Erastin (Cayman, 17754), RLS-3 (MedChemExpress, HY-100218A), ferrostatin-1 (Cayman, 17729), necrostatin-1 (Cayman, 11658), Z-VAD-FMK (Cayman, 14463), ionomycin (Sigma-Aldrich, I9657), staurosporine (MedChemExpress, HY-15141), GKT137831 (MedChemExpress, HY-12298), LY294002 (LC laboratories, L-7962), dasatinib (Cayman, 11498), FSEN1 (Cayman, 38025) and Trolox (MedChemExpress HY-101445) were all dissolved in DMSO and stored at −80 °C before usage. l-Buthionine sulfoximine (BSO) (Sigma-Aldrich, B2515), DFO mesylate salt powder (Sigma-Aldrich, D9533), Tiron (Sigma-Aldrich, 172553), TEMPO (Sigma-Aldrich, 176141), N-acetyl-l-cysteine (Sigma-Aldrich, A9165) and catalase (Sigma-Aldrich, C1345) were freshly prepared before each experiment by dissolving them in distilled H2O. FC (Sigma-Aldrich, 3522-50-7) was prepared in distilled H2O and stored at −20 °C. Sytox Green nucleic acid stain (Invitrogen, S7020), siR-DNA probe (Spirochrome, SC007), siR700-DNA probe (Spirochrome, SC015), CellROX deep red (Invitrogen, C10422), C11 BODIPY581/591 (Invitrogen, D3861), FeRhoNox-1 iron dye (Sigma-Aldrich, SCT030), DAPI (AAT Bioquest, 17513) and lucigenin (Cayman, 14872) were stored at −20 °C. NADPH (Sigma-Aldrich, N7505) was reconstituted in 10 mM Tris-HCl (pH 8) and stored at −80 °C. Phosphatase inhibitor cocktail (524629) and protease inhibitor cocktail (539134) were sourced from Calbiochem. Human holo-transferrin (R&D Systems, 2914-HT) was reconstituted in distilled H2O and stored at −80 °C. Phenol-red-free RPMI medium was made according to RPMI 1640 (Gibco, 11875) medium formulation using cell-culture-grade inorganic salts, amino acids and vitamins purchased from Sigma-Aldrich.

Cell culture

hTERT RPE-1 (ATCC, CRL-4000), 786-O (ATCC, CRL-1932), G-402 (ATCC, CRL-1440), HOS (ATCC, CRL-1543), LN-18 (ATCC, CRL-2610), U-118 MG (ATCC, HTB-15), PANC1 (ATCC, CRL-1469), MDA-MB-231 (ATCC, HTB-26), HT-1080 (ATCC, CCL-121), NCI-H1650 (ATCC, CRL-5883), A549 (ATCC, CRM-CCL-185) and U-2 OS (ATCC, HTB-96) cells were cultured in RPMI 1640 medium (Gibco, 11875) containing 5% fetal bovine serum (FBS) (Sigma-Aldrich, TMS-013-BKR). HuH-7 (JCRB Cell Bank, JCRB0403), A-172 (ATCC, CRL-1620), Hs 895.T (ATCC, CRL-7637), HeLa (ATCC, CCL-2) and SH-SY5Y (ATCC, CRL-2266) cells were cultured in DMEM (Gibco, 11965) with 5% FBS. All cell lines were grown at 37 °C under 5% CO2. Cells were passaged routinely to maintain around 80% confluency. All cell lines were tested and found to be free of mycoplasma.

RPE-1 cells with ERK2 overexpression

RPE-1 cell lines stably expressing ERK2 and mCherry (control) were generated by lentivirus infection according to a standard protocol. In brief, lentivirus production was performed by HEK-293T transfection with the target construct (ERK2-P2A-eGFP or mCherry), packaging vector (pVSV-G) and envelope plasmid (psPAX2) using FuGENE HD transfection reagent (Promega, E2311), followed by lentivirus infection in RPE-1 cells. To generate the ERK2-P2A-eGFP lentiviral construct, the ERK2 sequence (Addgene, 116760) was subcloned into a lentiviral backbone fused to a P2A-eGFP sequence using a Gateway recombination system (Invitrogen).

