Duplications and losses of genes encoding known elements of the stress defence system of the Aspergilli contribute to the evolution of these filamentous fungi but do not directly influence their environmental stress tolerance

Abstract

The contribution of stress protein duplication and deletion events to the evolution of the Aspergilli was studied. We performed a large-scale homology analysis of stress proteins and generated and analysed three stress defence system models based on Saccharomyces cerevisiae, Schizosaccharomyces pombe and Aspergillus nidulans. Although both yeast-based and A. nidulans-based models were suitable to trace evolutionary changes, the A. nidulans-based model performed better in mapping stress protein radiations. The strong Mantel correlation found between the positions of species in the phylogenetic tree on the one hand and either in the A. nidulans-based or S. cerevisiae-based models on the other hand demonstrated that stress protein expansions and reductions contributed significantly to the evolution of the Aspergilli. Interestingly, stress tolerance attributes correlated well with the number of orthologs only for a few stress proteins. Notable examples are Ftr1 iron permease and Fet3 ferro-O₂-oxidoreductase, elements of the reductive iron assimilation pathway, in the S. cerevisiae-based model, as well as MpkC, a HogA-like mitogen activated protein kinase in the A. nidulans-based model. In the case of the iron assimilation proteins, the number of orthologs showed a positive correlation with H₂O₂-induced stress tolerance while the number of MpkC orthologs correlated positively with Congo Red induced cell wall stress, sorbitol induced osmotic stress and H₂O₂ induced oxidative stress tolerances. For most stress proteins, changes in the number of orthologs did not correlate well with any stress tolerance attributes. As a consequence, stress tolerance patterns of the studied Aspergilli did not correlate with either the sets of stress response proteins in general or with the phylogeny of the species studied. These observations suggest that stress protein duplication and deletion events significantly contributed to the evolution of stress tolerance attributes of Aspergilli. In contrast, there are other processes, which may counterbalance the effects of stress gene duplications or deletions including (i) alterations in the structures of stress proteins leading to changes in their biological activities, (ii) varying biosynthesis of stress proteins, (iii) rewiring stress response regulatory networks or even (iv) acquiring new stress response genes by horizontal gene transfer. All these multilevel changes are indispensable for the successful adaptation of filamentous fungi to altering environmental conditions, especially when these organisms are entering new ecological niches.

Introduction

The Kingdom of Fungi is a large and diversified taxon with an estimated 2.2–3.8 million species (Lücking & Hawksworth 2018) occupying a breadth of ecological niches. Extensive fungal genome sequencing has led the construction of MycoCosm, a fungal genomics portal (https://genome.jgi.doe.gov/programs/fungi/index.jsf), which allows mycologists to gain a deeper and unique insight into the evolution of these organisms as new genome sequences continue to fill gaps in the Fungal Tree of Life (Grigoriev et al. 2014). These comparative genomics research projects are fuelled by the fact that the role of fungi in future bioeconomy including fermentation industry, biorefineries and agriculture cannot be overestimated (Baker et al., 2008, Grigoriev et al., 2011, Martin et al., 2011, Lange, 2014, Meyer et al., 2016).

Among filamentous fungi, the ascomycetous genus Aspergillus includes several hundreds of cosmopolitan asexual species with world-wide distribution. Although these fungi seem to occupy various soil habitats with preference (e.g. the black Aspergilli A. aculeatus, A. brasiliensis, A. niger; Supplementary Table S1; Samson et al. 2007) some Aspergillus species are also well-known opportunistic colonisers of animals or even humans (e.g. A. fumigatus, A. flavus, A. niger, A. terreus; Sugui et al. 2014), and some others are indispensable production hosts for a wide spectrum of industrial fermentation and biotechnological processes (e.g. A. niger, A. oryzae, A. terreus; Park et al. 2017). Most Aspergilli have outstanding capabilities for biomass deconstruction with high efficiency due to their unique hydrolytic enzyme repertoire (e.g. A. aculeatus, A. niger, A. oryzae, A. tubingensis; Benoit et al., 2015, Park et al., 2017, Souza Guimarães and da Costa Souza, 2017). Additionally, these fungi are also known to spoil corn, fruits as well as animal feed causing significant economic losses (e.g. A. carbonarius, A. flavus, A. niger; Perrone & Gallo 2016). The Aspergilli are ubiquitously present in indoor environments causing deterioration of artworks and also versatile health complications like asthma (e.g. A. clavatus, A. fumigatus, A. niger, A. versicolor; Egbuta et al., 2017, Mallo et al., 2017).

Not surprisingly, Aspergillus spp. have remarkable oxidative, osmotic, heavy metal and cell wall integrity stress tolerances, which help to explain the plethora of ecological niches these fungi occupy (de Vries et al., 2017, Orosz et al., 2018). As demonstrated by Orosz et al. (2018), some species grow remarkably fast at 37 °C (A. fisheri, A. acidus and A. nidulans) while others can tolerate osmolytes added at high concentrations or are even osmophilic in the presence of either non-ionic (sorbitol; A. glaucus, A. wentii, A. versicolor, A. oryzae) or ionic (NaCl; A. glaucus, A. sydowii, A. versicolor, A. wentii) osmolytes (Supplementary Table S2). Other species are surprisingly tolerant to other types of deleterious environmental stress like oxidative stress (A. nidulans, A. niger, A. oryzae to H₂O₂; A. brasiliensis, A. aculeatus to menadione sodium bisulfite), heavy metal stress (A. sydowii, A. fumigatus, A. terreus, A. versicolor and A. wentii to CdCl₂) and cell wall integrity stress (A. niger and A. glaucus to Congo Red) (de Vries et al., 2017, Orosz et al., 2018).

Previous work sheds light on the importance of both segmental and whole genome gene duplication events in the evolution of fungi (Wapinski et al. 2007). Gene duplications are important elements of evolutionary adaptation processes (Ames et al. 2010) and the duplicants produced by these events may undergo neofunctionalisation or subfunctionalisation processes (Levasseur & Pontarotti 2011) to avoid the disadvantageous consequences of increased and imbalanced gene dosages (Papp et al. 2003).

