Abstract
Streptococcus pneumoniae (‘pneumococcus’) is a leading cause of morbidity and mortality worldwide and a frequent coloniser of the nasopharynx. Competition among bacterial members of the nasopharynx is believed to be mediated by bacteriocins: antimicrobial toxins produced by bacteria to inhibit growth of other bacteria. Bacteriocins are also promising candidates for novel antimicrobials. Here, 14 newly-discovered bacteriocin gene clusters were identified among >6,200 pneumococcal genomes. The molecular epidemiology of the bacteriocin clusters was investigated using a large global and historical pneumococcal dataset. The analyses revealed extraordinary bacteriocin diversity among pneumococci and the majority of bacteriocin clusters were also found in other streptococcal species. Genomic hotspots for the integration of bacteriocin genes were discovered. Experimentally, bacteriocin genes were transcriptionally active when the pneumococcus was under stress and when two strains were competing in broth co-culture. These findings fundamentally expand our understanding of bacteriocins relative to intraspecies and interspecies nasopharyngeal competition.
Introduction
Pneumococci are a leading cause of severe infections such as pneumonia, bacteraemia and meningitis, and are among the most common causes of otitis media, sinusitis and conjunctivitis. All age groups are susceptible to pneumococcal infection, but young children, the elderly, and immunocompromised persons are most at risk (Bogaert et al, 2004). Despite the use of antimicrobials and pneumococcal conjugate vaccines, the pneumococcus remains a major global health problem, causing approximately 14.5 million cases of serious disease and 826,000 deaths annually in children <5 years of age (O’Brien et al., 2009). Antimicrobial-resistant pneumococci have been a serious and increasing concern for several decades (Doern et al., 2001; Klugman, 1990; Tadesse et al., 2017). The pneumococcus is now considered to be a ‘priority pathogen’ – antimicrobial-resistant bacteria that pose the greatest threat to global health – by the World Health Organisation (World Health Organization, 2017).
The pneumococcus is normally an asymptomatic coloniser of the nasopharynx in healthy young children; however, colonisation is also the initial stage of the disease process. The polysaccharide capsule is the main virulence factor of the pneumococcus: nearly 100 distinct capsular antigenic types (serotypes) have been described and certain serotypes are predominantly associated with disease whilst others are largely associated with nasopharyngeal colonisation (Brueggemann et al., 2003). Pneumococci frequently co-colonise with other pneumococci and non-pneumococcal bacterial species, and intraspecies and interspecies competition can influence colonisation dynamics, strain prevalence, serotype distributions and consequently, the potential for disease progression (Shak et al., 2013).
Competition among bacterial members of the nasopharyngeal microbiome is believed to be mediated by bacteriocins: ribosomally-synthesised antimicrobial toxins produced by bacterial species to inhibit the growth of other closely-related bacteria. The producer strain also encodes an immunity protein to protect itself from its own bacteriocin (Czaplewski et al., 2016; Dawid et al., 2006). Bacteriocin production has been associated with more efficient colonisation of a host by the producer strain, owing to the ability of these toxins to remove competitors (Dawid et al., 2006; Shak et al., 2013). Their ability to kill bacteria makes bacteriocins attractive potential candidates for the development of new antimicrobials. Several bacteriocins (e.g. nisin and pediocin PA-1) have already been commercialised and are widely used as food preservatives (Czaplewski et al., 2016).
From a genetic perspective, bacteriocins are found in gene clusters, whereby the genes involved in toxin production, immunity and transport (exporting and processing the toxin peptide) are situated adjacent to each other in the bacterial genome. The blp (bacteriocin-like peptides) cluster is the best-characterised bacteriocin in pneumococcus (Bogaardt et al., 2015; Czaplewski et al., 2016; Dawid et al., 2006; Reichmann et al., 2000). Previous work by our group showed that the blp cluster is ubiquitous among pneumococci recovered from the early 1900s onward and is highly diverse. We also identified a novel bacteriocin cluster that we named pneumocyclicin (Bogaardt et al., 2015). Five additional bacteriocins have been reported among pneumococci (Begley et al., 2009; Guiral et al., 2005; Hoover et al., 2015; Kadam et al., 2017; Maricic et al., 2016); however, their prevalence, genetic composition and molecular epidemiology in the context of the pneumococcal population are unknown.
