Determining data independence on a digitized membrane in three dimensions

A method for determining whether structures distributed along a cell's membrane represent a random spatial distribution is presented in this paper. Two three-dimensional (3-D) images are acquired from one cell by wide-field digital imaging of cells which have been labeled with two different fluorescent antibodies. Prior to spatial analysis, a constrained regularized least squares restoration of the images is performed. This is followed by registration via fiducial markers (dual-labeled beads). A deformable model is then used to map data near the surface to the surface. Finally, each resulting data set is analyzed to determine whether it is spatially random. To do this, we generalize the test for complete spatial randomness of points in a plane, to test voxels distributed along a voxelized membrane in three dimensions. We also test whether the distribution of one protein is independent of the distribution of a second protein. The method is applied to compare the distribution of the protein kinase C to that of vinculin. Vinculin is a protein which anchors intracellular filaments to the cell's plasma membrane. It is also used as a (sparse) membrane marker for the deformable model. Protein kinase C facilitates molecular motors inside the cell. These may be associated with actin and myosin filaments.