Gene duplication, diversification and differential gene loss processes also contributed significantly to the evolution of opportunistic human pathogenic fungi such as A. fumigatus (Fedorova et al. 2008). The rapid expansion and evolution of certain gene families functioning in the invasion of the host organisms by fungi typically takes place in genomic islands located at sub-telomeric regions, and which are also known as “gene factories” or “gene dumps” (Fedorova et al. 2008). Expansion of protein families, e.g. cell surface proteins and hydrolytic enzymes, was also reported in the near-obligate nematode endoparasitic fungus Drechmeria coniospora with the concomitant increase in the number of the orthologs of the S. pombe Mak1/2/3-type oxidative stress sensor kinases and also in that of the A. nidulans HogA-type mitogen activated protein kinases (MAPKs; Zhang et al. 2016). Importantly, the number of stress sensor proteins and stress response-related transcriptional regulators decreased, which indicated certain simplifications in the stress defence system of this endoparasite (Zhang et al. 2016). While core elements of stress signalling pathways seem to be evolutionarily well-conserved in fungi in general, up-stream stress sensor proteins and down-stream transcriptional regulators evolve rapidly presumably as a way for these eukaryotes to tailor and fine-tune their stress defence systems for an ecological niche (Nikolaou et al. 2009).

Previously we collected and classified a large group of fungal stress response proteins with verified physiological functions, in order to generate the Fungal Stress Response Database version 2 (Karányi et al., 2013, Zhang et al., 2016, de Vries et al., 2017, http://internal.med.unideb.hu/fsrd2/default.aspx?p=consortium). Moreover, the Fungal Stress Database was also set up by us, and currently incorporates Aspergillus stress tolerance data recorded in a number of agar plate experiments performed under various types of stress conditions (oxidative stress, high-osmolarity stress, cell wall stress and heavy metal stress) as well as at different incubation temperatures (25 and 37 °C) (de Vries et al., 2017, Orosz et al., 2018; http://www.fung-stress.org/). Based on the plethora of fungal stress data accommodated mainly by these two databases, we set the following aims in this study: (i) To find any correlation between gene duplication, diversification and differential gene loss processes concerning stress response genes/proteins and the evolution of Aspergillus species. (ii) To assess whether evolutionary changes in the Aspergillus stress defence systems affect directly or indirectly the environmental stress tolerances of these important ascomycetes. (iii) To estimate the applicability of Saccharomyces cerevisiae-based, Schizosaccharomyces pombe-based and Aspergillus nidulans-based stress defence system models to describe the stress defence systems operating in the Aspergilli.

Materials and methods

Homology search and counting Aspergillus orthologs of fungal stress proteins

In stress protein homology search, our fungal stress protein (FSP) collection was utilised. Our FSP collection contains 2 150 proteins with known/verified physiological functions (Karányi et al., 2013, Zhang et al., 2016). The distribution of the proteins among fungal species was the following: A. flavus: 1; A. fumigatus: 83; A. nidulans: 145; A. oryzae: 13; Candida glabrata: 31; C. neoformans: 79; F. graminearum: 13; F. oxysporum: 14; F. verticillioides: 4; N. crassa: 78; N. fischeri: 2; C. albicans: 210; S. cerevisiae: 921; S. pombe: 534; U. maydis: 22 (see “Stress Database” in Supplementary Table S3). Within the scope of this study, the set of FSPs was manually curated, increasing the reliability of and making any background literature search easier in the “Stress Database”.

Homology searches were performed in the fully sequenced genomes of 25 Aspergillus and Penicillium strains representing 22 species (de Vries et al. 2017). The following species were included in the study: A. aculeatus, A. brasiliensis, A. carbonarius, A. clavatus, A. fischeri, A. flavus, A. fumigatus, A. glaucus, A. kawachii, A. luchuensis, A. nidulans, A. niger represented by three strains (CBS 113.46/ATCC 1015, CBS 513.88 and NRRL3), A. oryzae, A. sydowii, A. terreus, A. tubingensis, A. versicolor, A. wentii, A. zonatus, Eurotium rubrum, P. chrysogenum, P. digitatum and P. rubens (see “Stress Protein Orthologs” in Supplementary Table S3). After clicking on “Links to genome sequences” in Supplementary Table S3, the list of links to the appropriate genome sequence resources will appear.

In the identification and counting of stress homologs of FSPs, the protocol of Miskei et al. (2009) and Karányi et al. (2013) was used with modifications. Briefly, (i) the set of FSPs was blasted against the selected 25 Aspergillus and Penicillium species using Blastp (protein-protein BLAST), (ii) the set of potential homologs was reverse blasted versus the set of FSPs with Blastp, (iii) for each protein A from FSP, the list of b₀, b₁, ..., b_N was gained from each of the 25 Aspergillus and Penicillium species, ranked by e-value, (iv) for the lowest e-value protein (or multiple proteins if there are ties) b₀, the ranked list of hits a₀, a1, ..., a_M, was obtained for the full protein sets of each organism in the FSP set, and (v) if a_i had best hit b_j, and b_j had best hit a_i, then we considered them to be best bidirectional BLAST hits, and a_i and b_j stress protein pairs were treated as putative “orthologs” in subsequent analyses. Although we use the expression of “ortholog” for clarity it is worth emphasising that the applied method does not differentiate between orthologs and paralogs. The complete list of orthologs is found in Supplementary Table S3.

To simplify stress defence system modelling in the Aspergilli, three groups of stress proteins were selected with the following features: Group 1 (Saccharomyces cerevisiae-based model): S. cerevisiae stress proteins with functionally characterised ortholog(s) in at least in one more fungal (e.g. Schizosaccharomyces, Candida, Neurospora, Aspergillus, etc.) species. Group 2 (Schizosaccharomyces pombe-based model): S. pombe stress proteins with functionally characterised ortholog(s) in at least in one more fungal species. Group 3 (Aspergillus nidulans-based model): all A. nidulans stress proteins functionally characterised before finalising the construction of the set of FSPs in this study (see the “S. cerevisiae-based model”, “S. pombe-based model” and “A. nidulans-based model” in Supplementary Table S3). In the case of the A. nidulans-based model, the relatively low number of known A. nidulans stress proteins did not allow us to make any further simplifications like we did in the yeast-based models.

In this study, we also collected stress protein orthologs for S. pombe and S. cerevisiae from the PomBase database (ftp://ftp.pombase.org/pombe/orthologs/cerevisiae-orthologs.txt). We collated this independently generated ortholog list by BLASTing S. cerevisiae proteins in S. pombe and vice versa. We regarded best bidirectional BLAST hits as confirmed orthologous stress protein pairs in this study but in addition, we also present PomBase orthologs for S. cerevisiae and S. pombe on worksheets “S. cerevisiae-based model” and “S. pombe-based model” without bidirectional BLAST confirmation.

