Cranial and trunk neural crest cells leave the dorsal neural tube and migrate as loosely connected streams toward targets such as the branchial arches or the heart. Three local rules, acting only between nearby cells and a diffusible chemokine field, are enough to reproduce this collective, directed behaviour (Carmona-Fontaine et al. 2008/2011; Theveneau et al. 2010):
v(t+dt) = v(t) + [ χ∇C + Σ_j F_co(r_ij) + Σ_j F_cil(r_ij) ] dt / τ
∇C = constant unit vector toward the target (SDF1/CXCL12 source)
F_co(r) = attractive, active only for R_cil < r < R_co (pulls neighbours into a cohesive group)
F_cil(r) = repulsive + repolarising, active for r < R_cil (Rac1 is suppressed at the contact edge,
so the cell's leading edge collapses and
re-forms pointing away from its neighbour)
- Chemotaxis (χ) — every cell reads the local SDF1 concentration gradient and biases its protrusions up-gradient, exactly as N-cadherin-mediated polarity sensing does in vivo.
- Contact inhibition of locomotion (CIL) — when two cells touch, the shared contact edge collapses (via a RhoA/Rac1 switch) and each cell repolarises away from the other, preventing cells from piling up or reversing into the group.
- Co-attraction — a shorter-range attractive signal (complement C3a, PDGF) keeps the group cohesive just outside CIL range; without it, CIL alone scatters the cells and directionality collapses even though chemotaxis is unchanged — this is the "co-attraction paradox" from the original neural-crest CIL papers.
Directionality index below is the population's mean velocity component along the gradient divided by the mean speed (1.0 = every cell moving straight toward the target, 0 = random). Cells that reach the target zone are counted as "arrived" and recycled to the source, keeping the stream continuous like a real cranial neural crest migration front.