The sensitivity of Turing self-organization to biological feedback delays: 2D models of fish pigmentation

Turing morphogen models have been extensively explored in the context of large-scale self-organization in multicellular biological systems. However, reconciling the detailed biology of morphogen dynamics, while accounting for time delays associated with gene expression, reveals aberrant behaviours that are not consistent with early developmental self-organization, especially the requirement for exquisite temporal control. Attempts to reconcile the interpretation of Turing's ideas with an increasing understanding of the mechanisms driving zebrafish pigmentation suggests that one should reconsider Turing's model in terms of pigment cells rather than morphogens (Nakamasu et al., 2009, PNAS, 106, 8429-8434; Yamaguchi et al., 2007, PNAS, 104, 4790-4793). Here the dynamics of pigment cells is subject to response delays implicit in the cell cycle and apoptosis. Hence we explore simulations of fish skin patterning, focussing on the dynamical influence of gene expression delays in morphogen-based Turing models and response delays for cell-based Turing models. We find that reconciling the mechanisms driving the behaviour of Turing systems with observations of fish skin patterning remains a fundamental challenge.