Two-stage linear models cannot capture desired properties of experimental clonal m burst data.

(a) Schematic representation of the two-stage model. The model describes immature (CD27+) cells and mature (CD27-) cells. Each cell type has a distinct growth rate (kI for immature, kM for mature), and immature cells differentiate to mature cells at rate r. (b) Experimental data from Flommersfeld et al. display negative value for the correlation Csize-CD27+ between clonal burst size and %CD27+ cells. (c) Schematic description of antigen specific clonal proliferation and differentiation in CD8+ T cells. Because mature CD62L-cells proliferate more rapidly compared to the immature CD62L+ cells, initial clones made primarily of CD62L-cells can grow to generate the larger size clones. (d) A parameter scan of all possible combinations of kI, kM, and r shows that negative correlations (Csize-CD27+ < 0) are not realized when kI > kM. Each point represents a value of Csize-CD27+ obtained from the model at a unique value of set of model parameters. The parameter configurations that populate the bottom-right quadrant satisfy our two constraints imposed by experimental observations regarding the negative values of Csize-CD27+ and higher growth rate of immature NK cells compared to their mature counterparts. (e) Schematic representation of the three-state model including cell death. The model has separate parameters for birth of immature (CD27+) cells (bI), death of immature cells (dI), birth of mature (CD27-) cells (bM), death of mature cells (dM), and differentiation of immature cells to mature (r). In this model, the growth rates are defined as kI=bI-dI and kM=bM-dM. (f) A parameter scan for this model shows that some parameter configurations can meet the two constraints where kI > kM and the parameters result in negative values for Csize-CD27+. Each point represents a unique parameter configuration. Red points denote parameter configurations where bM > bI and dM > dI. (g) Shows the best fit of the model in (e) to the moments with the constraints kI > kM and Csize-CD27+ < −0.2. Circles represent the fitted values of the first and second moments for the distribution of the NK cell clones obtained from the model. Blue and red circles represent mean populations of CD27+, and CD27-NK cells, respectively. The variances of the CD27+ and CD27-NK cells are shown in cyan and pink circles, and the covariance between the CD27+ and CD27-NK cells is shown in purple. Horizontal lines around the circles show the standard deviations of bootstrapped moments. The solid line is the line y=x, which demonstrates where values would lie if we had a perfect fit.

Best fit parameters to 3-stage model describing NK clonal bursts given in Fig. 2a.

A three-stage linear model can capture experimental observations of NK cell clones if intermediate double-positive NK cells are the fastest growing subset.

(a) Schematic representation of the three-stage model. In this model there are three stages of NK cell maturation: an immature (CD27+), intermediate (CD27-), and terminally mature (CD27-) subset. Each subset has a distinct proliferation and death rate, and cells progress from immature to intermediate maturity according to rate r1 and from intermediate to terminal maturity according to rate r2. (b) A parameter scan for the model in (a) shows that adding a third stage of maturation can account for the negative values in Csize-CD27+. Each point represents a unique parameter configuration. Positive values of Δk indicate that immature CD27+ cells grow faster than mature CD27-cells and vice versa. See the Materials and Methods for further details. (c) Best fit of this model to the moments with the constraints Δk > 0 and Csize-CD27+ < −0.2. Circles represent the fitted values of the moments to the model. Blue and red circles represent mean populations of CD27+, and CD27-NK cells, respectively. The variances of the CD27+ and CD27-NK cells are shown in cyan and pink circles, and the covariance between the CD27+ and CD27-NK cells is shown in purple. Horizontal lines around the circles show the standard deviations of bootstrapped moments. The solid line is the line y=x, which demonstrates where values would lie if we had a perfect fit. (d) Simulated clones from the three-stage model in (a) at the best fit parameter values shown in (c) when the three stages are taken as immature CD27+Ly6C-, mature CD27-LyC- and the terminally mature CD27-Ly6C+, respectively. Each point is a simulated clone resulting from a single NK cell.

Best fit parameters to homeostatic Ly49H+ and Ly49H-NK cells.

Kinetics of homeostatic NK cells and endogenous NK cells responding to MCMV infection.

(a-b) Best fit to (a) Ly49H+ and (b) Ly49H-homeostatic NK cells. Y axis refers to percentage of the total Ly49H+ or Ly49H-population occupied by that NK subset. Circles and Xs represent the mean values of tamoxifen-induced td-Tomato positive and negative NK cells observed in the data, respectively. Solid and dashed error bars represent standard deviations around the means of tamoxifen-induced positive and negative NK abundances respectively. Smooth curves represent model fits for tamoxifen-induced positive (solid) and negative (dashed) NK cells. (c) Best fit to profiled endogenous NK cells responding to MCMV infection. Points represent mean cell abundances, and error bars represent standard deviations of bootstrapped means. Smooth curves represent model fit.

Best fit parameters to endogenous NK cells responding to MCMV infection with constrained r1.

Mature CD27-NK cells undergo rapid death during the expansion phase.

(a) Schematic of experimental setup. (b) Relative abundances of dead cells for CD27+ (blue) and CD27-(red) ex vivo NK cell subsets as measured by flow cytometry experiment. Data are representative of experiments with n = 4-5 mice per timepoint. Graph shows means ± SEM; *P <0.033, and ***P <0.001 represent statistically significant difference between CD27+ and CD27− NK cells as determined by 2-way ANOVA. (c) Parameter scans for determining percentage of live cells for CD27+ and CD27-subsets using the model shown in Fig. S8c. Blue points represent a parameter scan where birth and death rates were varied by random sampling such that the growth rates kI = bI-dI, kINT = bINT-dINT, and kM = bM-dM are equivalent to the kinetic estimates for endogenous NK cells shown in Table 3. Red points represent randomly sampled dead cell clearance rates with other rates set to those describing adoptive transfer kinetics in Table 1. Black dotted line is y=x, and points below this line show a higher percentage of live cells for immature CD27+ cells than for mature CD27-cells.

Proposed mechanism of NK clonal expansion in response to MCMV infection.

Three distinct subsets of NK cells are necessary to generate full NK response to infection. The first is CD27+, Ly6C-, and moderately proliferative, with a doubling time of ~0.3 days and negligible cell death. The second is CD27-, Ly6C-, and highly proliferative, with a doubling time of ~0.2 days. The last is CD27-, Ly6C-, and prone to rapid cell death with a half-life of ~0.45 days. This picture paints CD27-Ly6C-NK cells as having a highly proliferative and highly effective phenotype, similar to effector CD8+ T cells, and CD27+Ly6C-cells as long-lived, similar to memory precursor CD8+ T cells.