CELL-DIFFERENTIATION RULES THAT GENERATE REGULAR MOSAIC PATTERNS - MODELING MOTIVATED BY CONE MOSAIC FORMATION IN FISH RETINA

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.