Before starting deeper bioinformatic analyses, some more simplifications were done on both the yeast-based and A. nidulans-based models. At first, ortholog protein sets, which came up with S. cerevisiae or S. pombe paralog pairs in the Aspergilli (e.g. orthologs of Ptc3/Ptc2, Grx1/Grx2, Trr1/Trr2 in baker’s yeast and those of Win1/Wis4, Pyp1/Pyp2, Ptc3/Ptc2, in fission yeast), were combined (see the S. cerevisiae-based and S. pombe-based models in Supplementary Table S4). Apparently highly expanding stress proteins with more than four putative orthologs in at least one Aspergillus species were excluded from further analyses. In these cases, it became highly uncertain whether or not all stress protein functions had been retained or diverged considerably in the corresponding paralogs. Moreover, these stress proteins with a high number of putative orthologs would have caused a very biased statistical analysis although the number of such proteins was relatively low. Similarly, stress proteins with exceptionally high Expect (E) value orthologs only (E typically higher than 10⁻¹⁰) were not analysed further.

The number of the studied Aspergillus species was limited to 18 in this part of the project (Supplementary Table S4). Please note that only data gained with the strain CBS 513.88 was processed for A. niger. The gene models for A. carbonarius have not been recently updated and were therefore excluded due to artefacts related to the use of an early generation gene modelling pipeline. Finally, all Aspergillus stress protein orthologs identified in the three models were manually checked and curated using the genome analysis tools available in the Aspergillus Genome Database (AspGD; http://www.aspgd.org/).

Construction of phylogenetic tree

Phylogeny of the Aspergillus spp. included in the study of de Vries et al. (2017) was inferred from 149 conserved protein sequences. After clustering proteins using the Markov Cluster (MCL) algorithm (Enright et al. 2002), clusters with only one protein from each species were selected (149 such clusters in total). Protein sequences were aligned with MAFFT multiple sequence alignment software (Nakamura et al. 2018), trimmed to well-aligned regions using Gblocks (Castresana 2000) with default parameters. The phylogenetic tree was constructed with the RAxML phylogenetic analysis program (Stamatakis 2014) using the PROTMIXWAG model, Batrachochytrium dendrobatidis set as an outgroup, and 100 rounds of bootstrapping.

Cluster analysis of stress tolerances

To estimate and present the differences in the stress tolerances of the studied Aspergillus species, growth data available in the Fungal Stress Database (FSD, Orosz et al. 2018; http://www.fung-stress.org/) for the following strains in the presence of various stressors were processed and analysed: A. aculeatus (CBS 172.66), A. brasiliensis (CBS 101740), A. carbonarius (CBS 141172 = DTO 115-B6), A. clavatus (CBS 513.65 = NRRL1), A. fischeri (CBS 544.65), A. flavus (CBS 128202 = NRRL 3357), A. fumigatus (CBS 126847 = Af293), A. glaucus (CBS 516.65), A. luchuensis (CBS 106.47), A. nidulans (FGSCA4), A. niger represented by two strains (CBS 113.46 and N402), A. oryzae (Rib40), A. sydowii (CBS 593.65), A. terreus (NIH2624), A. tubingensis (CBS 134.48), A. versicolor (CBS 795.97), A. wentii (CBS 141173 = DTO 134-E9). Growth data recorded in cultures exposed to H₂O₂ (oxidative stress, increases intracellular peroxide concentration), menadione sodium bisulfite (MSB, oxidative stress, elevates intracellular superoxide level) and CdCl₂ (heavy metal stress) as functions of stressor concentrations were fit by second order polynomials to calculate MIC₅₀ and MIC₉₀ values. MIC₅₀ and MIC₉₀ were defined as the lowest concentration of a given stress initiating agent, which caused 50 % or 90 % decreases in colony growth, respectively. For sorbitol (non-ionic hyperosmotic stress), NaCl (ionic hyperosmotic stress) and Congo Red (cell wall integrity stress) treatments, relative growth values (% of those recorded in unstressed control cultures) measured at 2.0 mol/L, 1.0 mol/L and 108 μmol/L concentrations, respectively, were calculated and taken into consideration in further analyses. Please note that only growth datasets recorded on nitrate minimal medium at 25 ^°C (5 and 10 days of incubation) and at 37 ^°C (5 d of incubation) were chosen and processed for each species. Conidia were always produced on malt extract––mycological peptone sporulation agar medium (1.5 % agar, 25 °C in the dark, 6 days) and, in the case of the osmophilic fungus A. glaucus, all sporulation and culture media were supplemented with 1.0 mol/L NaCl.

After mathematical standardisation (with “scale” function of R project) of growth values recorded in unstressed cultures as well as MIC₅₀, MIC₉₀ and relative growth data calculated for stress exposed cultures, the Euclidean distances of the species were determined in a multidimensional space (“dist” function of R project). These distances were used to perform cluster analysis and construct a dendrogram (“hclust” functions of R project) to demonstrate similarities and differences in the overall stress behaviours of the studied Aspergillus species. Multidimensional scale (MDS) plots were also generated to demonstrate the versatility of the stress tolerances of these Aspergilli (with “cmdscale” function of R project). Normalised data are available in Supplementary Table S5.

Gene onthology term (GO) enrichment analysis

Significant enriched GO terms within a subset of the S. cerevisiae-based, S. pombe-based and A. nidulans-based models were identified with the SGD Gene Ontology Term Finder (Saccharomyces Genome Database; https://www.yeastgenome.org/), Generic Gene Onthology Term Finder of Princeton University (http://go.princeton.edu/cgi-bin/GOTermFinder) and AspGD Gene Ontology Term Finder (Aspergillus Genome Database; http://www.aspergillusgenome.org), respectively. Default settings were employed with the following exceptions: The p value was set to 0.05 as well as genes from the appropriate model were used as background gene set in each case.

Determination of interacting partners of stress proteins

The String Database (https://string-db.org/) was used to count the number of interacting partners of stress proteins in the three, S. cerevisiae-based, S. pombe-based and A. nidulans-based stress defence system models. Only interactions determined experimentally and scored with at least 0.8 confidence values were taken into consideration.

