Inferring nuclear movements from fixed material

We describe a technique for inferring the typical movement of nuclei in Drosophila blastoderm using nuclear positions extracted from a large number of images of fixed embryos. Embryos are sorted into temporal cohorts and each cohort is represented by the average blastoderm shape and average density of nuclei along the blastoderm surface. To find cell movements, we formulate a cost function that measures how well a given placement of a set of "synthetic nuclei" respects the measured average density for the cohort. This function is optimized for each cohort in turn, initialized with the results of the previous time step. The result is a synthetic time series of changing nuclear locations which recapitulates average nuclear density and blastoderm shape seen under the microscope.