A. Takesue et al., CELL-DIFFERENTIATION RULES THAT GENERATE REGULAR MOSAIC PATTERNS - MODELING MOTIVATED BY CONE MOSAIC FORMATION IN FISH RETINA, Journal of theoretical biology, 194(4), 1998, pp. 575-586
study characteristics of cell-differentiation rules that realize stabl
e formation of regularly arranged checker-board patterns, exemplified
by cone ''mosaic'' zebrafish retina, or the regular arrangement of con
e photoreceptor cells. We consider the situation in which cells are ar
ranged on a square lattice and are initially undifferentiated. Later e
ach cell becomes one of the two differentiated states, affected by the
state of the neighboring cells. The cells that undergo differentiatio
n form a ''morphogenetic cell row'' which sweeps from one end to the,o
ther end of the lattice through time. This models an outward sweep of
the margin of expanding mosaic region of the retina which occurs as un
differentiated photoreceptor cells become differentiated in concentric
circles, joining the mosaic. We introduce an index to measure the abi
lity of cell-differentiation rules to generate regular checker-board p
atterns from irregular initial patterns, and attempt to characterize t
he successful rules. We first show the importance of six ''preservatio
n conditions'' which guarantee perfectly regular photoreceptor arrange
ment for all the rows after a regular row. Then we select an additiona
l six ''optimizing conditions'' for responses to configurations that a
re consistently shown by the rules of high average scores. We also exa
mine the effect of interaction between responses to different configur
ations. Finally we examine the concept of morphogenetic row precedence
, i.e, that the successful rules generating a high score tend to treat
the consistency with neighbors in the newly differentiated cells (tho
se in the morphogenetic cell row) as more important than the consisten
cy with previously differentiated neighbors. (C) 1998 Academic Press.