Live-cell fluorescence microscopy

Time-lapse imaging experiments were performed using a Zeiss Axio Observer 7 inverted microscope equipped with a X-Cite Xylis (Excelitas Technologies, XT720S) LED illumination system, Definite Focus 2 system and a Prime BSI Scientific CMOS camera (Photometrics), under controlled temperature (37 °C), atmosphere (5% CO2) and humidity (90–100%) in an environmental chamber. Images were taken with 2 × 2 binning using either a Zeiss ×10/0.45 M27 or ×20/0.8 M27 Plan-Apochromat objective. The fluorescence filter sets used for imaging experiments were as follows: Cy5 (Semrock, LED-Cy5-A-000), iRFP (Semrock, Cy5.5-C-000), FITC (Semrock, LED-FITC-A-000) and mCherry (Semrock, LED-mCherry-A-000).

Enhanced nuclear dye fluorescence as a cell death reporter

To simplify imaging experiments, cell death was monitored according to the increased nuclear dye (siR-DNA or siR700-DNA dye) fluorescence that co-occurs with cell rupture (Extended Data Fig. 1a). To further validate this approach, we compared the increase in nuclear dye fluorescence with that of a cell death indicator, Sytox Green (3 nM), during ferroptosis. The increase in nuclear fluorescence consistently occurred 1–2 h earlier than the increase in Sytox Green fluorescence in all dead cells (Extended Data Fig. 1a,b). Sytox Green, siR-DNA and siR700-DNA were imaged using the FITC, Cy5 and iRFP filter sets, respectively.

Comparison of cell death kinetics of different death types in RPE-1 cells

Cells (5.4 × 104 cells per cm2) were seeded on a 96-well μ-plate (Ibidi, 82406) in phenol-red-free RPMI medium with 5% FBS and siR-DNA (1 μM) 1 day before treatment with different death inducers (Extended Data Fig. 1d–j). For the cystine-starvation experiments, cells were washed three times and treated with cystine-free RPMI medium with 5% dialysed FBS (Gibco, 26400-044).

Ferroptosis death kinetics in different cell lines

To obtain the death kinetics of erastin-induced (10 μM) ferroptosis in 16 different cell lines, and RSL3-induced (0.15 μM) ferroptosis in U-2 OS and A549 cells, the cells were seeded at densities of 25% confluency, followed by the indicated treatments after 2 days.

Cell-based assay for ferroptotic trigger waves in RPE-1 cells

Two days before time-lapse imaging, 5.4 × 104 cells per cm2 were seeded on a 24-well μ-plate (IBIDI, 82406) or a 96-well μ-plate coated with Matrigel matrix (Corning, 356231). Cells were grown in DMEM/F12 (Gibco, 21041025) supplemented with physiological levels of holo-transferrin (0.8–1.3 mg ml−1). One day after seeding, the growth medium was replaced with homemade phenol-red-free RPMI with 0.15% FBS and the nuclear dye siR-DNA (1 μM). Cells were treated with erastin (10 μM) the next day, and imaged by fluorescence microscopy. To initiate ferroptotic death propagation, blue-light photoinduction (see the next section for details) was performed 8 h after erastin treatment. Generally, tiled (3 × 3 or 5 × 5) images were collected with a ×10 objective at a 1 h time interval.


For our standard photoinduction experiments, cells were exposed to blue light (Semrock, FF01-432/36-25) using a ×20 objective (60 mW for 10 s), unless otherwise stated. The size of the exposed area (~0.2 mm2) was adjusted with an aperture diaphragm slider. To experimentally test ROS responses after light irradiation at different wavelengths (Extended Data Fig. 3e), we applied different filters (Semrock, FF01-378/52-25, FF01-432/36-25, FF01-474/27-25, FF01-509/22-25, FF01-554/23-25, FF01-578/21-25, FF01-635/18-25) to irradiate cells. A Gigahertz Optik Radiometer (PT-9610) was used to measure light power.

Chemical perturbation of ferroptotic trigger waves

To quantify changes in trigger wave speed after chemical perturbations, we applied chemical inhibitors 11–15 h after photoinduction in 24-well μ-plates. To obtain the dose–response curves of wave speed in response to chemical inhibitors, experiments were performed in 96-well μ-plates into which chemical inhibitors had been added 4 h after photoinduction. To prevent potential toxicity, the final DMSO concentration was kept below 0.1%.

Imaging cellular ROS and lipid peroxidation

To image cellular ROS and lipid peroxidation during ferroptosis propagation, cells were stained with CellROX (0.6 μM) or C11-BODIPY581/591 (1.25 μM), respectively, in phenol-red-free RPMI medium with 0.15% FBS for 30 min. After staining, cells were washed twice with the growth medium before imaging. Filter sets were Cy5 for CellROX, and FITC and mCherry for C11-BODIPY581/591.

