Section: New Results

Microtubules modeling for variational assimilation analysis

Participants : Pierre Allain, Charles Kervrann.

Microtubules (MT) are highly dynamic tubulin polymers that are involved in many cellular processes such as mitosis, intracellular cell organization and vesicular transport. Nevertheless, the modeling of cytoskeleton and MT dynamics based on physical properties is difficult to achieve. We proposed to model microtubules as rigid and growing cylinders alike (Nedelec and Foethk 2007) [45] but including Newtonian dynamics. Using the Euler-Bernoulli beam theory, we have proposed then to model the rigidity of microtubules on a physical basis using forces, mass and acceleration. In addition, we linked microtubules growth and shrinkage to the presence of molecules (e.g. GTP-tubulin) in the cytosol. The overall model enables linking cytosol to microtubules dynamics in a constant state space, thus allowing usage of data assimilation techniques (see Fig. 17 ).

Figure 17. Left: Simulation of a 2D radial microtubule network. The results show growing and shrinking phases yielding inhomogeneous “pseudo-tubulin” concentration in the cytosol. MTs are bended according to fluid forces. Right: 3D simulation of MT nucleation and growth that mimics MT dynamics seeded onto a two vertical bar-shaped fibronectin pattern and observed in TIRF microscopy (courtesy of iRTSV/LPCV/PCM CEA-Grenoble).