Human liver tissues
Table of Contents
All human samples were de-identified and exempted (exemption 4). Human liver samples were obtained from the Stanford Diabetes Research Center (SDRC), Donor Network West (DNW), Stanford Tissue Bank and Clinical Biospecimen Repository and Processing Core (CBRPC) of the Pittsburgh Liver Research Center (PLRC). This was approved by Stanford University Institutional Review Board (IRB, 67378) and the Pittsburgh Liver Research Center Review Board. Histology was evaluated for necroinflammation, hepatocellular ballooning, ductular reaction and fibrosis by a hepatopathologist in a blinded manner, and non-alcoholic fatty liver disease activity score (NAS) scores were provided. Detailed information about the donors, including sex, age, diagnosis and NAS score, are summarized in Supplementary Table 1.
Animal studies
All animal experiments were conducted according to the experimental procedures approved by the Institutional Animal Care and Use Committee at Stanford University and Palo Alto VA. Mice were maintained at temperatures and humidity ranges of 20 to 26 °C and 30% to 70%, respectively. Mice were housed in standard cages under 12 h–12 h light/dark cycles with ad libitum access to water and food unless otherwise indicated. Mice were placed on control chow or a FFD (17.4% protein, 20% fat and 49.9% carbohydrate, AIN-76A) supplemented with high-fructose corn syrup in the drinking water at a final concentration of 42 g l−1 for up to 14 weeks, or HiAD (prepared by cooking FFD at 120 °C for 20 min) as previously described49 supplemented with high-fructose water. Wild-type C57BL/6J male mice (aged 8 to 10 weeks) were purchased from the Jackson Laboratory. RAGEfl/fl mice on the C57B6 background were gifted by B. Arnold. RAGEHepKO mice were generated by crossing RAGEfl/fl mice with Albumin-cre mice (Jackson Laboratory) for several generations. Male RAGEfl/fl mice and RAGEHepKO mice aged 8 to 10 weeks were used. To generate hepatocyte transgenic AGER1 (Ddost) mice, wild-type mice were injected with adeno-associated virus 8 (AAV8)-control green fluorescent protein (AAV8-control) or AAV8-thyroxine-binding globulin-AGER1 recombinase (AAV8-AGER1) (5 × 1011 genome copies, Vector BioLabs) at the end of week 5 of feeding (the rationale of the specific targeting in hepatocyte has been previously reported)50. To study the inhibition of AGE formation or AGE–protein cross-linking, wild-type mice fed with HiAD were injected intraperitoneally daily with pyridoxamine hydrochloride (Sigma-Aldrich) (60 mg per kg, daily)51, alagebrium (ALT-711) (Sigma-Aldrich, 1 mg per kg)52,53 or vehicle (Tris-HCl), from the fifth week of feeding. At the time of euthanasia, photographs of the livers were taken, and the number and the size of lesions on the surface were recorded.
Hydrodynamic tail vein injection and plasmid preparation
Oncogenic plasmids were delivered to the mouse liver by hydrodynamic tail vein injection as previously described20. In brief, pT3-EF1α-h-hMET, pT3-EF1αh-WT-β-catenin-MYC-tag, pT3-EF1α-h-S45Y-mutant-β-catenin-MYC-tag and pCMV/SB transposase were from S. P. S. Monga’s laboratory. Plasmids used for in vivo experiments were purified using the Invitrogen Endotoxin-free Maxi prep kit (Sigma-Aldrich). A combination of 20 µg of pT3-EF5-hMET and 20 µg of pT3-EF5α-WT-β-catenin-MYC or pT3-EF5α-S45Y-β-catenin-MYC, along with 1.6 µg of SB (25:1) was diluted in 1 ml of endotoxin-free saline (AdipoGen), filtered through 0.22 mm filter (Millipore), and injected into the tail vein of mice in 5 to 7 s at the at the end of week 7 of chow, FFD or HiAD feeding. To inhibit YAP activity, the mice were injected with dn-TEAD2 (pT3-EF1α-h-dnTEAD2, 60 µg)54 or negative control vector (empty pT3-EF1α, 60 µg), (from S. P. S. Monga’s laboratory) by hydrodynamic tail vein injection at the end of week 7 of chow or HiAD feeding with hMET, S45Y-mutant-β-catenin and SB. To knockdown TNS1, mice were injected with a CRISPR–Cas9-based vector linking two sgRNAs targeting Tns1 exon 1 and exon 7 (pX333-TNS1, 50 µg) or negative control vector (empty pX333, 50 µg) by hydrodynamic tail vein injection at the end of seventh week of chow or HiAD feeding at the same time as with hMET, S45Y-mutant-β-catenin and SB. The sequences of the sgRNAs used in this study are provided in Supplementary Table 2.