Intercellular gap creation

Intercellular gaps were created by scratching the bottom of the plate with needles of different tip sizes (20 μm to 400 μm) after wave initiation.

Characterization of conditioned medium from ferroptotic cells

The cell death induced by conditioned medium from ferroptotic cells was assessed in a similar manner to a protocol described previously27 with some modifications. Specifically, the recipient and donor RPE-1 cells were seeded at 4.5 × 103 cells per cm2 and 5.4 × 104 cells per cm2, respectively, according to the assay described in the ‘Cell-based assay for ferroptotic trigger waves in RPE-1 cells’ section above. Two days after seeding, the donor RPE-1 cells were treated with erastin (10 µM). After 12 h of treatment, when around 50% of cells were dead, erastin was washed out and replaced with erastin-free medium. After 4 h, these conditioned media were collected and pretreated with different ROS scavengers (Trolox, Fer-1, TEMPO and Tiron) (Extended Data Fig. 5b). In a separate experiment (Extended Data Fig. 5c), the conditioned media and H2O2-containing (100 µM) media underwent centrifugal filtration with a molecular mass cut-off of 30 kDa (Amicon ultracentrifugal filter). These ROS-scavenger-treated or filtered conditioned media were transferred to the recipient cells, before undergoing time-lapse imaging. As an erastin-wash control, we used a culture dish without cells to prepare the conditioned medium.

GSH measurement

Total GSH level was measured using the GSH/GSSG-Glo Assay kit (Promega) according to the manufacturer’s protocol. In brief, cells were seeded for 2 days in white-walled 96-well plates (Thermo Fisher Scientific, 136101). Before GSH measurement, cells were treated with erastin for 8 h. Luminescence signals were measured in relative light units using a SpectraMax Paradigm (Molecular Devices) microplate reader at 1 s integration time per well. GSH concentrations were interpolated from the linear range of the standard curve (R2 = 0.99).

Measurement of cellular labile iron

Intracellular labile iron (Fe2+) levels were measured in RPE-1 cells 8 h after erastin treatment (Extended Data Fig. 11c and 11f (bottom)). Cells were stained with FeRhoNox-1 (5 μM) in phenol-red- and FBS-free RPMI medium. After incubation for 1 h, the cells were washed twice with the growth medium, then fixed (4% paraformaldehyde) and imaged. For image analysis, DAPI staining (30 nM) was applied to stain nuclei. FeRhoNox-1 and nuclear DAPI fluorescence signals were acquired using mCherry and DAPI filter sets, respectively. Similarly, to measure iron levels during cell death propagation, cells were stained as described above, and then photoinduced and processed for time-lapse imaging (Extended Data Fig. 6a,b).

Measurement of NOX activity

NOX activities were measured using a lucigenin-derived chemiluminescence assay, as described previously50 with some modifications. After 8 h of erastin treatment, whole-cell homogenates were collected with modified HEPES buffer (140 mM NaCl, 5 mM KCl, 0.8 mM MgCl2, 1.8 mM CaCl2, 1 mM Na2HPO4, 25 mM HEPES, 1% glucose, pH 7) supplemented with phosphatase inhibitor cocktail and protease inhibitor cocktail. After three freeze (−80 °C)–thaw cycles, lucigenin was added to the homogenates to a final concentration of 5 μM and incubated at 37 °C for 30 min in the dark. The homogenates were then added into 96-well plates (equivalent to 2 × 105 cells per well). Immediately before luminescence measurement, 400 μM NADPH was added to each well. Luminescence was measured every 3 min using the EnSpire Multilabel Plate Reader with an integration time of 1 s per well and the temperature was maintained at 37 °C. Data are presented as relative luminescence units after 30 min of recording.

DPPH assay

The antioxidant potential of small molecule inhibitors (GKT137831, LY294002, dasatinib) was determined using a 2,2-diphenyl-1-picrylhydrazyl (DPPH) assay kit (Dojindo) according to the manufacturer’s protocol. The absorbance at 517 nm was measured using the EnSpire Multilabel Plate Reader.

