In 1933 Henri Cartan proved a fundamental theorem in Nevanlinna theory, namely a generalization of Nevanlinna's second fundamental theorem. Cartan's theorem works very well for certain kinds of problems. Unfortunately, it seems that Cartan's theorem, its proof, and its usefulness, are not as widely known as they deserve to be. To help give wider exposure to Cartan's theorem, the simple and general forms of the theorem are stated here. A proof of the general form is given, as well as several applications of the theorem.

The cytoskeleton plays an important role in cell structure, polarity, locomotion and division. Individual elements of the cytoskeleton are composed of subunit proteins which assemble and disassemble in specific places and times within the cell. Knowledge of the temporal and spatial regulation of subunit assembly and disassembly is essential to understanding how the cytoskeleton contributes to cellular activities. The assembly and dynamics of two cytoskeletal structures, namely adhesion plaques (APs) and intermediate filaments (IFs), have been difficult to study by traditional methods. We have generated GFP-chimeras to label these structures and to study their dynamics in motile fibroblasts.

To study the dynamics of APs, we prepared stable 3T3 cell lines expressing a GFP-β1 integrin chimera. The chimera was prepared by fusing GFP to the transmembrane and cytoplasmic portions of β1 intergrin, since previous studies had shown that the cytoplasmic tail of β integrins is sufficient to direct integrins to APs.