The abundance of whole genome sequence data expedites the detection and genetic analysis of bacteriocin clusters. Here, we report 14 newly-discovered pneumococcal bacteriocin clusters and describe the molecular epidemiology of all the currently known bacteriocins within a collection of pneumococci isolated over the past 90 years. We also provide transcriptomic evidence that multiple bacteriocin clusters were induced in response to external stress and also in response to competition for space and nutrients in broth co-culture.
Results
Genome mining triples the number of known bacteriocins among pneumococci
Our investigation of a large and diverse dataset of 571 historical and modern pneumococcal genomes resulted in the identification of 14 newly-discovered bacteriocin clusters, increasing the number of known bacteriocins in this species to 21 (Table 1). We identified several clusters similar to lactococcin 972, sactipeptide and lassopeptide bacteriocins (Arnison et al., 2013; Letzel et al., 2014; Martinez et al., 1999), which were hitherto not known to be harboured by the pneumococcus (Table 1; Supplemental Table 1). We subsequently expanded our search for bacteriocins to a much larger dataset of 5,673 published pneumococcal genomes, but no additional bacteriocins were found; thus, the detailed description of the bacteriocins here is restricted to those identified in the dataset of 571 genomes.
BLAST searches of the NCBI database of non-redundant nucleotide sequences revealed that the majority of these clusters were not exclusive to pneumococcus, but that identical or similar versions were present in other streptococci (Supplemental Table 2). Therefore, we used the prefix “strepto” and named each cluster according to its type of bacteriocin (see Materials and methods). Among the putative bacteriocins, five were similar to lactococcin 972 (Martinez et al., 1999) and we called these streptococcins (Fig. 1). Despite gene synteny among the streptococcins (Fig. 1A), nucleotide sequence similarity was low: toxin genes, 37-59%; immunity genes, 27-48%; and transporter genes, 49-63% (Fig. 1B). Different streptococcins were found in different, but consistent, locations within the bacterial chromosome (Fig. 1A and 1C). Eleven different streptolancidins, one streptosactin, one streptolassin and one streptocyclicin (what we previously called pneumocyclicin) were also identified among pneumococcal genomes (Fig. 2; Arnison et al., 2013). The bacteriocin clusters were commonly flanked by genes predicted to encode CAAX proteins (possibly involved in self-immunity from bacteriocin toxins; Kjos et al., 2010), Rgg and PlcR transcriptional regulators (implicated in bacterial quorum sensing; Perez-Pascual et al., 2016), transporters, lipoproteins and mobilisation proteins.
Further support for interspecies exchange of bacteriocin gene clusters was provided by the guanine (G) and cytosine (C) content of the bacteriocin clusters. The average GC-content of all pneumococcal genomes in this dataset was 39.6%, whereas the range of values for different bacteriocin groups was as follows: streptococcins, 36.3-42.4%; streptolancidins subset 1, 31.2-33.4%; streptolassin, 31.2%; streptolancidins subset 2, 28.9-29.6%; streptocyclicin, 27.0%; and streptosactin, 25.5% (Supplemental Fig. 1). By comparison, the GC-content of other non-pneumococcal Streptococcus species in another study ranged between 33.2-44.6% (Kurioka et al., 2017).
Extraordinary bacteriocin diversity within a globally-distributed pneumococcal dataset dating from 1916
We further assessed these bacteriocins in the context of the pneumococcal population structure. The study dataset consisted of a diverse collection of 571 pneumococci isolated between 1916 and 2009 from patients and healthy individuals of all ages residing in 39 different countries across six continents. 88 pneumococcal serotypes and 99 different clonal complexes were represented (Table 1; Supplemental Table 3). All bacteriocins detected more than once in the dataset were identified among pneumococci isolated over several decades and from a variety of different countries (Table 1). Some bacteriocins were present in all pneumococci, whilst others were limited to specific clonal complexes (genetic lineages). Bacteriocin clusters missing one or more genes were defined as partial. The percentages of partial and complete clusters varied between different bacteriocins, e.g. streptococcin E was present in all but one pneumococcal genome but was missing one or more genes in the majority (83.5%) of genomes, while streptococcin C was found as a complete cluster in all genomes (Table 1 and Fig. 3A). We constructed a core genome phylogenetic tree of all isolates and labelled each genome according to the presence or absence of each bacteriocin cluster (Supplemental Fig. 2). Overall, we found that the number of bacteriocins within each genome varied from 5 to 11 per genome and that certain combinations of bacteriocins were well represented in the dataset (Fig. 3B, 3C and Supplemental Fig. 2).
