The wild types AX2 and AX3, and the flavohemoglobin null mutants fhbA ^-, fhbB ^- and fhbA ^- B ^- strains of Dictyostelium cells were provided by the National BioResource Project (NBRP Nenkin, Japan) and cultured axenically with HL5 medium (HLF2; Formedium, United Kingdom) containing 100 mM glucose and 1/1,000 penicillin-streptomycin (P/S) (15140-122; Gibco, United States) on cell culture dishes at 22°C or under agitation. PhyA-strain is a kind gift from C. West (University of Georgia, United States).

Sodium nitroprusside dihydrate (SNP) (71778; Sigma-Aldrich, United States), which releases NO, was added at 10–100 µM to the culture medium to investigate the effect of RNS on the aerotaxis. H₂O₂ (18084-00; Kanto Chemical, Japan) was added at 100–500 µM to investigate the effect of ROS on the aerotaxis. Ethidium bromide (EtBr) (E1510, Sigma-Aldrich), which inhibits mitochondria DNA replication, was added to the culture medium 24 h before experiments at 30 μg/mL for pretreatment of the cells. Oligomycin (O4876, Sigma-Aldrich) was used at 10 μg/mL, and antimycin A (A8674, Sigma-Aldrich) was used at 37.5 µM. Tiron (4,5 dihydroxy-1,3-benzene-disulphonic acid; D7389, Sigma-Aldrich) was used at 10 mM.

A double-layer microfluidic device with oxygen-controllability was used (Supplementary Figure S1) (Hirose et al., 2022). The device was 30 × 30 mm square, and the thickness was 4 mm. Inside the device, two gas channels in a 1-mm interval were located at 0.5 mm from the bottom surface, perpendicularly crossing above three parallel media channels on the bottom (Supplementary Figure S1A). The width and height were 2 mm and 0.15 mm for all channels, respectively. The device mainly consisted of polydimethylsiloxane (PDMS, Sylgard 184 Silicone Elastomer Kit, The Dow Chemical Company, United States) and contained a polycarbonate film to prevent gas infusion from the atmosphere. The x and y-axes were defined to be parallel and perpendicular to the media channels, respectively, and the z-axis was in the vertical direction. The origin was set at the center of the device. The oxygen concentration in the device was controlled by gas exchange between the channels, supplying gas mixtures at predefined oxygen concentrations to the gas channels. The oxygen concentration in the device was computed by three-dimensional numerical simulation using commercial multiphysics software (COMSOL Multiphysics ver. 5.5, COMSOL AB, Sweden) and verified using an oxygen-sensing film which emitted phosphorescence quenched by oxygen (Hirose et al., 2021). The computational and experimental results showed almost the same tendency especially for the minimum value of oxygen concentration, showing an oxygen concentration gradient from 0.4% to 21% O₂ was generated along each media channel in the x-direction when the gas mixtures containing 0% and 21% O₂ were supplied to the left and right gas channels, respectively (gray solid line in Supplementary Figures S1B–F). At the most hypoxic location at x = −1.6 mm, the slope of the oxygen concentration gradient inverted.

Dictyostelium cells were harvested from the culture dishes and introduced into the media channels in the microfluidic device at 2 × 10⁶ cells/mL (400 cells/mm²) with the HL5 culture medium. After incubation for 20 min to adhere Dictyostelium cells to the bottom surface of the media channels, the HL5 culture medium was replaced by fresh one. Here, depending on the experimental conditions, reagents were added to the HL5 culture medium. For accurate comparisons, each device was set to have channels for control condition and each of another two conditions at the same time. The device was placed in a stage incubator (TP-CHSQ-C, Tokai Hit, Japan) mounted on an inverted microscope (IX83, Olympus, Japan), and controlled at 22°C. Just after gas mixtures of oxygen and nitrogen were supplied at 30 mL/min to the left and right gas channels, time-lapse imaging was started.

