  We present a theoretical model for retinocollicular map development, which
can account for intriguing behaviors observed in gain-of-function experiments
in knock-in mice by Brown et al., including bifurcation in heterozygous
Isl2/EphA3 knock-ins. The model is based on known chemical labels, axonal
repulsion/competition, stochasticity and uses Markov chain description. Our
model suggests that the map in heterozygotes is single-valued in the temporal
region of retina due to reduced gradient of ephrin in the corresponding region
of SC. The remaining map is double-valued since the gradient of ephrin is high
there. We predict therefore that if gradient of ephrin is reduced by a genetic
manipulation, the single-valued region of the map should occupy a larger
portion of temporal retina, i.e. the point of transition between single- and
doulble-valued maps should move to a more nasal position in Isl2-EphA3
heterozygotes. We also discuss the importance of inhomogeneous EphA gradient
and mapping in Isl2/EphB knock-ins.
