(683f) Image Mining and the Temporal Evolution of Protein Spatial Patterns: A Case Study in Drosophila Embryogenesis

    The Extracellular Signal Regulated Kinase (ERK) pathway controls a wide range of processes in cells and tissues. Multiple lines of evidence suggest that biological effects of ERK depend on dynamics of its activation, but experimental studies of ERK dynamics have been largely limited to cells in culture. We study the dynamics of the activation of the epidermal growth factor receptor (EGFR) in the ERK pathway in the Drosophila embryo. Because ERK is double-phosphorylated (dpERK) directly downstream of the EGFR pathway, we follow the dynamics of dpERK in order to study the activation of the EGFR pathway. 
    Microfluidic arrays are used to collect dpERK concentration profiles from multiple embryos; because each embryo must be fixed prior to staining for dpERK, it is impossible to obtain dynamic trajectories of the dpERK concentration profiles from a single organism followed over time. Instead, we obtain concentration profiles for many different embryos, with each embryo fixed at a slightly different developmental time. We are interested in reconstructing dynamics from such "cross-sectional" data. We use linear (PCA) as well as nonlinear (diffusion maps) dimensionality reduction techniques to extract the relevant dynamics. Spatial symmetries within the embryo have important implications in this process: an "angular synchronization" problem must be solved to correctly align the data before extracting the dynamics. We discuss the algorithms involved in the process, and we illustrate their use in analyzing the evolution of concentration profiles along the circumference of the embryo, as well as in direct embryo images.