Abstract
Background
Microbial communities play fundamental roles in industrial processes and ecosystem stability. However, understanding how individual members and their interactions give rise to community-level function remains challenging because such functions emerge from complex interactions among diverse members.
Results
In this study, we developed SubCom analysis, a subcommunity-based experimental–computational workflow for inferring candidate taxon-specific contributions and interaction contexts underlying microbial community function. Using an aniline-degrading microbial community, we generated paired composition–function data from 558 randomly assembled, low-complexity subcommunities constructed using a dilution-and-dispense strategy. We then trained decision-tree-based models to predict community function from composition, achieving high predictive performance (r = 0.77–0.89). Interpretation of the learned decision rules identified taxa with consistent functional association: specific Pseudomonas and Acinetobacter taxa were associated with increased community-level aniline utilization, whereas an Achromobacter taxon exhibited a negative association despite its presumed role in downstream metabolism. The models further suggested potential functional interactions, including attenuation of the positive contributions of Pseudomonas and Acinetobacter in the presence of a Corynebacterium taxon, highlighting functional relationships that are not readily inferred from genome-based approaches alone. An augmentation assay using representative isolates supported the predicted direction of several effects and enabled targeted improvement of community function.
Conclusions
These results demonstrate the potential of SubCom analysis as a practical framework for inferring taxon-specific contributions and interaction contexts in complex, nonsynthetic microbial communities.
Video Abstract
Supplementary Information
The online version contains supplementary material available at 10.1186/s40168-026-02460-3.
Background
Microbial communities perform emergent functions, such as coordinated substrate conversion and host phenotype modulation, that are not attributable to individual microbes alone. These functions are widely leveraged in industry (e.g., agriculture, wastewater treatment, human healthcare) and tightly linked to environmental outcomes (e.g., greenhouse-gas emissions), making predictive microbial community science an urgent need [1–4]. However, mechanistic dissection of microbial community function remains difficult because it emerges from complex interspecies interactions, including metabolic cooperation, cross-feeding, competition, and antagonism [5–7]. Consequently, bulk community profiling (e.g., metagenomics) can link community composition to function, but inferring the mechanistic contributions of individual taxa and their interactions remains difficult. Conversely, isolation-based approaches can miss behaviors that manifest only within multispecies assemblages. Therefore, a mechanistic, predictive understanding of microbial community function requires methods that can disentangle taxon-specific contributions and interactions within their ecological context.
Existing efforts to dissect microbial community functions have largely relied on genomic information, metabolic models, and/or cultivation data from monocultures or pairwise cocultures [8–13]. However, recent work suggests that systematic analysis of low-complexity subcommunities (typically containing 3–10 species) offers a viable alternative [14, 15]. In this approach, numerous subcommunities containing different subsets of members from a target community are assayed for the function of interest. By measuring function across diverse but simplified compositional contexts, this strategy can help disentangle taxon-specific associations without requiring detailed prior knowledge of genomes or metabolic pathways. In addition, reduced community complexity can make composition–function relationships more statistically tractable, whereas inference from whole-community data is often more difficult [16, 17]. Consistent with this idea, several studies using synthetic microbial communities have demonstrated that measurements from simple subcommunities can enable bottom-up prediction of community-level functions and the underlying taxon-specific roles and interaction contexts [18–23].
However, such subcommunity-based approaches have been developed primarily in low-diversity synthetic communities (typically containing ≤ 10 species), and their applicability to diverse natural microbial communities remains unclear. To realize their potential in real-world communities, at least two challenges must be addressed. First, scalable methods are needed to generate and phenotype hundreds to thousands of subcommunities within practical time, labor, and financial constraints. Second, the validity and robustness of models that infer functional outcomes, influential taxa, and interaction contexts from subcommunity data have not been established for natural microbial communities, in which measurements may be incomplete or noisy.
Here, we developed SubCom analysis, an experimental–analytical workflow for subcommunity-based analysis of a complex, nonsynthetic microbial community (Fig. 1). As a model system, we used a previously established aniline-degrading microbial community [23]. Aniline is a common organic pollutant that persists in soil and aquatic environments, making it a priority target for bioremediation [24, 25]. Prior metagenomic and isolation-based studies suggested coordinated degradation in this community: a Caballeronia taxon initiates degradation by converting aniline to catechol, and several taxa (Caballeronia, Achromobacter, Pseudomonas, and Pseudorodoferax) harbor catechol degradation genes and participate in downstream metabolism [23]. Nevertheless, taxa beyond these core degraders might directly or indirectly shape community function [26–28], yet their roles remain difficult to elucidate.
Fig. 1.
Schematic diagram of the SubCom analysis performed in this study. a–c The bulk community was randomly partitioned into simplified subcommunities (typically 3–10 species), followed by independent cultivation and functional output measurement. Compositional profiles were determined via multiplexed sequencing. d–f Paired composition-function datasets were used to train a decision-tree model, mapping community structures to functional outcomes. Candidate taxon-specific contributions and interaction contexts associated with community function were inferred by interpreting the model’s decision criteria
We generated paired composition–function data from 558 randomly assembled subcommunities using a dilution-and-dispense strategy and trained decision-tree-based models to predict subcommunity function from composition. We then interpreted the learned decision rules to identify candidate taxa and compositional contexts associated with increased or decreased function, and tested these predictions by targeted augmentation of the original community using representative isolates. Together, these analyses demonstrate the potential of SubCom analysis as a practical framework for inferring candidate taxon-specific contributions and interaction contexts underlying community function in a diverse nonsynthetic microbial community.
Methods
Aniline-degrading microbial community
A previously established aniline-degrading microbial community was used [23]. The community was enriched from a soil microbial community using minimal salt medium (MSM) [29] supplemented with 0.5 mM aniline (hereafter, MSM–aniline medium). After stable aniline degradation was observed, the community was preserved as multiple stocks at −80 °C in 16.7% glycerol.
