Gap-gap cross-regulation in mid-embryo pattern formation: deterministic and stochastic modelling of hunchback-Krüppel interactions. David M. Holloway¹, Alexander V. Spirov^2,3. 1) Dept Mathematics, British Col Inst Tech, Burnaby, BC, Canada; 2) Computer Science and CEWIT, Stony Brook University, NY, USA; 3) Sechenov Institute for Evolutionary Physiology and Biochemistry, St. Petersburg, Russia.

   hunchback (hb) is an evolutionarily conserved gap gene involved in early specification of anterior-posterior (AP) position in the embryo. In previous work, we used a stochastic model of hb cis-regulation to characterize the relative contributions of maternal Bicoid (Bcd) activation and hb self-regulation to hb expression noise, suggesting selective influences for multiple cooperative Bcd binding and hb autofeedback. Here, we explore the role of gap-gap interactions in constraining expression noise at the mid-embryo, at the sharp Hb transition from high anterior expression. Krüppel (Kr) is a gap gene expressed just posterior to this boundary, which has long been known to interact with hb. We build on a recently published model incorporating experimental evidence for dual action of Hb on Kr expression - activating at low concentration, inhibiting at high concentration. We find that inhibitory feedback of Kr on hb can play a role in decreasing expression noise (e.g. between- and within-nucleus mRNA variability). We find that the observed loss of the mid-embryo (parasegment 4) hb stripe in Kr- embryos can be accounted for by a reciprocal dual action of Kr on hb. The model gives quantitative predictions for both the averaged expression patterns and the stochastic variability of these patterns.