A second type of microfluidic device, with a Y-shape channel was used to generate a chemical gradient of soluble molecules (Figure 3A). The device was placed in the same stage incubator mounted on the microscope, and controlled at 22°C. The x and y-axes were defined to be perpendicular and parallel to the merged channel, respectively. The origin was set at the junction of the channels from the two inlets. Dictyostelium cells were first allowed to adhere on the microchannel in HL5 culture medium for 20 min. HL5 culture media without and with a pharmacological substance at a concentration C ₀ (SNP at 100 µM or H₂O₂ at 500 µM) were injected from the left and right inlets, respectively, at 1 mL/h, and time-lapse imaging was then started. The average velocity was U ₀ = 0.37 mm/s in the merged channel inducing a wall-shear stress around 4.4 mPa low enough not to affect cell migration and adhesion on the bottom glass (Rupprecht et al., 2012). The profile of chemical concentration C (x, y) at a given position (x, y) was calculated by the following equation: C x , y = C 0 2 1 + erf x 2 U 0 D y (1) where D is the diffusion coefficient of the chemical substance in water. For the H₂O₂ gradient we used D = 1.4 × 10⁻³ mm²/s (van Stroe-Biezen et al., 1993). Addition of 100 µM SNP leads to rapid increase of NO in the media to reach a prolonged plateau after 25 min (Bradley & Steinert, 2015). As the experimental set-up require 30 min, we expect a constant level of NO for the duration of the assay, hence for the SNP gradient experiment. We used the diffusion constant of NO, D = 2.2 × 10⁻³ mm²/s (Zacharia & Deen, 2005), to compute the relative NO concentration profile. Cells were imaged and tracked between 1 h and 2 h after starting the media flow.

Phase-contrast microscopic images of the central part of each media channel including the region of interest (ROI) displayed in Supplementary Figure S1A and were taken by the microscope with a ×4 objective lens (UPLFLN4XPH, Olympus) every 30 s for 2 h. The positions of Dictyostelium cells were detected at each time step by analyzing the images using ImageJ (National Institutes of Health, United States) with its built-in plugin, Find Maxima. Then, the individual cells were tracked using MATLAB (MathWorks, United States) by minimizing the total of squared displacements with a published tracking code (Blair and Dufresne, 2008). All trajectory data were analyzed using in-house MATLAB programs. The migration distance in 1 min between the time steps t _i and t _i+1 was defined as dl _i , which was decomposed into the x and y-directional displacements dl _x,i and dl _y,i , respectively (dl _i ² = dl _x,i ² + dl _y,i ²), where the x-direction is defined as the gradient direction for both devices. The average speed v = d l i ¯ and the average x-directional velocity v _x = d l x , i ¯ were averaged from all 1-min cell displacements in Δx = 200 µm wide slabs as a function of x-position. The aerotactic index was defined as AI = d l x , i / d l i ¯ referring to a chemotactic index normally used as a metric for chemotaxis (Amselem et al., 2012). The maximal AI _max was measured in each individual experiment as the maximum value of AI on the positive side (x > −1.6 mm) since the oxygen gradient was better controlled than on the negative side. A chemotaxis index CI = d l x , i / d l i ¯ was computed to analyze the data by experiments with the Y-shaped microfluidic devices.

The confined spot assay offers a quick and robust way to test whether cells can generate oxygen gradients and move aerotactically (Deygas et al., 2018; Biondo et al., 2021; Cochet-Escartin et al., 2021). A drop of either 2, 3 or 5 µL of a cell suspension containing 2,000, 3,000 or 5,000 cells respectively was carefully deposited on a dish. The drop was incubated for 30 min in humid atmosphere at 22°C before adding 2 mL of HL5 culture medium. An 18 mm or 22 mm diameter round glass coverslip cleaned with ethanol then thoroughly rinsed in HL5 was gently deposited on top of it. Image acquisition was performed using a lens-free imaging device (Cytonote 6W, Iprasense, France) or the aforementioned inverted microscope. Images were taken every 5–15 min for 24 h. The software Horus (Iprasense, France) was used to process and reconstruct the Cytonote images, and a homemade ImageJ macro based on the polar transformer plug-in was used to construct kymographs from the original images by polar transformation and z-stacking of frames. The ring speed was determined by calculating the slope of the front density band associated with ring propagation on these kymographs between 16 h and 24 h. To improve signal to noise ratio in kymographs, images were filtered from their background by using the Find-Edges function of ImageJ before applying the polar transformation.