Before use, 1.2 mL of the community stock was thawed on ice, and added to 10 mL of MSM, and cells were pelleted (10,000 × g, 4 °C, 10 min). The pellet was washed twice with MSM and resuspended in 5 mL of MSM. Next, 1 mL of the cell suspension was inoculated into 50 mL of MSM–aniline medium and incubated for 48 h at 30 °C with shaking at 150 rpm. These procedures were previously demonstrated to restore the aniline-degrading community with generally consistent aniline degradation capacity and community structure [23].
Subcommunity cultivation and phenotyping
To generate subcommunity cultures, the restored aniline-degrading community was diluted and added to MSM–aniline medium containing 2 mg/L resazurin, and 20 µL of the suspension was dispensed into each well of a 384-well plate. The dilution factor was adjusted to yield an expected inoculum of 3–10 cells per well, based on the community cell density estimated by spectrophotometry and optical microscopy using a Petroff–Hausser counting chamber. Plates were incubated in a microplate reader (Synergy HTX, Agilent Technologies, Santa Clara, CA, USA) at 30 °C for 72 h with shaking at 237 rpm to allow randomly assembled subcommunities to degrade aniline. During incubation, fluorescence (Ex/Em 528/590 nm) was measured every 15 min to quantify the reduction of resazurin, a widely used indicator of microbial respiratory activity [30, 31]. Under the present medium and culture conditions, in which aniline was the sole carbon and energy source, resazurin reduction was previously found to correlate with HPLC-based measurements of residual aniline content across a large set of synthetic microbial communities, prompting its use as a proxy for community-level aniline utilization [23]. In most wells, fluorescence increased monotonically over time, and we used the maximum relative fluorescence units as a summary metric of subcommunity function.
Amplicon sequencing
High-throughput amplicon sequencing was performed to profile the bacterial community composition of cultured subcommunities. For DNA extraction, 3 µL of each culture were mixed with 17 µL of extraction buffer (Cica Genius DNA extraction solution, Kanto Chemical, Tokyo, Japan) in a 96-well PCR plate, incubated at 72 °C for 20 min, and heat-treated at 94 °C for 3 min. The resulting lysate was used as the PCR template. The V4 region of the 16S rRNA gene was amplified using primers 515 F and 806R carrying internal index sequences (Supplementary Table S1). Amplicons were purified using AMPure XP beads (Beckman Coulter, Brea, CA, USA) and subjected to a second round of PCR to add sequencing adapters and 5–8-mer index sequences (Supplementary Table S1). Second-round products were size-selected by gel electrophoresis, excised, and purified using the NucleoSpin Gel and PCR Clean-up kit (Macherey–Nagel, Düren, Germany). The purified linear library was converted to DNA nanoballs using the DNBSEQ™ OneStep DNB Make Reagent Kit V4.0 (MGI Tech, Shenzhen, China) and 300 bp paired-end reads were obtained on the DNBSEQ-G400 platform (MGI Tech). PCR setup and cleanup steps were performed using an automated liquid-handling system as described in Supplementary Text 1. The community composition of the original aniline-degrading community prior to subset cultivation was analyzed using the same workflow, except that 300 bp paired-end sequencing was performed on the NextSeq1000 platform (Illumina, San Diego, CA, USA) using a linear DNA library.
Sequence data processing
Sequence reads from the subcommunities were demultiplexed and processed using DADA2 [32] to generate an amplicon sequence variant (ASV) table. In this table, we observed multiple instances in which ASVs differing by a single nucleotide co-occurred across communities at an approximately constant ratio, suggesting that a single genotype had been split into multiple ASVs because of 16S rRNA gene polymorphism and/or artifacts of ASV inference. Therefore, we reclustered ASVs into k-mer taxonomic units (KTUs) using the “KTU” R package (v1.0.3) [33]. This approach typically merges small groups of highly similar ASVs (often > 99% sequence identity), thereby converting a sparse ASV table into a biologically more meaningful KTU table [33, 34]. The taxonomy of KTU representative sequences was assigned against the SILVA v138 database [35]. Subcommunity samples with sufficient sequencing depth to evaluate diversity (> 3800 reads) were retained for subsequent analyses.
XGBoost model
To build a decision-tree–based classifier that predicts whether each subcommunity exhibits aniline-utilization activity, we trained an XGBoost model using the “xgboost” R package. XGBoost is a gradient-boosting algorithm that combines multiple decision trees to improve predictive accuracy [36]. Prior to training, the compositional profile of each subcommunity was binarized using a relative-abundance threshold. This representation was adopted to emphasize community membership while reducing sensitivity to fluctuations in relative abundance during cultivation. To account for class imbalance, the positive class was up-weighted by the negative-to-positive ratio (negative/positive). Hyperparameters (max_depth, eta, nrounds, and the binarization threshold) and the random seed were selected via grid search to obtain a well-performing model for subsequent interpretation. Using the selected settings (max_depth = 5, eta = 0.18, nrounds = 30, threshold = 0.04%), model performance was evaluated by fivefold cross-validation with an 80/20 train/test split in each fold. Because the primary goal of the modelling was to construct a well-performing model for subsequent interpretation rather than to provide a benchmark of predictive accuracy, the cross-validation results were reported as descriptive indicators of predictive signal.
For the regression task, we trained an XGBoost model on the 87 subcommunities that exhibited aniline utilization. As in the classification analysis, the same hyperparameters were tuned via grid search to minimize RMSE, yielding max_depth = 2, eta = 0.24, nrounds = 50, and threshold = 1%. Predictive performance was assessed by leave-one-out cross-validation.
Interpretation of the fitted XGBoost models was performed by computing SHAP values using the “SHAPforxgboost” R package from models trained on the subcommunity datasets. SHAP values were used to identify taxa whose presence or absence contributed strongly to model predictions thereby identifying candidate KTUs associated with functional outcomes.
RuleFit model
To derive interpretable rules linking community composition to subcommunity function, we fitted a RuleFit model to the 87 subcommunities that exhibited aniline utilization using the “pre” R package, with the maximum depth of the decision trees set to 3. RuleFit is an interpretable modeling approach that combines simple “if–then” rules extracted from decision trees with a linear model to predict the response [37]. Predictive performance was evaluated via leave-one-out cross-validation. The extracted rules and their coefficients were used to infer putative taxon-level contributions and interaction contexts associated with aniline utilization. To evaluate the robustness of the extracted rules, RuleFit models were generated 100 times using random seed values.
