ANTISYMMETRY, DIRECTIONAL ASYMMETRY, AND DYNAMIC MORPHOGENESIS

Fluctuating asymmetry is the most commonly used measure of development al instability. Some authors have claimed that antisymmetry and direct ional asymmetry may have a significant genetic basis, thereby renderin g these forms of asymmetry useless for studies of developmental instab ility. Using a modified Rashevsky-Turing reaction-diffusion model of m orphogenesis, we show that both antisymmetry and directional asymmetry can arise from symmetry-breaking phase transitions. Concentrations of morphogen on right and left sides can be induced to undergo transitio ns from phase-locked periodicity, to phase-lagged periodicity, to chao s, by simply changing the levels of feedback and inhibition in the mod el. The chaotic attractor has two basins of attraction-right side domi nance and left side dominance. With minor disturbance, a developmental trajectory settles into one basin or the other. With increasing distu rbance, the trajectory can jump from basin to basin. The changes that lead to phase transitions and chaos are those expected to occur with e ither genetic change or stress. If we assume that the morphogen influe nces the behavior of cell populations, then a transition from phase-lo cked periodicity to chaos in the morphogen produces a corresponding tr ansition from fluctuating asymmetry to antisymmetry in both morphogen concentrations and cell populations. Directional asymmetry is easily m odeled by introducing a bias in the conditions of the simulation. We d iscuss the implications of this model for researchers using fluctuatin g asymmetry as an indicator of stress.