For consumption measurements of fhb null mutant and for those of the respiratory inhibitors oligomycin and antimycin A (Supplementary Figure S6C), about 10⁶ total cells suspended in HL5 culture medium were placed in a respirometer (Oxygraphs 2k high-resolution respirometers, Oroboros Instruments, Austria) to determine oxygen concentration changes over time. After the measurement of the basal respiration, oligomycin (10 μg/mL) or antimycin A (37.5 µM) were added successively. Oxygen consumption were calculated using the change of oxygen level over time and normalized per cell. For consumption measurements of EtBr treated cells or in presence of SNP or H₂O₂ (Supplementary Figure S6D), a 6-mL glass vial was filled with 2 × 10⁷ cells suspended in HL5, and closed it with a cap through which an optical oxygen probe was plunged. The cap was carefully sealed around the probe to avoid external oxygen entering the bottle. We measured the change of oxygen level over time with this probe coupled to its oxymeter (OXROB3 robust probe and Firesting oxymeter, Pyroscience, Aachen, Germany).

For proliferation experiments, cells were plated at about 10⁴ cells/cm² in 6-well plates, and imaged and counted with the lens-free imaging device or the inverted microscope every 30 min for 24 h.

Four plates containing 2.3 × 10⁶ A×3 cells in 1.5 mL HL5 culture medium were prepared with either no chemicals, 100 µM SNP or 100 µM H₂O₂. The two plates containing SNP or H₂O₂ and a plate without chemical were placed at 22°C and 21% O₂. The last plate containing cells in HL5 culture medium was incubated at 22°C and 0.4% O₂. After 3 h, total RNA was extracted (RNeasy Plus Mini Kit, 74134, Qiagen, Germany), quantified and adjusted at 1 µg to synthesise cDNA (First Strand cDNA Synthesis Kit for RT-PCR, 11483188001, Roche, Switzerland). Then a qPCR was performed (DyNAmo Flash SYBR Green qPCR Kit, F415L, Thermo Fisher Scientific, United States) using the following primers: rnlA-F (5′-GCA​CCT​CGA​TGT​CGG​CTT​AA-3′), rnlA-R (5′-CAC​CCC​AAC​CCT​TGG​AAA​CT-3′), cxgE-F (5′-ATG​TCC​CAC​GCA​TTA​CCA​G-3′), cxgE-R (5′-CAT​AGG​CAG​CGT​AAA​AAT​CTT​CTC-3′), cxgS-F (5′-AAG​TTG​TTA​AAT​CTC​AAC​TC-3′), cxgS-R (5′-TTT​ATC​AAC​GCC​ATA​TTT​AA-3′), fhbA-F (5′-GAA​CTC​ACA​TCA​GAC​ATT​AC-3′), fhbA-R (5′-CTA​CAT​AGT​CAC​CAG​CTG​GA-3′), fhbB-F (5′-GAT​GGT​AAA​GAG​ATA​GCT​AC-3′), and fhbB-R (5′-CTG​ATA​AAC​TGT​AAT​GTC​TGA​C-3′). The experiments were performed in duplicate for each gene. The relative gene expression was determined using the 2^−ΔΔCt method (Livak & Schmittgen, 2001) using rnlA as a housekeeping gene.

