DOI: 10.1021/la900509r 8817 Langmuir 2009, 25(15), 8817–8823 Published on Web 05/13/2009 pubs.acs.org/Langmuir © 2009 American Chemical Society Vimentin Intermediate Filament Formation: In Vitro Measurement and Mathematical Modeling of the Filament Length Distribution during Assembly † St  ephanie Portet,* ,‡,# Norbert Mu¨cke, §,# Robert Kirmse, §,3 Jo¨rg Langowski, § Michael Beil, ^ and Harald Herrmann* , ) ‡ Department of Mathematics, 342 Machray Hall, University of Manitoba, Winnipeg, MB, Canada R3L 2N2, § Division of Biophysics of Macromolecules and ) Division of Molecular Genetics, German Cancer Research Center (DKFZ), Im Neuenheimer Feld 580, Heidelberg D-69120, Germany, and ^ Department of Internal Medicine I, University Hospital Ulm, D-89070 Ulm, Germany. # These authors contributed equally to this work. 3 Current address: Research Group Microenvironment of Tumor Cell Invasion, German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, Heidelberg D-69120, Germany. Received February 10, 2009. Revised Manuscript Received April 10, 2009 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 μm 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.; Mu¨cke, 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. Introduction Intermediate filaments (IF) constitute, in addition to micro- tubules (MTs) and microfilaments (MFs), the third principal filament system of the cytoskeleton-structuring metazoan cells. In particular, IFs form, together with several cross-bridging molecules, the cytoskeleton proper. They are highly resistant to disruptive treatments such as the extraction of cells with buffers containing high concentrations of salt and nonionic detergents in the cold, which are conditions that lead to the disassembly of MTs and MFs. 22 Accordingly, strong denaturants have to be employed to dissociate filaments and to obtain monomeric subunits. Also, in contrast to MTs and MFs, whose subunit proteins tubulin and actin are globular, IFs assemble from fibrous molecules exhibiting an approximately 45-nm-long central R-helical, coiled-coil-forming domain (“rod”). These parallel coiled-coils associate into antiparallel, approximately half-staggered tetra- meric complexes already at a relatively high concentration of † Part of the Molecular and Polymer Gels; Materials with Self-Assembled Fibrillar Networks special issue. *Corresponding authors. E-mail: portets@cc.umanitoba.ca; h.herrmann@ dkfz-heidelberg.de. (1) Abumuhor, I. A.; Spencer, P. H.; Cohlberg, J. A. J. Struct. 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