IS-capades of Klebsiella pneumoniae: Insertion sequences drive metabolic loss in obscure sub-lineages
Department of Infectious Diseases, School of Translational Medicine, Monash University, Melbourne, Victoria, Australia
Centre to Impact AMR, Monash University, Clayton, Victoria, Australia
Department of Infection Biology, London School of Hygiene and Tropical Medicine, London, UK
*Corresponding authors Ben Vezina (benjamin.vezina@monash.edu); Margaret M. C. Lam (margaret.lam@monash.edu)Abstract
Introduction
Klebsiella pneumoniae is an opportunistic pathogen which causes a wide spectrum of infections within healthcare settings and the community. Four K. pneumoniae sub-lineages defined with cgMLST/LINcodes are known to cause distinct infections of the nasal and/or upper respiratory passages: SL91 and SL10031 (also referred to as subspecies ozaenae), SL10032 (subspecies rhinoscleromatis) and SL82. These sub-lineages have also demonstrated reduced carbon source utilisation, which in other species has been linked with high loads of insertion sequences (IS).
Methods
We performed comparative genomics, analysed IS and constructed genome-scale metabolic models for available public sequences from these four sub-lineages and compared them to other sub-lineages from the wider K. pneumoniae population.
Results
The four focal sub-lineages displayed significantly higher IS loads (median range 88 to 120 per genome) compared to other K. pneumoniae sub-lineages (median range 12 to 73). Notably, each K. pneumoniae sub-lineage had unique IS profiles, consistent with distinct evolutionary trajectories of IS acquisition and expansion. Across sub-lineages, higher IS loads were inversely associated with the number of metabolic model genes per genome (R2 = 0.16, p <0.001), as well as predicted aerobic substrate utilisation for phosphorus sources (R2 = 0.39, p<0.001) as per a second-degree polynomial regression model (n = 1,664 genomes). Additionally, the four IS-dense sub-lineages displayed a combination of convergent sub-lineage-specific substrate utilisation losses including parallel loss of 3-Phospho-D-glycerate, D-Glycerate-2-phosphate, Phosphoenolpyruvate utilisation as carbon/phosphorus sources. Finally, inspection of IS insertion sites demonstrated frequent and non-destructive insertion next to transcriptional, carbohydrate and amino acid metabolism genes.
Conclusions
IS loads were significantly and inversely associated with metabolic substrate usage within K. pneumoniae, whereby sub-lineages that had higher numbers of IS also had reduced metabolic capacity. We hypothesise that an insertional tolerance model explains these findings, whereby IS can only insert into “metabolically-tolerable” sites for the individual cell and any impacts on metabolism are not detrimental for survival.
Article notes
Competing Interest Statement
The authors have declared no competing interest.
Introduction
Klebsiella pneumoniae is an opportunistic pathogen which causes a diverse range of infections within healthcare settings such as pneumonia, bloodstream, surgical site and urinary tract infections. It is also a causative agent of infections in the community, associated with a unique subset of K. pneumoniae sub-lineages distinct from those that cause healthcare-associated infections (1). As a species, K. pneumoniae exhibits a remarkable amount of genome diversity, with hundreds of unique ‘deep-branching’ sub-lineages and significant variation in its accessory genome content (1, 2). This diversity is likely an important driver of the different lifestyles and variable virulence profiles of K. pneumoniae.
Two sub-lineages of K. pneumoniae, clonal groups CG67 and CG90/91 based on 7-gene MLST and formally designated as subspecies rhinoscleromatis and ozaenae, respectively, cause rare but unique chronic infections typically associated with the nasal and/or upper respiratory passages. Whole genome sequencing has since clarified that both are divergent sub-lineages of K. pneumoniae rather than separate subspecies as previously characterised Error! Reference source not found.(3). The K. pneumoniae LINcode taxonomic scheme (based on a 629-loci core genome MLST) assigns K. pneumoniae into >705 discrete sub-lineages (4). Our sub-lineages of interest are SL10032 (previously rhinoscleromatis or CG67) and SL10031/SL91 (previously ozeanae or CG90/CG91). SL10032 strains cause a chronic granulomatous disease described as rhinoscleroma, whereas SL91 and SL10031 typically cause atrophic rhinitis or ozena. There have been at least 63 cases of rhinoscleromatis (5-9) and 45 ozaenae (8-22) infections documented in modern medical literature dating back to 1944, although there appears to be archaeological evidence of rhinoscleroma as far back as 300-600 AD from Maya (modern day Guatemala) (23). While these sub-lineages are usually associated with the nasopharyngeal sites, there is strong historical proof that they are able to colonise other body sites including the urinary tract, soft tissue, blood, cerebral spinal fluid and gastrointestinal tract (11, 12, 18, 21, 24, 25). Additionally, these sub-lineages have also been found in non-human hosts, isolated from cockroaches, cattle and chicken meat (13, 21, 22).
