Influence of gene expression gradients on positional information content in fly embryos

Abstract

The concept of positional information was introduced to qualitatively explain how individual cells are involved in forming patterns. Recent experimental and theoretical developments have made studying specific biological systems in a quantitative manner possible using the framework of positional information. Much previous work has focused on using the full gene expression profiles when calculating the available positional information. In an attempt to simplify the model a discretized version, where the gene expression profiles are simplified to a binary system, was proposed. Binarizing, however, results in a significant loss of information over using the full profiles. The question remains how coarsely can we discretize the full model without losing essential positional information. Recent work has shown the importance of concentration gradients in impacting the folding of proteins during embryonic development. Based on this work we posit that the gradients of gene profiles might be an important addition to the discretized model. Using data provided by the Gregor lab at Princeton University we test this hypothesis on the gap gene network of Drosophilia embryos. In order to implement the addition of gradients to the positional information requires producing an algorithm that can efficiently take meaningful derivatives of noisy data, which is done using Chebyshev interpolation. An adaptation of Monte Carlo methods to find maxima of multidimensional functions is also implemented. We find that the derivatives can account for over one bit of the information lost by the discretization process. Allowing the cells to locate themselves with an average precision close to one internuclear spacing. This suggests that a binary model using gradients may be almost as efficient as the model that uses the full gene profiles. We propose that a discrete model of positional information that includes gradients does not lose significant information over a model that uses full profiles.