Due to their relative simplicity (containing only three genes), we chose streptococcins as models for further investigating the pattern of missing genes in partial clusters (Fig. 3A). Scrutinising these clusters revealed that the majority of the partial clusters lack the toxin gene, while still retaining the immunity and/or the transporter genes. This could support the general idea of a ‘cheater’ phenotype, whereby the immunity and transporter genes are conserved to protect the pneumococcus from neighbouring bacteria that express the bacteriocin toxin protein, but the cheater strain does not bear the cost of producing the bacteriocin toxin (Brown et al., 2009; Son et al., 2011).
Multiple hotspots for the integration of bacteriocin clusters in the pneumococcal genome
By conducting a population genomics-based assessment of the bacteriocin cluster insertion sites, we identified three genomic regions that are putative hotspots for the integration of bacteriocin clusters in the pneumococcal chromosome. These bacteriocin cluster hotspots (BCHs) are specific locations in the genome where different bacteriocin clusters were found in different pneumococci (Fig. 4). This suggested a switching mechanism, whereby different clusters can replace one another via homologous recombination. Up to three different bacteriocin clusters were found to be associated with a single BCH (Fig. 4C). The acquisition of streptolancidin G appears to have rendered the streptococcin E partial by replacing the toxin and part of its immunity gene (Fig. 4A), which is in accordance with the fact that streptolancidin G could not be found in genomes that harboured a complete streptococcin E cluster (Supplemental Fig. 1). Nonetheless, the remnant genes of the streptococcin E partial clusters were conserved in samples collected over many decades (Fig. 3A).
Bacteriocin gene expression in response to heat stress and strain competition
To explore whether the bacteriocin clusters were transcriptionally active, we analysed a whole-genome RNA sequencing dataset from a broth culture of pneumococcal strain 2/2, which was incubated at a higher than normal temperature (40°C vs 37°C) to induce a bacterial stress response (NCBI GEO accession number GSE103778; Kurioka et al., 2017). Multiple genes in the bacteriocin clusters were differentially expressed compared to the control over several time points, indicating that many of these bacteriocin genes were transcribed in response to external stress (Fig. 5).
Notably, there were two bacteriocin clusters (streptolancidin J and streptococcin E) that were missing genes and yet the remaining genes were clearly being upregulated. Moreover, the timing of gene expression varied across bacteriocin clusters, e.g. genes within a cluster were induced in a specific pattern, whilst at any particular time point during the sampling period several genes in different clusters were upregulated simultaneously. The regulatory governance over which bacteriocin genes are expressed at any given point during bacterial growth remains to be determined.
A second whole-genome RNA sequencing experiment was designed to test whether bacteriocin genes were transcribed when two genetically-different reference strains, PMEN-3 and PMEN-6, were cultured together in the same broth culture using standard incubation conditions. These strains were competing for space and nutrients as the incubation time progressed and cell density increased. Samples were taken for RNA sequencing at multiple time points and sequenced. Sequencing reads from all time points were combined in silico. The sequencing reads were mapped to a pseudo-reference genome that was constructed to include the genes unique to PMEN3 and PMEN6 plus the genes shared between both strains (see Materials and methods).
Pneumococcal genes that were significantly upregulated included many genes that would be expected to be expressed during growth (e.g. metabolic genes), in addition to the significant upregulation of 29 bacteriocin genes (Figure 6; Supplemental Table 5). Many of the bacteriocin genes were present in highly similar allelic versions in both PMEN-3 and PMEN-6, thus it was not possible to determine with confidence whether both versions were upregulated or whether one strain overexpressed a similar gene. However, there were three genes within the bacteriocin clusters that were unique: PMEN-3 significantly upregulated the bacteriocin toxin gene of streptococcin A (scaA) and a putative immunity gene (pncM) from the blp bacteriocin cluster, and PMEN-6 significantly upregulated the bacteriocin toxin gene of streptococcin E (sceA).