Augmentation assay
Bacterial strains previously isolated from the same aniline-degrading community—Caballeronia cordobensis MA074 (Cab074), Pseudomonas monteilii MA033 (Pse033), and Pseudomonas sp. MA056 (Pse056)—were selected from our earlier work [23]. In addition, two bacterial strains were newly obtained using R2A agar plate and identified as Achromobacter veterisilvae MA059 (Ach059) and Acinetobacter pittii MA036 (Aci036), respectively, based on Sanger sequencing of the 16S rRNA gene (Table S2). The 16S rRNA gene sequences of all five strains exhibited either a perfect match or a single-nucleotide mismatch with the representative sequences of the top six KTUs identified in the subcommunity dataset, excluding KTU004 (Corynebaterium).
For the augmentation assay, colonies of each isolate were inoculated into oligotrophic medium (MSM supplemented with 0.1% R2A) and cultured for 48 h to obtain carbon-starved cell suspensions. Cells were then harvested, washed, and resuspended in MSM. For cultivation, the restored community was inoculated into 96-well plates containing 100 µL of MSM–aniline medium supplemented with 2 mg/L resazurin per well, at an initial optical density at 600 nm (OD600) of 0.01. For augmented cultures, an additional aliquot of isolate cell suspension was added to achieve a restored community:isolate ratio of 1:1 based on OD600. The augmented and nonaugmented control cultures were incubated at 30 °C with orbital shaking at 237 rpm for 48 h to permit aniline degradation by the communities. During incubation, fluorescence (Ex/Em 528/590 nm) was measured every 10 min to quantify the reduction of resazurin to resorufin. The area under the fluorescence time-course curve (AUC) was calculated from the fluorescence trajectories using the “gcplyr” R package [38]. AUC was used as a metric of community performance because it captures both the rate and maximum extent of fluorescence increase. AUCs were compared with those of nonaugmented controls using one-way ANOVA followed by Dunnett’s post hoc test, implemented in the “multcomp” R package. Each condition was tested in eight replicate wells. To handle occasional wells exhibiting an unusually large AUCs, suggestive of technical artefact (e.g., condensation on the plate lid) rather than biological variation, up to one replicate per condition was excluded using Grubbs’ test criterion (P < 0.01). The overall pattern was unchanged when all wells were included (Fig. S1).
Results
Subcommunity cultivation and phenotyping
To implement SubCom analysis, a liquid culture of a previously characterized aniline-degrading microbial community was diluted and dispensed into a 384-well plate to generate subcommunities containing approximately 3–10 cells per well. The original community was dominated by KTUs assigned to Caballeronia and Achromobacter within Betaproteobacteria and to Acinetobacter and Pseudomonas within Gammaproteobacteria (Fig. 2a). This moderately diverse composition was expected to allow random combinations of 3–10 cells to generate broad compositional variation. The subcommunities were cultivated for 72 h in the same medium as the original community, with aniline as the sole carbon and energy source. During cultivation, aniline-utilization activity was monitored using fluorescence associated with resazurin reduction, which served as a proxy for overall metabolic activity. The taxonomic composition of each subcommunity was determined after cultivation by multiplexed sequencing of the 16S rRNA gene.
Fig. 2.
Subcommunity dataset derived from a natural aniline-degrading community. a Community structure of the original aniline-degrading community used to generate subcommunities. Amplicon sequencing results from three replicate communities are presented. b Overview of the composition–function dataset obtained from 558 subcommunities. Functional performance (aniline-utilization activity) was quantified by fluorescence measurements during microplate cultivation, and community composition was determined by 16S rRNA gene amplicon sequencing. KTUs were used as biologically relevant taxonomic units. c Histogram showing the distribution of functional performance across subcommunities. Most subcommunities (n = 471) were functionally negative, whereas a subset (n = 87) exhibited positive activity. d Histogram showing the distribution of taxonomic richness across subcommunity, presented as the number of KTUs detected in each subcommunity. e Relationship between the relative abundance of KTU003 (Caballeronia) and functional output
After filtering by the read-count threshold, paired composition–function data were obtained for 558 subcommunity combinations (Fig. 2b). Among these, 471 subcommunities (84.4%) displayed negligible aniline utilization, whereas 87 exhibited detectable activity (Fig. 1c). Dominant taxa from the original aniline-degrading community were consistently detected across subcommunities, with the top 15 KTUs accounting for 85.2–89.0% of the original community composition. Accordingly, subsequent analyses focused on these 15 KTUs as major features, whereas all remaining KTUs were grouped into an “others” category. Based on a presence/absence threshold of 0.04%, individual subcommunities contained between 1 and 13 KTUs (mean = 7.87; Fig. 1d).
Prior shotgun-metagenomic analysis revealed the distribution of genes involved in aniline degradation and downstream catechol metabolism across metagenome-assembled genomes (MAGs; Table S3) [23]. Among the reconstructed MAGs, only the Caballeronia MAG (corresponding to KTU003) contained genes putatively responsible for the initial oxidation of aniline to catechol. This was supported by cultivation-based assays, in which Caballeronia was the only isolate capable of degrading aniline in monoculture [23]. In fact, subcommunities composed solely of KTU003 exhibited measurable aniline-utilization activity (Fig. 2b). However, many subcommunities containing KTU003 exhibited no detectable activity, suggesting that the co-existence of other taxa inhibited aniline degradation by KTU003. Moreover, the relative abundance of KTU003 tended to be lower in more active subcommunities, and was nearly absent (< 0.04%) in highly active subcommunities (Fig. 2e; Corresponding plots for other KTUs are provided in Fig. S2). In these communities, KTUs presumably possessing catechol degradation genes but lacking aniline degradation genes, e.g., KTU001 (Achromobacter) and KTU006 (Pseudomonas), displayed high relative abundance (Fig. S3). This pattern suggests that, in high-activity subcommunities, KTU003 was initially present and converted aniline to catechol, but it was subsequently outcompeted during cultivation, possibly because it was less competitive than other strains at utilizing downstream metabolites.
