T. gondii is an opportunistic pathogen that causes encephalitis in patients with acquired defects in T-cell function11. Several studies have established that resistance to this parasite in the central nervous system (CNS) relies on T-cell production of interferon (IFN)-γ and cytotoxic T cells, but little is known about the factors that regulate the behaviour of effector T cells at this site12,13,14. To understand the role of chemokines in directing T cells to regions of infection during toxoplasmic encephalitis, real-time PCR (rtPCR) was performed to assess changes in chemokine-receptor expression in the brains of infected mice (Supplementary Fig. 1a). Notably, messenger RNA transcripts for CXCR3, a receptor expressed by activated and memory T cells and associated with T-helper 1 (T H 1)-type responses15,16 and its ligands, CXCL9 and CXCL10, were highly expressed during toxoplasmic encephalitis (Fig. 1a). Previous studies have demonstrated extensive production of Cxcl10 mRNA by activated astrocytes during toxoplasmic encephalitis17. Analysis of lymphocytes isolated from the brains of mice infected with ovalbumin (OVA)-expressing Prugniaud-strain (PruOVA) tachyzoites showed that CD8+ T cells, including those specific for ovalbumin, express CXCR3 (Fig. 1b) and migrate towards CXCL10 ex vivo (Fig. 1c). Thus, parasite-specific CD8+ T cells present in the CNS during toxoplasmic encephalitis are responsive to CXCR3 ligands.

Figure 1: Chemokine and chemokine receptor expression in the brain during chronic toxoplasmosis. C57BL/6 mice were infected with PruOVA and RNA was isolated from whole brain tissue. a, rtPCR specific for Cxcl9, Cxcl10 and Cxcr3 was performed and normalized to Hprt mRNA. Results are depicted as mean and s.e.m. of fold increase over uninfected brain. Data are representative of two independent experiments with three mice per group. RQ, relative quantity. b, Brain mononuclear cells were purified on day 35 after infection. CXCR3 expression (solid line) by CD8+ and Kb-SIINFEKL+ (tet+) cells was measured by flow cytometry. The grey histogram represents the fluorescence minus one control. Data are representative of three independent experiments. c, Purified brain mononuclear cells were used in ex vivo chemotaxis assays. The mean and s.e.m. percentage of cells that migrated towards CXCL10 are depicted. Results are representative of three independent experiments. Full size image Download PowerPoint slide

Although CXCL10 is required for resistance to acute T. gondii infection18, little is known about how this molecule affects T-cell responses during chronic toxoplasmic encephalitis. Therefore, we treated chronically infected mice with anti-CXCL10 antibodies. One week later, mononuclear cells from the brain were isolated, and T cells were quantified by flow cytometry. Anti-CXCL10 treatment led to a 40% decrease in the number of CD8+ T cells (Fig. 2a, P = 0.04) and an increase in parasite burden (Fig. 2b, P = 0.04). Immunohistochemical staining for T. gondii showed latent cyst forms in control mice (Fig. 2c), whereas regions of active parasite replication were observed in the brains of anti-CXCL10-treated mice (Fig. 2d). To address the role of CXCL10 in the recruitment and maintenance of antigen-specific T cells in the CNS, we used an adoptive-transfer system. In vitro-activated OVA-specific OT-I cells were transferred to mice chronically infected with PruOVA, resulting in the migration and accumulation of these cells within the CNS19. When OT-I T cells were transferred to chronically infected wild-type C57BL/6 or Cxcl10-deficient mice, knockout mice had 60% fewer transferred cells in the brain in comparison to wild-type mice, whereas equivalent numbers were recovered from the spleen and lymph node in both groups (Supplementary Fig. 1b, c). Similar results were obtained when Cxcr3−/− and wild-type OT-I cells were transferred to wild-type mice chronically infected with PruOVA (Supplementary Fig. 1d, e).

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) and parasite burden was measured in the brain using rtPCR (b). Results are depicted as mean and s.e.m. of three independent experiments, with 3–4 mice per group. *P ≤ 0.05, paired Student’s t-test. c, d, Immunohistochemical staining of brain sections for T. gondii (green), CD8 (red) and 4′,6-diamidino-2-phenylindole (DAPI; blue) in anti-CXCL10-treated mice (c) and control animals (d). Scale bar, 20 μm. OT-IGFP cells were expanded in vitro and transferred to mice chronically infected with PruOVA parasites. On day 7 after transfer, brains from mice that received PBS (control), 300 µg anti-CXCL10, or 8 μg PTX intraperitoneally (i.p.) were imaged in three dimensions over 10 min. e–g, Representative cells tracks from control (e), anti-CXCL10-treated (f), and PTX-treated (g) mice are shown. Scale bar, 100 μm. h, 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). Ctrl, control. i–k, Cell motility was visualized by plotting individual cell tracks from the origin from control (i), anti-CXCL10-treated (j) and PTX-treated (k) mice. ***P < 0.001 by one-way analysis of variance. Cell track data were 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. Full size image Download PowerPoint slide

