Run-and-Tumble Dynamics and Mechanotaxis Discovered in Microglial Migration

Microglia are resident macrophage cells in the central nervous system that search for pathogens or abnormal neural activities and migrate to resolve the issues. The effective search and targeted motion of macrophages mean dearly to maintaining a healthy brain, yet little is known about their migration dynamics. In this work, we study microglial motion with and without the presence of external mechanostimuli. We discover that the cells are promptly attracted by the applied forces (i.e., mechanotaxis), which is a tactic behavior as yet unconfirmed in microglia. Meanwhile, in both the explorative and the targeted migration, microglia display dynamics that is strikingly analogous to bacterial run-and-tumble motion. A closer examination reveals that microglial run-and-tumble is more sophisticated, e.g., they display a short-term memory when tumbling and rely on active steering during runs to achieve mechanotaxis, probably via the responses of mechanosensitive ion channels. These differences reflect the sharp contrast between microglia and bacteria cells (eukaryotes vs. prokaryotes) and their environments (compact tissue vs. fluid). Further analyses suggest that the reported migration dynamics has an optimal search efficiency and is shared among a subset of immune cells (human monocyte and macrophage). This work reveals a fruitful analogy between the locomotion of 2 remote systems and provides a framework for studying immune cells exploring complex environments.

: Distribution of ∆r max win . Each column corresponds to results obtained from cells in a specific motility state; while each row corresponds to a specific setting of the state marker.
Parameter determination. The detected motion of a cell's center consists of three parts: the ac-38 tual displacement, the displacement due to cell deformation, and tracking noise due to pixel value 39 fluctuation. Parameters can be empirically determined by categorizing typical cell displacement in 40 different states. Here we characterize typical displacement for runs, tumbles, deformation, and pixel 41 fluctuation. 42 We prepare four training sets. The first one consists of dead cells or dirt that have similar sizes 43 to microglia (N=19 in total, ∼ 80 h of video) to benchmark the noise level of pixel fluctuation, see 44 Figure S1(a1-3). The second one includes live cells that tumble throughout the recording without 45 obvious shape change (N=21, ∼ 80 h); and this is to obtain the typical tumble motility, see Fig-46 ure S1(b1-3). The third is comprised of tumbling cells that change shapes frequently (N=10, ∼ 20 h of video). This set is used to evaluate displacement induced by cell deformation, see Figure S1(c1-3).

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The fourth dataset includes 85 min of recordings wherein the cells only run, see Figure S1(d1-3). In 49 Figure S1, rows from top to bottom display distributions of the ∆r max win of frame-to-frame displace-50 ment (N win = 1 frame), displacement over t win = 1 min (N win = 3 frames), and displacement over 51 t win = 2 min (N win = 5 frames) respectively. The blue dashed lines mark the R thres implemented in 52 this study. Figure S1(b1) and (d1) highlight the necessity of not using the frame-to-frame displace-53 ment for state marking. The single-frame step sizes for the most motile cells (d1) overlap greatly 54 (c1-3) do not significantly alter the detected tumbling motility (b1-3).

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Lastly, we characterize the fraction of mis-marked states for the shown settings. For (t win , R thres ) =

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(1 min, 5µm), almost no tumbles will be mistaken as runs, as the total probabilities to the right of 58 the dashed lines in Figure S1(b2) and (c2) are less than 1%. Meanwhile, ∼8% run will be marked 59 as tumble. Note that this setting only applies short tracks (T tot ≤ 12.5 min) which accounts for only 60 4% (N=15/369) of the cells used in the main text. For the majority (N=354/369) of the tracks,

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(t win , R thres ) = (3 min, 5µm). This leads to maximum 5% tumbles being mistaken as runs, see 62 Figure S1(c3) and less than 1% runs being mistaken as tumbles (d3). Understand the parameters. Here we show how R thres and t win are associated with the cells' motility. 64 We simulate run-and-tumble tracks with known parameters. In the simulation, the particle (cell) switches between run and tumble at constant probability rates (p R,T ), giving rise to an exponential 66 distribution of the state intervals. The characteristic time τ R /τ T is set to 1:4. The particle runs at a 67 constant speed v R without turning. In tumbles, it changes direction randomly per time interval and 68 moves one step forward at the speed of v R . We apply the state marker to the simulated tracks and 69 show how the marked run-time fraction T R /T tot varies with R thres , see Figure S2 increasing R thres , T R /T tot decreases slowly around the set value Lastly, there is a cutoff at v R t win , as no particle will be able to move longer than that within t win .

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Adding rotational diffusion to the runs, the abrupt cutoff will be smeared, see the Figure S2(a) inset.

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To summarize, by setting the threshold at R thres ≳ v R t win , one will be able to separate the runs 76 from tumbles.

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Therefore, we determine the R thres for experimental data to be approximately 6 µm for t win = 78 2 min, see Figure S2(b). Due to the stronger noise in the experimental data, we examined the state 79 marker working with R thres ranging from 5 to 7 µm. No significant differences are found for the data 80 presented here and for those in the main text. In Figure S3 In the main text, the reported time scale for losing angular persistence during runs (τ rot ) is 99 approximately 2 min [ Figure 3]. This time scale is larger than yet comparable to our sampling time Figure S6: Correlation between ϕ in and ϕ out for tumbles (a-b) and runs (c-d) during mechanotaxis. Note that ϕ = 0 is now the direction towards the mechanostimuli. Each point represents an event colored by its duration. Crosses: mean of binned events. Horizontal bar: range in T R,T to compute the mean for the rightmost symbol.
Angular correlation in mechanotaxis. We confirm that microglial migration during mechanotaxis 113 still bears the features of run-and-tumble motion. Figure S6 Super-diffusive behavior. The 3D run-and-tumble motion of E.coli in chemotaxis is recently reported 120 to be supper-diffusive with a MSD of ⟨∆r 2 ⟩ ∝ t 1.66 [5]. We find a similar trend in microglia 121 performing mechanotaxis. Figure S7  In Ref.
[6], the authors provide an analytical expression for the optimal time for run (τ R ) and tumble 140 (τ T ) to minimize the first-passage time in a 2D diffusive searching process: The coefficients C = 4 ln w − 5 + c and w are obtained by solving a equation solely dependent on (2) Here c = 4(γ − ln 2) ≈ −0.4637 with γ the Euler constant.