Binary classification of subcommunity performance
To link community composition to functional outcomes, we trained machine-learning models to predict subcommunity performance from taxonomic composition. Because functional outcomes were strongly skewed towards inactive subcommunities (Fig. 1b), we adopted two complementary modelling strategies: namely a binary classification model predicting whether a subcommunity exhibits detectable aniline utilization and a regression model trained exclusively on functionally positive subcommunities. For both tasks, we employed XGBoost and the presence or absence of each KTU as an input feature.
For the binary classification task, the trained model achieved an accuracy of 92.1% (balanced accuracy = 85.5%) under five-fold cross-validation (Fig. 3a), indicating that compositional information contains substantial predictive signal. The remaining false-negative (3.8%) and false-positive predictions (4.1%) likely reflect uncertainty arising from both microbial dynamics, such as stochastic variation in functional expression among subcommunities and technical limitations in phenotyping and sequencing-based detection. In particular, the primary aniline degrader KTU003 (Caballeronia), although functionally essential, was often present at an extremely low or undetectable level in highly active subcommunities (Fig. 2e), potentially contributing to classification uncertainty.
Fig. 3.
XGBoost-based binary classifier for subcommunity function. The model predicts whether a subcommunity exhibits aniline-utilization activity (positive vs negative) from composition data (presence/absence of the top 15 KTUs). a Prediction performance evaluated by fivefold cross-validation on the subcommunity dataset (n = 558). b Interpretation of the model using SHAP values. For each individual prediction, positive SHAP value indicates that the presence or absence of a feature pushes the prediction toward the positive class, whereas negative values push it towards the negative class. Features were ranked by their global importance, presented at the top as the mean absolute SHAP value
Given the strong predictive performance of the classifier, we reasoned that interpreting learned decision rules in the trained model could provide insight into candidate taxon-specific functional associations and interaction contexts underlying community function. To interpret the trained XGBoost classifier, we computed SHAP values for all 558 prediction events. SHAP values, derived from cooperative game theory, decompose each prediction into additive contributions of individual features [39], which in this study represented the presence or absence of each KTU. Positive SHAP values indicate that a given feature state (presence or absence) increases the predicted probability of a positive functional outcome, whereas negative values indicate a decrease. Using this framework, several KTUs, e.g., KTU008 (Paucibacter), KTU009 (Aeribacillus), and KTU010 (Escherichia), showed predominantly negative SHAP values when present (Fig. 3b). Although SHAP values are model-derived measures and do not directly represent biological causality, this pattern implies that these KTUs may be associated with reduced functional outcomes. In contrast, KTU012 (Acidovorax) and KTU014 (Acinetobacter) displayed mainly positive SHAP values when present, suggesting a supportive association with functional expression. Notably, some KTUs, e.g., KTU002 (Acinetobacter) and KTU006 (Pseudomonas) exhibited SHAP values spanning both positive and negative ranges across samples, suggesting context-dependent functional associations that varied with community composition.
Quantitative prediction of subcommunity performance
We next trained an XGBoost regression model to predict quantitative functional levels of aniline-utilization activity among the 87 functionally positive subcommunities. The model achieved high predictive performance under leave-one-out cross-validation (Pearson’s r = 0.894; Fig. 4a), indicating that subcommunity composition contained substantial predictive signals informative of functional variation, thereby supporting the interpretation of the fitted model to nominate candidate taxa and compositional contexts.
Fig. 4.
XGBoost-based regression model for subcommunity function. The model predicted the level of aniline-utilization activity from compositional data (presence/absence of the top 15 KTUs) specifically within functionally positive subcommunities. a Prediction performance evaluated by leave-one-out cross-validation on the active subcommunities (n = 87). b Model interpretation using SHAP values. For each individual prediction, a positive SHAP value indicated that a feature contributes to higher predicted activity, whereas a negative value indicated a contribution to lower activity. Features are ranked by their global importance, as indicated by the mean absolute SHAP value presented at the top
SHAP analysis of the regression model revealed a distinct pattern from that observed in the binary classification task (Fig. 4b). In particular, dominant KTUs (KTU001–KTU007) showed the largest influence on predicted functional levels, with both positive and negative contributions depending on the community context. Three Pseudomonas KTUs (KTU005, KTU006, and KTU007) showed predominantly positive SHAP values when present, consistent with metagenomic evidence indicating their involvement in catechol degradation (Table S3). The aggregated “others” feature showed consistently negative SHAP values when present. This association might reflect either negative functional association of minor taxa or an indirect relationship in which their persistence at high abundance indicates lower metabolic flux that reduces competitive exclusion.
Identifying functional interactions using the RuleFit algorithm
To further explore interaction patterns among dominant KTUs, we applied the RuleFit framework. Unlike XGBoost, which relies on multiple decision trees, RuleFit identifies a small set of explicit, human-readable rules, facilitating direct interpretation of interaction-like dependencies. When trained on the regression task, the RuleFit model yielded 13 rules, each defined by the presence or absence of no more than three KTUs (Fig. 5a). The predictive performance was lower than that of the XGBoost regression model; nevertheless, the RuleFit predictions remained correlated with observed functional levels across the 87 positive subcommunities (r = 0.766; Fig. 5b). Although the extracted rules depended on the random seed used for model construction, eight of the nine rules with mean coefficients greater than 0.05 were selected in at least 88 of the 100 trials, supporting the robustness of the analysis (Table S4).
Fig. 5.