These studies show that CXCL10 and CXCR3 are required for optimal recruitment and/or retention of antigen-specific CD8+ T cells in the CNS during toxoplasmic encephalitis. To determine whether CXCL10 and chemokine signals also affect the migration of CD8+ T cells once they enter the CNS, we used multi-photon imaging to track green fluorescent protein (GFP)-expressing OT-I T cells (OT-IGFP) in explant brain after short-term anti-CXCL10 treatment (Supplementary Movies 1 and 2). In addition, chemokine signals were inhibited using pertussis toxin (PTX), an inhibitor of Gα i signalling2 (Supplementary Movie 3). We imaged cells for 10–30 min because cells migrate out of the field of view during longer imaging periods, biasing our sample towards cells that are less motile. Analysis of the cell tracks (Fig. 2e–g) showed that anti-CXCL10 treatment reduced the average cell velocity by 23%, from 6.35 μm min−1 in control-treated mice to 4.88 μm min−1 (Fig. 2h), whereas PTX reduced the track velocity by 46% to 3.45 μm min−1. Plots of individual cell tracks demonstrate that cells cover less area over a 10-minute time span in the absence of CXCL10 or when treated with PTX (Fig. 2i–k).

We performed a standard analysis to determine quantitatively how chemokines affect the migratory behaviour of CD8+ T cells by extracting the motility coefficient (Supplementary Fig. 2). This analysis implicitly assumes a Brownian walk, as the motility coefficient is extracted from the slope of the best linear fit to the mean-squared displacement (m.s.d.), , as a function of time, t (ref. 20). However, when we plot the m.s.d. on a log–log plot, it grows with time approximately as tα, with α ≈ 1.4 (Fig. 3a). This finding suggests that the T-cell tracks are not Brownian walks.

Figure 3: CD8+ T-cell migration tracks are consistent with generalized Lévy walks. a, We compare experimental data for cells in control (black circles), anti-CXCL10-treated (green squares), and PTX-treated (blue triangles) mice with results for the generalized Lévy walk model (solid lines). The m.s.d. grows nonlinearly in time, scaling approximately as tα, where α ≈ 1.4 (dashed line). Inset shows linear plot of the m.s.d. Error bars denote s.e.m. b, The probability distributions, , of T-cell displacements at several different times, t, for cells from control mice only. To avoid artefacts30, histograms were constructed by placing 2,500, 2,000, 1,500, 1,300 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 shows that displacement probability distributions at different times collapse onto a single curve when the displacement is scaled by ζ(t). For comparison, a scaled Gaussian distribution is shown (dashed line). c, ζ(t), used to rescale displacements in b increases approximately as a power law, tγ, where γ ≈ 0.63. Inset shows that normalized displacement correlations, , for control cells decay more slowly than exponentially (dashed line) with time τ. Full size image Download PowerPoint slide

To determine the type of random walk that best describes the migration data, we focused not only on the behaviour of the m.s.d., but also on the shape of the tracks; the probability distribution of cell displacements, , as a function of the time interval, t; and the decay of normalized displacement correlations, , as a function of τ, where is the displacement between times τ and τ + t. Together, these properties provide a more complete description of the walk statistics than the m.s.d. alone, and therefore provide far more constraints that must be satisfied by a candidate random-walk model. First, by analysing statistics of the cell-trajectory shapes, we established that CD8+ T cells do not exhibit directional migration on the time and length scales relevant to this experiment (see Supplementary Fig. 3 and Supplementary Discussion). To analyse the displacement distribution, we introduced a time-dependent variable, ζ(t), to scale the cell displacements. For Brownian walks, the distribution, , of scaled displacements, , should be Gaussian, , and the scale factor, ζ(t), should be the root m.s.d. (r.m.s.d.). However, for the migrating CD8+ T cells, the distribution is not Gaussian (Fig. 3b, inset); the probability of large displacements is much larger than expected at all times studied. Notably, has the same shape at all times, indicating that the tracks are also not well described by persistent random walks. Moreover, the scale factor obeys , with γ = 0.63, and not γ = 1/2, as expected for Brownian walks (Fig. 3c), and clearly differs from the r.m.s.d. (Supplementary Fig. 4) at all times studied. Finally, the displacement correlations do not decay exponentially in time, as for Brownian walks (Fig. 3c, inset). Thus, Brownian walks do not describe effector T-cell migration during toxoplasmic encephalitis.

