Vimentin intermediate filament formation: in vitro measurement and mathematical modeling of the filament length distribution during assembly.

The salt-induced in vitro assembly of cytoplasmic intermediate filament (IF) proteins such as vimentin is characterized by a very rapid lateral association of soluble tetrameric subunits into 60-nm-long full-width "unit-length" filaments (ULFs). We have demonstrated for this prototype IF protein that filament elongation occurs by the longitudinal annealing of ULFs into short IFs. These IFs further longitudinally anneal and thus constitute a progressively elongating filament population that over time yields filaments of several microm in length. Previously, we provided a mathematical model for the kinetics of the assembly process based on the average length distribution of filaments as determined by time-lapse electron and atomic force microscopy. Thereby, we were able to substantiate the concept that end-to-end-annealing of both ULFs and short filaments is obligatory for the formation of long IFs (Kirmse, R.; Portet, S.; Mücke, N. Aebi, U.; Herrmann, H.; Langowski, J. J. Biol. Chem. 2007, 282, 18563-18572). As the next step in understanding the mechanics of IF formation, we have expanded our mathematical model to describe the quantitative aspects of IF assembly by taking into account geometry constraints as well as the diffusion properties of rodlike linear aggregates. Thereby, we have developed a robust model for the time-dependent filament length distribution of IFs under standard conditions.