RuleFit-based regression model of subcommunity function. The model extracted a limited number of interpretable rules that predict the level of aniline-utilization activity from compositional data (presence/absence of the top 15 KTUs) within functionally positive subcommunities. a Extracted logical rules and corresponding coefficients. For each subcommunity, prediction was made by adding coefficients of satisfying rules. b Prediction performance evaluated by leave-one-out cross-validation of active subcommunities (n = 87). c Candidate functional contributions and interaction contexts within the original aniline-degrading community produced by the interpretation of extracted rules and predicted metabolic roles of taxa from shotgun-metagenomic analysis
The rule with the highest positive coefficient was "KTU004 = 0 & KTU005 = 1", indicating that predicted functional output increases when KTU005 is present and KTU004 is absent (Fig. 5a). As KTU005 (Pseudomonas) is predicted to harbor catechol-degradation genes and that KTU004 (Corynebacterium) was identified by SHAP analysis as a strong negative factor (Fig. 4b), this rule suggests that the positive functional association of KTU005 to downstream metabolism might be suppressed in the presence of KTU004. Interpreting the extracted rules in this manner enabled functional inference that explicitly incorporates interaction contexts among dominant KTUs (Fig. 5c). Together, the RuleFit and SHAP analyses support a community model in which KTU003 (Caballeronia) initiates aniline oxidation, downstream degraders such as Pseudomonas contribute to intermediate metabolism, and specific co-occurring taxa modulate these processes through inhibitory interactions. Although KTU001 (Achromobacter) harbors catechol-degradation genes and was therefore expected to show positive functional association (Table S3), both modelling frameworks consistently associated this KTU with reduced community-level activity, underscoring the importance of interaction context in shaping functional expression.
Validation of model interpretation through augmentation tests
Although the subcommunity–based models provided insights into taxon–function relationships, the extent to which these model-based predictions translate to the original, more complex aniline-degrading community required experimental validation. To address this, we isolated bacterial strains corresponding to dominant KTUs and conducted augmentation assays by adding each isolate back into the original community to test whether increasing its abundance affected community-level performance in the predicted direction.
Five isolates whose 16S rRNA gene sequences perfectly matched, or differed by a single nucleotide from, representative KTU sequences were selected. These strains were inoculated into the original community at an approximate 1:1 ratio based on OD₆₀₀. Aniline utilization was monitored over 48 h using fluorescence measurements, and community performance was quantified as the AUC (Fig. 6a). Augmentation with each isolate significantly altered community-level activity relative to the unamended control (one-way ANOVA with Dunnett’s post hoc test; Fig. 6b), indicating that changes in the abundance of individual taxa can measurably influence overall community function.
Fig. 6.
Augmentation assay of bacterial isolates added back to the original aniline-degrading community. a Fluorescence trajectories of augmented and control cultures during cultivation. Fluorescence reflects resazurin reduction, used in this study as a proxy for metabolic activity in medium containing aniline as the sole carbon source. Shaded areas indicate standard deviations (n = 7–8). b Effects of the five strains summarized as the AUC presented in panel (a). Error bars indicate standard deviations (n = 7–8). Asterisks denote significance levels (*P < 0.05; **P < 0.01; ***P < 0.001; one-way ANOVA with Dunnett’s post hoc test). c Summary of model-based inferences of taxon roles and the corresponding effects observed in the augmentation tests. In the constructed XGBoost and RuleFit models, the predicted effect of each KTU was evaluated based on SHAP values or extracted rules
For three strains corresponding to KTU001 (Achromobacter), KTU002 (Acinetobacter), and KTU006 (Pseudomonas), the direction of the experimentally observed effects were consistent with model-based predictions (Fig. 6c). KTU005 (Pseudomonas) exhibited opposing functional associations in the binary classification and regression models, suggesting context-dependent effects on community-level activity. The augmentation assay supported the prediction by the binary classification model, suggesting that inhibitory effects dominated under our experimental conditions. This may be attributable to the relatively high inoculum of the added strain (1:1), which may have strongly influenced community states during the early phase that determined whether aniline degradation was initiated. KTU003 (Caballeronia) was also predicted to show varying functional associations across models, likely reflecting its tendency to occur at very low abundance in highly active communities and consequent limitations in sequencing-based detection. In the augmentation assay, KTU003 consistently increased community-level activity, in agreement with the RuleFit prediction and its expected role in aniline degradation.
Taken together, these augmentation experiments supported the directions of several taxon-level effects inferred by decision-tree models, while also underscoring the importance of context dependence and sequencing-related limitations when interpreting model-based predictions. Furthermore, these results suggest that information derived from SubCom analysis can guide targeted community manipulation to improve microbial community functions.
Discussion
Prior work involving synthetic communities found that measurements from simple subcommunities enable bottom-up inference of complex microbial community functions [16–23]. Building on this foundation, we demonstrated a practical implementation of SubCom analysis in complex, nonsynthetic microbial communities. Specifically, combining subcommunity data with tree-based models enables the extraction of interpretable, rule-like dependencies between community composition and function, which we used to nominate key taxa and interaction signatures linked to community-level performance. A subset of these predictions was supported by targeted augmentation experiments. Together, our results offer a proof-of-concept for SubCom analysis as a workflow that offers a potential bridge between whole-community profiling and isolation-based approaches while also clarifying current limitations that motivate future methodological improvements.
Aniline is a toxic environmental pollutant that is frequently used as a reference compound to assess biodegradability in microbial communities [40], yet its degradation has often been reported to be unstable [41–43]. Our SubCom analysis offers a potential mechanistic perspective on such instability by revealing that community-level aniline utilization is strongly modulated by interspecies interactions. This observation is consistent with the metabolic structure of aniline degradation: while the initial conversion of aniline to catechol requires specialized enzymes [44, 45], this step yields little or no usable carbon or energy. As a result, competition over downstream metabolites can strongly influence the growth and persistence of the primary aniline degrader, making its activity and abundance prone to instability across community contexts. Among dominant members of our community, certain Pseudomonas and Acinetobacter KTUs were associated with enhanced functional performance, consistent with their genetic potential to degrade catechol. Conversely, KTU001 (Achromobacter) consistently exhibited a negative association with community-level function despite its high relative abundance in the original community and predicted capacity for catechol degradation. This discrepancy highlights that genetic potential inferred from metagenomics does not necessarily translate into a positive functional association, potentially because of comparatively slow metabolic flux and/or inhibitory effects on other key community members. Furthermore, a RuleFit model suggested that the positive functional associations of KTU005 (Pseudomonas) and KTU002 (Acinetobacter) might be attenuated in the presence of other community members, such as KTU004 (Corynebacterium). These context-dependent contributions and interactions, which are difficult to infer from metagenomic or isolation-based approaches alone, underscore the value of SubCom analysis in generating mechanistic hypotheses that can inform the rational control and design of functional microbial communities.