Aside from their characteristic clinical presentations, these sub-lineages display a reduced metabolic capacity in biochemical tests compared to other K. pneumoniae sub-lineages (3, 26), explaining why they were originally considered distinct sub-species. These sub-lineages, along with SL82 (ST82 or CG82 based on 7-gene MLST), have demonstrated reduced phenotypic carbon source utilisation (3). A link between this metabolic reduction and niche/pathogenic lifestyle adaptation has been posited (3). This phenomenon has also been observed in other bacterial pathogens such as Shigella species and Bordetella pertussis (27). Shigella in particular is associated with the accumulation of insertion sequences (IS) (28). Reduced carbon utilisation is also seen in SL82 (3), which along with ozaenae were unique amongst K. pneumoniae in lacking the mrkD type III fimbrial adhesin. SL82 expressed the virulence-associated K1 capsule serotype. Similar to the other sub- lineages of interest, SL82 was noted to be strongly associated with respiratory infections (8/11 BioSample IDs with sample metadata).
In this study, we performed a systematic analysis on a dereplicated collection of 1,664 completed and 210 draft K. pneumoniae genomes, to investigate the prevalence and impacts of IS on metabolic capacity in these four sub-lineages of interest. We hypothesised that, similar to Shigella, IS caused genome degradation and the loss of metabolic capabilities in these sub-lineages.
Methods
Genome acquisition, assembly and annotation
Complete K. pneumoniae genome assemblies (n=2,302) were initially downloaded from NCBI RefSeq (accessed on 04/07/2024, Table S1). To further expand genome numbers and improve robustness of population-level inferences, 210 dereplicated NCBI BioSample IDs of target sub-lineages were obtained from BIGSdb (29) by selectively downloading genomes which matched the 4 sub-lineages of interest and their associated Sequence Types when no LINcode was determined, including SL10032 (ST67, ST3818, ST3819), SL91 (ST91, ST381, ST3766, ST3768), SL10031 (ST91) and SL82 (ST82, ST3764). Where available, short-read sequence reads were downloaded from SRA (n=201), otherwise assembled sequences were downloaded from Genbank (n=20) (accessed on 29/10/2024, Table S1).
Short-read sequence data were assembled with Unicycler v0.5.1 (30). Low quality genomes were removed if they had >300 graphical fragment assembly dead ends, or in absence of assembly graphs, an N50 of <65,000. This threshold was more lenient than previously defined quality control metrics (31), to account for IS fragmenting short read draft assemblies, resulting in larger contig numbers and dead end counts. Remaining genomes (n=2,108) were then dereplicated using Assembly-Dereplicator v0.1.0 (32) using the following specifications: ‘--threshold 0.0003’. This resulted in a collective dataset of 1,874 dereplicated genomes. All genomes were annotated using Bakta v1.8.1 (33).
Lineage assignment and genotyping
Dereplicated genomes were uploaded to Pathogenwatch (https://pathogen.watch/) for genotyping; namely to confirm species and assign sub-lineage, clonal groups and LIN codes (4, 34). A neighbour-joining tree was generated with PopPUNK v2.4.0 (35) as follows. The ‘create-db’ function was used with the following options: ‘--sketch-size 1000000 --min-k 15 -- max-k 29 --qc-filter prune’. The ‘fit-model’ function was subsequently used with the following options: ‘bgmm --ranks 1,2,3,5 --graph-weights --K 3’. Additionally, the ‘poppunk_visualise’ function was used, with the ‘--distances’ and ‘--previous-clustering’ parameters, to output a neighbour joining tree. Kaptive v3.1.0 (36, 37) was used to identify capsule synthesis loci (KL), and genotyping was performed with Kleborate v3.1.3 (38).
