  Live cell microscopy captures 5-D $(x,y,z,channel,time)$ movies that display
patterns of cellular motion and signaling dynamics. We present here an approach
to finding 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 proposed cell signaling structure function
(SSF) is 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. SSF
kymographs store at each spatiotemporal cell centroid the SSF value, 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 SSF 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 how meaningful an embedding from the RKHS representation.
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 .