This study represents a single implementation of SubCom analysis, reflecting specific choices in cultivation, phenotyping, and data processing, and it highlighted several practical challenges. A key challenge is that community composition was profiled after cultivation, which increased uncertainty in sequence-based characterization of subcommunity composition. This issue was illustrated by the potential loss or lack of detection of specific taxa, e.g., KTU003 (Caballeronia), that might have contributed functionally during the early stages of cultivation but were absent or rare in the sequencing data used for model inference. To address such community dynamics, community composition should ideally be profiled before or during functional readouts. One approach is to pre-culture subcommunities under conditions that mimic the original environment (e.g., in filter-sterilized supernatant from the parental community) and then splitting each culture for sequencing and functional assays.
In addition, extending this approach to a wider range of microbial communities will require further optimization of three key aspects: the number and diversity of subcommunities, culture conditions, and functional assessment. First, although we performed the present analyses using 558 subcommunities (including 87 functional subcommunities) from this enrichment-derived, moderately diverse community, the sample size required for reliable inference in more diverse communities remains unclear. Larger datasets would likely generate a wider range of subcommunity compositions and improve the coverage of low-prevalence taxa, permitting more confident estimation of candidate taxon effects. Although increasing the diversity within each subcommunity may improve taxonomic coverage, it can also reduce interpretability by making functional variation more difficult to associate with individual taxa [23] and by reducing stochastic compositional variation among subcommunities. Future studies should therefore improve scalability of SubCom analysis by integrating higher-throughput phenotyping and profiling platforms, such as microdroplet-based technologies [46].
Second, optimizing culture conditions is essential because SubCom analysis currently relies on cultivation-dependent functional assessment. In this study, most constituent taxa were recovered using the same medium as that used for the original community. However, for microbial communities from more natural environments, media that better mimic the original environment, such as filter-sterilized supernatant, may be required. Although laboratory batch cultivation cannot fully reproduce environmental fluctuations or the continuous influx and diffusive loss of substrates and metabolites, incorporating in situ cultivation strategies [47] may help address this limitation. In addition, because many microbial communities exert beneficial or detrimental functions in biofilm states, future studies should examine whether SubCom analysis can be extended to culture conditions that allow biofilm formation.
Third, functional assessment of subcommunities requires high-throughput readouts, and there remains room for improvement beyond spectroscopic measurements. For example, high-throughput mass spectrometry [48] or Raman spectroscopy [49] could provide more detailed molecular-level readouts, potentially helping to elucidate detailed metabolic dynamics or pathways within communities. It is also important to generate an appropriate degree of functional variation among subcommunities. In this study, KTU003 (Caballeronia) appeared to be essential for aniline degradation; consequently, many subcommunities lacking this taxon were classified as nonfunctional. Thus, depending on the functional architecture of the target community, it may be necessary to design subcommunities so that they include the minimum set of taxa required for functional expression.
In addition to experimental considerations, analytical choices also influenced the implementation and interpretation of SubCom analysis. For data analysis, we used binary (0/1) compositional features rather than raw relative abundance data. Relative abundance profiles can be influenced by transient fluctuations and by the inherent interdependence of taxa in compositional datasets, in which an increase in one member necessarily reduces the relative abundance of others [50]. Presence/absence representations therefore provide a more robust summary of community membership. Building on this representation, we evaluated two tree-based models suited to binary compositional inputs, XGBoost and RuleFit. Although the models were broadly consistent, they yielded some divergent taxon-level contributions. Moreover, the more interpretable RuleFit model showed lower predictive performance (r = 0.766) than XGBoost (r = 0.894), highlighting an inherent trade-off between interpretability and predictive reliability. More broadly, machine-learning–based analysis of microbial community datasets is becoming increasingly active, and many studies have attempted to learn predictive relationships directly from whole-community profiles [51–53]. Against this backdrop, our results suggest that combining subcommunity measurements with tree-based models provides a practical route to inferring taxon-specific contributions and interaction contexts from microbial community data.
Conclusions
This study provided a practical implementation of SubCom analysis using an aniline-degrading microbial community as a model system. By combining scalable subcommunity construction and phenotyping with interpretable modelling, this framework enables the inference of candidate taxon-specific contributions and interaction contexts associated with community-level function in a complex that are difficult to infer from existing meta-omics or culture-dependent approaches alone. Although SubCom analysis identifies statistical associations rather than direct biological causality, when combined with such approaches, it might contribute to a more mechanistic understanding of community function. With continued advances in high-throughput cultivation, phenotyping, and modelling, this framework might provide a useful basis for understanding and, ultimately, manipulating a broad range of microbial community functions.
Supplementary Information
Acknowledgements
Not applicable.
Authors’ contributions
H.I. conceived the study. M.K., S.N., and K.K. conducted lab work. H.I., S.N., and M.T. analyzed and interpreted the data. H.I. wrote the manuscript. All authors reviewed and edited the manuscript.
Funding
This work was supported by JST, ACT-X (JPMJAX22B1), Research Grants by Kurita Water and Environment Foundation (22E053, 23K008), and Gene-grant 2023 by Nippon Genetics Co., Ltd. to Hidehiro Ishizawa.
Data availability
The 16S rRNA gene sequences of the bacterial isolates were deposited in the DDBJ/EMBL/GenBank database under accession numbers LC921213–LC921214. Raw sequence reads were deposited under the accession number PRJDB40535. All experimental data and analytical codes have been deposited in Zenodo [54].
Declarations
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Hidehiro Ishizawa, Miku Kito and Sunao Noguchi contributed equally to the work.
