Cell migration and antigen capture are antagonistic processes coupled by myosin II in dendritic cells

The immune response relies on the migration of leukocytes and on their ability to stop in precise anatomical locations to fulfil their task. How leukocyte migration and function are coordinated is unknown. Here we show that in immature dendritic cells, which patrol their environment by engulfing extracellular material, cell migration and antigen capture are antagonistic. This antagonism results from transient enrichment of myosin IIA at the cell front, which disrupts the back-to-front gradient of the motor protein, slowing down locomotion but promoting antigen capture. We further highlight that myosin IIA enrichment at the cell front requires the MHC class II-associated invariant chain (Ii). Thus, by controlling myosin IIA localization, Ii imposes on dendritic cells an intermittent antigen capture behaviour that might facilitate environment patrolling. We propose that the requirement for myosin II in both cell migration and specific cell functions may provide a general mechanism for their coordination in time and space.

of a Lifeact-GFP immature DC before and after wash out. The compartment retaining the antigen correspond to endolysosomes as it appears lysotracker positive. D/ Volume of 10kDa AF647-dextran internalized by immatures DCs migrating into micro-channels treated either with DMSO or several doses of Latrunculin A or EIPA. We observed high mortality at 100µM EIPA. (n=20-80 cells per condition from 2 independent experiments. A Kruskal-Wallis test was applied for statistical analyses). E/ Sequential images (60X, middle plane) of a neutrophil stained with AF488-WGA for membrane visualization migrating along micro-channels filled with 10kDa AF647-dextran. Scale bars = 10µm. The optimal search strategy, defined as the minimum of the mean search time is characterized by τ1,min and τ2,min.
It is given for each concentration, and is well predicted by Eq.

Supplementary Methods: physical model for the migratory behavior of DCs as an intermittent search strategy
The data presented in this paper show that immature DCs migrate by alternating high motility phases with low motility phases during which macropinosomes are resorbed and their content transported to endolysosomes promoting antigen retrieval. We suggest here that such biphasic mode of locomotion belongs to the class of "intermittent random walks 1-4 . The intermittent random walk model relies on the assumption that efficient probing of the environment by an agent looking for a target is incompatible with a fast motion: search trajectories are in that case characterized by an alternation of slow motion with high detection abilities, and fast motion with reduced detection. The analysis of the intermittent random walk model then demonstrates on general grounds that adjusting the durations of the slow and fast phases can minimize the search time for randomly hidden targets 3 . We here briefly recall the intermittent random walk model in its minimal version, as depicted in Figure 8A. We assume that a DC evolves in a 2dimensional environment, where antigen are present with effective concentration c=a 2 /b 2 where a is the detection radius and b is the typical distance between antigen locations. The DC alternates slow phases (i) during which we assume that antigen capture occurs with rate k within the detection radius a, and fast phases (ii) during which we assume that antigen uptake occurs with rate k'<<k. The mean duration of a phase (i) (resp. (ii)) is denoted by 1 (resp. 2); the velocity in phase (ii) has a random direction and modulus v and motion in phase (i) is neglected in a first approximation. Following Benichou et al., 2011 3 , the efficiency of the search process is quantified by the mean search time <t> for a target, which is then given analytically by: (1) where Ik denote modified bessel functions and (2) The mean search time <t> can then be shown (in the limit of low antigen concentration) to be minimized for the following values of the mean durations 1 and 2 of the slow and fast phases: (3) Equation (3) defines the optimal search strategy of the model. Figure S7 shows that the analytical prediction of Eq. (1) is in very good agreement with numerical simulations. In particular, the mean search time for a target antigen can be clearly minimized as a function of 1 and 2. While the model is presented here in its minimal version, qualitatively similar results can be obtained under much less restrictive hypothesis 3 .

Supplementary References
Solving this linear system of four equations with four unknowns, and then averaging over the initial position of the searcher, we finally obtain for the search time

Comparison with numerical simulations
Here again, this expression (45)is in very good agreement with numerical simulations for a wide range of parameters (see figure 5 and table 2). The agreement is quantitatively supported by calculating d = ( 1 where N is the number of couples (τ 1 , τ 2 ) for which we have calculated t in the simulation and f is the function given by equation (45). The error is about 5-8%, and does not seem to depend on a as in the 'dynamic' mode, but rather on a/ b.Once again, the minimum obtained from the simulations is very well described by the analytical approximate.

Optimization of the search time
In this case, intermittence is trivially necessary to find the target: indeed, if the searcher does not move, the MFPT is infinite. Once again, we have three characteristic lengths a, b and v/ k.        6).

7.
Comparison with systematic search strategies