# Two-exponential models of gene expression patterns for noisy experimental data

## TL;DR

This paper introduces a two-exponential model for accurately quantifying bcd mRNA gradients in Drosophila embryos, enabling analysis of variability, classification, and robustness in developmental gene expression patterns.

## Contribution

The authors develop a biologically relevant, invariant two-exponential modeling technique for quantifying and analyzing gene expression gradients in noisy experimental data.

## Key findings

- Robust gradient quantification method developed
- Ability to classify embryos by developmental stage
- Quantifies embryo-to-embryo variability in gene expression

## Abstract

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.