On the basis of these walk statistics, we considered several variations of Lévy walks (see Supplementary Table 1, Supplementary Fig. 5 and Supplementary Discussion). We find that, consistent with early observations of runs and pauses in lymphocytes21, T-cell migration is well described by the following model of a generalized Lévy walk22. Walkers make straight runs at fixed velocity in random directions over distances chosen randomly from a Lévy distribution, , with μ run = 2.15. After each run, a walker pauses for a duration of time that is drawn from a Lévy distribution with μ pause = 1.7. The values of the exponents μ run and μ pause were determined from a maximum-likelihood analysis23 (see Supplementary Discussion). The model captures quantitatively the observed displacement distributions at different times (Fig. 3b), the time evolution of the m.s.d. and scale factor (Fig. 3a and c, respectively), the decay of displacement correlations (Fig. 3c, inset), and qualitative features of cell tracks (Supplementary Fig. 6). An Akaike weight analysis24 indicates that the generalized Lévy walk model does a better job of fitting the displacement distributions than any of the other models we have considered, including, for example, bimodal correlated random walks25 (see Supplementary Table 1, Supplementary Fig. 5 and Supplementary Discussion). The generalized Lévy walk model is consistent with our data over 30 min (Supplementary Fig. 7), and also describes the behaviour of polyclonal CD8+ T cells, transgenic lymphocytic choriomeningitis virus-specific CD8+ T cells migrating in the absence of cognate antigen, and CD8+ T cells migrating in the brains of live animals (Supplementary Fig. 8).

In the absence of CXCL10 or signals through Gα i -coupled receptors, the migration statistics for CD8+ T cells are well described by the same generalized Lévy walk model, characterized by μ run = 2.15 and μ pause = 1.7 (Supplementary Figs 6 and 8), as for control cells, but with either a reduced instantaneous speed during runs or longer pauses. Therefore, the chemokine CXCL10 and signals through Gα i -coupled receptors speed up migration without otherwise changing the walk statistics. This result, together with the fact that we find no evidence of directed migration over the timescales investigated (see Supplementary Discussion), suggests a chemokinetic role for CXCL10 during toxoplasmic encephalitis.

Previous studies have demonstrated that neutrophil or CD8+ T-cell control of bacteria or tumour cells, respectively, can be understood by a rate equation in which the killing of targets is modelled as a collision-based process26,27. We incorporated the generalized Lévy walk statistics into a similar model to predict the time required to find rare target cells. In our model, we placed N generalized Lévy walkers randomly in a sphere of volume V with a target of radius a at the origin (Supplementary Fig. 9a). We find that cells migrating by generalized Lévy walks are considerably more efficient in finding target cells than those performing Brownian walks (Fig. 4 and Supplementary Fig. 9b, c). Here, the efficiency is the inverse of the sum of the displacements of all the walkers at the instant when the first walker reaches the target28. In the absence of CXCL10 or signals through Gα i -coupled receptors, our model predicts that for estimated values of a, V and N, the capture time for a CD8+ T cell to reach the target is increased by factors of 1.9 or 3.0, respectively, in comparison to the control setting (see Supplementary Fig. 9d–f and Supplementary Discussion). These results suggest that the ability of CD8+ T cells to find and control T. gondii-infected targets in the CNS is aided by a generalized Lévy walk search strategy, and the capture time is shortened by CXCL10, and probably by other chemokines as well. We emphasize that the generalized Lévy walk is not necessarily an optimal search strategy, and a model with μ run = 2.0 would be more efficient according to this definition28. Moreover, the efficiency is highly dependent on details of the environment and search/capture process29 that are not presently known, so determination of the optimal search strategy remains an open question.

Figure 4: Generalized Lévy walks find targets more efficiently than random walks. We determined efficiency, η, 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 denote s.e.m. Small inset shows an example trajectory for Brownian walks and the large inset shows the generalized Lévy walk model. Full size image Download PowerPoint slide

Lévy search strategies may be used by diverse species, including microzooplankton, fruitflies, honeybees, mussels, predatory fish, sea turtles, penguins and spider monkeys4,5,6,7,8,9,10. Our results show that a generalization of this search strategy seems to be relevant, at the single-cell level, to the ability of effector cells to find rare targets. In addition, our findings provide a new insight into the role of CXCL10 as a chemokine that specifically influences the capture time for CD8+ T cells to find infected targets during toxoplasmic encephalitis. Altogether, our findings raise several fundamental questions as to whether lymphocytes execute generalized Lévy walks in other environments, how activation status affects walk statistics, and whether the pauses suggested by our model arise from factors internal to the cell or from interactions of the cells with their external environment.