For each measurement type, experiments were repeated three to six times. Significant differences between three or more conditions were evaluated by one-way ANOVA or two-way ANOVA followed by a post-Tukey test for multiple comparisons. In each test, statistical significance and the tendency toward significance were inferred at *p < 0.05 and †p < 0.1, respectively.

The simulations were performed using a numerical mean-field “Go-or-Grow” model coded in the Python language, which we recently introduced to explain ring propagation in confined spot experiments (Cochet-Escartin et al., 2021). The mean field model used for the aerotactic dispersion consisted of coupled reaction-diffusion equations for both oxygen and cell concentrations respectively: ∂ C ∂ t = D O 2 Δ C − b 0 C ρ (2) ∂ ρ ∂ t = D c e l l s   Δ ρ + r o C ρ − ∇ . → J → a e r o (3) where C is the oxygen concentration, t is the time, D O 2 is the oxygen diffusion constant, b ₀ is the cell oxygen consumption, ρ is the cell density, D _cells is the cellular diffusion constant, r ₀ is the cell proliferation rate, and J → a e r o is the advection term. From our recent observations that the aerotactic displacements are more correlated to the relative oxygen gradient ∇ → C C than to the absolute gradient ∇ → C (Hirose et al., 2022), we propose a slight modification to the advection term in the shape of J → a e r o = ρ v → a e r o , with: v → a e r o = χ   l ∇ → C C ) 1 1 + e C − C 0 s (4) χ is a proportionality constant called aerotactic bias (unique for each experimental condition, see below), l = 10 µm is the approximate cell size, and the latter two terms comprise the response function to oxygen relative gradient. We choose an initial cell distribution and a boundary condition for oxygen C (L = 9 mm) = 21% O₂ mimicking the experimental situation. Mesh sizes of Δx = 10 µm and Δt = 0.05 min were used. To avoid negative O₂ values a threshold C ₁ = 0.5% O₂ was chosen below which cells consume oxygen relative to the local ambient oxygen concentrations. We also used a proliferation threshold below which cells stop dividing C ₂ = 0.2% O₂ as recently measured (Carrère et al., 2023). This is also a slight modification to our initial Go-or-Grow model for which C ₀ = C ₂ (Cochet-Escartin et al., 2021).

The aerotactic bias, the oxygen threshold, and the steepness factor in Eq. 4 were respectively updated to χ ₀ = 30 μm/min, C ₀ = 0.4% O₂ and s = 0.1% O₂ upon further analysis of density accumulation of cells and maximum aerotactic displacement along the gradient perceived in the microfluidic device experiments with the AX2 in HL5 control condition (Ghazi et al., in preparation). For other conditions, C ₀ and s were kept constant as we never observed any shift in the range of oxygen concentrations triggering an aerotactic response, but χ was set proportional to the measured aerotactic x-directional velocity v _x (Supplementary Figure S1C; Supplementary Table S1), as χ = χ 0 v x v x 0 where v _x0 is the aerotactic speed of the control condition reported in Figures 2E, H. The cellular diffusion constant D _cells plays a minor role on the ring propagation speed or ring formation time (Ghazi et al., in preparation). It was not systematically measured but we used a scaling relation motivated by former studies (Golé et al., 2011), D c e l l s D 0 = v v 0 where D ₀ = 30 μm²/min (Cochet-Escartin et al., 2021) and v ₀ = 5 μm/min (Supplementary Figure S3D) are the diffusion constant and average speed of the AX2 control condition in the ring region. All parameter values, cell oxygen consumption b ₀, aerotactic x-directional velocity v _x , absolute displacement speed v, cell proliferation rate r ₀, were taken directly from experimental observations discussed in this article and summarized in Supplementary Table S1. Oxygen diffusion constant in HL5 medium at 22°C was taken from the one in pure water at 20°C: D O 2 = 2,000 μm²/s (Cochet-Escartin et al., 2021). On one hand, salt and sugar present in HL5 decrease D O 2 by about 100 μm²/s, but on the other hand, temperature increases D O 2 by about 50 μm²/s/°C (Goldstick et al., 1976; Jamnongwong et al., 2010).

