Influence of cell-to-cell variability on spatial pattern formation
Many spatial patterns in biology arise through differentiation of selected cells within a tissue, which is regulated by a genetic network. This is specified by its structure, its parameterisation, and the noise on its components and reactions. The latter, in particular, is not well examined because it is rather difficult to trace. Using experimental data on trichomes, i.e., epidermal plant hairs, as an example, we examine the variability in pattern formation that is due to small differences among the cells involved in the patterning process. We employ suitable local mathematical measures based on the Voronoi diagram of the trichome positions to determine the noise level in of the pattern. Although trichome initiation is a highly regulated process we show that the experimentally observed trichome pattern is substantially disturbed by cell-to-cell variations. Using computer simulations we find that the rates concerning the availability of the protein complex which triggers trichome formation plays a significant role in noise-induced variations of the pattern. The focus on the effects of cell-to-cell variability yields further insights into pattern formation of trichomes. We expect that similar strategies can contribute to the understanding of other differentiation processes by elucidating the role of naturally occurring fluctuations in the concentration of cellular components or their properties.