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Plant material
Z. japonica used in this study was collected from Fangchenggang, Guangxi, China.
DNA extraction and primer design
Leaves of Z. japonica were used as materials to extract genomic DNA from young leaves that had grown well. A MiniBEST Plant Genomic DNA Extraction Kit (TaKaRa, 9768) was used to extract genomic DNA from the leaves of Z. japonica following the manufacturer’s instructions. Based on the full-length cDNA sequence of ZjFes1 obtained by RACE18, three identical and high annealing temperature specific primers (SP Primer) were designed, and four specifically designed degenerate primers, AP1, AP2, AP3 and AP4, were used for thermal asymmetric interlaced PCR (TAIL-PCR). Typically, at least one of these degenerate primers can react with specific primers by TAIL-PCR based on the difference of annealing temperature, and the flanking sequence of known sequence can be obtained by three nested PCR reactions. Because the length obtained in one experiment cannot meet the experimental requirements, we continue to acquire the flanking sequence according to the sequence information obtained in the first genome walking. Four genome walkings were conducted. Twelve SP Primers were designed. DNAMAN software was used to combine the four fragments described above into a consensus sequence by combining overlapping fragments. Specific primers were designed to amplify 2 kb sequences according to the results (Table 1), and the experimental results were verified.
Table 1 PCR primer sequences.
Full size table

Cloning and construction of the plant expression vector and sequence analysis of promoter
The full-length promoter sequence was amplified using high fidelity polymerase 2 × TransStart FastPfu PCR SuperMix (-dye) (TRANSGEN BIOTECH, AS221-01) using the DNA of Z. japonica as a template following the manufacturer’s instructions. The PCR products were detected using 1% gel electrophoresis. The results showed that the size of the bands was the same as that of the target fragments, and the PCR products were recovered using a MiniBEST Agarose Gel DNA Extraction Kit Ver. 4.0 (TaKaRa, 9762). The pCXGUS-P plasmid is a vector designed to detect the activity of plant promoters. The promoter activity is detected by the dyeing intensity of GUS. We used XcmI to digest the empty vector to obtain T vector. After recovery, the product was recombined with T vector, and then the recombinant vector was transformed into E. coli DH5α Competent Cells (TaKaRa, 9057) following the manufacturer’s instructions. The positive samples identified by PCR were verified by sequencing at the Guangzhou Sequencing Department of Invitrogen. The sequencing results were compared using DNAMAN software. The plasmid was extracted from the correct bacterial solution and designated pZjFes1::GUS. The sequence analysis of cis-acting elements that could possibly be found in the promoter was performed using the plant-CARE online prediction database (plant cis-acting regulatory element, https://bioinformatics.psb.ugent.be/webtools/plantcare/html/)20.
Agrobacterium-mediated genetic transformation of pZjFes1::GUS into Arabidopsis thaliana
The fusion vector pZjFes1::GUS was transformed into Agrobacterium Rhizobium strain GV3101 chemically competent cells (Biomed, BC304) using the freeze–thaw method following the manufacturer’s instructions. Transgenic plants of A. thaliana were obtained by floral dipping. Plants in nutrient soil were cultured to form a large number of immature flower clusters. The monoclone of A. tumefaciens GV3101 was selected and inoculated in liquid LB medium containing kanamycin and rifampicin (50 µg/mL). The monoclone was cultured overnight at 200 rpm and 28 °C. A volume of 2 mL bacterial solution was transferred to a 500 mL flask culture (containing 200 mL liquid LB with 50 µg/mL kanamycin and rifampicin added) and was cultured overnight at 200 rpm and 28 °C. The next day, the OD600 of Agrobacterium solution was 1.8–2.0. The solution was centrifuged at 5000 rpm for 15 min at 4 °C. The supernatant was discarded, and the precipitate of A. tumefaciens was resuspended in 1/2 volume (100 mL) osmotic medium (1/2 Murashige-Skoog, 5% sucrose, 0.5 g/L MES, 10 µg/mL 6-BA, 200 µl/L Silwet L-77, and 150 µM acetyleugenone, pH 5.7), resulting in an OD600 of approximately 1.6. The bacterial solution was adsorbed on the transformed plants using the floral dip method (5 min), wrapped with film to keep it fresh, and cultured overnight, followed by the removal of the film. The plants were cultured until the seeds were ripe, and they were harvested. A mixed disinfectant consisting of 70% ethanol and 30% bleaching water was used to soak the seeds for 3 min, suspend them continuously, and wash them three times with anhydrous ethanol. The dried seeds were evenly dispersed on the surface of solid screening medium containing hygromycin (25 µg/mL). After stratification at 4 °C for 2 days, the seeds were germinated in a light incubator and cultured for 2 weeks at 21 °C and 16 h light/8 h darkness. The development of seedlings and length of roots were used to determine whether they were transformants.
GUS dyeing and activity analysis
The expression of GUS reporter gene in Arabidopsis tissues was determined using a GUS staining kit (Solarbio, G3060) following the manufacturer’s instructions. The seedlings, leaves, flowers and siliques to be dyed were immersed in GUS dye solution and incubated overnight at 37 °C. The chlorophyll was removed with 75% ethanol until the background color disappeared completely. The results were documented by photography using a Canon 60d camera.
The material needed to determine Gus enzyme activity was frozen rapidly with liquid nitrogen, and then ground into powder by ball mill. The extraction buffer solution (50 mM NaH2PO4 (pH 7.0), 10 mM EDTA, 0.1% Triton X-100, 0.1 (w / v) sodium dodecyl sulfonate, 10 mM β-mercaptoethanol) were added to extract protein. After centrifugation at 4 °C, 12,000 r/min for 10 min, the supernatant was taken as protein extract. The protein concentration was determined by Bradford method. 4-MUG, the substrate of GUS reaction, was added and reacted at 37 °C for 30 min. Fluorescence measurement was carried out under the condition of 365 nm excitation light and 455 nm emission light. Three independent biological repeats were conducted. Finally, the GUS enzyme activity value was calculated according to the relative change of product in unit time. More