Micro-colonies of various strains were confined with a glass coverslip and observed by videomicroscopy. The behavior of the PhyA null mutant or of the one of the wild type AX3 cells were similar to the one previously described with AX2 cells (Figures 1A–D; Supplementary Figure S2). After less than an hour, the oxygen depletion at the center of the colony induced an increase of aerokinetic motility and the formation of an expanding ring of aerotactic cells. This resulted in a sharp density profile, the ring being two to three times of higher density than the interior of the colony. All of fhb null mutants presented a much slower and rougher ring of cells than the AX3 strain (Figure 1), the slowing down of the ring being especially more marked and significant for the fhbB ^- and fhbA ^-B^- (Supplementary Figure S3C). Furthermore, small aggregates of cells were frequently observed inside the mutant colonies while they were very rare for the wild type.

In order to test solely the aerotaxis of fhb null mutants in imposed oxygen gradients, and not the intermingled response to self-generated gradients with oxygen consumption and cell proliferation, we used a double-layer microfluidic device generating a 0.4%–21% O₂ gradient (Supplementary Figure S1A). In such a device, at the most hypoxic location where the slope of the oxygen concentration gradient was inverted, the directionality of the cell migration was changed from the -x direction for x < −1.6 mm to +x direction for x > −1.6 mm, implying migration toward higher oxygen levels [Supplementary Figure S1B with the already reported AX2 strain (Hirose et al., 2022)]. The existence of such an inversion even when the signal-to-noise in cell displacement is low is a signature of an aerotactic response. Cells migrated also in the y-direction but the average of the y-directional displacements were almost zero regardless of the position (Supplementary Figure S1B). The AX2 strain migrated faster in the hypoxic region than in the normoxic region (positive aerokinesis, Supplementary Figure S1C).

The parental AX3 strain presented a higher non-directional motility than the mutants in all oxygen concentrations (Figure 2A) and displayed a strong aerotactic bias when the oxygen level was under 1.5% O₂ (Figure 2B), resulting in a maximal aerotactic index AI _max of 0.13 (Figure 2C). The average speed of all fhb null mutants was significantly reduced (Figure 2A), but all exhibited an aerotactic displacement. Even if for the fhbB ^- and fhbA ^- B ^- strains, it was just measurable (see inset of Figure 2B). As a result, the AI _max was slightly reduced in fhbA ^- strain comparatively to wild type, but reduced by more than half for the fhbB ^- and fhbA ^- B ^- strains, indicating a strong reduction in the ability of the cells to properly sense or respond to oxygen gradients in these mutants. We performed a comparative random motility assay in plastic dishes at 21% and 0.4% O₂ (Supplementary Figure S4). The AX3 strain exhibited a higher motility in the hypoxic condition confirming the results of Figure 2A and the flavohemoglobin mutants motility was normal in normoxia but slightly reduced by hypoxia (Supplementary Figure S4).

In many organisms, flavohemoglobins expression is induced by NO, while induction upon hypoxia is uncommon (reviewed in Forrester and Foster, 2012). Therefore, the level of expression of fhbA and fhbB genes in wild type cells were tested by RT-qPCR in response to hypoxia and SNP, a chemical source of NO or H₂O₂ as a generic source of ROS (Table 1). Both flavohemoglobins expression were strongly induced after 3 h in 0.4% O₂. Strong induction was also observed for cxgS, an optional subunit of cytochrome c oxidase induced by hypoxia, used here as positive control (Bisson et al., 1997). As expected, cxgE, the alternate optional subunit of cytochrome c oxidase expressed only during growth in normoxia was sharply downregulated at 0.4% O₂ (Bisson et al., 1997). On the other hand, treatment with SNP, a classical source of NO, did not induce fhbB expression and rather slightly repressed fhbA. As mitochondria also release ROS, H₂O₂ effect was tested but did not affect the flavohemoglobins expression. Thus, low oxygen concentration appears to be key to induce the expression of flavohemoglobin genes, reinforcing the possibility that the proteins are important in this condition required for aerotaxis to appear.