Western blot analysis

Cells were lysed in RIPA buffer supplemented with phosphatase and protease inhibitor cocktails, and then allowed to homogenize on ice for 30 min. Protein lysates were collected from the supernatants after centrifugation at 14,000g for 10 min. After protein quantification using the BCA assay kit (Thermo Fisher Scientific, 23227), protein lysates (15 μg per lane) were mixed with sample buffer and then incubated at 70 °C for 10 min before loading. Proteins were separated by 10% SDS–PAGE and blotted onto PVDF membranes (Millipore, IPFL85R). After blocking with 5% bovine serum albumin at room temperature for 30 min, the membranes were incubated with primary antibodies against ERK (1:2,000, Cell Signaling Technology, 9102) and phosphorylated-ERK (1:1,000, Cell Signaling Technology, 9106S) at 4 °C overnight, followed by incubation with secondary antibodies (IRDye 680RD goat anti-mouse IgG, LiCOR, 926-68070; IRDye 800CW donkey anti-rabbit IgG, LiCOR, 925-32213) at room temperature for 1 h. The bands were visualized using the Typhoon laser scanner. Finally, the membranes were stained with Ponceau S to validate the transfer efficiency and to quantify protein loading.

RT–qPCR analysis

Total RNA was extracted with TRIzol reagent (Invitrogen, 15596018) and reverse transcribed using the iScript cDNA synthesis kit (Bio-Rad, 1708891). Quantitative PCR with reverse transcription (RT–qPCR) was performed with iTaq Universal SYBR Green (Bio-Rad, 1708882) and monitored with a BioRadCFX96 system equipped with CFX Maestro software 2.3 (v. The primers for qPCR were as follows: NOX1, fw: 5′-GTCTGCTCTCTGCTTGAAT-3′, rv: 5′-ATGAGATAGGCTGGAGAG-3′; NOX2, fw: 5′-CCCTTTGGTACAGCCAGTGAAGAT-3′, rv: 5′-CAATCCCGGCTCCCACTAACATCA-3′; NOX3, fw: 5′-ATGAACACCTCTGGGGTCAGCTGA-3′, rv: 5′-GGATCGGAGTCACTCCCTTCGCTG-3′; NOX4, fw: 5′-CAGAAGGTTCCAAGCAGGAG-3′, rv: 5′-GTTGAGGGCATTCACCAGAT-3′.

TUNEL staining of chicken limbs

No ethical approval was required for experiments on chicken embryos at the desired Hamburger–Hamilton (HH) stage51 30–33. Fertilized Leghorn chicken eggs were incubated at 37.5 °C in a humidified incubator. Chicken hindlimbs were dissected and fixed for 12 h with 4% paraformaldehyde. The terminal deoxynucleotidyl-transferase-mediated dUTP-TRIC nick-end labelling (TUNEL) assay was performed using the In Situ Cell Death Detection Kit (Roche) according to the manufacturer’s protocol. In brief, limbs and tissue sections were permeabilized at 37 °C with 2% Triton X-100 in PBS for 12 h. Antigen retrieval was performed by incubating in 0.1 M sodium citrate with 0.1% Triton X-100 in PBS at 70 °C for 30 min. TUNEL staining was conducted at 37 °C for 1 h, followed by imaging under the Zeiss LSM980 confocal microscope equipped with Zen Blue software (v.3.8). For tissue sections (Extended Data Fig. 12b,c), limbs were sliced to a thickness of 200 µm using a vibratome. Immunostaining was applied to the tissue sections (see the ‘Immunostaining of chicken limbs’ section below), followed by double-labelling with TUNEL.

Immunostaining of chicken limbs

Chicken limbs were fixed for 12 h with 4% paraformaldehyde at the indicated embryonic stages. For immunostaining of tissue sections, limbs were sliced to a thickness of 200 µm using a vibratome. Limbs and tissue sections were permeabilized with 2% Triton X-100 in PBS for 12 h. After permeabilization, blocking was conducted for 8 h with 10% FBS in PBS, followed by incubation with primary antibodies for 2 days, and with secondary antibody for 12 h in 2% Triton X-100 in PBS with 20% DMSO, unless otherwise specified. Whole-mount immunostaining of 4-HNE (Fig. 5c) was done in 0.5% Triton X-100 in PBS. All of the incubation steps were performed at room temperature. Imaging was conducted under the Zeiss LSM980 confocal microscope.

The following primary antibodies were used: anti-4-HNE (1:250, Abcam, ab46545; and 1:250, Abcam, ab48506) and anti-myosin heavy chain (2 µg ml−1, Developmental Studies Hybridoma Bank, MF20). The following secondary antibodies were used: goat anti-rabbit IgG Alexa Fluor Plus 488, goat anti-mouse IgG Alexa Fluor Plus 647 and goat anti-rabbit IgG Alexa Fluor 568 (1:500, Invitrogen, A32731, A32728, A11036). The results of 4-HNE staining using anti-4-HNE (Abcam, ab46545) antibody was further validated with an additional anti-4-HNE antibody (Abcam, ab48506) in 2% Triton X-100 in PBS with 1% FBS.

