A compartmental model for the bicoid gradient

The anterior region of the Drosophila embryo is patterned by the concentration gradient of the homeodomain transcription factor bicoid (Bcd). The Bcd gradient was the first identified morphogen gradient and continues to be a subject of intense research at multiple levels, from the mechanisms of RNA localization in the oocyte to the evolution of the Bcd-mediated patterning events in multiple Drosophila species. Critical assessment of the mechanisms of the Bcd gradient formation requires biophysical models of the syncytial embryo. Most of the proposed models rely on reaction-diffusion equations, but their formulation and applicability at high nuclear densities is a nontrivial task. We propose a straightforward alternative in which the syncytial blastoderm is approximated by a periodic arrangement of well-mixed compartments: a single nucleus and an associated cytoplasmic region. We formulate a compartmental model, constrain its parameters by experimental data, and demonstrate that it provides an adequate description of the Bcd gradient dynamics.