Interestingly, other genes that were significantly upregulated were genes associated with unique prophages present in each of the PMEN strains. We have recently demonstrated that prophage genes are ubiquitous among pneumococcal genomes, but to what extent prophages are influencing pneumococcal biology and perhaps competition between strains is not yet understood (Brueggemann et al., 2017). Overall, the data from this experiment demonstrate proof-of-principle that such methodology can be used to test for the differential expression of key bacterial genes within a competitive environment.
Discussion
A clear understanding of the role bacteriocins play in pneumococcal biology is central to understanding microbial interactions within the ecological niche (the nasopharynx). The importance of intraspecies competition to pneumococcal ecology is reflected in the changes in prevalence of different pneumococcal serotypes and genotypes in the nasopharynx over time, and understanding competition dynamics is important in the context of understanding vaccine impact (Auranen et al., 2009; Crook et al., 2004; Garcia-Rodriguez et al., 2002). Pneumococcal conjugate vaccines are disruptive to the pneumococcal population structure and alter the composition of microbes competing for space and nutrients in the nasopharynx. The effects of this disruption are not yet fully understood but can lead to increased disease in human populations (Aguiar et al., 2010; Huang et al., 2005; Kaplan et al., 2010).
We revealed here that not only do pneumococci possess a substantially greater and more varied array of bacteriocins than previously recognised, the bacteriocins (often in a particular combination) are associated with specific genetic lineages. This is fundamental, as it provides the framework on which to investigate the mechanisms underpinning specific bacteriocin-pneumococcus combinations, particularly among epidemiologically-successful genetic lineages, and the activity of specific bacteriocin and immunity genes. RNA sequencing clearly demonstrated that bacteriocin genes were transcriptionally active when the pneumococcus was under stress or in competition with another strain during bacterial co-culture. The in vivo production of bacteriocin gene products and their functional activities is under further investigation.
Interestingly, we identified several specific locations in the pneumococcal genome that harboured different bacteriocin clusters, which suggested that recombination events had occurred at these locations and resulted in a switching of bacteriocin clusters. The profound impact of recombination on the pneumococcal genome has been described for >25 years and recombination events are well documented in other locations within the pneumococcal genome, most commonly at the capsular polysaccharide locus (conferring a change of serotype) and at penicillin binding protein genes (conferring penicillin resistance if the proteins are altered) (Coffey et al., 1991; Golubchik et al., 2012; Laible et al., 1991; Maynard Smith et al., 1991; Wyres et al., 2012). Similarly, the DpnI, DpnII and DpnIII clusters, each containing a distinct restriction modification system, can replace one another at the dpn locus. This is believed to be of protective value in mixed pneumococcal populations against bacteriophages, which are constant invaders of pneumococcal genomes (Brueggemann et al., 2017; Eutsey et al., 2015; Johnston et al., 2013).
We found several examples of presumed bacteriocin cluster switching events that had occurred adjacent to distinct quorum-sensing transcriptional regulators TprA and Rgg. Intriguingly, while the genes that are known to be under the control of TprA and Rgg were replaced, the quorum-sensing transcriptional regulators remained conserved. It is known that TprA controls the expression of its downstream bacteriocin genes: it induces them when pneumococcal cells are at high density in the presence of galactose and represses them when under high glucose growth conditions (Hoover et al., 2015). Galactose is plentiful in the nasopharynx, whereas glucose is scarce (although abundant in the blood), suggesting that the TprA may mediate the expression of its adjacent bacteriocin genes to aid pneumococci to compete for resources during nasopharynx colonisation (Bidossi et al., 2012; Hoover et al., 2015). Likewise, the Rgg quorum-sensing transcriptional regulator has been shown to mediate the expression of its adjacent genes, and this is thought to be directed by sensing amino acid levels in the cellular community (Cuevas et al., 2017). An explanatory hypothesis might be that bacteriocin cluster switching provides a mechanism by which the existing intricate quorum-sensing signalling network required for coordinating population-level behaviours is accessible by the newly-acquired bacteriocin cluster. This remains to be experimentally verified.
Our current work is significant for the broader community in that among the 21 different pneumococcal bacteriocin clusters now identified, many homologues are found in other unrelated streptococcal species. We also provide here a unified nomenclature for the pneumococcal bacteriocin clusters and their genes. Finally, the fact that any single pneumococcal genome possesses multiple bacteriocin clusters should be carefully considered when designing laboratory experiments aimed at assessing the activity of an individual bacteriocin.
