Functional Data Clustering of Filopodia Dynamics
Notch signaling plays a significant role in tissue patterning. During patterning of the fruit fly dorsal thorax peripheral nervous system, basal filopodia extend the spatial range of cell-cell communication, yet it is still unclear how Notch is activated in long range signaling via filopodia interaction. Filopodia undergo dynamic length changes during their lifetime, which could supply the mechanical pulling force required for notch activation. However, their dynamics are often characterized using individual scalar values such as maximum length and extension rate which could obscure more intricate dynamics. Our hypothesis is that signaling filopodia exhibit distinct and recurrent temporal patterns which can be identified by a consideration of their complete lifetime trajectories. Our work analyzes 60 filopodia trajectories at the basal surface of the fly dorsal thorax during patterning. Length profiles were smoothed using cubic B-splines and clustered by first reducing them to their dominant functional principal component followed by the application of various clustering algorithms. We found that 94.29% of the overall trajectory variation is explained by the first four functional principal components which account for variations in maximal length, extension and retraction rate, duration of stationary phase and length fluctuation frequency. Five recurrent temporal profiles (dynamic extension modes) with varying trajectory shapes and physical attributes, were identified using trimmed K-means. These findings demonstrate that whereas the major source of structural variation in filopodia profiles remains the length, extension rate and retraction rate, nontrivial combinations of these create distinct dynamic modes of extension which provide new insight into their length profiles. Our work thus offers a quantitative framework for future research connecting filopodia dynamic extension modes to productive Notch activation.