Time-lapse imaging of cell death in chicken limb ex vivo

Chicken limbs were dissected at stage HH31 and cultured in DMEM/F12 with 5% FBS and siR-DNA (5 μM). For imaging purposes, limbs were anchored to the bottom of the glass-bottomed plate (Mattek, P24G-1.0-13-F) by applying silicon glue (Picodent Twinsil, 13001000) to the farthest proximal region of the limb. To further stabilize the limb, we added a cover glass above the distal region of the limb. Time-lapse imaging experiments were performed using a Zeiss LSM980 confocal microscope or a Zeiss Axio Observer 7 inverted microscope under controlled temperature (35 °C), atmosphere (5% CO2) and humidity (90–100%). Cell death was detected as increased fluorescence signal of siR-DNA dye, as described above. Images were taken every 1.5 h with a 639 nm laser (LSM980) and Cy5 filter set (Axio Observer 7) using the Zeiss ×10/0.45 M27 Plan-Apochromat objective.

In ovo injection of ferroptosis inhibitor UAMC-3203

In ovo injection into the amniotic sac was conducted on stage HH30 embryos. Egg candling was performed to locate the target amniotic sac, and a hole was created using a 26 G 1/2 needle. Solutions of UAMC-3203 (4 mM) and DMSO (vehicle control) were prepared in saline (0.9% sodium chloride), and 120 µl of either solution was injected into the amniotic sac using a 26 G 1/2 needle. The success rate (>90%) of in ovo injection into the amniotic sac was determined by trial injections of a food dye solution. Chicken limbs were dissected at stage HH33 and fixed with 4% paraformaldehyde, before undergoing immunostaining.

PALP assay

PALP assays44 were performed using the Zeiss LSM980 confocal microscope equipped with Chameleon Ultra (Coherent) for two-photon laser excitation. Specific circular areas (98 μm2) were stimulated by an 800 nm two-photon laser at 5% power output with eight iterations (scan speed = 7 fps; pixel time = 0.51 μs). To acquire images for C11-BODIPY fluorescence, 488 nm and 561 nm lasers were used.

Computation of the travelling distances of diffusive molecules

The travelling distances for diffusive molecules in Fig. 1e were calculated using the diffusion equation \(d=\sqrt{2Dt}\), where d is the distance, D is the diffusion coefficient and t is time (D of calcium = 200 µm2 s−1 and D of a small globular protein = 10 μm2 s−1).

Summary of image processing and data analysis

The image preprocessing procedures—including flatfield correction, ratiometric image calculation, image alignment and stitching of tiled images—were implemented using ImageJ (v.1.54 f). For image presentation, raw images were median-filtered with a circular area of 20 μm2.

Wave outlines, representing the boundaries of wave propagation, were generated by identifying the top 1% of the image’s fluorescence intensity by image binarization, followed by pixel dilation and mean filtering to visualize wavefronts of cell death (Fig. 1b,c), lipid peroxidation (Fig. 1g,h) and ROS (Fig. 2a and Extended Data Fig. 4a,b). The wavefronts of lipid peroxidation and ROS represent the increase in their signals, obtained by the fluorescence intensity difference between two consecutive images along time. Size filters were applied to exclude debris from analysis.

Fluorescence intensities of cell death, lipid peroxidation (Fig. 1f (bottom)) and cellular ROS (Extended Data Fig. 4a (bottom)) across space were obtained by calculating the mean signal intensities along the indicated distance with width (250 μm), and normalizing to their minimum and maximum intensities. The same procedure was done for quantifying ROS across space in Fig. 2a, but without signal normalization. The mean fluorescence intensities were smoothed with a window size of 50 μm.

To analyse the spatial and temporal patterns of cell death events, vector fields (Extended Data Fig. 1c) were constructed from the cell death outlines described above. The vectors, which indicate the directionality between death events, were generated based on two consecutive cell death outlines using the gradient function in MATLAB (v.R2023b). As an index to quantify spatial and temporal associations between death events, we computed the entropy of the vectors’ angle distribution along different directions from an initial cell death event. Specifically, a distribution of vectors along a specific direction was obtained from the initial death event to the next successive death events across 3 h within its neighbourhood (typically 100 μm × 350 μm). The entropy of the vectors was calculated as \(H=-{\sum }_{i=1}^{30}{p}_{i}{\log }_{2}{p}_{i}\), where pi is the frequency that the angle of vector falls in the ith bin (30 bins in 360°).