Gene duplication and gene deletion based multidimensional scaling and cluster analysis of the Aspergillus species

The numbers of ortholog genes were used to calculate Manhattan distances between the studied Aspergillus species in each stress defence system model. These distance matrices were used to perform cluster analysis and construct dendrograms using complete linkage. Distance matrices and dendrograms were constructed with the “dist” and “hclust” functions of the R project, respectively. To show similarities and differences between the Aspergillus species, distance matrices were also used to generate multidimensional scale (MDS) plots. MDS plots were created with the “cmdscale” function of the R project.

Mantel test

Pairwise Mantel tests {implemented in the R package “ade4” by Dray & Dufour (2007)} were applied to rank-transformed versions of the distance matrices. The number of permutations for the tests of significance was 9 999. Holm corrected one-tailed p-values, associated with the Mantel correlations were calculated to test the alternative hypothesis that the Mantel correlation under test is positive. Only Mantel correlations with Holm adjusted p < 0.05 were regarded as significant positive correlation. The origins of the compared distance matrices were as follows:

• -Manhattan distance matrices of the normalised stress-related physiological features of 16 Aspergillus species. (A. carbonarius and the strain A. niger N402 were omitted from these analyses.)
• -Manhattan distance matrices of the S. cerevisiae-based, S. pombe-based and A. nidulans-based stress defence system models, which covered the same 16 Aspergillus species presented in the above mentioned stress physiology matrices.
• -Cophenetic distance matrices originated from the dendrogram representing phylogenetic relationships of the 16 Aspergillus species (de Vries et al. 2017).

Results

Three stress protein groups were selected based on S. cerevisiae, S. pombe or A. nidulans stress proteins with experimentally verified functions (Supplementary Table S4). By definition, the physiological functions of selected S. cerevisiae and S. pombe stress proteins were also confirmed in at least one more fungal species through the functional characterisation of their appropriate orthologs. Because the number of already characterised A. nidulans stress proteins was dwarfed by known stress proteins in both S. cerevisiae and S. pombe this restriction was not employed for this species. The selected stress protein groups were regarded as elements of S. cerevisiae-based, S. pombe-based and A. nidulans-based stress defence system models. The uniqueness (specificity) of the stress models is summarised in Table 1. According to these data, the overlap between the two yeast-based models was much larger than those calculated between the A. nidulans-based model and any of the two yeast-based stress defence system models. The overlap between the S. cerevisiae-based and S. pombe-based models came from the fact that the stress defence systems of baker’s yeast and fission yeast are by far the most extensively studied among fungi and, as a consequence, orthologous stress protein pairs are most often characterised in these two species (Supplementary Tables S3 and S4).

Table 1.

Specificities of the S. cerevisiae-based, S. pombe-based and A. nidulans-based stress response system models.

Compared models1	Number of proteins in the compared two models		Number and per cent ratio of unique stress proteins in the
	former model	latter model	former model	latter model
S. cerevisiae vs. S. pombe	301	248	89 (30 %)	39 (16 %)
S. cerevisiae vs. A. nidulans	301	133	238 (79 %)	70 (53 %)
S. pombe vs. A. nidulans	248	133	195 (79 %)	79 (59 %)

¹– Note that direct relationships between the models cannot be calculated because one protein present in a given stress defence system model may have more than one ortholog in the other models. Therefore, only the number of unique proteins present merely in one of the two compared stress defence models can be counted. By definition, a unique protein has no ortholog in the other analysed stress defence system model.

Orthologs of the selected S. cerevisiae, S. pombe and A. nidulans stress response proteins were identified in 18 Aspergillus species (Supplementary Table S3). The stress proteins in the stress defence system models were grouped into three subsets referred to as “deleted”, “duplicated” and “conserved” proteins in accordance with the number of their orthologs found in the Aspergilli. These stress protein subgroups were defined as follows:

“Deleted” protein – a stress protein in the employed stress defence system model, which has no ortholog in at least one Aspergillus species. It can be the consequence of losing the gene encoding the protein in some species or gaining a gene in other species. Note that a “deleted” stress protein may arise as the consequence of either a gene deletion event or substantial changes in its gene sequence or even fusion with another gene, which made the identification of the orthologous stress protein impossible. It can also not be fully excluded that some genes are missing due to gaps in the genome sequence.

“Duplicated” protein – a stress defence system model protein, which has more than one ortholog in at least one Aspergillus species.

“Conserved” protein – a stress model protein, which has exactly one ortholog in each Aspergillus species.

It is important to note that genes coding for either “duplicated” proteins or “conserved” proteins may also have paralog(s) in the genomes of the model yeasts S. cerevisiae and S. pombe.

Characterisation of the “deleted”, “duplicated” and “conserved” stress proteins

Interestingly, the ratio of the “deleted” proteins (20–26 %) did not differ significantly in the three studied stress defence system models (Table 2). In contrast, the ratio of the “duplicated” proteins varied between 4 and 18 %, with the highest ratio of “duplicated” proteins observed in the A. nidulans-based model (Table 2).

Table 2.

Number and ratio of “conserved”, “deleted” and “duplicated” proteins in the studied stress defence system models.

Model	Number of proteins in the model	Number (percentage) of
		“conserved” proteins	“deleted” proteins	“duplicated” proteins
S. cerevisiae	301	197 (65 %)1	78 (26 %)1	29 (10 %)1
S. pombe	248	184 (74 %)2	54 (22 %)1	11 (4 %)2
A. nidulans	133	88 (66 %)1,2	27 (20 %)1	24 (18 %)3

^1-3 – Ratios marked with the same superscript within a column are not significantly different, as indicated by the Fisher’s exact test (p < 0.05).

Only few GO terms showed significant enrichment within the “deleted”, “duplicated” and “conserved” protein subgroups (Table 3, Supplementary Table S6). It is noteworthy that in the case of the S. cerevisiae-based model the set of “deleted” proteins was enriched in “transcription factors”, while the set of “duplicated” proteins was enriched in “ion transporters” and also in proteins involved in “carbohydrate metabolism” (Table 3). In the S. pombe-based and A. nidulans-based models, the GO terms “phagophore assembly site membrane” and “intracellular organelle” were significantly enriched in the “deleted” and “conserved” proteins, respectively.

Table 3.

Enriched GO terms in the sets of “conserved”, “deleted” and “duplicated” proteins.