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Human gut microbiome data and preprocessing
The publicly available data that we re-analyzed here were generated by David et al.32 accessible on the European Nucleotide Archive (ENA) under the accession number ERP006059, and by Hsiao et al.31 on the NCBI Short Read Archive (SRA) under the accession number PRJEB6358. The downloaded reads were trimmed with V-xtractor version 2.146 a HMM scan based method of isolating variable regions from 16S rRNA sequences) to ensure the amplicon sequences could be aligned across consistent fractions of the 16S rRNA variable regions. Trimmed reads were then clustered into OTUs using usearch v9.2.6447 with a minimum cluster size of two. Representative sequences from each OTU were classified using mothur v1.36.148 and the RDP reference 16S rRNA sequences v1649.
Prochlorococcus data
Data from Malstrom et al.33 was obtained from the Biological and Chemical Oceanography Data Management Office (https://www.bco-dmo.org), accession number 3381.
Mapper
Conceptually, the Mapper algorithm accepts as input a matrix of distances or dissimilarities between data, and aims to represent the shape of the distribution of data points in high-dimensional phase space as an undirected graph. In this graph, vertices represent neighborhoods of phase space spanned by subsets of adjacent data points, and edges represent connectivity between neighborhoods. In brief, it does this by dividing the data into overlapping subsets that are similar according to the output of at least one filter function that assigns a scalar value to each data point, performing local clustering on each subset, and representing the result as an undirected graph, where each vertex represents a local cluster of data points, and edges between vertices represent at least one shared data point between clusters.
Distance matrix
We interpreted microbiome relative abundances to be probability distributions, and thus used the square root of the Jensen-Shannon divergence as a metric50. However, it is important to note that any other metric can be used in place of the Jensen-Shannon distance, such as the Aitchison distance51, calculated from centered10 or isometric12 log-transformed relative abundances.
Filter functions and binning
For the filter functions used by Mapper to bin data points, we performed principal coordinate analysis (PCoA, also known as classical multidimensional scaling) in two dimensions on the pairwise distance matrix, and used the ranked values of principal coordinates (PCo) 1 and 2 as the first and second filter values for Mapper, following Rizvi et al.28. PCo ranks are an appropriate filter for our purposes, as it assigns similar filter values to points that are relatively close together in the original phase space. We wish to note that while PCoA leads to loss of information, the following local clustering step is performed using subsets of distances from the original distance matrix, and is thus not affected. The data points were then binned by overlapping intervals of the two ranked principal coordinates. For hyperparameters specifying these bins and their overlaps, see Table 1.
Table 1 Hyperparameters used to generate the Mapper representation of each data set.
Full size table