Mice were monitored 3 days per week for any sign of pain or distress, and the body weight and body condition score were evaluated after hydrodynamic tail vein injection. The mice were immediately euthanized if they lost more than 10% of their body weight or if they had a body condition score of 2 or less during that time. The tumour size (macroscopic) never reached more than 3 mm.
Histology, immunohistochemistry and early focus quantification
Paraffin-embedded tissue samples were cut into 5 µm sections, deparaffinized and rehydrated. For antigen retrieval, slides were boiled in citrate buffer (0.01 M, pH 6.0) using a microwave oven on high power for 5 min and cooled down to room temperature. After incubation in 3% aqueous H2O2 to quench the endogenous peroxidase, the sections were washed in PBST (PBS with 0.1% Tween-20, v/v) washing buffer, blocked with 5% goat serum (EMD Millipore) diluted in PBST at room temperature for 1 h and incubated with primary antibodies diluted in 2% goat serum in PBST at 4 °C overnight.
For immunohistochemistry, slides were incubated with appropriate biotinylated secondary antibodies (Supplementary Table 3) for 1 h, and then processed according to the ABC Peroxidase Standard Staining Kit (Thermo Fisher Scientific) for 30 min. The slides were stained with 3,3′-diaminobenzidine (Abcam) for 5 s to 5 min and counterstained with haematoxylin (Thermo Fisher Scientific) for 45 s. The images were scanned using the Leica Aperio AT2 system at Stanford Human Pathology/Histology Service Center. Serial sections were incubated with GS and MYC-tag primary antibodies, and a cluster of cells (at least 20 cells) positive both for GS and MYC-tag were counted as early foci. The antibodies used in this study are shown in Supplementary Table 3.
Measurement of AGE content
AGEs were measured using the OxiSelect Advanced Glycation End Product Competitive ELISA Kit (Cell Biolabs) in the serum and the liver homogenate according to the manufacturer’s instructions. In brief, 10 mg liver samples were homogenized in PBS. After measuring the protein concentration, 300 µg protein was added to a 96-well ELISA plate and incubated for 1 h at room temperature. After incubation with the secondary HRP-conjugated anti-AGE antibodies, the reaction was halted with a stop solution, and the plates were read at 450 nm.
RNA extraction, reverse transcription and RT–qPCR
According to the manufacturer’s recommendations, total RNA was extracted from snap-frozen liver tissues and cells using the RNeasy mini kit (Qiagen). Complementary cDNA was created from an identical amount of RNA using the iScript cDNA synthesis kit (Bio-Rad). The PowerUp SYBR Green PCR Master Mix (Applied Biosystems) was used for quantitative PCR with reverse transcription (RT–qPCR) on the 7900HT machine (Applied Biosystems), and the data were evaluated using the 2−Ct technique. As an endogenous control, Arbp (also known as Rplp0) and GAPDH were used to standardize the data in mouse and human, respectively. A list of the primer sequences used in this study is provided in Supplementary Table 4.
AFM
Measurements on frozen liver tissues were performed on livers embedded in OCT compound (Sakura), snap frozen by direct immersion into liquid nitrogen and cut into 100 μm sections on the Leica CM1900-13 cryostat. The samples were kept in a protease inhibitor cocktail during the AFM analyses (Roche Diagnostic). For the hydrogel mapping collagen or AGE-modified collagen was neutralized with 5× DMEM and 1× NaOH and the hydrogels were kept overnight on 37 °C. The Bruker Resolve BioAFM system was used to take measurements (Bruker). For the indentation, Novascan Tech modified silicon nitride cantilevers (k = 0.01 N m−1, k = 0.06 N m−1) with a borosilicate glass spherical tip (diameter 10 and 5 μm, respectively) were used.
For each session, cantilevers were calibrated using the thermal oscillation method. AFM force maps were performed on 94.7 μm × 94.7 μm fields. Each experimental group included at least four different human or mouse samples, with two sections from each, and three different areas generated per section. For hydrogel mapping, each group included at least four different gels, and five different areas generated per gel. Data analyses were performed using the Hertz model in NanoScope Analysis v.1.9. and Mountains SPIP v.9.
