Properties of morphogen gradients and positional information. (A): Morphogen concentrations as a function of distance along a tissue, represented by exponentially decreasing profiles. Red (A1) and black (A2) profiles differ with respect to their characteristic lengths, λ1=30 μm (red arrow) and λ2=10 μm (black arrow), respectively, which on a log-linear plot (inset) corresponds to the inverse of the slope of the morphogen profiles (; with slope α1for A1 and α2for A2). Positional information is conveyed through the graded distribution of morphogens, by means of concentration thresholds that activate different genes (‘high’ and ‘low’ gene thresholds, indicated by the green and blue lines). The spatial range of the gene expression within the tissue is affected by λ, as is schematically shown beneath the graph, causing differential gene activation regions. Differences in gene expression in its turn steers differentiation of a field of cells, reacting in an equivalent manner to the morphogen, into different regions, as schematically indicated in the lowermost panel. (B): Exponential gradients can also differ with respect to the maximum concentration (C0): even when the λ’s of two morphogen gradients (B1, B2) are equivalent (λ1,2=λ=30), the maximum concentrations (here, C0,B1=1, C0,B2=0.5) influence the positional information experienced by the tissue. This is due to the dependency of the gene expression on the absolute morphogen concentrations, as depicted in the schematic drawing below. (C): Comparison between an exponential (red) and a power-law morphogen profile (blue); both profiles have the same concentration value at the characteristic length of the exponential gradient (λ=30). (D): The exponential gradient presents a linear profile in the log-linear representation, whereas the power-law profile has relatively higher values at larger distances from the maximum (i.e. the profile has a long-tail distribution).