Model	Significantly (p < 0.05) enriched GO terms1 in the set of
	“conserved” proteins	“deleted” proteins	“duplicated” proteins
S. cerevisiae	–	“transcription regulatory region DNA binding”	“ion transmembrane transporter activity”, “carbohydrate metabolic process”
S. pombe	–	“phagophore assembly site membrane”	–
A. nidulans	“intracellular organelle”	–	–

¹- The full data set is available in Supplementary Table S6.

Stress proteins with five or more known interacting partners were enriched within the “conserved” proteins subgroup in the S. cerevisiae-based model and were depleted within the “duplicated” and “deleted” proteins subgroups in the S. cerevisiae-based and S. pombe-based models, respectively (Table 4; Supplementary Fig. S1). This means that stress proteins located at network nodes tend to preserve their doses, i.e. they are unlikely to go through deletions or duplications, which would jeopardise their distinguished and delicate positions in the stress response network.

Table 4.

Duplications and deletions of important stress proteins locating at the nodes of the stress defence system networks.

Model	Number of proteins with at least 5 known interacting partners1 in the protein sets of
	“conserved” proteins	“deleted” proteins	“duplicated” proteins	whole stress defence systems
S. cerevisiae	1052	335	113	149
S. pombe	544	83	4	66
A. nidulans	16	5	4	25

¹The number of interacting partners was identified using the String database (https://string-db.org/). Only interacting partners identified experimentally and scored with at least 0.8 confidence values were counted.

²Significant enrichment within the protein set (Fisher’s exact test, p < 0.05).

³Significant depletion within the protein set (Fisher’s exact test, p < 0.05).

⁴Enrichment within the protein set (Fisher’s exact test, 0.05 < p < 0.10).

⁵Depletion within the protein set (Fisher’s exact test, 0.05 < p < 0.10).

Characterisation of the evolution of stress proteins and stress tolerances in selected Aspergillus species

Hierarchical cluster analysis of the 18 studied Aspergilli was carried out to map the distances of the species, based on protein duplications and protein deletions. The similarities and differences between the species are visualised in Fig. 1, Fig. 2. Stress tolerances and phylogenetic relationships of the selected Aspergillus species were also summarised in dendrograms and, in the case of stress tolerances, in an MDS plot as well (Fig. 3).

Fig. 1.

Hierarchical cluster analysis of the Aspergillus species using complete linkage and Manhattan distances calculated from the features (numbers of ortholog genes) of the three stress defence system models. Part A: S. cerevisiae-based model, Part B: S. pombe-based model and Part C: A. nidulans-based model.

Fig. 2.

Multidimensional scaling of Manhattan distances between Aspergillus species, calculated from the features (numbers of ortholog genes) of the three models. Part A: S. cerevisiae-based model, Part B: S. pombe-based model and Part C: A. nidulans-based model.

Fig. 3.

Comparison of the phylogenetic positions and the stress tolerances of the Aspergilli. Part A: Maximum likelihood phylogeny of the Aspergillus spp. as published in the study of de Vries et al. (2017). The phylogenetic tree was deduced from 149 conserved protein sequences. Newly sequenced species are shown in bold. Note, A. niger ATCC 1015 is identical to CBS 113.46. Part B: Cluster analysis dendrogram constructed on the stress tolerance data reposited in the Fungal Stress Database (Orosz et al. 2018; URL: http://www.fung-stress.org/). Part C: Multidimensional scale plot presentation of the stress tolerance variability of the Aspergillus species tested (de Vries et al., 2017, Orosz et al., 2018).

Pairwise Mantel tests were applied to compare the results coming from the S. cerevisiae-based, S. pombe-based and A. nidulans-based stress response system models as well as to elucidate whether the stress protein deletions and duplications found in these models reflect phylogenetic relationships or physiological (stress tolerance) similarities between the studied Aspergillus species. The strongest Mantel correlation was observed between the two yeast models (0.74, p = 0.001) (Fig. 4), which can be explained well with the high overlap between the stress protein sets of these models (Table 1). A strong correlation was also found between the positions occupied in the phylogenetic tree and in the A. nidulans-based model (0.6, p = 0.001) (Fig. 4). Positions in the S. cerevisiae-based model correlated well with those in the A. nidulans-based model (0.57, p = 0.001) and in the phylogenetic tree (0.51, p = 0.0014) (Fig. 4). The positions of the Aspergilli in the dendrogram (Fig. 3B) constructed from the stress physiological data accommodated by FSD (http://www.fung-stress.org/) did not correlate at all with the observed positions of the same species in the yeast-based or A. nidulans-based stress response system models (Fig. 1, Fig. 2) or on the phylogenetic tree in general (Fig. 3, Fig. 4). Nevertheless, some closely related species like A. aculeatus – A. carbonarius, A. sydowii – A. versicolor, A. luchuensis – A. tubingensis as well as the two A. niger strains (CBS 113.46 and N402) showed remarkably similar overall stress tolerances (Fig. 3B). On the other hand, some other species like A. brasiliensis and A. fumigatus showed highly anomalous stress tolerance patterns (Fig. 3B; de Vries et al., 2017, Orosz et al., 2018).

Fig. 4.

Mantel correlations between the distance matrices of the studied Aspergillus species calculated on the S. cerevisiae-based, S. pombe-based and A. nidulans-based stress defence system models (Fig. 1, Fig. 2), distance matrix based on stress tolerance data (“Stress”; Fig. 3B) and cophenetic distance matrix of the phylogenetic tree (“Phylogeny”; Fig. 3A). Non-significant correlations (p ≥ 0.05) are indicated by crosses (X).

Importantly, Mantel correlations did not show any significant correlations between the positions occupied by the Aspergillus spp. studied in the stress tolerance-based dendrogram and their positions either in the phylogenetic tree or in any of the yeast-based and A. nidulans-based stress response system models. Therefore, we examined individual stress proteins in the latter models to determine whether some of them would go along with any of the stress tolerance property of the studied Aspergillus spp. For most stress proteins we found that the copy number of genes coding for them did not show any strong correlation with any stress parameters tested (Supplementary Fig. S2, Supplementary Table S7). Those proteins which showed significant correlation with a certain stress condition generally also correlated well with other stress conditions as well (Supplementary Fig. S2, Supplementary Table S7). Remarkably, changes in the copy numbers of only few proteins could be linked specifically to one tested stress condition. For example, 10 proteins in the A. nidulans-based model and 17 proteins in the S. cerevisiae-based model formed groups, in which the copy numbers indicated a positive correlation with cadmium stress only (Supplementary Fig. S2, Supplementary Table S7). However, the correlation coefficients usually did not reach the value of 0.6. Out of these stress proteins, only Vma1 (locus ID S000002344, subunit of the vacuolar membrane ATPase) has been demonstrated to be involved in cadmium stress response (Ruotolo et al. 2008) so far, to the best of our knowledge. Considering the few stress proteins, which were linkable to certain stress conditions with high correlation coefficients (Supplementary Fig. S2, Supplementary Table S7) the following were especially interesting:

