dots) we found no evidence for mass-action killing kinetics at the whole spleen level aer correcting for multiple comparisons (p>0.05), either for CTL measured as total numbers (le column) or as a fraction of total splenocytes (right column). Conjugates involving multiple cells (>2) were also identi ed. Since effector cells were in excess in these assays (B), it is likely that these multiples consist of two or more effectors bound to a single target. However, the exact number and identity of individual cells within these multiples could not be determined from the available data. Multiples accounted for approximately 10% of all conjugates, and their numbers remained roughly constant over the course of the assay.