title: Positional information, positional error, and readout precision in morphogenesis: a mathematical framework.
abstract: The concept of positional information is central to our understanding of how cells determine their location in a multicellular structure and thereby 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 the features of expression patterns that affect positional information quantitatively. 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 nearly single-cell resolution. Our approach can be generalized to a variety of different model systems; procedures and examples are discussed in detail.
authors.affiliation: Institute of Science and Technology Austria, A-3400 Klosterneuburg, Austria gasper.tkacik@ist.ac.at.
authors.forename: Gašper
authors.initials: G
authors.lastname: Tkačik
authors.affiliation: Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey 08544 Lewis Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544.
authors.forename: Julien O
authors.initials: JO
authors.lastname: Dubuis
authors.affiliation: Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey 08544.
authors.forename: Mariela D
authors.initials: MD
authors.lastname: Petkova
authors.affiliation: Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey 08544 Lewis Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544.
authors.forename: Thomas
authors.initials: T
authors.lastname: Gregor
mesh_terms: D000818:Animals; D004330:Drosophila / Q000196:embryology / Q000235:genetics*; D018507:Gene Expression Regulation, Developmental; D008957:Models, Genetic; D009024:Morphogenesis
keywords: development; patterning; positional information; precision