The number of

• -Ftr1 {high affinity iron permease (Stearman et al. 1996); locus ID S000000947; S. cerevisiae model} orthologs showed positive correlation (correlation coefficients > 0.6, p-values < 0.006) with sorbitol and H₂O₂ induced stress tolerance;
• -Fet3 {ferro ion-O₂-oxidoreductase (Askwith et al. 1994); locus ID S000004662; S. cerevisiae model} orthologs showed positive correlation (correlation coefficients > 0.67, p-values < 0.004) with H₂O₂ induced stress tolerance at 25 °C;
• -Gpp1 {glycerol-3-phosphate phosphatase (Norbeck et al. 1996); locus ID S000001315; S. cerevisiae model} orthologs correlated (correlation coefficients > 0.63, p-values < 0.009) with Congo Red induced cell wall stress tolerance or sorbitol induced osmotic stress tolerance at 25 °C;
• -Ena1 {P-type ATPase sodium pump (Haro et al. 1991); locus ID S000002447; S. cerevisiae model} orthologs showed positive correlation (correlation coefficients > 0.66, p-values < 0.005) with CdCl₂ tolerance characterised with MIC₅₀ values;
• -Dis2 {serine/threonine protein phosphatase PP1 (Ohkura et al., 1988, Grallert et al., 2015); locus ID SPBC776.02c; S. pombe model} orthologs positively correlated (correlation coefficients > 0.54, p-values < 0.031) with Congo Red induced cell wall stress tolerance;
• -MpkC {putative HogA-like mitogen activated protein kinase (Furukawa et al., 2005, Jaimes-Arroyo et al., 2015, Bruder Nascimento et al., 2016, Pereira Silva et al., 2017); locus ID AN4668; A. nidulans model} orthologs correlated positively (correlation coefficients > 0.53, p-values < 0.036) with Congo Red induced cell wall stress tolerance or sorbitol induced osmotic stress tolerance and also showed a some positive correlation (correlation coefficients between 0.54 and 0.60, p < 0.03 with three out of the six attributes) with H₂O₂ induced stress tolerance;
• -CatB {hyphal catalase (Kawasaki et al. 1997); locus ID AN9339; A. nidulans model} orthologs also showed positive correlation (correlation coefficients > 0.57, p-values < 0.021) with Congo Red induced cell wall stress tolerance and or sorbitol induced osmotic stress tolerance at 25 °C;
• -NikA {putative histidine-specific protein kinase (Hagiwara et al. 2007); locus ID AN4479; A. nidulans model} orthologs correlated (correlation coefficients > 0.53, p-values < 0.034) with H₂O₂ stress tolerance detected at 25 °C.

Among the above-mentioned proteins, the involvement of MpkC in the cell wall and osmotic stress responses of A. fumigatus (Pereira Silva et al. 2017) and the contribution of NikA to the regulation of oxidative stress response in A. nidulans (Hayashi et al. 2014) have been experimentally verified. In the case of A. fumigatus frtA (an frt1 ortholog) and fetC (an fet3 ortholog) Kurucz et al. (2018a) found that a combined iron starvation – oxidative stress treatment up-regulated both genes markedly, however, iron starvation alone had no significant effect on the expression of these genes. These data suggest the potential involvement of FrtA and FetC (proteins in the reductive iron assimilation pathway) in oxidative stress response under iron deprivation. Skamnioti et al. (2007) demonstrated that CatB of Magnaporthe grisea (an ortholog of A. nidulans CatB) contributed to strengthening the cell wall during cell wall stress. Interestingly, similar physiological function for CatB orthologs has not been described in the Aspergilli.

It is worth noting that due to the huge number of investigated proteins, the Holm-corrected p value of the correlation coefficients were always higher than 0.05 with the exception of the copy number of AN0554 (aldA; aldehyde dehydrogenase gene) orthologs which correlated significantly (correlation coefficient: −0,87; p = 0.0129) with the normalised relative growth values of Congo Red treated cultures (37 °C 5 d) (Supplementary Table S7).

Discussion

Gene duplications – originating from either segmental or whole genome duplications – are common events in fungi and represent one of the most effective evolutionary driving forces operating in these wide-spread eukaryotes (Wapinski et al., 2007, Ames et al., 2010, Levasseur and Pontarotti, 2011). Of course, imbalanced gene doses can be harmful for the organism (Papp et al. 2003) but neofunctionalisation or subfunctionalisation processes may stabilise duplicated genes (Shertz et al., 2010, Giacometti et al., 2011, Levasseur and Pontarotti, 2011). The radiation of certain gene families likely plays a role in how fungi change life styles, e.g. towards parasitism (Fedorova et al., 2008, Jackson et al., 2009, Moran et al., 2011, Gabaldón et al., 2013, Maguire et al., 2013, Zhang et al. 2016). Comparative genomics is an outstanding tool to track evolutionary changes proceeding via gene duplication events (Fedorova et al., 2008, Jackson et al., 2009, Moran et al., 2011, Gabaldón et al., 2013). Erosion, pseudogenisation and eventual loss of superfluous gene copies are also among the predominant processes reshaping fungal genomes (Fedorova et al., 2008, Jackson et al., 2009, Shertz et al., 2010).

Considering the Aspergilli, an exceptionally important group of filamentous ascomycetous fungi (de Vries and Visser, 2001, Sugui et al., 2014, Perrone and Gallo, 2016, Egbuta et al., 2017, Mallo et al., 2017, Park et al., 2017, Souza Guimarães and da Costa Souza, 2017), gene duplication and gene deletion events have contributed significantly to the evolution of this taxon (Table 2, Supplementary Tables S3 and S4). Importantly, the positions occupied by the Aspergilli on dendrograms and MDS plots constructed taking into consideration stress gene duplications and stress gene deletions (Fig. 1, Fig. 2) correlated well with the positions of the same species on the phylogenetic tree deduced from 149 conserved protein sequences (Fig. 3, Fig. 4). This correlation demonstrates the importance of the radiation and reduction of stress protein families in the evolution of the Aspergilli. Similar results were found by Zhang et al. (2016) for the nematode endoparasitic fungus D. coniospora. Moreover, some recent laboratory evolution experiments have also demonstrated the importance of gene amplification and gene deletion events in stress adaptation processes. In the case of the baker’s yeast S. cerevisiae, amplification of hxt5 and hxt6 genes (encoding high affinity hexose transporters) and sul1 (coding for a high affinity sulfate permease) was observed under glucose- and sulfate-limited conditions, respectively (Gresham et al. 2008). Meanwhile both amplification and complete deletion of the pho5 (extracellular acid phosphatase) gene were reported in phosphate limited cultures (Gresham et al. 2008).