Rheometry analysis of the human and mouse livers
Measurements were optimized to assess storage modulus, loss modulus, loss tangent and stress relaxation based on methods previously described55. In brief, liver samples were prepared using an 8 mm diameter punch (Integra Miltex). The height of the slices ranged from 3 to 5 mm in the uncompressed state. The samples were kept hydrated during all of the experiments with DMEM. Parallel plate shear rheometry was performed on the ARES-G2 rheometer (TA instruments) at room temperature using TA TRIOS software v.5.1.1 (TA instruments). For all of the measurements, the upper plate was initially lowered to touch the sample, and 0.01 N of nominal initial force (~300 Pa) was applied to ensure adhesive contact of the sample with the plates. Measurements were taken first with a dynamic time sweep test (2% constant strain, oscillation frequency 1 radian s−1, measurements taken for 600 s), then stress relaxation (10% initial strain, measurements taken for 600 s).
Measurement of total and insoluble collagen
The hydroxyproline assay for total liver collagen was performed as previously described56. In brief, liver samples were homogenized and denatured in 6 N HCl. Hydrolysed samples were then dried and washed three times with deionized water, followed by incubation in 50 mM chloramine T oxidation buffer for 20 min at room temperature. The samples were incubated with 3.15 M perchloric acid (Sigma-Aldrich) for 5 min, then with p-dimethylaminobenzaldehyde (Sigma-Aldrich). The absorbance of each sample was measured.
For insoluble collagen, the liver or collagen gel was first homogenized in 0.5 M acetic acid at a 1:4 ratio (for example, 800 μl for 200 mg liver) to make 20% liver homogenate. Next, 500 μl of 20% liver homogenate was added onto 1 ml of 0.5 M acetic acid and the tubes rotated at 4 °C overnight. The samples were centrifuged at 20,000g for 30 min to collect the pellet, resuspended in pepsin (2 mg ml−1 in 0.5 M acetic acid) and incubated at 4 °C overnight. The next day, the samples were centrifuged and the pellets were collected. The samples were then analysed using the hydroxyproline assay, described previously56.
Preparation of AGE-BSA
AGE-BSA was prepared as previously described57,58. In brief, glycolaldehyde (Sigma-Aldrich) was dissolved in 10 mg ml−1 BSA/PBS to a final concentration of 33 mM. The solutions were incubated at 37 °C for 72 h, followed by dialysis against PBS. The dialysed solutions were sterilized with 2 µM filters, and aliquots were stored at −80 °C.
Preparation of AGE-modified collagen and gels
Collagen type I (telopeptide intact, Corning, 354236, Corning collagen I, rat tail, used in all experiments) was incubated with 2.5 mg ml−1 in AGE-BSA 0.1% acetic acid (Merck) to obtain 3 mg ml−1 collagen solution at 4 °C for 4 weeks. BSA was mixed with collagen as the control. Alagebrium chloride (ALT-711, 20 mg ml−1) was added as the AGE cross-linking inhibitor. Collagen gels were polymerized by mixing 3 mg ml−1 AGE-modified or non-modified collagen solution with 10× PBS and neutralized with 1× NaOH (Merck) and incubated at 37 °C for 90 min leading to the formation of gels. For most gels, 1.6 mg ml−1 collagen was used.
Alginate preparation
According to the manufacturer, low-molecular-mass, ultrapure sodium alginate (Provona UP VLVG, NovaMatrix) with a molecular mass of <75 kDa was used for fast-relaxing substrates. For slow-relaxing substrates, sodium alginate (high molecular mass) was used (FMC Biopolymer, Protanal LF 20/40, high molecular mass, 280 kDa). Alginate was treated with activated charcoal, dialysed against deionized water for 3–4 days (molecular mass cut-off, 3,500 Da), sterile-filtered, lyophilized and then reconstituted to 3.5 wt% in serum-free DMEM (Gibco). The use of low/high-molecular-mass alginate resulted in high/low viscoelasticity IPNs.
Imaging of collagen fibrils
Mouse livers were decellularized in situ by detergent (0.5% (w/v), sodium deoxycholate, 250 ml per mouse) and water (50 ml per mouse) perfusion at a pump speed of 0.2 ml min−1. After the final perfusion, the livers were removed and washed overnight in PBS. For AGE-modified collagen gels, the samples were prepared as previously described. Gels were imaged 1 day after formation.