Micro-colonies of wild type AX2 cells were confined in HL5 supplemented with either H₂O₂ as a source of ROS or with SNP as a source of RNS by generating NO in the media. Neither product prevented the formation of the expanding ring of cells even though the ring speed was reduced with SNP or H₂O₂ (Supplementary Figures S3A, S5). It was not possible to use much higher concentrations of these chemicals as they prevented cell adhesions or killed the cells at 1 mM. As an alternate way to change the potential effect of ROS, we used Tiron, a free radical scavenger that had previously been used to prevent oxidative stress in Dictyostelium (Bloomfield & Pears, 2003). Addition of 10 mM Tiron to confined wild type cell had no visible effect on ring formation appearance or migration speed (Supplementary Figure S5).

To detect eventual fine effect of free radical, SNP and H₂O₂ were applied to wild type cells placed in the microfluidic device previously described. However, lower concentration had to be used as they impair cell adhesion to the glass bottom of the device. The 100 µM H₂O₂ did not affect migration speed or response to oxygen gradient of the cells (Figures 2D–F). On the other hand, the 100 µM SNP reduced only slightly the cell speed at 21% O₂ (3.5 μm/min versus 4.5 μm/min) but dramatically at 0.4% O₂ (1.5 μm/min versus 5 μm/min) (Supplementary Figure S3D). Despite this strong speed reduction, the SNP-treated cells still responded to oxygen gradients and the maximum aerotactic index remained similar to that of untreated cells (Figure 2F).

To further exclude a role of ROS and RNS in controlling aerotaxis, wild type cells were placed in a Y-shaped microfluidic device generating a chemical gradient of soluble molecules: either SNP or H₂O₂. Higher levels of NO (Figure 3B) or of H₂O₂ (Figure 3D) induce a lower motility of Dictyostelium cells (negative chemokinesis) but cells did not show specific chemotaxis towards or away from either product, up to 100 µM for SNP and 500 µM for H₂O₂ as exemplified by the chemotactic index (Figures 3C, E). These experiments unambiguously indicate that cells do not respond to direct ROS or RNS gradients. As ROS/RNS are not implicated in the observed aerotactic responses, we investigate whether mitochondria are involved in any other way.

As mitochondria are major oxygen sinks and are potentially involved in direct or indirect oxygen sensing for aerotaxis, three different mitochondrial inhibitors were used on confined wild type cells. Treatment with 10 μg/mL of the mitochondria replication inhibitor EtBr for 5 days was shown to inhibit mitochondrial respiration in Dictyostelium cells by 75% and to prevent cell division (Kobilinsky and Beattie, 1977). For our experiments, a pretreatment of 24 h with 30 μg/mL EtBr was used as it results into a strong reduction of cell growth (Chida et al., 2004). This resulted into a reduction of total respiration by 35% comparatively to their untreated control (Supplementary Figure S6D). The confined colony of EtBr-treated cells formed an expanding ring (Figures 4E–H) but with a decreasing migration speed with respect to the non-treated AX2 cells tested (Figures 4A–D; Supplementary Figure S3B) and a slight delay of ring formation time (compared Figures 4D, H). Although it was not measured, cell growth was expected to be strongly reduced since the media contained EtBr during the confinement assays. The EtBr-treated cells were also tested for their aerotactic response in an oxygen gradient (Figures 2D–F). There was no reduction of the aerotactic response and the aerotactic index was similar to untreated cells. Interestingly, on the normoxic side, the addition of EtBr markedly reduced the migration speed of the cells but with no significant reduction on the hypoxic side (Figure 2D).