The number of duplicated Aspergillus stress proteins revealed by S. cerevisiae-based, S. pombe-based and A. nidulans-based stress defence system models varied significantly (10, 4 and 18 % of total stress proteins analysed; Table 2), which was attributed to two factors: (i) The S. cerevisiae-based and S. pombe-based models contained more conserved stress proteins, because only stress proteins with functional ortholog(s) in at least one additional fungal species were taken into consideration in setting up the models (Supplementary Tables S3 and S4). (ii) Paralog genes (proteins) are quite difficult to identify using evolutionarily distant model species like S. cerevisiae or S. pombe (Wang et al. 2009), especially when one of the paralogs has been eroded e.g. in “gene dumps” (Fedorova et al. 2008). This observation strongly supports the urgent need for good-quality A. nidulans-based models in future evolutionary studies, which will be carried out in filamentous ascomycete taxa (Miskei et al. 2009).

Considering the evolution of Aspergillus stress proteins, conserved proteins located at network nodes with at least 5 known interacting partners in the S. cerevisiae-based model (Table 4, Supplementary Fig. S1) appear more recalcitrant to either duplications or deletions. This observation seems reasonable as deletions would result in serious functional disorders in any kind of environmental stress defence system while duplications could significantly disturb the stoichometry of a number of protein complexes (protein “dosage imbalances”; Papp et al. 2003). GO term enrichment analyses indicate that stress proteins with functions in “intracellular organelle” are especially “conserved” (Table 3). Not surprisingly, transcriptional regulators with “transcription regulatory region DNA binding” are among the most often deleted genes, which is in line with previous observations (Nikolaou et al., 2009, Zhang et al., 2016). The evolution of transcription factors is rapid in fungi, similar to that of stress stimuli sensors (Nikolaou et al., 2009, Zhang et al., 2016). Further studies are needed to shed light on the significance of the enrichment of those “deleted” stress proteins, which are functionally coupled to “phagophore assembly site membrane” (“a cellular membrane associated with the pre-autophagosomal structure”; https://www.yeastgenome.org/go/34045) in the Aspergilli, because autophagy is a crucial element of stress defence in both baker’s and fission yeasts (Thorpe et al., 2004, Su et al., 2015). The enrichment of “duplicated” stress proteins with “ion transmembrane transporter activity” or with function in “carbohydrate metabolic process”, which includes proteins (e.g. Tdh3, Gpp1, Gpd2, Dak2, Tps1 and Tps3) involved in the metabolism of glycerol or trehalose as well known “stress metabolites”, is not surprising and obviously will contribute to the evolution of the Aspergillus stress defence system (Table 3). These duplicated proteins are likely selected to reach/maintain higher ion and metabolic fluxes (Papp et al. 2004).

Although some closely related Aspergillus species like A. aculeatus – A. carbonarius, A. sydowii – A. versicolor, A. luchuensis – A. tubingensis as well as the two tested A. niger strains (CBS 113.46 and N402) showed similar stress tolerance patterns (Fig. 3) there was no significant correlation between the positions of the studied Aspergillus species in the dendrogram constructed from the stress physiological data (Fig. 3) and their positions in the yeast-based or A. nidulans-based stress response system models (Fig. 1, Fig. 2) or in the phylogenetic tree (Fig. 3, Fig. 4). Nevertheless, we cannot rule out that either addition of further stress proteins (when their involvement in stress tolerance is justified) or studying and including additional stress tolerance data to the analysis will modify these results in the future. However, according to Supplementary Fig. 2, which demonstrates that gene duplications and deletions do not show any strong correlation (correlation coefficients lower than −0.6 or higher than 0.6) with any of the studied stress tolerances for the vast majority of stress genes, addition of few new stress proteins or new stress conditions are unlikely to result in significantly different conclusions. The lack of significance could indicate that the deletion or alteration of a single stress response protein causes profound changes in the stress tolerance of an Aspergillus species, and as a consequence, tolerances against various specific types of environmental stress may correlate well with the copy numbers of few selected stress proteins rather than the total number of stress protein duplications and deletions. E.g. the number of MpkC orthologs correlated positively with cell wall stress tolerance, osmotic stress tolerance and oxidative stress tolerance (Supplementary Table S7, Supplementary Fig. S2). The osmophility of A. glaucus and A. wentii could be attributed simply to the lack of their A. nidulans GfdB NAD-dependent glycerol-3-phosphate dehydrogenase orthologs while the remarkable superoxide tolerance of A. brasiliensis was related to the appearance of two new sod genes in the genome of the fungus (de Vries et al., 2017, Orosz et al., 2018).

Processes other than gene duplications or deletions contribute to stress adaptation and may substitute or even counterbalance the effects of the altered copy numbers of a stress gene which may also explain the lack of correlations we found in this study. These processes likely include the following:

• (i)Changes in the stress protein structure/activity can increase resistance.

Several examples have been reported in the literature that mutations in genes encoding stress defence proteins, e.g. against an antifungal agent, led to acquired resistance (Revie et al. 2018). As an example, Bódi et al. (2017) found in laboratory-based evolution experiments performed with S. cerevisiae that increased fluconazole resistance was frequently accompanied with mutations in the pdr5 gene encoding a fluconazole efflux pump.

• (ii)Changes in the expression level of a stress gene can be an alternative of gene duplication/deletion events.