For SHG imaging, all of the samples were imaged using the Leica TCS SP5 multiphoton confocal microscope or the Leica Stellaris 8 DIVE upright confocal microscope. The excitation wavelength was tuned to 840 nm, and a 420 ± 5 nm narrow band-pass emission controlled by a slit was used for detecting the SHG signal of collagen. The images were recorded using an inverted confocal laser-scanning microscope (Leica TCS SP8) equipped with a ×20 water-immersion objective for confocal reflection imaging. An Ar+ laser at 488 nm was used to illuminate the sample, and the reflected light was detected with photomultiplier tube (PMT) detectors. Scans were at 1,024 × 1,024 pixels, and all of the images were taken 80–100 μm into the samples. Collagen measurements were performed using CT-Fire software (v.2.0 beta) (https://loci.wisc.edu/software/ctfire) and ImageJ v.1.53t (https://imagej-nih-gov.stanford.idm.oclc.org/ij/).
IPN 3D hydrogel formation
Alginate was transferred to a 1.5 ml Eppendorf tube (a polymer tube) and kept on ice for each viscoelastic gel. For rBM-IPNs, alginate was mixed 30 times before adding rBM (Corning) at 4 °C. Collagen-IPNs were created by diluting and neutralizing AGE-modified or AGE-unmodified collagen gels with 10× DMEM and 1 M NaOH (Merck) at 4 °C. All substrates had a final concentration of 10 mg ml−1 alginate, 4.4 mg ml−1 rBM or 1.6 mg ml−1 collagen after additional DMEM was added. This was pipette-mixed, and the resulting mixture was kept on ice. Calcium sulfate was added to 1 ml Luer lock syringes (Cole-Parmer) and stored on ice to maintain the constant Young’s moduli of the substrates with high and low viscoelasticity. The polymer mixes were divided into individual 1 ml Luer lock syringes (polymer syringes) and placed onto ice as well. The polymer syringe was linked to the calcium sulfate syringe to create gels. The two solutions were quickly combined using 30 pumps on the syringe handles, and the resulting mixture was placed into a well of an eight-well Lab-Tek plate (Thermo Fisher Scientific) that had been precoated with rBM. After moving the Lab-Tek dish to a 37 °C incubator, the gel was allowed to form for 1 h before a full medium was added.
Mechanical characterization of IPNs
Rheology experiments were performed using a stress controlled AR2000EX rheometer (TA Instruments). IPNs were directly deposited onto the lower Peltier plate for rheology testing. The gel was then slowly contacted by a 25 mm flat plate, creating a 25 mm disk gel. To stop dehydration, mineral oil (Sigma-Aldrich) was applied to the gel’s edges. The storage and loss moduli had equilibrated by the time the time sweep was done, which was at 1 rad s−1, 37 °C and 1% strain.
For the stress relaxation experiments, after the time sweep, a constant strain of 5% was applied to the gel at 37 °C, and the resulting stress was recorded over the course of 4 h.
Cell culture, transfection and CRISPR–Cas9-mediated TNS1 and integrin β1 knockdown
Human HCC cell lines Huh7 (gift from P. Sarnow) and Hep3B (purchased from ATCC) were cultured in high-glucose DMEM (Gibco) with 10% fetal bovine serum (FBS, Gibco) with 1% penicillin–streptomycin (Life Technologies). All cells were cultured at 37 °C in 5% CO2.
TNS1 was knocked down in Huh7 and Hep3B cells using TNS1 sgRNAs or integrin β1 sgRNAs. A control sgRNA sequence was used as the negative control. sgRNAs were cloned into pMCB306 (Addgen plasmid 89360, sgRNA expression vector with GFP, puromycin resistance), then co-transfected into cells with lentiCas9-Blast (Addgen plasmid 52962, expresses human codon-optimized Streptococcus pyogenes Cas9 protein and blasticidin resistance from the EFS promoter). Transfected cells were selected by puromycin and tested for TNS1 or integrin β1 expression 2 days after transfection. A list of the sequences of the sgRNAs used in this study is provided in Supplementary Table 2.
For PTB-domain-deleted TNS1 (dd-TNS1) assays, dd-TNS1 or a full-length TNS1 was cloned into a tdTomato-N1 vector (gift from S.-H. Lo). Huh7 cells were transfected with these plasmids and cultured for 24 h before encapsulation in IPNs hydrogels.
Huh7 or Hep3B cells were transfected with plasmids containing the human TKS5 (also known as SH3PXD2A) with either mNeonGreen or mScarlet tag (gift from L. Hodgson) for all invadopodia analyses.