Kymographs were generated using an array of cropped images of the fluorescent signals (cell death, lipid peroxidation, ROS or iron) along the direction of wave propagation (y axis). For each cropped image, the value for each pixel on the y axis represents the maximum signal along its width (250 μm). This operation was repeated on each cropped image for all timepoints, and the intensity lines were stacked along the x axis. For speed measurement, we first marked the earliest time for each position on the y axis that the threshold of fluorescence signals was reached (defined as the top 10% of the signal intensity for the kymograph). This yielded a distribution of spatial locations representing the wavefront for each timepoint. The top 11 locations closest to the mode of the distribution at each timepoint were used to estimate the wave speed using the polyfit function in MATLAB.

To characterize the ferroptosis initiation sites (Extended Data Fig. 2), a threshold-based segmentation was initially applied to binarized bright-field images to identify dead cells. We define a ferroptosis initiation site as the area where: (1) >5 dead cells are initially found within a circle of 40 μm radius, and (2) the cell death area increases (less than 20-fold) over time. All automatically identified initiation sites were manually inspected to eliminate false-positive sites (such as debris). In total, 761 ferroptosis initiation sites across 756 positions (area of 1.26 × 1.26 mm2) were identified over a 5 h period. The distribution of the number of ferroptosis initiation sites was then compared with a Poisson distribution with the same mean (1.01 initiation events per 5 h) with P = 1 using a two-sample Kolmogorov–Smirnov test. To examine the distribution of time interval between two consecutive initiation events, we randomly combined the 756-time series of ferroptosis initiation events to calculate the time interval distribution. When compared with a geometric distribution with the same mean (5.16 h), we determined a P = 0.23 using a two-sample Kolmogorov–Smirnov test.

The dose–response curves in Fig. 3j–n were obtained by fitting the data to a Michaelian inhibition function, \(y={y}_{0}+(\,{y}_{M}{-y}_{0})\frac{K}{K+x}\), for DFO, LY294002 and GKT137831; to a Michaelian activation function, \(y={y}_{0}+(\,{y}_{M}{-y}_{0})\frac{x}{K+x}\), for FC; and to a biphasic inhibition function, \(y={y}_{0}+{y}_{M}\left(1-{f}_{1}\frac{x}{{K}_{1}+x}-(1-{f}_{1}\,)\frac{x}{{K}_{2}+x}\right)\), for dasatinib49, where y is the trigger wave speed, x is the drug concentration, and all of the other parameters are determined by model fitting.

In Fig. 4c, the ROS levels in individual cells were quantified 1 h before and after photoinduction using a semi-automatic cell tracking program, as described previously41. The slope of increased ROS was computed as an estimate for the ROS steady state.

The mean intensities of ROS and iron dye fluorescence (Extended Data Fig. 11c,e) were quantified in whole cells by nuclear segmentation using the ImageJ StarDist plugin, followed by nuclear dilation 7 pixels from the nuclear border. Size filtering was applied to exclude incorrect segmentation and dividing cells.

The widths and amplitudes of a ROS wavefront (Fig. 4f,g) were measured as the distances and the maximal intensities of ROS signal between two consecutive ROS outlines in multiple directions.

Maximum intensity projections of confocal (Fig. 5a–d,g,h,j and Extended Data Fig. 12) and epifluorescence (Fig. 5e) image stacks were obtained using the ImageJ Stack Focuser plugin. The margins of the limbs were outlined by threshold-based segmentation.

To quantify the co-localization of degenerating muscles (myosin heavy chain-positive and rounded cells) with 4-HNE, the images were initially binarized on the basis of the thresholds of their respective backgrounds, which enabled identification of signal-positive regions. The binary images of degenerating muscles were then used to construct 3D objects using the regionprops3 function in MATLAB, followed by dilation (3 μm from the object). The percentage of 4-HNE colocalization with the degenerating muscles was calculated as the ratio of the number of 4-HNE-positive degenerating muscles to the total number of degenerating muscles.

