Extended Data Fig. 10: Mathematical modelling reveals that fibroblasts direct collective CD8⁺ T cell local activity.

a, The mathematic model developed to predict local CD8+ T cell recruitment and clonal expansion behaviour. The model is a 3D square lattice with two layers. The upper epidermal layer contains T cells and melanocytes. The lower dermal layer contains fibroblasts with different chemotactic abilities. The CD8+ T cell population in skin is considered to be a decentralized system. Each CD8+ T cell is equipped with the means of sensing a change in density. Over time, the behaviour of each cell changes according to its state and the states of its neighbouring cells and the surrounding signals. The collective pattern can be globally modulated by changing the parameters governing local cell-cell interactions. Once the T cell surrounding a melanocyte exceeds a threshold number, melanocyte death and IFNγ secretion occur. The IFNγ signal induce neighbouring fibroblast chemotactic effect to recruit nearby CD8+ T cells, reaching the local CD8+ T cell density threshold for adjacent melanocyte cytotoxicity and IFNγ secretion. This positive feedback loop between CD8+ T cells and fibroblasts could ensure T cell clonal expansion and vitiligo progression. b, The mathematic model predicts the expansion process of a single T cell clone. Five representative time points from T0 to T80 show the initial T cell cluster state and the subsequent T cell expansion process over 80 time units. In model 1 with normal chemotactic fibroblasts, full spectrum of T cell cluster formation and expansion patterns observed in WT vitiligo mouse model were reproduced (first row, fibroblasts with normal chemotactic effect, also shown in Supplementary Videos 1, 2). In model 2, in which the fibroblasts were incapable of chemotaxis, we obtained patterns observed in Pdgfra^CreER;IFNGR1^fl/fl cKO mice. In this model, although T cells could still randomly aggregate in the epidermis, they failed to propagate this effect and recruit more T cells to the initial site (second row, fibroblasts with no chemotactic effect, also shown in Supplementary Videos 3, 4). In model 3, in which the chemotactic effect of fibroblasts was turned down to 1/2 of the normal value, random CD8+ T cell aggregates only recruited a limited number of T cells, resulting in slow T cell cluster expansion and melanocyte loss in one or two directions (third row, fibroblasts have 1/2 normal chemotactic effect, also shown in Supplementary Videos 5, 6). c, The mathematic model predicts large-scale T cell clone expansion over the long term. Four representative time points from T0 to T450 show the initial state and the subsequent T cell cluster expansion process over 450 time units. CD8+ T cells in the normal chemotaxis model efficiently coordinate so as to achieve clonal expansion and melanocyte clearance. CD8+ T cells in the no chemotaxis model fail to undergo clonal expansion and melanocyte death is detected. CD8+ T cells in the weak chemotaxis model (migration ability decreases to 1/2) generate small T cell clones and expand slowly. d, The mathematic model predicts the T cell clone distribution pattern under regional variant fibroblasts with different levels of chemotactic effect to T cell. In this model, the fibroblasts marked in blue have a normal chemotactic effect, and those marked in green have a weak chemotactic effect. In this region, T cell chemotaxis (migration ability) decrease to 1/2 of normal value. Six representative time points from T0 to T600 show the initial state and subsequent T cell cluster expansion (also shown in Supplementary Video 7). The results show that the T cell clones are more likely to expand and generate white patches on the normal chemotactic region. Both white patches and T cell clone patterns are highly correlated with the regional fibroblast variants. e, f, QPCR analysis validated high knockdown efficiency (e) and the effect blocking IFNγ downstream signal (f) in vitro for shRNAs targeting IFNGR1, JAK1, or STAT1. g, Representative epidermis whole-mount immunofluorescent staining images and density plot of shRNA-mediated knockdown assay, relative to the corresponding dermis in Fig. 4k. h, Box-whisker plots and correlation analysis of T cell number versus percentage of infected fibroblasts (upper panels), and melanocyte number versus percentage of infected fibroblasts (lower panels) in each scale of in vivo mosaic fibroblast knockdown experiment. i, Scatter plots of median of melanocyte number versus percentage of infected fibroblasts in each scale of in vivo mosaic fibroblast knockdown experiment. Scale bars, 500 µm(g). For exact p values, see Source Data. For statistics, p summary and sample sizes, see Methods.

Source data