Local clustering
The algorithm first performs hierarchical clustering from all pairwise distances between data points within a bin of filter values. Then, it creates a histogram of branch lengths using a predefined number of bins, and uses the first empty bin in the histogram as a cutoff value, separating the hierarchical tree into single-linkage clusters. The algorithm thus finds a separation of length scales within each neighborhood of phase space represented by a bin of the filter values. We used the default number of histogram bins, 10, for each data set (Table 1).
Creating the undirected Mapper graph
The final output is produced by representing each local cluster of data points as a vertex, and drawing an edge between each pair of vertices that share at least one data point. When plotting, the size of each vertex represents the number of data points therein. Layout and visualization of the Mapper graph may be performed with any graph layout algorithm; we used the Fruchterman-Reingold force-directed layout algorithm52. It is important to note that the visualized shape of the Mapper graph depends on the algorithm used, and may not be deterministic. When performing a Mapper analysis, one should rely on the connectivity of the graph rather than the overall shape.
Selection of hyperparameters
The Mapper algorithm is relatively new, and there are currently no standard protocols to optimize the values of the hyperparameters. For our purposes, it was important that the algorithm achieved a sufficiently high resolution in partitioning data, but also adequately represented connections between regions of phase space. We thus used the following heuristic to set the number of intervals and percent overlap for each data set.
1.
The largest vertex in the resultant Mapper graph should represent no more than ≈10% of the total number of data points in the set;

2.
the number of connected components representing only one data point should be minimized.

We acknowledge that a heuristic determination of appropriate hyperparameter values leaves much to be desired; as such, we recommend future in-depth theoretical explorations of how the Mapper output depends on the choice of hyperparameters.
Density estimation
We estimated the inverse density for each vertex by calculating the k-nearest neighbors (kNN) distance53 for each constituent data point i.
We first define the k-neighborhood N(k)i of a point i, to be the set of k nearest neighbors of i, choosing k equal to 10% of the number of samples in each data set, rounded to the nearest integer. Then the kNN distance of point i is defined as:

$${rm{kNN}}(i,k)=frac{{sum }_{jin N{(k)}_{i}}{d}_{ij}}{k}$$
(1)

where dij is the distance between points i and j.
For a vertex V representing n points, we define its inverse density as

$${D}_{{rm{inv}}}(V)=frac{{sum }_{iin V}{rm{kNN}}(i,k)}{{n}^{2}}$$
(2)

The n2 term in the denominator compensates for the differing sizes of vertices. Finally, we invert the inverse density to obtain the estimated density:

$$D(V)=frac{1}{{D}_{{rm{inv}}}}$$
(3)

State assignment
We then defined states as topological features of the density surrounding local maxima of D. We designated each vertex with higher D than its neighbors to be a local maximum of the potential. Connected vertices tied for maximum D were each assigned to be a local maximum. To approximate a gradient, we converted the undirected Mapper graph to a directed graph, with each edge pointing from the vertex with lower D to the one with higher D. For each non-maximum vertex, we found the graph distance dg to each local maximum constrained by edge direction. We defined the state Bx of a maximum Vx as the set of vertices V with uniquely shortest graph distance to Vx:

$$Vin {B}_{x},{rm{if}},{d}_{g}(V,{V}_{x}), More

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A high pressure experiment reveals the world’s first room-temperature superconductor, and a method to target ecosystem restoration.

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00:44 Room-temperature superconductivity
For decades, scientists have been searching for a material that superconducts at room temperature. This week, researchers show a material that appears to do so, but only under pressures close to those at the centre of the planet. Research Article: Snider et al.; News: First room-temperature superconductor puzzles physicists
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The Coronapod team revisit mask-use. Does public use really control the virus? And how much evidence is enough to turn the tide on this ongoing debate? News Feature: Face masks: what the data say
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A new method provides 3D printed materials with some flexibility, and why an honest post to Facebook may do you some good. Research Highlight: A promising 3D-printing method gets flexible; Research Highlight: Why Facebook users might want to show their true colours
22:11 The best way to restore ecosystems
Restoring degraded or human-utilised landscapes could help fight climate change and protect biodiversity. However, there are multiple costs and benefits that need to be balanced. Researchers hope a newly developed algorithm will help harmonise these factors and show the best locations to target restoration. Research Article: Strassburg et al.; News and Views: Prioritizing where to restore Earth’s ecosystems
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We discuss some highlights from the Nature Briefing. This time, a 44 year speed record for solving a maths problem is beaten… just, and an ancient set of tracks show a mysterious journey. Quanta: Computer Scientists Break Traveling Salesperson Record; The Conversation: Fossil footprints: the fascinating story behind the longest known prehistoric journey
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