For the images in Fig. 5j, 3D median filter and background subtraction was applied using ImageJ. To further remove the background signals, threshold-based 3D surface segmentation was performed in Imaris (v.10.0.1). To quantify the numbers of muscle fibres and their orientations (Extended Data Fig. 12i,j), we better visualized the fibre structures by applying a tubeness filter (ImageJ), followed by ridge detection (ImageJ) to identify individual muscle fibres. The muscle fibre count (Extended Data Fig. 12i) represents the total number of detected fibres across all z stacks encompassing the ventral foot muscles. The muscle fibre orientations were determined using the ImageJ OrientationJ plugin and are colour coded in Fig. 5j. To quantify the entropy of the fibre orientations, fibres within a 900 μm2 area were considered, and the entropy of the fibre orientations was calculated as \(H=-{\sum }_{i=1}^{90}{p}_{i}{\log }_{2}{p}_{i}\), where pi is the frequency with which the fibre orientation falls in the ith bin (90 bins from 0° to 180°).

In Fig. 5h,i, lipid peroxidation was quantified using the following formula: \(\frac{{\rm{O}}{\rm{x}}{\rm{i}}{\rm{d}}{\rm{i}}{\rm{z}}{\rm{e}}{\rm{d}}\,{\rm{C}}11-{\rm{B}}}{{\rm{O}}{\rm{x}}{\rm{i}}{\rm{d}}{\rm{i}}{\rm{z}}{\rm{e}}{\rm{d}}\,{\rm{C}}11-{\rm{B}}+{\rm{r}}{\rm{e}}{\rm{d}}{\rm{u}}{\rm{c}}{\rm{e}}{\rm{d}}\,{\rm{C}}11-{\rm{B}}}\). The mean intensities of lipid peroxidation were quantified at the laser target sites before and after photoinduction.

The wave speed in Fig. 5e was measured by generating kymographs as described above. To quantify the area of cell death in Fig. 5f, a threshold was applied to identify the area of cell death, which was normalized to the total limb area. For image presentation in Fig. 5e, the debris outside the limb were threshold-filtered followed by manual removal.

Computational modelling of ROS trigger waves

We developed a reaction–diffusion model to model propagation of ROS trigger waves. Two types of ROS feedback loops were considered, that is, positive-feedback loops (through NOX and Fenton loops) and a double-negative feedback loop (through GSH). For simplicity, we modelled the two positive-feedback loops as a single term. The resulting partial differential equation is:

$$\begin{array}{c}\frac{{\rm{\partial }}{\rm{R}}{\rm{O}}{\rm{S}}}{{\rm{\partial }}t}=D\frac{{{\rm{\partial }}}^{2}{\rm{R}}{\rm{O}}{\rm{S}}}{{\rm{\partial }}{x}^{2}}+\mathop{\bar{{k}_{{\rm{p}}{\rm{o}}{\rm{s}}{\rm{i}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}\frac{{{\rm{R}}{\rm{O}}{\rm{S}}}^{{n}_{{\rm{p}}{\rm{o}}{\rm{s}}{\rm{i}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}}}{{\rm{E}}{\rm{C}}{50}_{{{\rm{p}}{\rm{o}}{\rm{s}}{\rm{i}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}^{{n}_{{{\rm{p}}{\rm{o}}{\rm{s}}{\rm{i}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}}+{{\rm{R}}{\rm{O}}{\rm{S}}}^{{n}_{{{\rm{p}}{\rm{o}}{\rm{s}}{\rm{i}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}}}}}\limits^{\text{positive-feedback loop}}\,-\mathop{\overline{{k}_{{\rm{d}}-{{\rm{n}}{\rm{e}}{\rm{g}}{\rm{a}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}\left({c}_{{\rm{G}}{\rm{S}}{\rm{H}}}+\frac{{{\rm{E}}{\rm{C}}50}_{{\rm{e}}{\rm{r}}{\rm{a}}{\rm{s}}{\rm{t}}{\rm{i}}{\rm{n}}}}{{{\rm{E}}{\rm{C}}50}_{{\rm{e}}{\rm{r}}{\rm{a}}{\rm{s}}{\rm{t}}{\rm{i}}{\rm{n}}}+E}\right)\frac{EC{50}_{{\rm{d}}-{{\rm{n}}{\rm{e}}{\rm{g}}{\rm{a}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}^{{n}_{{\rm{d}}-{{\rm{n}}{\rm{e}}{\rm{g}}{\rm{a}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}}}{{{\rm{E}}{\rm{C}}50}_{{\rm{d}}-{{\rm{n}}{\rm{e}}{\rm{g}}{\rm{a}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}^{{n}_{{\rm{d}}-{{\rm{n}}{\rm{e}}{\rm{g}}{\rm{a}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}}+{{\rm{R}}{\rm{O}}{\rm{S}}}^{{n}_{{\rm{d}}-{{\rm{n}}{\rm{e}}{\rm{g}}{\rm{a}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}}}{\rm{R}}{\rm{O}}{\rm{S}}}}\limits^{\text{double-negative-feedback loop}}\\ \,\,-{k}_{{\rm{d}}{\rm{e}}{\rm{g}}}{\rm{R}}{\rm{O}}{\rm{S}}+{k}_{{\rm{s}}{\rm{y}}{\rm{n}}{\rm{t}}{\rm{h}}}\end{array}$$

