MATHEMATICAL BIOSCIENCES http://www.mbejournal.org/ AND ENGINEERING Volume X, Number 0X, XX 200X pp. X–XX AN IN VIVO INTERMEDIATE FILAMENT ASSEMBLY MODEL St´ ephanie Portet Department of Mathematics University of Manitoba, Winnipeg, MB, Canada Julien Arino Department of Mathematics University of Manitoba, Winnipeg, MB, Canada (Communicated by the associate editor name) Abstract. A model is developed to study the in vivo intermediate filament organization in terms of repartition between four different structural states: soluble proteins, particles, short and long filaments. An analysis is conducted, showing that the system has a unique, globally asymptotically stable equilib- rium. By means of sensitivity analysis, the influence of parameters on the system is studied. In agreement with biological observations, it is shown that post-translational modifications of intermediate filament proteins resulting in filament solubilization are the main regulators of the intermediate filament or- ganization. A high signalling-dependent solubilization of filaments favours the intermediate filament aggregation in particles. 1. Introduction. The cytoskeleton is a complex arrangement of structural pro- teins organized in three different networks: microfilaments, intermediate filaments and microtubules. Each network has specific physical properties and spatial organi- zation, and plays particular roles in the cell. Here, the focus is on the intermediate filament network, which is involved in the stabilization and mechanical resilience of the cell, cell migration, and signal transduction [6, 8]. Intermediate filaments are cell type and differentiation stage dependent. They are classified in five different types: Types I-IV are cytoplasmic filaments; Type V, lamins, are nuclear filaments. Intermediate filament proteins share a central rod domain that forms a highly conserved α−helix involved in the formation of coiled-coil structures [11]. The central rod domain is flanked by the head and tail domains, which are less conserved and confer specific structural properties to the different types of intermediate filament proteins. Mutations occur at the conserved central rod domain, which modulates the assembly; they then lead to defaults in the organization of intermediate filament networks [1]. The head and tail domains contain the sites that can undergo post-translational modifications [16, 18]; there- fore, the terminal domains have mainly regulatory roles. The α−helical coiled-coil structures, called dimers, laterally associate to form tetramers. The latter are con- sidered as the soluble subunits of intermediate filaments. Depending on the type of intermediate filament proteins, dimers are hetero- or homopolymers. 2000 Mathematics Subject Classification. Primary: 92C37. Key words and phrases. Cytoskeleton assembly dynamics, intermediate filaments. Research supported in part by NSERC. 1