Insertion Sequence analysis
Plasmids were filtered out from the complete genome sequences using seqtk v1.3 (41), with the following command: “seq -L 4500000”. Genomes were rotated to dnaA at base pair position 1 using rotate v1.0 (42) with the following command: “-s gtgtcactttcgctttggcagcagtgtcttgcccgattgcaggatgagtt -m 5”, to facilitate comparison of chromosomal synteny. Rotated, plasmid-free genomes (i.e. the chromosome) were used for the remaining analyses.
ISEScan v1.7.2.3 (43) was used to identify IS elements, which also identifies novel IS elements with divergence from known IS in the ISEScan database. For comparisons within SL82, SKA v1.0.0 (44) was used to determine single nucleotide variants (SNV) using ska fasta followed by ska distance -s 25. Within sub-lineages, specific phylogenetic minimum evolution trees were constructed using SNV distances inferred from SKA, optimized via Nearest Neighbour Interchange (NNI) with the fastme.bal command from R package ape v5.8 (45), then midpoint rooted via midpoint.root from phytools v2.3-0 (46). All-vs-all whole genome alignments were performed using MUMmer4 v4.0.0 (47) using “nucmer -p”, then coordinates extracted using “show-coords -d -l -T”.
Genome locus comparisons were performed by extracting gene coordinates via slice_multi_gbk.py (https://github.com/bananabenana/slice_multi_gbk) and Clinker v0.0.31 (48) was used for visualisation.
Statistical analysis and code
R v4.4 (49) and RStudio v2024.04.2+764 (50) were used for statistical analysis and visualisation. R packages tidyverse v2.0,0 (51), ggtree v3.12.0 (52), colorspace v2.1-0 (53), ggpmisc v0.6.0 (54), ggpubr v0.6.0 (55), ggh4x v0.2.8 (56), rstatix v0.7.2 (57), gggenomes v1.0.0 (58) and patchwork v1.2.0 (59) were used. All R code can be found at Figshare (doi: 10.6084/m9.figshare.28341917).
Linear regression was performed between IS loads and the ratio of nucleotides assigned to IS vs total chromosomal sequence. IS loads between sub-lineages were compared using a Kruskal-Wallis test with Holm adjustment for multiple comparisons, followed by a Dunn’s post hoc test with Holm adjustment for multiple comparisons.
Results
Dataset description
To explore the impact of IS in K. pneumoniae, we utilised two dereplicated datasets: i) a collection of complete genomes (n=1,664) used to quantify the exact numbers of IS within chromosomal sequences and phylogenetic clusters; and ii) an expanded collective dataset (n=1,874) which included targeted inclusion of draft assemblies. Throughout the manuscript, we will explicitly state which dataset was used. We found that 26 draft assemblies failed Pathogenwatch’s quality control measures (Table S1), as they had >500 contigs, despite having high levels of genome completeness (≤300 graphical fragment assembly dead ends). We suspected high contig numbers may be caused by large numbers of IS and these assemblies were kept for analysis.
Significant diversity was observed in the expanded dataset (n=1,874), which was made up of 244 sub-lineages (based on cgMLST). To ensure appropriate population-level inferences, only sub-lineages with n≥3 genomes were included for further analysis, resulting in a dataset of n=1,441 genomes representing 65 sub-lineages. The majority of genomes were from sub-lineages associated with known multi-drug resistant (n=1,013 across 14 MDR SLs; 61.69%) or hypervirulent clones (n=129 from 4 hypervirulent SLs; 7.86%) as defined by Wyres et al (1) (Table S1).
Some sub-lineages display unusually high IS loads
Plasmid-free complete genomes (n=1,664) were screened for IS, and the numbers and types (i.e. IS families) were compared across the 65 sub-lineages with n≥3 genomes (Fig. 1). As expected, linear regression indicated a strong, positive correlation (R2 = 0.89, p<0.001) between IS loads and the ratio of nucleotides assigned to IS vs total chromosomal sequence (Fig. S1). Across each sub-lineage, the number of IS per genome (i.e. IS-load) varied from 10 to 131 (median 31). A total of 132 unique IS from 23 distinct IS families were detected across this dataset. Sub-lineages contained 3 to 20 distinct IS families, of which only three IS families (IS3, IS21 and ISNCY) were found in every sub-lineage. Lineage-specific IS patterns were identified (Fig. S2, Table S2). Aside from five novel IS (Novel 20, 24, 189, 272 and 348, which were detected in sub-lineages SL43, SL91, SL107, SL147 and SL17, respectively. No other IS families were restricted to a single sub-lineage. An additional 19 IS were rarely detected across the population (i.e. found in <10 sub-lineages).
