Assessing the Reproducibility of Developmental Time and Spatial Patterns in Drosophila melanogaster Embryogenesis

Abstract

Pattern formation in nature is a long-studied phenomenon for its precision and reproducibility, and self-organization is a subcategory that is particularly notable. Embryo development is a canonical example of biology beautifully performing this non-equilibrium pattern formation. During embryo development, an unorganized mass of cells self-assembles into an organism that is then set on a trajectory of further growth and development. This process must be highly regulated to ensure the appropriate growth and correct body formation is undergone to produce a viable embryo. Such precise regulation brings into conversation the concept of non-equilibrium pattern formation, or the phenomena that stereotyped patterns can emerge in a system being driven by mechanical forces or chemical gradients. We consider how embryo development can itself be considered a pattern on the basis of its precision and conservation across many individuals of one species. We consider the concept of reproducibility as one facet of pattern formation, as well as an interesting physical phenomenon to explore. The reproducibility of embryos has been quantified on small scales, specifically in the spatial reproducibility of single developmental landmarks or cells at a single point in time, but it has yet to be extended and robustly characterized on the entirety of a developing embryo. Here, we seek to quantitatively assess and characterize the spatial and temporal variability in embryo development, measuring both processes and anatomy to argue for pattern-like reproducibility despite the system being far from equilibrium. We first develop an analysis pipeline to standardize the data and then align the developmental movies in space via conformal mapping. Time alignment is done by an adapted form of dynamic time warping using developmental epochs. In order to do this, we develop a method to view development as a one-dimensional “trajectory,” enabling quantitative identification of epochs. Biologically, we find that in the temporal domain, D. melanogaster embryogenesis displays periods of striking intra- organism reproducibility, completing some developmental stages in a tight timing window while other stages appear to be more variable. In the spatial domain, we recapitulate earlier reproducibility measurements, make new measurements, and make initial moves towards a more comprehensive view of spatial reproducibility that is not feature-based.