  Signal transduction and cell function are governed by the spatiotemporal
organization of membrane-associated molecules. Despite significant advances in
visualizing molecular distributions by 3D light microscopy, cell biologists
still have limited quantitative understanding of the processes implicated in
the regulation of molecular signals at the whole cell scale. In particular,
complex and transient cell surface morphologies challenge the complete sampling
of cell geometry, membrane-associated molecular concentration and activity and
the computing of meaningful parameters such as the cofluctuation between
morphology and signals. Here, we introduce u-Unwrap3D, a framework to remap
arbitrarily complex 3D cell surfaces and membrane-associated signals into
equivalent lower dimensional representations. The mappings are bidirectional,
allowing the application of image processing operations in the data
representation best suited for the task and to subsequently present the results
in any of the other representations, including the original 3D cell surface.
Leveraging this surface-guided computing paradigm, we track segmented surface
motifs in 2D to quantify the recruitment of Septin polymers by blebbing events;
we quantify actin enrichment in peripheral ruffles; and we measure the speed of
ruffle movement along topographically complex cell surfaces. Thus, u-Unwrap3D
provides access to spatiotemporal analyses of cell biological parameters on
unconstrained 3D surface geometries and signals.