Sub-lineages SL82, SL91-ozaenae, SL10031-ozaenae and SL10032-rhinoscleromatis carried the highest IS loads, with median 88 to 120 IS per genome compared to other SLs (median 12 to 73, Fig. 1). Kruskal-Wallis with Holm error correction indicated sub-lineages had significantly different IS loads (p < 0.0001). This was followed by a Dunn’s post hoc test with Holm error correction, showing SL82 had significantly more IS per genome than 37 other sub-lineages (p-values <0.05), while SL91-ozaenae, SL10031-ozaenae and SL10032-rhinoscleromatis had significantly higher IS loads than 25, 5 and 6 other sub-lineages, respectively (Table S2). There were no significant differences between SL0032-rhinoscleromatis (median 120 ± 2 IQR), SL91-ozaenae (median 113 ± 21.5 IQR), SL82 (median 112 ± 7 IQR) or SL10031-ozanae (median 88 ± 1). We focused on these four IS-dense sub-lineages for the remaining analyses. The complete genome set was supplemented with additional short-read assemblies that could be assigned LINcodes, resulting in a total of n=1,874 genomes, which included n=4 SL10032-rhinoscleromatis, n=15 SL91-ozaenae, n=5 SL10031-ozaenae, and n=36 SL82.
This statistical analysis also revealed that several other sub-lineages displayed significantly higher IS loads compared to others (Table S2). This included genomes that corresponded to MDR (SL258, SL15, SL395), hypervirulent (SL65) and common clones (SL34, SL3010), although there appeared to be within-clone variation in many sub-lineages. For example, the number of IS per genome within sub-lineage SL258 ranged from 22 to 80. Within sub-lineage variability in IS loads was typically larger for sub-lineages represented by more genomes. With the exception of our four sub-lineages of interest, the IS loads were generally similar across other clones regardless of MDR or hypervirulence status.
Aside from isolates of unknown sampling site (n=42, 70% of genomes from the four sub-lineages of interest), the remaining isolates were recovered from human nasopharyngeal sites including sputum (n=8), nasopharynx (n=6), maxillary sinuses (n=2), pleural cavity (n=1) and throat (n=1) (Table S1). One additional isolate was isolated from blood (n=1). While source metadata was missing for many of the SL10032-rhinoscleromatis and SL91-ozanae isolates, sampling dates indicated collection between 1920 to 1952. Many samples collected during this period were generally of clinical origin. While there is likely a sequencing bias for clinical isolates, these sub-lineages have previously been isolated from a variety of non-human sources including chicken meat, cattle and cockroaches (13, 21, 22), although no such isolates are currently represented in public genome repositories.
IS profiles varied within IS-dense sub-lineages
The four focal IS-dense sub-lineages contained 16 (SL91-ozaenae), 15 (SL82), 13 (SL10031-ozaenae) and 10 (SL10032-rhinoscleromatis) IS families (Fig. 2). Of these, seven IS families (IS1, ISL3, IS21, IS66, IS256, ISNCY and IS200/IS605) were detected across all four lineages (Fig. S2). The IS profile of SL10032-rhinoscleromatis was the most distinct from the others while the closely-related ozaenae sub-lineages and SL82 shared highly similar IS profiles, consistent with their divergence from a more recent common ancestor.
Most notable is the considerable expansation of IS1 in SL82 (mean 71.53±6.31 SD copies per genome), SL91-ozaenae (70.14±7.9) and SL10031-ozaenae (51.3±3.5) genomes, while it was conversely rarer in SL10032-rhinoscleromatis; (1±0). IS1 expansion (mean ≥10 copies) was not specific to these sub-lineage and was found in six others including hypervirulent SL25 and other clones SL10022 and SL383.
