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. 2012 Jun 28;486(7404):545-8.
doi: 10.1038/nature11098.

Generalized Lévy walks and the role of chemokines in migration of effector CD8+ T cells

Tajie H Harris  1 , Edward J Banigan, David A Christian, Christoph Konradt, Elia D Tait Wojno, Kazumi Norose, Emma H Wilson, Beena John, Wolfgang Weninger, Andrew D Luster, Andrea J Liu, Christopher A Hunter
Affiliations

Generalized Lévy walks and the role of chemokines in migration of effector CD8+ T cells

Tajie H Harris et al. Nature. .

Abstract

Chemokines have a central role in regulating processes essential to the immune function of T cells, such as their migration within lymphoid tissues and targeting of pathogens in sites of inflammation. Here we track T cells using multi-photon microscopy to demonstrate that the chemokine CXCL10 enhances the ability of CD8+ T cells to control the pathogen Toxoplasma gondii in the brains of chronically infected mice. This chemokine boosts T-cell function in two different ways: it maintains the effector T-cell population in the brain and speeds up the average migration speed without changing the nature of the walk statistics. Notably, these statistics are not Brownian; rather, CD8+ T-cell motility in the brain is well described by a generalized Lévy walk. According to our model, this unexpected feature enables T cells to find rare targets with more than an order of magnitude more efficiency than Brownian random walkers. Thus, CD8+ T-cell behaviour is similar to Lévy strategies reported in organisms ranging from mussels to marine predators and monkeys, and CXCL10 aids T cells in shortening the average time taken to find rare targets.

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Figures

Figure 1
Figure 1. Chemokine and chemokine receptor expression in the brain during chronic toxoplasmosis
C57BL/6 mice were infected and RNA was isolated from whole brain tissue. Real time PCR specific for cxcl9, cxcl10, and cxcr3 was performed and normalized to hprt mRNA. Results are depicted mean ± s.e.m. of fold increase over uninfected brain. Data is representative of two independent experiments with three mice per group (a). c-d, Brain mononuclear cells (BMNC) were purified on day 35 post-infection. CXCR3 expression (solid line, mean ± s.e.m.) by CD8+ and Kb-SIINFEKL+ (tet+) cells was measured by flow cytometry (c). The gray histogram represents the FMO control. Data is representative of three independent experiments. Purified BMNC were used in ex vivo chemotaxis assays. The mean ± s.e.m. percentage of cells that migrated toward CXCL10 are depicted (d). Results are representative of three independent experiments, n=3.
Figure 2
Figure 2. CXCL10 affects the CD8+ T cell population and the control of parasite replication
a-b, Mice chronically infected with PruOVA were treated with anti-CXCL10 (+) antibody or control antibody (-). T cells isolated from the brain were identified by flow cytometry (a). Parasite burden was measured in the brain using real time PCR (b). Results are depicted as mean ± s.e.m. of three independent experiments, n=3-4 per group. *p≤0.05, paired student's t-test. c-d, Immunohistochemical staining of brain sections for T. gondii (green), CD8 (red), and DAPI (blue) in anti-CXCL10-treated mice (c) and control animals (d). Size bar = 20μm. OTIGFP cells were expanded in vitro and transferred to mice chronically infected with PruOVA parasites. On day 7 post-transfer, brains from mice that received PBS (con), 300 μg of anti-CXCL10 (anti-CXCL10), or 8 μg pertussis toxin (ptx) i.p. were imaged in 3 dimensions over 10 minutes. Representative cells tracks from control (e), anti-CXCL10 (f), and pertussis-toxin-treated mice (g) are shown (size bars, 100 μm). Volocity software was used to calculate the average track velocity (the average over all cells of the total displacement divided by the total observation time) (h). Cell motility was visualized by plotting individual cell tracks from the origin from control (i), anti-CXCL10-treated (j), and pertussis-toxin-treated (k) mice. **p<0.01, ***p<0.001 by one way ANOVA. Cell track data was obtained from three independent experiments with two mice per group. Control, 12 movies, n=507 cells; anti-CXCL10, 10 movies, n=280 cells; and ptx, 7 movies, n=192 cells.
Figure 3
Figure 3. CD8+ T cell migration tracks are consistent with generalized Lévy walks
We compare experimental data for cells in control (black circles), anti-CXCL10-treated (green squares), and pertussis toxin-treated (blue triangles) mice with results for the generalized Lévy walk model (solid lines). (a) The mean squared displacement (MSD) grows nonlinearly in time, scaling approximately as tα, where α≈1.4 (dashed line). Inset: Linear plot of the MSD. Error bars depict s.e.m. (b) The probability distributions, P(r→(t)), of T cell displacements at several different times, t, as indicated in the legend, for cells from control mice only. In order to avoid artifacts, histograms were constructed by placing 2500, 2000, 1500, 1300, or 600 displacements in each bin for t=0.37 min, 1.1 min, 2.9 min, 4.8 min, or 9.9 min, respectively. Inset: The displacement probability distributions at different times t collapse onto a single curve when the displacement is scaled by ζ(t). For comparison, a scaled Gaussian distribution is displayed (dashed line). (c) The scale factor, ζ(t), used to rescale displacements in (b) increases approximately as a power law, t, where γ≈0.63. Inset: Normalized displacement correlations, 〈K(τ,t)〉 = 〈r(0,t) · r(τ,τ + t)〉 / 〈r2(0,0)〉, for control cells decay more slowly than exponentially (dashed line) with time τ.
Figure 4
Figure 4. Generalized Lévy walks find targets more efficiently than random walks
We determined efficiency for generalized Lévy walkers (black circles) and Brownian walkers (open red squares) as a function of the target radius, a. The generalized Lévy search is considerably more efficient, especially when the targets are small. Error bars are the s.e.m. Examples of trajectories for Brownian walks (small inset) and the generalized Lévy walk model (large inset) are shown.
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