Defining the quantitative limits of intravital two-photon lymphocyte tracking

Abstract

Two-photon microscopy has substantially advanced our understanding of cellular dynamics in the immune system. Cell migration can now be imaged in real time in the living animal. Strikingly, the migration of naive lymphocytes in secondary lymphoid tissue appears predominantly random. It is unclear, however, whether directed migration may escape detection in this random background. Using a combination of mathematical modeling and experimental data, we investigate the extent to which modern two-photon imaging can rule out biologically relevant directed migration. For naive T cells migrating in uninfected lymph nodes (LNs) at average 3D speeds of around 18 μm/min, we rule out uniform directed migration of more than 1.7 μm/min at the 95% confidence level, confirming that T cell migration is indeed mostly random on a timescale of minutes. To investigate whether this finding still holds for longer timescales, we use a 3D simulation of the naive T cell LN transit. A pure random walk predicts a transit time of around 16 h, which is in good agreement with experimental results. A directional bias of only 0.5 μm/min-less than 3% of the cell speed-would already accelerate the transit twofold. These results jointly strengthen the random walk analogy for naive T cell migration in LNs, but they also emphasize that very small deviations from random migration can still be important. Our methods are applicable to cells of any type and can be used to reanalyze existing datasets.

Fig. 1.

Quantitative bounds for taxis in two-photon data. (A) x and y projections of 1,355 naive T cell tracks. (Inset) A 40 × 40 × 40 μm subvolume for comparison. (B) The tracks from A with aligned starting positions. No preferential direction is apparent by eye. The small square corresponds to the coordinate system in D. (C) Scatter plot of cell steps (duration = 60.9 s) extracted from the tracks in B. (D) Hotelling's T² test gives a confidence region (ellipsoid) for the mean step (υ_mean). Because the null vector (cross) is inside the confidence region, data are consistent with random motion. The point in the confidence region that is farthest from the null vector (υ_max) gives an upper speed bound for taxis that may escape this analysis. Data are shown for the x and y dimensions, and 3D values are in the text.

Fig. 2.

Benchmarking two-photon data analysis methods. The power of two-photon data analysis methods can be evaluated systematically using computer-generated data (Materials and Methods) as shown here for the three methods discussed in this paper. (A) Naive T cell data (red; 1,132 tracks) are displayed for comparison alongside three simulated datasets: random walk (black; 842 tracks), random walk with taxis (blue; 3 μm/min along z axis, 897 tracks), and a mixed population with 50% taxing cells and 50% randomly walking cells (green; 5.1 μm/min along z axis, 893 tracks). Simulated cells were tracked in a finite volume having the size of our two-photon imaging region. (B) Mean square displacement of the data in A plotted as a function of time. (C) Cell steps extracted from the tracks in A. Crosses indicate the null vector (red = 703 steps; black = 693 steps; blue = 773 steps; green = 749 steps). (D) Analysis of the mean angle between the cell steps (C) and the taxis direction, which is known only for the simulated data. A mean angle of less than 90° indicates taxis (mean angles and 95% confidence intervals are shown; asterisk indicates significance). (E) Hotelling's T² test applied to the y and z dimensions (compare with Fig. 1D).

Fig. 3.

Displacement analysis can lead to wrong conclusions. (A) For example, assume that one subset of T cells (black) migrates purely randomly, whereas another subset (blue) performs taxis to the medulla. (B) If one could follow the cell populations for a very long time, the difference could be detected using a mean square displacement (MSD) plot, which is shown here for two simulated cell populations tracked for 6 h without placing bounds on the trajectories. Pure random walk (black; M = 100 μm²/min) leads to a linear MSD, and taxis (3 μm/min) gives a curved MSD. Data are averaged over 10,000 simulated cells, giving a negligibly small SEM. (C) Two-photon imaging is limited to a finite region in which faster cells are underrepresented, because they exit more quickly. (D) This effect can be reproduced by truncating the simulated data from B to a finite region (shading ± SEM for 10,000 simulated cells; region size = 492 × 492 × 40 μm as in our experimental setup). If we compared the two populations based on this plot alone, we would conclude that the blue population has lower motility (slope) and persistence (curvedness) than the black one, when in fact, the opposite is true.

Fig. 4.

Modeling the naive T cell LN transit. (A) Microtome slice from a mesenteric rat LN with B cells stained in brown and macrophages stained in blue. (B) Using image processing algorithms (SI Text), the lymph node volume was divided into three compartments: sinus (blue; abundant macrophages), paracortex (green; few macrophages and B cells), and follicles (red; few macrophages and abundant B cells). 3D renderings of the reconstructed compartments are shown. (C) The 3D reconstruction was used to simulate the transit of naive T cells from paracortex to sinus (a 2D projection of the central LN slice is shown). The model assumes that naive T cells are released uniformly in the paracortex (green), transit to a nearby sinus region (blue), and then, exit after around 1 h. For simulating taxis, a hypothetical chemokine gradient (arrows) pointing from paracortex to sinus was created. Arrows indicate direction of the gradient and taxis speed per minute, with arrow lengths magnified 250-fold based on a mean taxis speed of 0.5 μm/min.

Fig. 5.

Impact of taxis on the LN transit. (A) 2D snapshots of T cell concentrations from the central slice of the reconstructed LN (Fig. 4C) superimposed on grayscale images of the slice. Intensity of the red color is proportional to T cell concentration. Top corresponds to random T cell motility as estimated from our data. In the biased population (Middle), cells perform taxis to the sinuses with 0.5 μm/min on average. Bottom shows the effect of a 50% lower motility coefficient. (B) Detailed exit kinetics of the three simulated populations (symbols on the curve indicate the matching populations in A). For random T cell migration (squares), our simulation gives a realistic median transit time of 16.1 h, which taxis accelerates roughly twofold (7.33 h). (C) Transit time quantiles as a function of the taxis speed with M = 100 μm²/min. Squares and triangles mark the same values as in A. (D) Transit time as a function of the random walk motility coefficient in the absence of taxis. Squares and circles mark the same values in A.