There were, however, notable differences between the four focal sub-lineages and which IS families had undergone significant expansions. For example, expansion of IS3 was observed in SL10032-rhinoscleromatis (mean of 53±1 SD copies per genome) and SL82 (12.8±3.2), while SL91-ozanae and SL10031-ozanae carried 3.7±1 or no IS3, respectively. ISL3 was highly expanded in SL10032-rhinoscleromatis (24±1), SL91-ozaenae (10.57±10.81), SL10031-ozaenae (9±2), but was largely absent in SL82 (1±0). In SL10032-rhinoscleromatis, IS3, ISL3 and IS21 comprised the largest proportions of IS (mean 53±1, 24±1 and 22.7±0.6 SD copies per genome, respectively), while carrying fewer IS1 (mean 1±0 copies).
Discussion
Reduced metabolic versatility has previously been documented in select sub-lineages of K. pneumoniae: SL10032-rhinoscleromatis, SL10031-ozaenae, SL91-ozaenae and SL82 (3). This is thought to be an important driver of their unique ecological and pathogenic profiles, particularly as these strains are often isolated from the upper respiratory tract but are by no means restricted to these sites or human host (13, 21, 22). In this study, application of genome-scale metabolic modelling supported significant loss of substrate usage across SL82, SL10031-ozaenae, SL91-ozaenae and SL10032-rhinoscleromatis compared to other K. pneumoniae sub-lineages. In particular, these sub-lineages appear to have lost the ability to utilise gut microbe/human metabolites for energy including 3-Phospho-D-glycerate, D-glycerate-2-phosphate, phosphoenolpyruvate, 3-hydroxyphenylacetic acid and 5-aminopentanoate (64-68), along with myo-Inositol hexakisphosphate found in plant tissues and human diet (70) and human metabolites (R)-3-hydroxybutanoate (liver) (71) and 4-Aminobutanoate (neurotransmitter) (72). These hint that these sub-lineages have deviated from other K. pneumoniae sub-lineages that readily colonise the gut prior to infection (69).
We demonstrate for the first time that these four sub-lineages also have significantly higher IS loads (Fig. 1), which has been linked to streamlining of metabolic profiles in Bordetella pertussis and various Shigella species (27, 28). IS has been previously quantified within K. pneumoniae SL258 (ST258) (73), which found a stable repertoire of IS elements and small within-lineage variation (specifically, an increase in IS load in one subclade of SL258, referred to as ST258B). This is consistent with the IS profiles and within-sub-lineage variation that were observed in our study (Fig. 1, Fig. 2, Table S2), such as intermediate rather than complete loss of core K. pneumoniae substrates within a sub-lineage (Fig. 5). Notably, the lack of impact IS had on the metabolism of SL258 differed from that of the four focal sub-lineages. This indicated that K. pneumoniae sub-lineages have different relationships and IS-mediated evolutionary trajectories. This analysis was limited by the sampling biases of public data, and the relative rarity of these particular sub-lineages.
Direct IS interruptions of metabolic genes were detected in only a few instances (only 5/323 examples were found). We hypothesize that IS may have been responsible for the initial disruption of other key metabolic genes, whose loss was selectively tolerated at the time of transposition, leading to subsequent genetic degradation of the associated metabolic loci over time. The inverse relationship between IS loads and substrate usage, primarily aerobic carbon and phosphorus usage (Fig. 3, Fig. S4) is consistent with this hypothesis. Insertion of an IS may have caused the initial interruption of the gene but have been subsequently purged from the genome over time -either via recombination, rearrangement or genome degradation. Additionally, higher IS loads potentiate a higher rate of genomic rearrangement (74), deleting genes without direct insertion. This highlighted that DNA sequence analysis of isolated pathogens cannot capture the in vivo conditions or genetic history which shaped the organism even when historical isolates are used. Hawkey et al. noted significant genome degradation from IS insertions in Shigella species which caused metabolic usage losses (28). We did not observe any correlation between IS load and genome length in our dataset, contrasting to Shigella where the two appeared to be related. The metabolic gene losses in both Shigella and the four K. pneumoniae sub-lineages of interest provide insight into the cellular processes required for these pathogens to colonise and progress to invasive human disease. Our data show that while these sub-lineages displayed loss of some K. pneumoniae-specific core traits, they retained use of 552 to 587 core metabolic traits. Given conservation of these core metabolic traits across all K. pneumoniae sub-lineages, these are likely key to the species’ ability to colonise and/or cause infections.
