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PLoS One
2014 Jan 01;99:e104969. doi: 10.1371/journal.pone.0104969.
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Directional collective cell migration emerges as a property of cell interactions.
Woods ML
,
Carmona-Fontaine C
,
Barnes CP
,
Couzin ID
,
Mayor R
,
Page KM
.
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Collective cell migration is a fundamental process, occurring during embryogenesis and cancer metastasis. Neural crest cells exhibit such coordinated migration, where aberrant motion can lead to fatality or dysfunction of the embryo. Migration involves at least two complementary mechanisms: contact inhibition of locomotion (a repulsive interaction corresponding to a directional change of migration upon contact with a reciprocating cell), and co-attraction (a mutual chemoattraction mechanism). Here, we develop and employ a parameterized discrete element model of neural crest cells, to investigate how these mechanisms contribute to long-range directional migration during development. Motion is characterized using a coherence parameter and the time taken to reach, collectively, a target location. The simulated cell group is shown to switch from a diffusive to a persistent state as the response-rate to co-attraction is increased. Furthermore, the model predicts that when co-attraction is inhibited, neural crest cells can migrate into restrictive regions. Indeed, inhibition of co-attraction in vivo and in vitro leads to cell invasion into restrictive areas, confirming the prediction of the model. This suggests that the interplay between the complementary mechanisms may contribute to guidance of the neural crest. We conclude that directional migration is a system property and does not require action of external chemoattractants.
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25181349
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Figure 2. Calibration to in vitro data.(a). Relative angle of the normal force elastic collision model, representing equal mass impulse momentum. (b). Relative angle of the repolarization model. (c). Relative angle of the biological data. (d). Contact time for the normal force elastic collision model. (e). Contact time for the repolarization model. (f). Contact time for the real cell data. (g). Mean speed after contact separation of the normal force elastic collision model. (h). Mean speed after contact separation for the repolarization model. Note that the speed does not increase past the default migratory speed due to the self-propulsion force term. (i). Mean speed after contact separation for the real cell data, average over 4 cells.
Figure 3. Relationship between CIL, co-attraction and collective migration.(a–d). Images taken at approximately half of the baseline collective target time. (a). −CIL,−CoA, where migration can be seen to be less efficient than in (b) and (d). (b). +CIL,−CoA (c). −CIL,+CoA, (d). +CIL,+CoA. (e). Table of coherence measures for the four cases. (f). Table of collective target times for the four mutually exclusive cases. (g). Collective target time for the cases +CIL,+CoA and +CIL,−CoA. The cases −CIL,−CoA and −CIL,+CoA are omitted as the time was greater than 150 hours. (h). Coherence measure of the four cases, shown in black. Blue star indicates the automated tracking value for the model and the red star shows the experimental data tracking software value.
Figure 4. Coherence measure and collective target time.Data points represent the mean value over 10 independent simulations and error bars represent one standard deviation from the mean. Black arrows represent baseline parameter values. (a). Variation of 1/(RT rate) showing coherence. (b). Variation of the angle by which the cells can deviate during RT showing coherence. (c). Variation of 1/(CoA rate) showing coherence. (d). Variation of the diffusion length showing coherence. (e). Variation of the domain width showing coherence for weak (dashed) and strong co-attraction (solid line). (f). Variation of 1/(RT rate) showing collective target time. (g). Variation of the angle by which the cells can deviate during RT showing collective target time. (h). Variation of 1/(CoA rate) showing the collective target time. (i). Variation of the diffusion length, showing the collective target time. (j). Variation of the domain width showing the collective target time for weak (dashed) and strong co-attraction (solid line).
Figure 5. Optimal rate of response to co-attraction.System behaviour for strong co-attraction, showing an optimal rate at 1/(CoA rate). (a). Coherence is maintained for high rates of co-attraction. (b). Speed is reduced as the rate of co-attraction increases. (c). Collective target time. The smallest target time occurs at 1/(CoA rate).
Figure 6. Co-attraction facilitates stream guidance.(a). +CIL,+CoA, cells respond to the restrictive cues and remain in the migratory region. (b). +CIL,−CoA, cells neglect restrictive cues and migrate into the restricted region. (c). Control NC cells migrating in vivo. (d). C3aR MO cells migrating in vivo. In this case single cells cross into restricted regions. (e). Quantification on the percentage of the population that has moved into the restricted region throughout simulation (blue) and in vitro experiment (red).
Figure 1. Discrete element model.Disks (broken lines) represent simulated cells, with cartoon NC cells overlaid. The polarity of each cell is shown (black arrow) and the forces attenuating or amplifying protrusion formation are indicated with red and blue arrows (respectively). (a). Self-propulsion and rotational turning (blue dashed arrow) force terms: cells attempt to maintain an intrinsic speed and polarity by acceleration (blue arrow), and deceleration (red arrow). (b). CIL: as cells come into contact, contact forces exist at the contact region. In addition, biological intracellular communication promotes the retraction of protrusions near the contact site (red region). Intracellular communication affected by contact promotes protrusion formation at the free edge (blue region). (c). Forces applied during CIL: classical overlap and repolarization are indicated (solid red and blue arrows). Deviation from the classical theory of contact is represented as a random angle (blue dotted arrows). (d–f). Frames of a time-lapse movie of zebrafish NC migrating in vivo. Green labels GFP expressed in the NC under Sox10 regulatory elements; Red: cell protrusions. Two cells (1 and 2) are shown. Arrow: direction of migration for cell 1. (d). Before contact. (e). During contact protrusions collapse. (f). After CIL, protrusions are generated at the free edge. (g). Secretion of co-attractant: at the single cell level the cell experiences a retraction of protrusion. (h). Co-attraction for multiple cells: individual cells experience the co-attractant generated by the whole population and attempt to align their polarity to the gradient with the sensing ray (green line, star indicates the location of the measurement). (i). Typical surface profile of the co-attractant: individual sources and their sum are shown (colour and grey plots resp.). (j). Simulation set up, designed to represent NC streams in vivo: Cell positions represent the origination and initial conditions of the NC. The vertical borders represent the restrictive cues that surround the migratory stream. (k). Diagram representing the computational overlap, where overlap represents the deformation of the cells.
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