Spatial Correlations in the Drosophila Embryo

Abstract

One of the foremost endeavors in modern biophysics is to elucidate the broad principles underlying the fundamental biological process of DNA transcription, whereby information is first extracted from an organism's genetic code of DNA into the usable form of mRNA. Much about the basic properties of DNA transcription still remains unknown. In particular, physical analysis of molecular mRNA correlations---which would yield fundamental insight into the physical manifestation of genetic information---has thus far been confined only to unicellular organisms, which are wholly uninformative about the subtle effects of continuous spatial inputs on correlated transcriptional activity. In this theoretical project, we have used recent data that provides the positional coordinates of single mRNA molecules to calculate spatial correlations in a multicellular system, the Drosophila Melanogaster embryo, whose lack of cell walls at early stages of development creates a freely-diffusive environment which is highly amenable to transcriptional study. By adapting the idealized approach of standard statistical mechanics to this complex system of irregular geometry and non-uniform density, we have developed a generalized methodology to construct meaningful correlation functions for any gene of choice in the embryo. We have applied these techniques to analyze the entire regulatory Gap Gene network, and have found that while in unregulated regions, the mRNA distributions are perfectly uncorrelated, in regulated regions the distributions all show a dichotomy of length scales about a transition length of approximately 80 micrometers, with significant correlations at lower length scales and significant anti-correlations at higher length scales. Astoundingly, we also find that in both the unregulated and regulated regions, correlation functions for all four gap genes in the network collapse onto two respective master curves. The results provide unexpected, yet promising indications of universal transcriptional modes in the network, and illuminate future paths to uncover the physical principles linking molecular correlations with the information flow of life.