A metric embedding kernel for live cell microscopy signaling patterns

Live cell microscopy captures 5-D $(x,y,z,channel,time)$ movies that display patterns of cellular motion and signaling dynamics. We present here a metric kernel function for spatiotemporal patterns of cell signaling dynamics in 5-D live cell microscopy movies unique in requiring no a priori knowledge of expected pattern dynamics, and no training data. The approach uses Kolmogorov complexity theory to compute a metric distance between movies and to measure the meaningful information among subsets of movies. Cell signaling kymographs store at each spatiotemporal cell centroid the cell signaling state, or a functional output such as velocity. Patterns of similarity are identified via the metric normalized compression distance (NCD). The NCD is a reproducing kernel for a Hilbert space that represents the input cell signaling kymographs as points in a low dimensional embedding that optimally captures the pattern similarity identified by the NCD throughout the space. The only parameter is the expected cell radii ($\mu m$). A new formulation of the cluster structure function optimally estimates the meaningful information captured by the embedding. Also presented is the cell signaling structure function (SSF), a Kolmogorov structure function that optimally measures cell signaling state as nuclear intensity w.r.t. surrounding cytoplasm, a significant improvement compared to the current state-of-the-art cytonuclear ratio. Results are presented quantifying the impact of ERK and AKT signaling between different oncogenic mutations, and by the relation between ERK signaling and cellular velocity patterns for movies of 2-D monolayers of human breast epithelial (MCF10A) cells, 3-D MCF10A spheroids under optogenetic manipulation of ERK, and human induced pluripotent stem cells.