References
- 1.Gilbert JA, Blaser MJ, Caporaso JG, Jansson JK, Lynch SV, Knight R. Current understanding of the human microbiome. Nat Med. 2018;24:392–400. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 2.Wu L, Ning D, Zhang B, Li Y, Zhang P, Shan X, et al. Global diversity and biogeography of bacterial communities in wastewater treatment plants. Nat Microbiol. 2019;4:1183–95. [DOI] [PubMed] [Google Scholar]
- 3.Singh BK, Trivedi P, Egidi E, Macdonald CA, Delgado-Baquerizo M. Crop microbiome and sustainable agriculture. Nat Rev Microbiol. 2020;18:601–2. [DOI] [PubMed] [Google Scholar]
- 4.Bahram M, Espenberg M, Pärn J, Lehtovirta-Morley L, Anslan S, Kasak K, et al. Structure and function of the soil microbiome underlying N2O emissions from global wetlands. Nat Commun. 2022;13:1430. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 5.Sanchez-Gorostiaga A, Bajić D, Osborne ML, Poyatos JF, Sanchez A. High-order interactions distort the functional landscape of microbial consortia. PLoS Biol. 2019;17:e3000550. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 6.Bergelson J, Kreitman M, Petrov DA, Sanchez A, Tikhonov M. Functional biology in its natural context: a search for emergent simplicity. eLife. 2021;10:e67646. [DOI] [PMC free article] [PubMed]
- 7.Yang X, Yang T, Zhang Z, Zhang Y, Mei X, Gao Y, et al. Substrate utilization and cross-feeding synergistically determine microbiome resistance to pathogen invasion. Nat Ecol Evol. 2026;10:211–20. [DOI] [PubMed] [Google Scholar]
- 8.Kalyuzhnaya MG, Lapidus A, Ivanova N, Copeland AC, McHardy AC, Szeto E, et al. High-resolution metagenomics targets specific functional types in complex microbial communities. Nat Biotechnol. 2008;26:1029–34. [DOI] [PubMed] [Google Scholar]
- 9.Garza DR, van Verk MC, Huynen MA, Dutilh BE. Towards predicting the environmental metabolome from metagenomics with a mechanistic model. Nat Microbiol. 2018;3:456–60. [DOI] [PubMed] [Google Scholar]
- 10.Clark RL, Connors BM, Stevenson DM, Hromada SE, Hamilton JJ, Amador-Noguez D, et al. Design of synthetic human gut microbiome assembly and butyrate production. Nat Commun. 2021;12:3254. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 11.Gowda K, Ping D, Mani M, Kuehn S. Genomic structure predicts metabolite dynamics in microbial communities. Cell. 2022;185:530-46.e25. [DOI] [PubMed] [Google Scholar]
- 12.Zhou Z, Tran PQ, Breister AM, Liu Y, Kieft K, Cowley ES, et al. METABOLIC: high-throughput profiling of microbial genomes for functional traits, metabolism, biogeochemistry, and community-scale functional networks. Microbiome. 2022;10:33. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 13.Bald S, Zhang J, Nelson R, Scott DC, Dukovski I, de Raad M, et al. Metabolic blueprints of monocultures enable prediction and design of synthetic microbial consortia. bioRxiv. 2026:2026.01.11.698878.
- 14.Friedman J, Higgins LM, Gore J. Community structure follows simple assembly rules in microbial microcosms. Nat Ecol Evol. 2017;1:0109. [DOI] [PubMed] [Google Scholar]
- 15.Ishizawa H, Tashiro Y, Inoue D, Ike M, Futamata H. Learning beyond-pairwise interactions enables the bottom-up prediction of microbial community structure. Proc Natl Acad Sci U S A. 2024;121:e2312396121. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 16.Pinto S, Benincà E, van Nes EH, Scheffer M, Bogaards JA. Species abundance correlations carry limited information about microbial network interactions. PLoS Comput Biol. 2022;18:e1010491. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 17.Poupin MJ, González B. Embracing complexity in plant-microbiome systems. Environ Microbiol Rep. 2024;16:e70000. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 18.Skwara A, Gowda K, Yousef M, Diaz-Colunga J, Raman AS, Sanchez A, et al. Statistically learning the functional landscape of microbial communities. Nat Ecol Evol. 2023;7:1823–33. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 19.Sanchez A, Bajic D, Diaz-Colunga J, Skwara A, Vila JCC, Kuehn S. The community-function landscape of microbial consortia. Cell Syst. 2023;14:122–34. [DOI] [PubMed] [Google Scholar]
- 20.Ruiz J, de Celis M, Diaz-Colunga J, Vila JC, Benitez-Dominguez B, Vicente J, et al. Predictability of the community-function landscape in wine yeast ecosystems. Mol Syst Biol. 2023;19:e11613. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 21.Emmenegger B, Massoni J, Pestalozzi CM, Bortfeld-Miller M, Maier BA, Vorholt JA. Identifying microbiota community patterns important for plant protection using synthetic communities and machine learning. Nat Commun. 2023;14:7983. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 22.Diaz-Colunga J, Skwara A, Vila JCC, Bajic D, Sanchez A. Global epistasis and the emergence of function in microbial consortia. Cell. 2024;187:3108-19.e30. [DOI] [PubMed] [Google Scholar]
- 23.Ishizawa H, Noguchi S, Kito M, Nomura Y, Kimura K, Takeo M. Decoding emergent properties of microbial community functions through subcommunity observations and interpretable machine learning. ISME J. 2025;19:wraf236. [DOI] [PMC free article] [PubMed]
- 24.Kulkarni M, Chaudhari A. Microbial remediation of nitro-aromatic compounds: an overview. J Environ Manage. 2007;85:496–512. [DOI] [PubMed] [Google Scholar]
- 25.Ye J-C, Zhao Q-S, Liang J-W, Wang X-X, Zhan Z-X, Du H, et al. Bioremediation of aniline aerofloat wastewater at extreme conditions using a novel isolate Burkholderia sp. WX-6 immobilized on biochar. J Hazard Mater. 2023;456:131668. [DOI] [PubMed]
- 26.Hu B, Wang M, Geng S, Wen L, Wu M, Nie Y, et al. Metabolic exchange with non-alkane-consuming Pseudomonas stutzeri SLG510A3–8 improves n-alkane biodegradation by the alkane degrader Dietzia sp. strain DQ12–45–1b. Appl Environ Microbiol. 2020;86:e02931–19. [DOI] [PMC free article] [PubMed]