where ROS denotes the cellular ROS level and E denotes the erastin concentration. The parameters were as follows: D = 178 μm2 min−1, \({k}_{{{\rm{p}}{\rm{o}}{\rm{s}}{\rm{i}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}\) = 1.2 μM min−1, \({{\rm{E}}{\rm{C}}50}_{{{\rm{p}}{\rm{o}}{\rm{s}}{\rm{i}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}\) = 1 μM, \({n}_{{{\rm{p}}{\rm{o}}{\rm{s}}{\rm{i}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}\) = 3, \({k}_{{\rm{d}}-{{\rm{n}}{\rm{e}}{\rm{g}}{\rm{a}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}\)= 1.5 min−1, cGSH = 0.1, EC50erastin = 0.27μM, \({{\rm{E}}{\rm{C}}50}_{{\rm{d}}-{{\rm{n}}{\rm{e}}{\rm{g}}{\rm{a}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}\) = 2 μM, \({n}_{{\rm{d}}-{{\rm{n}}{\rm{e}}{\rm{g}}{\rm{a}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}\) = 3, kdeg = 0.26 min−1 and ksynth = 0.1 μM min−1.

The ROS positive and double-negative feedback loops were modelled as hyperbolic functions with Hill coefficients (\({n}_{{{\rm{p}}{\rm{o}}{\rm{s}}{\rm{i}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}\) and \({n}_{{\rm{d}}-{{\rm{n}}{\rm{e}}{\rm{g}}{\rm{a}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}\)) equal to 3. The impact of erastin on the ROS double-negative feedback loop follows a hyperbolic response, with EC50erastin = 0.27 μM. cGSH represents the basal production of GSH independently of cystine import.

In our simulations, the diameter of a cell was assumed to be 16 µm with an intercellular distance of 5 µm. To simulate the initiation of ROS trigger waves, we allowed all cells to first reach their lower ROS steady states as a function of erastin concentration. A local ROS elevation (photoinduction area = 0.2 mm2) was simulated to surpass the USS threshold, mimicking blue light irradiation in the initiating cells (Fig. 4a (blue arrow)). When the USS threshold was surpassed, ROS underwent a bistable switch to its higher steady state (Fig. 4a (red arrow)). We defined the ROS threshold for cell death to be 90% of the higher steady state. After reaching this ROS threshold for 30 min, ROS production was stopped by setting \({k}_{{{\rm{p}}{\rm{o}}{\rm{s}}{\rm{i}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}\), \({k}_{{\rm{d}}-{{\rm{n}}{\rm{e}}{\rm{g}}{\rm{a}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}-{\rm{f}}{\rm{b}}}_{}}\) and ksynth to be zero, representing cell death.

Reproducibility and statistical analysis

All experiments were independently performed at least three times with similar results. Technical repeats were performed in independent wells, and all the data from technical repeats are consistent across different biological replicates. The number of biological replicates is indicated in the figure legend as n. Details of statistical testing can be found in the corresponding figure legends. Wilcoxon rank-sum tests and the two-sample Kolmogorov–Smirnov tests were conducted in MATLAB. The wave propagation probability (Fig. 2b) was obtained by fitting the data to a logistic model using the fitglm function in MATLAB. The dose–response curves (Fig. 3j–n) were obtained by fitting the data to hyperbolic functions (indicated in the Methods above) using the nlinfit function in MATLAB.

Data reporting

No statistical method was used to predetermine sample size. For the animal experiment in Fig. 5f, the left and right limbs of an individual animal were randomly allocated in control and experimental groups. For Fig. 5j and Extended Data Fig. 12h,i, animals were randomly allocated in control and experimental groups. Investigators were not blinded during data collection. However, data quantification was performed automatically using computational algorithms as described.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

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