  Motivation: Spatial pattern formation of the primary anterior-posterior
morphogenetic gradient of the transcription factor Bicoid (Bcd) has been
studied experimentally and computationally for many years. Bcd specifies
positional information for the downstream segmentation genes, affecting the fly
body plan. More recently, a number of researchers have focused on the
patterning dynamics of the underlying bcd mRNA gradient, which is translated
into Bcd protein. New, more accurate techniques for visualizing bcd mRNA need
to be combined with quantitative signal extraction techniques to reconstruct
the bcd mRNA distribution.
  Results: Here, we present a robust technique for quantifying gradients with a
two-exponential model. This approach: 1) has natural, biologically relevant
parameters; and 2) is invariant to linear transformations of the data which can
arise due to variation in experimental conditions (e.g. microscope settings,
non-specific background signal). This allows us to quantify bcd mRNA gradient
variability from embryo to embryo (important for studying the robustness of
developmental regulatory networks); sort out atypical gradients; and classify
embryos to developmental stage by quantitative gradient parameters.
