Emergence of embryonic pattern through contact inhibition of locomotion

Abstract

The pioneering cell biologist Michael Abercrombie first described the process of contact inhibition of locomotion more than 50 years ago when migrating fibroblasts were observed to rapidly change direction and migrate away upon collision. Since then, we have gleaned little understanding of how contact inhibition is regulated and only lately observed its occurrence in vivo. We recently revealed that Drosophila macrophages (haemocytes) require contact inhibition for their uniform embryonic dispersal. Here, to investigate the role that contact inhibition plays in the patterning of haemocyte movements, we have mathematically analysed and simulated their contact repulsion dynamics. Our data reveal that the final pattern of haemocyte distribution, and the details and timing of its formation, can be explained by contact inhibition dynamics within the geometry of the Drosophila embryo. This has implications for morphogenesis in general as it suggests that patterns can emerge, irrespective of external cues, when cells interact through simple rules of contact repulsion.

Fig. 1.

In vivo tracking of Drosophila haemocytes during contact inhibition. (A) A red fluorescent nuclear marker and a GFP microtubule label (green) were driven specifically in Drosophila haemocytes to observe acquisition of the three-line pattern (arrows). (B) Stills from a time-lapse movie of a haemocyte collision pair. Nuclei were tracked and the collision was defined by microtubule alignment (white arrowhead). (C) Sketch of colliding haemocytes at the moment of microtubule alignment (time t), illustrating how the acceleration vector a_t is calculated as its change in velocity v_t–v_t–1. Note that all vectors were oriented so that the cell on the right is in horizontal alignment with that on the left (dashed grey line). (D) Five samples of acceleration vectors surrounding a collision from t–1 to t+3 minutes. The x-components of the accelerations showed no significant bias to left or right except at the collision time t, when there was a highly significant bias away from the target cell [two-tailed t-tests: df=53, t-statistic=–1.68, –5.33, –0.69, 1.08, –1.34, respectively; P>0.05 except in the second case (collision time) when P<<0.001]. Scale bars: 10 μm.

Fig. 2.

Mathematical modelling of non-colliding and colliding haemocyte motility. (A) Illustration of the successive velocities v_t–1 and v_t (black vectors) in the free motility model, showing how the dark grey vectors ϕv_t–1 andσn_t sum together to give v_t in each iteration. Sinceσn_t is a random noise vector, the cloud of grey points shows a sample of other possible end points for v_t. (B) Sample of v_t data from non-colliding haemocyte tracks where each pair of successive vectors (v_t–1, v_t) has been oriented so that v_t–1 points to the right. Taking expectations of the x-components we get E[vx_t]=ϕE[vx_t–1]+σE[nx_t]. Since we know that E[nx_t]=0, the estimate of ϕ becomes ϕ_estimate=mean[vx_t]/mean[vx_t–1] and we obtained a value of 0.73. The two estimates ofσ are given by:σx_estimate=s.d.[vx_t–ϕ_estimate vx_t–1] andσy_estimate=s.d.[vy_t]; these estimates, 1.44 and 1.06, were not significantly different at the 1% level [two-sided Fisher’s variance ratio test: variance ratio=1.86; df=(49,49), 0.05>P>0.01] and the mean of the two estimates (1.25) was used for simulations. (C) Illustration of the successive velocities v_t–1 and v_t (black vectors) in the collision model showing how the dark grey vectors ψr_t, ϕv_t–1 andσn_t sum together to give v_t in each iteration. (D) v_t data from multiple collisions where each pair of vectors (v_t–1, v_t) has been oriented so that v_t–1 points to the right. We first took expectations of the y-components: E[vy_t]=ψE[ry_t]+ϕE[vy_t–1]+σE[ny_t]. Since all aspects of the motility were expected to be symmetrical about the x-axis, these terms would normally vanish; however, we have biased the data by flipping some collisions about the x-axis so that all target cells (grey arrows) lie to the right of the oncoming cell. This resulted in two terms vanishing, leaving E[vy_t]=ψE[ry_t], which enabled us to estimate ψ as mean[vy_t]/mean[ry_t]. The estimated value of ψ (1.25) was next used to calculate new vectors, v_t–ψ_estimate r_t, which have the influence of the direction of the target cell removed. We used these modified vectors to estimate ϕ andσ by the methods used for the free motility model. We obtained an estimate for ϕ of 0.51, and the two estimates forσ (1.73 and 1.24) were again not significantly different at the 1% level [two-sided Fisher’s variance ratio test: variance ratio=1.94; df=(52,52), 0.05>P>0.01].

Fig. 3.

Simulated haemocyte dispersal recapitulates reality. (A) Haemocyte dispersal was simulated within a space of approximate geometry to real embryos. Cells were run down the midline for a period of 40 minutes before being allowed to freely disperse, when they rapidly developed a stable three-line pattern. (B) Real and simulated cells were tracked during the dispersal process. The insets highlight the repeating lateral movements (arrows) that emerged in both real and simulated cells. Scale bar: 20 μm. (C) Quantification of angles off the midline as cells migrate laterally revealed no significant difference (n.s.) between real and simulated cells (83±25° versus 87±31°, respectively; P>0.6, df=45, unpaired t-test). (D) A time-lapse movie (supplementary material Movie 5) was thresholded and flattened with a mean intensity to reveal the average spacing of haemocytes. (E) Flattening of the same movie with a maximum intensity revealed that haemocytes covered the entire surface of the embryo. (F) Domain maps from simulations were generated in the same way as from real cells using halos to approximate the actin region. (G) The domain map in D was analysed by contour plotting to reveal the peaks of the haemocyte domains. (H) The distance between the haemocyte domains was ∼34 μm. The asterisk indicates a breakdown in the haemocyte domain pattern, which was analysed further in supplementary material Movie 10.

Fig. 4.

Reduction of cell number prevents pattern development. (A) Example embryo containing haemocytes overexpressing Cyclin A, along with a red nuclear marker and GFP-labelled microtubules. Cells were tracked for 2 hours as they developmentally dispersed. Right-hand panel shows cell tracks over the duration of the time-lapse movie. (B) Contour plot of a domain map of Cyclin A-expressing haemocytes containing labelled actin (generated from supplementary material Movie 14). (C) Contour plot of a domain map of a simulation containing half the number of cells as found in wild type. Scale bars: 10 μm.