In the above-mentioned experiment by Bódi et al. (2017), another frequently mutated gene was the rox1, which encodes a repressor of hypoxic genes (including ergosterol biosynthesis genes; Montañés et al. 2011) suggesting that beside altered protein activities, altered expression levels were also important in the adaptation to fluconazole in these experiments. (In fact, in laboratory evolution experiments, most of the analysed endpoint mutants had mutations in a regulatory gene (Conrad et al., 2009, Conrad et al., 2011). Pca1 is another good example for the importance of the transcriptional activity of a stress gene : S. cerevisiae Pca1 is a cadmium efflux pump (Adle et al. 2007) and its ortholog in A. fumigatus (PcaA) is also involved in cadmium tolerance (Bakti et al. 2018). Genome analysis studies demonstrated that the most cadmium tolerant Aspergillus spp. (A. fumigatus, A. versicolor, A. sydowii) have a pca1 ortholog (in the case of A. sydowii two orthologs), while the most Cd sensitive species (A. carbonarius, A. aculeatus, A. glaucus) have no pca1 ortholog (de Vries et al. 2017). However, in spite of the exceptions, A. niger, having no pca1 ortholog, generally showed higher cadmium tolerance than A. flavus, harboring one pca1 ortholog (de Vries et al. 2017). Not surprisingly, the Kruskal-Wallis test did not show any significant difference in the cadmium tolerance among the Aspergillus species possessing two, one or even zero pcaA orthologs (Kurucz et al. 2018b). Moreover, the MIC_50,cd values of 10 A. fumigatus isolates varied within a wide range (0.25 mM–>2 mM) and showed strong positive correlation with the relative transcription of the pcaA gene (Kurucz et al. 2018b). All these data demonstrated that harbouring a pca1 ortholog is not necessarily accompanied with an outstandingly high cadmium tolerance and, vice versa, losing the pca1 ortholog not necessarily increase cadmium sensitivity.

• (iii)Rewiring stress response regulatory networks can also be an inherent part of genetic adaptation to stress.

Evolution of stress responding pathways in fungi demonstrates that – in addition to gene expansion/gene loss events as well as gene structure diversification – functional changes in signalling pathways is an important element of the adaptation to changing environment (Pusztahelyi and Pócsi, 2013, Hagiwara et al., 2016, Xu et al., 2017). In contrast to mitogen-activated protein kinases which seem to be evolutionarily stable, up-stream (e.g. sensors of various environmental stress stimuli) and down-stream (e.g. transcriptional regulators) elements of the same stress sensing, signal transduction and stress response regulatory pathways tend to undergo rapid changes (Nikolaou et al., 2009, Zhang et al., 2016).

Positive feedback mechanisms commonly cause phenotypic heterogeneity (Becskei et al. 2001), which can be important in physiological adaptation to stress and can also contribute to genetic adaptation to a stress condition via compensating possible negative effects of mutations on fitness (Mustonen and Lässig, 2010, Sánchez-Romero and Casadesús, 2014, Bódi et al., 2017). Development or cessation of these autoregulatory mechanisms may therefore significantly influence the (evolution of) stress tolerance of microbes.

• (iv)Acquiring new genes via horizontal gene transfer can be an efficient alternative of gene duplication and subsequent neofunctionalisation/subfunctionalisation events.

It is well documented that horizontal gene transfer significantly contributes to the evolution of fungi (Fitzpatrick 2012). As an example, the genome of the commercial wine yeast S. cerevisiae EC118 contains 34 genes that have been transferred horizontally from other fungal species (Novo et al. 2009). These genes contribute to the adaptation to various types of stress induced by high-osmolarity, nitrogen starvation or high ethanol concentrations (Novo et al. 2009).

Taking into consideration the outcomes of the comparative stress protein and stress tolerance analyses, we suggest the following:

Gene duplication events support successful stress adaptation in new habitats by modulating the dose of important genes (Wapinski et al., 2007, Fedorova et al., 2008, Ames et al., 2010, Shertz et al., 2010, Giacometti et al., 2011, Levasseur and Pontarotti, 2011). Changing environmental conditions may trigger the erosion (e.g. pseudogenisation) and even the loss of certain genes, which lost their significance, with the concomitant arise of new ones, e.g. via new gene duplications (Fedorova et al., 2008, Jackson et al., 2009, Moran et al., 2011). These changes contribute to the expansion or reduction of certain stress response gene families (Nikolaou et al., 2009, Zhang et al., 2016) and, as a consequence, to reshaping the genome of the organism, which may lead to the evolution of new species (Fig. 4). Beside gene duplication and deletion events, other processes can also significantly affect the adaptation of fungi to new habitats which generally prevents any significant correlation between the copy numbers of proteins and stress tolerances (Fig. 4). These processes include (i) alterations in the structure of stress proteins, which has an impact on their activity, (ii) varying biosynthesis of these proteins, (iii) rewiring stress response regulatory networks, or (iv) acquiring new genes through horizontal gene transfer. All these multilevel changes seem to be indispensable for the successful adaptation of filamentous fungi when they are entering new ecological niches.

Considering the future applications of yeast-based models to gain a deeper insight in the stress defence systems of the Aspergilli we can conclude that both S. cerevisiae-based and S. pombe-based models are suitable to identify Aspergillus stress response proteins and also to reconstruct their interactions. Nevertheless, because of the significant evolutionary distances between ascomycetous yeasts and filamentous Aspergilli (Wang et al. 2009), stress protein paralog pairs are often difficult to identify using yeast-based models. Not surprisingly, Aspergillus orthologs of yeast stress proteins may even have modified or altered physiological functions (Balázs et al. 2010). In addition, Aspergillus genomes harbour significantly more genes than those of S. cerevisiae and S. pombe and, hence, many important Aspergillus stress proteins do not have any yeast counterparts (Supplementary Tables S3 and S4). Therefore, further efforts are needed to speed up the functional characterisation of Aspergillus (especially A. nidulans) stress response proteins and set up a detailed stress defence system model preferentially based on A. nidulans, which will be at least equivalent to or even better than today’s frequently used yeast-based models in either quality or applicability (Miskei et al., 2009, Karányi et al., 2013).

Appendix A. Supplementary data

The following are the Supplementary data to this article:

figs 1.

Simplified representation of the stress responsive protein networks of S. cerevisiae (A) and S. pombe (B). Networks were generated using the String Database (https://string-db.org/), with stress response proteins included in the two yeast-based models. Pebbles symbolize nodes (proteins) meanwhile lines indicate interactions, which were experimentally verified between two nodes with confidence value of 0.8. In the case of the A. nidulans-based model, the number of interactions between nodes was too low to generate any similar network. Not connected nodes and connections to nodes, which are outside the model, are not shown here for clarity.