Positional information, positional error, and read-out precision in morphogenesis: a mathematical framework

TL;DR

This paper introduces a mathematical, information-theoretic framework to quantify positional information and error in developmental gene expression, demonstrating its application in Drosophila embryo patterning.

Contribution

It provides the first formal mathematical definition of positional information and tools to measure it from experimental data in developmental biology.

Findings

Four genes' expression patterns suffice for single-cell resolution in Drosophila.

The framework links positional information with positional error.

Tools are developed for direct measurement from experimental data.

Abstract

The concept of positional information is central to our understanding of how cells in a multicellular structure determine their developmental fates. Nevertheless, positional information has neither been defined mathematically nor quantified in a principled way. Here we provide an information-theoretic definition in the context of developmental gene expression patterns and examine which features of expression patterns increase or decrease positional information. We connect positional information with the concept of positional error and develop tools to directly measure information and error from experimental data. We illustrate our framework for the case of gap gene expression patterns in the early Drosophila embryo and show how information that is distributed among only four genes is sufficient to determine developmental fates with single cell resolution. Our approach can be generalized to a variety of different model systems; procedures and examples are discussed in detail.