Are embryonic gene networks optimal encoders of position?
In plain words
In the fruit-fly embryo, a few genes switched on in graded patterns tell each cell where it is with about 1 percent precision. One hypothesis is that these networks are tuned to carry the most positional information possible given their noise.
Precise statement
For the Drosophila gap-gene network (hunchback, Kruppel, knirps, giant) driven by maternal gradients, maximize the mutual information $I(x; g)$ between position $x$ and expression vector $g$ at a fixed budget of molecules and the measured noise, and test whether the optimal network, with no parameters fitted to gap-gene profiles, predicts the measured profiles, the positional error of about $0.01\,L$ ($L$ = egg length), and mutant phenotypes. Answer: yes or no for wild type and for mutants or other species.
What would settle it
Parameter-free predictions of the optimized network compared with measured expression profiles in mutants and in other fly species.
Status in the literature
An optimization-based derivation (Sokolowski, Gregor, Bialek, Tkacik; arXiv 2302.05680, 2023) reproduced key features of the wild-type network; out-of-sample tests remain open.