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## Section: New Results

### Connecting trajectories in TIRF images of rod-shaped bacteria

Participants : Yunjiao Lu, Charles Kervrann.

In this work, we investigate the role of MreB protein involved in the cell wall construction in rod-shaped bacteria Bacillus. Previous work concerning the quantification of dynamics of MreB is performed from 2D TIRFM image sequences, ignoring the curvature of the rod-shaped cell wall and the thickness of TIRFM plane. To evaluate the effect of these approximations, we have developed a simulator to generate the trajectories on the surface of the cylinder. We assume that trajectories are modeled as:

$dX=b\left(X\right)dt+\sqrt{2}B\left(X\right)dW,$

where $b\left(X\right)$ is the drift tangent to the surface, $W$ is a white noise, and $\sigma \left(X\right)=\frac{1}{2}B\left(X\right)B{\left(X\right)}^{T}$ is the diffusion tensor assumed to be isotropic. In our approach, the drift and diffusion tensor on the surface and on the projected plane are estimated respectively. Moreover, we propose to extrapolate the drift and diffusion tensor to the hidden region, to reconnect the segments we observe in the visible region, and then, to recover the entire trajectory on the surface of the cylinder in 3D (see Fig. 8).

Collaborators: Alain Trubuil and Pierre Hodara (INRA UR MAIAGE, Jouy-en-Josas),

Rut Carbllido-López and Cyrille Billaudeau (INRA, UR MICALIS, Jouy-en-Josas).

Figure 8. (A): Trajectories generated on the surface of the cylinder and (B): the view of TIRF microscope which is the projection of the dynamics on the cylinder near the support surface. The unity in the two figures is in pixel and in our TIRF images 1 pixel $\approx 64$ nm. As the theoretical thickness of TIRF is 200 nm, the trajectories whose $z$ coordinate is under 3.125 pixels are projected onto $x-y$ plan. Colors for different trajectories are random. (C): The connection result through the hidden region of three segments (light blue, dark blue and yellow in order of passage). Red points represent the extrapolated points using drift and diffusion tensor of segments on the surface, while blue points are the extrapolated points using projected drift and diffusion tensor on 2D plan.