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## Section: New Results

### Probabilistic overall reconstruction of membrane-associated molecular dynamics from partial observations in rod-shaped bacteria

Participants : Yunjiao Lu, Charles Kervrann.

Understanding the mechanisms that maintain the structure of rod-shaped bacteria is a challenging problem in cell biological research. Thanks to progress in molecular biology and microscopy (e.g Total Internal Reflection Fluorescence (TIRF) microscopy), we have the opportunity to observe the dynamics of the cell wall construction workers, that is the membrane-associated molecular machines (MMs). Due to the cylindrical form of the bacteria and the 2D selective visualization in TIRF microscopy, only around one third of the perimeter can be observed at a given time. Nevertheless, from the partial observed bacteria surface images, earlier studies showed that a fraction of the MMs performs directed motion, across the image field quasi-orthogonally to the cylinder axis.

Accordingly, we addressed the problem of the connection of motion segments on a cylindrical surface, assuming that one MM may re-enters into the observed region (OR), a certain period of time after having left the field of view. The directed MM motions are assumed as Brownian motion with drift. The birth and death events of the MMs are supposed to happen independently and uniformly on the surface. Given a set of observed segments entering and exiting the OR, we proposed a probabilistic framework to calculate the probabilities of the events of birth, death and re-entry, based on speed and diffusion of the motion and the time of exit and entry. Even though two third of the surface is hidden as shown in Figure 8, this framework allows us to derive a computational procedure aiming at connecting segments belonging to the same trajectory, and then recovering directed MMs dynamics on the whole surface. The performance of the method has been demonstrated on appropriate simulation data that mimics MMs dynamics observed in TIRF microscopy.

Collaborators: A. Trubuil and P. Hodara (INRA MaIAGE unit, Jouy-en-Josas),

R. Carballido-López and C. Billaudeau (INRA, UR MICALIS, Jouy-en-Josas).

Figure 8. Trajectories on the cylinder and its 2D representation. The unobserved region is $\left(-L,-l\right]×\left[0,H\right]$ and the observed region is $\left(l,0\right]×\left[0,H\right]$.