Oligomycin and antimycin are fast acting inhibitors of mitochondrial respiration that reduce considerably oxygen consumption: by nearly 60% with oligomycin, and 85% with antimycin as measured in this study (Supplementary Figure S6C). As expected, these drugs also reduce considerably cell division (Supplementary Figure S6B). Despite this strong inhibition, an expanding ring of cells was formed in the confined spot assay (Figures 4I–O), but with a 5 h (oligomycin) to 6 h delay (antimycin) as shown with the kymographs of Figures 4D, L, P. In addition, the ring expansion speed was slower than for the untreated AX2 cell colony (control) especially for the antimycin treatment (Figures 4M–P; Supplementary Figure S3B). In the microfluidic assay, oligomycin treated cells (red curves in Figures 2G, H) responded as did the EtBr-treated cells (green curves in Figures 2D, E) with a similar aerotactic displacement along the direction of the gradient but a slightly reduced migration speed on the normoxic side. On the other hand, both migration speed and aerotactic response were reduced by the antimycin treatment (blue curves in Figures 2G, H). Such general reduction of motility is not unexpected as antimycin prevents the cytochrome c oxidase to generate ATP which is required for motility (Wilson et al., 1992).

To interpret experiments, we used the numerical mean-field version of the Go-or-Grow model (Cochet-Escartin et al., 2021). Briefly, the rapid oxygen consumption by cells in the confined area and the very selective aerotactic cell response are the two key ingredients for ring formation and propagation. Ring formation may occur even in the absence of proliferation (Biondo et al., 2021; Cochet-Escartin et al., 2021). However, proliferation is necessary to sustain a stable long-lived ring (Rieu et al., 2022). The ring speed depends mostly on the aerotactic speed and slightly on the proliferation rate. Here, we simulated the experiments with various O₂ diffusion constants values taken from literature and found that the changes in the ring speed between the various extreme literature values were negligible (Supplementary Figure S7 and its caption). The ring speed also did not depend on initial cell density, only the formation time depended on it: the denser, the quicker the ring formation and the more it appeared in the peripheral position of the initial spot (Supplementary Figure S8). After adjusting the aerotactic response from microfluidic experiments, and the initial cell density profile and other parameters from experiments, the model predicted a ring formation within an hour for AX2 and AX3 cell spots (Figures 5C, A) in agreement with experiments (Figures 4D, 1D). The simulated ring propagated at constant speeds of ∼1.1 and 1.2 μm/min for AX2 and AX3, respectively. These values were in good agreement with the range of measured ring speeds (Supplementary Figures S3A–C), given the experimental variability.

All other cell lines tested in this study presented an aerotactic response (i.e., v x > 0 ) in the region of 0%–2% O₂ (Figures 2B, E, H). Simulated rings of fhbB ^- mutant (Figure 5B) were 50% slower and much wider than those of the parent cell line AX3 (Figure 5A) as the x-directional velocity v _x was only 37% of their parent one. But, the rings appeared as quickly as their parent did as the cellular oxygen consumption or proliferation was not impaired. The rings of AX2 treated with 100 µM SNP (Figure 5D) were 21% slower than those of non-treated cell line (Figure 5C) as the x-directional velocity v _x was also reduced by 21% with respect to their parent. They were also wider but not significantly delayed as the oxygen consumption of this condition was only slightly decreased with respect to the control. These findings were in very good agreement with experimental observations (Figures 1D, L; Supplementary Figures S5D, H).

Oligomycin and antimycin treatments corresponded to a very different set of parameters. The aerotactic directional migration speed v _x of oligomycin-treated cells was similar to the non-treated AX2 (Figure 2H) but they did not proliferate at all (Supplementary Figure S6B). As a result, once initiated the ring expanded poorly (Figure 5E) and even stopped after a while. The ultra-low oxygen consumption of antimycin-treated cells made the ring appear at very late simulation times (about 7 h in Figure 5F) comparable to experimental observations (Figure 4P).

One can conclude from these simulations that.

(i) Rings formed only in presence of aerotaxis.