3D cell encapsulation in IPNs
For analyses of YAP activation, invadopodia formation and proliferation, Huh7 cells were serum-starved overnight and encapsulated in IPNs. In brief, cells were washed with PBS, trypsinized using 0.05% trypsin/EDTA, washed once, centrifuged and resuspended in serum-free medium. The concentration of cells was determined using the Vi-Cell Coulter counter (Beckman Coulter). After Matrigel was mixed with the alginate, cells were added to this polymer mixture and deposited into a cooled syringe. The solution was then vigorously mixed with a solution containing CaSO4 and deposited into wells of a chambered cover glass (LabTek). The final concentration of Matrigel and alginate was 4.4 mg ml−1 and 10 mg ml−1, respectively. 5 mM, 15 mM and 50 mM CaSO4 were used to generate varied stiffness of IPNs with 0.8 kPa, 2 kPa and 5 kPa, respectively. The final concentration of cells was 3 × 106 cells per ml of IPN. The cell-laden hydrogels were gelled in an incubator at 37 °C and 5% CO2 for 60 min and then were cultured in a DMEM medium containing 10% FBS. After 1 day, cells were collected for RT–qPCR, western blotting and immunostaining analysis.
Inhibitors
Inhibitors in the 3D cell culture were used at the following concentrations: 10 μM Y-27632 to inhibit ROCK (Abcam); 50 μM blebbistatin (Abcam) to inhibit myosin II; and 1 μg ml−1 monoclonal integrin-β1-blocking antibody (Abcam, P5D2). Vehicle-alone controls for these inhibitors were as follows: DMSO for blebbistatin, and latrunculin-a; deionized water for Y-27632; and IgG nonspecific antibody (Sigma-Aldrich, I5381) for integrin-β1-blocking antibody. Y-27632 and blebbistatin were added to the culture medium directly. Integrin β1-blocking antibody was incubated with Huh7 cells on ice for 1 h before encapsulation in IPNs and added to the culture medium directly.
RNA-seq, bioinformatics and KEGG analyses
RAGEfl/fl (wild-type) mice were fed chow, FFD or HiAD for 14 weeks. A group of HiAD-fed mice was injected intraperitoneally daily with PM. A cohort of RAGEHepKO mice was placed on a HiAD for 14 weeks as described previously10. RNA was prepared from 2–3 mice per group, and RNA-seq was performed at Novogene with paired-end 150 bp reads (NovaSeq 6000 Sequencing System, Illumina). Gencode gene annotations version M18 and the mouse reference genome major release GRCm38 was derived from https://www.gencodegenes.org/. Dropseq tools v.1.1249 were used for mapping the raw sequencing data to the reference genome. The resulting UMI-filtered count matrix was imported into R v.3.4.4. Before differential expression analysis using Limma v.3.40.650, sample-specific weights were estimated and used as coefficients alongside the experimental groups as a covariate during model fitting with Voom. t-tests were used for determining differentially (P < 0.05) regulated genes between all possible experimental groups. GSEA was conducted using the preranked GSEA method within the KEGG databases with the online tool g:Profiler (https://biit.cs.ut.ee/gprofiler/gost). RNA-seq heat maps and unsupervised hierarchical clustering was performed with g:Profiler. RNA-seq data are available under Gene Expression Omnibus accession number GSE245016.
Protein extraction and western blotting
Cells were washed with PBS and lysed with RIPA buffer. The homogenate was centrifuged, and the supernatant was collected. Protein concentrations were determined using the Pierce BCA Protein Assay Kit (Thermo Fisher Scientific). Protease inhibitor (Roche) and phosphatase inhibitor (Roche) were added to all the lysis procedures mentioned above, and 10–50 µg of the protein samples were loaded onto the SDS–polyacrylamide gel. The proteins were transferred to a polyvinylidene difluoride membrane or nitrocellulose membrane, which was blocked with 5% BSA in TBST and then incubated with primary antibodies at 4 °C overnight. The blots were washed with TBST and further incubated with horseradish-peroxidase-conjugated secondary antibodies. The signal was detected by adding Western-Bright enhanced chemiluminescence substrate (Advansta) or SuperSignal West Pico PLUS Chemiluminescent Substrate (Thermo Fisher Scientific) and imaged with film or the iBright CL1500 imaging system (Thermo Fisher Scientific). The images were processed and analysed using NIH ImageJ (v.1.53t) and iBright Analysis software v.5.2.1 (Thermo Fisher Scientific). The antibodies used in this study were shown in Supplementary Table 3.