As it currently stands, the metabolic models have broad agreement with previously published biochemical tests (3, 26) (Table 1) whereby these IS-dense sub-lineages exhibited considerable loss of metabolic potential (Fig. 5). The decaying, polynomial relationship between increased number of IS per genome and loss of substrate growth conditions, as well as metabolic genes and reactions (Fig. 3), demonstrates this effect. Lower accuracy scores were observed, (Table 1) and can be explained by various reasons. False positives are not always indicative of model inaccuracies, but usually indicate the presence of metabolic genes which failed to be expressed in the experimental condition due to gene regulation (40, 75), or phenotypically-tested isolates do not have intact copies of key genes. Discrepancies likely stem from strain choice used in biochemical tests, which may not be reflective of the larger population. In some cases, false-positives could be explained by IS interrupting the promoter/regulatory regions required for this expression to occur. For example, the genes required for L-histidine, L-tyrosine, ethanolamine, quinate, 2-Ketoglutarate and putrescine utilisation are all present in the genomes but phenotypically showed no growth. Alternatively, if these false positives did not arise from gene regulation issues, there may be incorrect assumptions being made in the metabolic models, such as over-assignment of metabolic genes. A metabolic model gene is considered ‘present’ if there is ≥25% bi-directional coverage (standard value) (31, 39, 76). This would indicate our model-based analysis is likely underrepresenting the impact of IS reducing the metabolic capacity of isolates. It is also possible that the four focal IS-dense sub-lineages may contain additional novel or specialised metabolism that are not accounted for in the current model.
Insertion of IS not only leads to genomic rearrangements as had been observed for SL82 (Fig. 6) but have also been shown to impact expression of neighbouring genes via their promoters. One prime example is IS1 (61, 62). Considering the vast numbers of IS found across these IS-dense sub-lineages and their close proximity to many regulatory, amino acid and carbohydrate metabolism loci (Fig. S2), it may be that IS are facilitating metabolic specialisation via provision of a selective advantage for organisms by transcriptionally upregulating remaining metabolic traits in addition to purifying unneeded metabolic traits. For example, a copy of IS1 was found directly upstream of the cra catabolite repressor/activator gene in an SL82 genome (accession GCF_900451215) that regulates the acetolactate ilvIN locus responsible for amino acid biosynthesis from pyruvate. Increasing expression of cra may provide a selective advantage for SL82 and balance the effects arising from usage loss of 17 core substrates.
The proximity of IS to metabolic genes could be interpreted as: i) IS ferrying these associated metabolic genes with them during insertion; or ii) IS can only insert into metabolically-tolerable sites for the individual cell, where only metabolism that is not essential for survival can be selectively purified. This insertional tolerance model, combined with potential upregulation of these operons is a compelling hypothesis, as this would improve the fitness of an individual strain via metabolic specialisation. This is consistent with the limited examples of directly interrupted, vestigial metabolic loci observed in our study. Future work could entail using transcriptional data to study the impact of insertions within intergenic regions (62).
Supporting information
Competing interests
The author(s) declare no competing interests.
Data availability
All data used in this study is available as supplemental material (Figs. S1-4, Tables S1-4). Additionally, all analysis code is available at Figshare (doi: 10.6084/m9.figshare.28341917).
Funding
MMCL is supported by an Australian National Health and Medical Research Council Investigator Grant [APP2009163]. JEH is supported by an Australian National Health and Medical Research Council Investigator Grant [APP2034741].
Acknowledgements
This research/work was supported by Monash eResearch capabilities, including M3 and Research Data Storage.
We thank the Institut Pasteur teams for the curation and maintenance of BIGSdb-Pasteur databases at http://bigsdb.pasteur.fr/
Supplemental material
Table S1: Metadata and strain information of all genomes used in this study. Includes BioSample and accession numbers.
Table S2: Results of Insertion Sequence analysis on genomes and statistical analyses
Table S3: Results of substrate usage predictions using metabolic models and comparisons to phenotypic tests
Fig. S1: Scatterplot of number of IS per genome compared to the IS bp:chromosomal bp ratio per genome. Linear regression model fitted to data.
Fig. S2: IS families present in each sub-lineage.
Fig. S3: Scatterplot comparing IS load and metabolic model features of SL258. Squared polynomial model fitted.
Fig. S4: Scatterplot comparing IS load and metabolic model features of all sub-lineages. Squared polynomial model fitted.