Anna Marciniak-Czochra

Pattern formation and regeneration in hydra: Mathematical modelling
versus new experimental findings

One of the crucial issues in developmental biology is
understanding how coordinated systems of positional information are
established during organism's development and how cells respond to them,
resulting in the subdivided and patterned tissues of multicellular organisms.
We approach the question of mechanisms responsible for formation of new
structures and regeneration of missing ones. The test organism for
mathematical modelling is a fresh-water polyp, hydra, a simple organism which
can be treated as a prototype for axis formation in higher organisms. We
propose models based on the idea that patterns are controlled by specific
cell-surface receptors, which transmit to the cells signals responsible for
their differentiation. We study two mechanisms of pattern formation,
diffusion-driven instability and hysteresis, and demonstrate their
possibilities and limitations as a means for explanation for
self-organisation and regeneration. We find stationary and oscillatory
patterns resulting from multiple steady states and switches in the production
rates. Our studies show that a hysteresis-driven mechanism is capable of
explaining the results of grafting experiments. We discuss our models in the
context of recent experimental findings of the Wnt and Dkk overexpression
during regeneration. We examine how the Wnt signalling pathway may be
responsible for spatial patterning, and how to incorporate processes on
different biological scales (inside the cell) to derive proper reaction
terms.