Fluorescence immunostaining and microscopy
Frozen sections of livers or gel-embedded cells were washed twice with PBS and fixed with 4% paraformaldehyde at 4 °C overnight. Sections were permeabilized in PBS with 0.4% (v/v) Triton X-100 for 10 min. After blocking with 5% goat serum in PBST at room temperature for 1 h, cells were incubated with primary antibodies (Supplementary Table 3) diluted in 2% goat serum in PBST at 4 °C overnight. The slides were washed and then incubated with secondary antibodies at room temperature for 1 h. Coverslips were washed with PBST between incubations and mounted with an anti-fade mounting medium with DAPI. Fluorescence images were taken using the Leica TCS SP8, multi-photon Leica Stellaris 8 DIVE upright Confocal, and Zeiss Airyscan2 LSM980 systems. Images were processed using NIH ImageJ (v.1.53t). To quantify cell circularity and cell area, the confocal images of cells were analysed in ImageJ v.1.53t (https://imagej-nih-gov.stanford.idm.oclc.org/ij/). Circularity, mathematically calculated as 4π × area × (perimeter)−2, ranges from 0 to 1, with a value of 1 being a perfect circle.
PLA
The Duolink proximity ligation assay kit (Sigma-Aldrich) was used to determine the interaction between TNS1 and integrin β1 in Huh7 cells. Reagents were used according to the manufacturer’s instructions, and the steps were optimized. In brief, anti-TSN1 and anti-integrin β1 were used as the primary antibodies. The primary antibodies bound to a pair of oligonucleotide-labelled secondary antibodies (PLA probes), the hybridizing connector oligos joined the PLA probes if they were close by and the ligase created the DNA template needed for rolling-circle amplification (RCA). Labelled oligos hybridized to the complementary sequences in the amplicon and produced discrete red fluorescent signals that could be seen by confocal microscopy (Leica Microsystems). NIH Image J (v.1.53t) software was used to count the signal, and the average counts were used for the plot.
Simulation modelling
In this study, we used an agent-based model for simulating the discrete structure of collagen matrices. Details of the model and all of the parameter values used in the model are provided in the Supplementary Methods and Supplementary Table 5. The computational domain is rectangular with 20 × 20 × 5 µm in the x, y and z directions. A periodic boundary condition exists only in the x and z directions. In simulations, the motions of the cylindrical elements are updated at each time step through the Langevin equation and the Euler integration scheme. Three types of matrices were used in this study: fibrillar matrix; long, tight-bundle matrix; and short, loose-bundle matrix. Fibril assembly is initiated by the nucleation of seed fibrils through the appearance of one cylindrical segment in random positions, followed by elongation up to either 3 µm or 5 µm through the addition of segments without consideration of depolymerization. Effective collagen concentration calculated using the specific volume of collagen (0.73 ml g−1) is 3.65 mg ml−1. The fibrillar matrix is constructed with cross-linkers in the absence of bundlers (Extended Data Fig. 4d,h). During the assembly of the fibrillar matrix, individual fibrils are interconnected by cross-linkers of which two binding sites bind to any part of two fibrils. There is no preference for a cross-linking angle in this process. The long, tight bundle matrix is assembled with cross-linkers in the presence of bundlers that connect individual fibrils in a parallel, staggering manner into tight bundles (Extended Data Fig. 4g,i). Cross-linkers connect fibrils within each bundle or fibrils belonging to different bundles. The short, loose-bundle matrix is created by bundlers that connect fibrils at their ends with a specific angle (Extended Data Fig. 4e,f,j). While the bundlers are permanently bound to fibrils, the cross-linkers can unbind from fibrils at a rate that exponentially increases with an increasing force, following Bell’s law. Fibrils are permanently bound to two boundaries normal to the y direction (that is, +y boundary located at y = 20 µm and −y boundary located at y = 0 µm). After completion of matrix assembly, 20% strain is applied to the +y boundary in the x direction, whereas the −y boundary is fixed. After reaching the 20% strain, the strain is held at a constant level to measure stress relaxation.
Statistical analyses
At least three biological replicates were performed for all in vivo experiments, and in vitro experiments were repeated at least three times. Data are presented as mean ± s.e.m. Statistical analyses were performed using GraphPad Prism v.10.0.3 (GraphPad Software). Normality distribution was assessed using the Kolmogorov–Smirnov test. Two-tailed unpaired t-tests and one-way ANOVA with Tukey tests were used to analyse data with a normal distribution. Data with a non-normal distribution were analysed using Wilcoxon rank-sum tests and Kruskal–Wallis tests with Dunn’s test. P < 0.05 was considered to be statistically significant.
Reporting summary
Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.