- 27.D’Souza G, Schwartzman J, Keegstra J, Schreier JE, Daniels M, Cordero OX, et al. Interspecies interactions determine growth dynamics of biopolymer-degrading populations in microbial communities. Proc Natl Acad Sci U S A. 2023;120:e2305198120. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 28.Peng Q, Zhao C, Wang X, Cheng K, Wang C, Xu X, et al. Modeling bacterial interactions uncovers the importance of outliers in the coastal lignin-degrading consortium. Nat Commun. 2025;16:639. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 29.Coleman NV, Mattes TE, Gossett JM, Spain JC. Biodegradation of cis-dichloroethene as the sole carbon source by a β-proteobacterium. Appl Environ Microbiol. 2002;68:2726–30. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 30.Sarker SD, Nahar L, Kumarasamy Y. Microtitre plate-based antibacterial assay incorporating resazurin as an indicator of cell growth, and its application in the in vitro antibacterial screening of phytochemicals. Methods. 2007;42:321–4. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 31.Balbaied T, Moore E. Resazurin-based assay for quantifying living cells during alkaline phosphatase (ALP) release. Appl Sci. 2020;10:3840. [Google Scholar]
- 32.Callahan BJ, McMurdie PJ, Rosen MJ, Han AW, Johnson AJA, Holmes SP. DADA2: high-resolution sample inference from Illumina amplicon data. Nat Methods. 2016;13:581–3. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 33.Liu P-Y, Yang S-H, Yang S-Y. KTU: K-mer Taxonomic Units improve the biological relevance of amplicon sequence variant microbiota data. Methods Ecol Evol. 2022;13:560–8. [Google Scholar]
- 34.Chen C-C, Xie Q-Y, Chuang P-S, Darnajoux R, Chien Y-Y, Wang W-H, et al. A thallus-forming N-fixing fungus-cyanobacterium symbiosis from subtropical forests. Sci Adv. 2025;11:eadt4093. [DOI] [PMC free article] [PubMed]
- 35.Quast C, Pruesse E, Yilmaz P, Gerken J, Schweer T, Yarza P, et al. The SILVA ribosomal RNA gene database project: improved data processing and web-based tools. Nucleic Acids Res. 2013;41:D590–6. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 36.Chen T, Guestrin C. XGBoost: a scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York (NY): Association for Computing Machinery; 2016:785–94.
- 37.Friedman JH, Popescu BE. Predictive learning via rule ensembles. Ann Appl Stat. 2008;2:916–54. [Google Scholar]
- 38.Blazanin M. gcplyr: an R package for microbial growth curve data analysis. BMC Bioinformatics. 2024;25:232. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 39.Lundberg S, Lee S-I. A unified approach to interpreting model predictions. arXiv 2017:1705.07874.
- 40.OECD. OECD Guidance for Testing Chemicals: Ready Biodegradability. 1992.
- 41.Ouchiyama N, Ohshima Y, Yonezawa Y, Omori T. Degradation of aniline in the biodegradation test: changes of bacterial population and isolation of aniline degradable bacteria from activated sludge. Environ Sci. 1996;9:35–43. [Google Scholar]
- 42.Vázquez-Rodríguez GA, Garabétian F, Rols J-L. Inocula from activated sludge for ready biodegradability testing: homogenization by preconditioning. Chemosphere. 2007;68:1447–54. [DOI] [PubMed] [Google Scholar]
- 43.Dalmijn J, Poursat BAJ, van Spanning RJM, Brandt BW, de Voogt P, Parsons JR. Influence of short- and long-term exposure on the biodegradation capacity of activated sludge microbial communities in ready biodegradability tests. Environ Sci Water Res Technol. 2021;7:107–21. [Google Scholar]
- 44.Takeo M, Fujii T, Maeda Y. Sequence analysis of the genes encoding a multicomponent dioxygenase involved in oxidation of aniline and o-toluidine in Acinetobacter sp. strain YAA. J Ferment Bioeng. 1998;85:17–24. [Google Scholar]
- 45.Takeo M, Ohara A, Sakae S, Okamoto Y, Kitamura C, Kato D, et al. Function of a glutamine synthetase-like protein in bacterial aniline oxidation via γ-glutamylanilide. J Bacteriol. 2013;195:4406–14. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 46.Hsu RH, Clark RL, Tan JW, Ahn JC, Gupta S, Romero PA, et al. Microbial interaction network inference in microfluidic droplets. Cell Syst. 2019;9:229-42.e4. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 47.Berdy B, Spoering AL, Ling LL, Epstein SS. In situ cultivation of previously uncultivable microorganisms using the ichip. Nat Protoc. 2017;12:2232–42. [DOI] [PubMed] [Google Scholar]
- 48.Dueñas ME, Peltier-Heap RE, Leveridge M, Annan RS, Büttner FH, Trost M. Advances in high-throughput mass spectrometry in drag discovery. EMBO Mol Med. 2022;15:e14850. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 49.Pezzotti G. Raman spectroscopy in cell biology and microbiology. J Raman Spectrosc. 2021;52:2348–443. [Google Scholar]
- 50.Roche KE, Mukherjee S. The accuracy of absolute differential abundance analysis from relative count data. PLoS Comput Biol. 2022;18:e1010284. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 51.Hernández Medina R, Kutuzova S, Nielsen KN, Johansen J, Hansen LH, Nielsen M, et al. Machine learning and deep learning applications in microbiome research. ISME Commun. 2022;2:98. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 52.Thompson J, Johansen R, Dunbar J, et al. Machine learning to predict microbial community functions: an analysis of dissolved organic carbon from litter decomposition. PLoS ONE. 2019;14:e0215502. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 53.Dutta A, Goldman T, Keating J, et al. Machine learning predictions biogeochemistry from microbial community structure in a complex model system. Microbiol Spectr. 2022;10:e01901-e1921. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 54.Ishizawa H. Data and analytical codes for: Ishizawa, Kito, Noguchi et al. SubCom analysis: dissecting microbial community functions into taxon-specific contributions and interaction contexts. Zenodo. 2026. [DOI] [PMC free article] [PubMed]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
The 16S rRNA gene sequences of the bacterial isolates were deposited in the DDBJ/EMBL/GenBank database under accession numbers LC921213–LC921214. Raw sequence reads were deposited under the accession number PRJDB40535. All experimental data and analytical codes have been deposited in Zenodo [54].