Overall, these population genomic and transcriptomic analyses reveal an extraordinary complexity of bacteriocins among pneumococci and underscore the need to determine precisely how these bacteriocins drive changes within the pneumococcal population and the wider microbial community. Such findings are interesting not only for their population biology and ecology insights, but also because bacteriocins potentially have a huge impact on public health. By directly influencing changes in microbial populations, bacteriocins might indirectly be affecting the effectiveness of vaccines in the longer term: after vaccine use in human populations, the target pneumococcal population is significantly changed and those pneumococci must now compete within the altered microbiome. If bacteriocins are essential to the pneumococcal competitive strategy, then the composition of bacteriocins possessed by the post-vaccination pneumococcal community is important to understand. Moreover, there is obvious potential for the development of bacteriocins as novel antimicrobials: at a time when the challenges of antimicrobial-resistant microbes have never been more acute, these data provide many new areas of investigation.
Materials and methods
Genome mining for bacteriocin clusters
In total, 6,244 assembled pneumococcal genomes from studies previously published by us and others (Brueggemann et al., 2017; Chewapreecha et al., 2014; Croucher et al., 2011; Croucher et al., 2013a; Croucher et al., 2013b; Gladstone et al., 2015; van Tonder et al., 2014; van Tonder et al. 2015) (Supplemental Table 4) were screened for the presence of bacteriocin clusters using a variety of bioinformatic tools and databases, including antiSMASH (Weber et al., 2015), BACTIBASE (Hammami et al., 2010), BAGEL (de Jong et al., 2006) and InterProScan (Jones et al., 2014) (data collected in March 2016). An in-house pipeline was developed to automate part of this process. Predicted gene clusters from each of the database outputs were examined manually and further scrutinised using extensive BLAST searches.
Analyses of the putative bacteriocin genes
Putative bacteriocin genes were annotated using homology to other known bacteriocin genes (not shown) in all available databases mentioned above, as well as structure-based searches. Protein domains were examined using the Conserved Domain search feature at NCBI (Marchler-Bauer et al., 2010). Genes of interest were screened against the STRING database (Szklarczyk et al., 2015) to search for any previously reported relationship to other genes. Multiple sequence alignments of the genes in streptococcin clusters were performed in Geneious version 9.1 (Biomatters Ltd) using the ClustalW algorithm (Larkin et al., 2007) with default parameters (Gap open cost=15, Gap extend cost=6.66). The multiple sequence alignment output was used within the Geneious environment to calculate percentage identity matrices. The figures of the coding regions of the bacteriocin clusters and their flanking genes were generated in Geneious and edited using Inkscape (http://inkscape.org).
Classification and nomenclature of bacteriocin clusters
Putative bacteriocin clusters were classified based on their predicted biosynthetic machinery and structural features (Arnison et al., 2013) and their corresponding genes were designated per the standards of nomenclature for bacteriocins (Supplemental Table 1). BLAST searches in the NCBI database revealed that the majority of these clusters are also present in other closely related streptococci (Supplemental Table 2); therefore, the clusters were named using the prefix “strepto-” followed by an abbreviation of their bacteriocin class: “streptococcins” for those that were lactococcin 972-like, “streptolancidins” for lanthipeptides, “streptocyclicins” for the head-to-tail cyclized peptides, “streptosactins” for the sactipeptides and “streptolassins” for the lassopeptide group of bacteriocins. When more than one bacteriocin cluster from the same class was present, they were lettered alphabetically by the order of their discovery in our analyses.
Molecular epidemiology of the bacteriocin clusters
We compiled a global and historical dataset (n=571) by selecting a diverse set of pneumococcal genomes isolated between 1916 and 2009 from people of all ages residing in 39 different countries. Samples from both carriage and disease, 88 pneumococcal serotypes and 99 different clonal complexes were represented in this dataset (Supplemental Table 3). Genomes and their associated metadata were stored in a BIGSdb database (Jolley et al., 2010). The BIGSdb database platform was used to generate a presence/absence matrix of all the known bacteriocin genes in all 571 genomes. (Note that there were two small frameshifted gene remnants of both streptolancidins C and E present in some genomes, but these were not analysed further in this study.) Using this matrix (79,940 genes) as an input, an in-house python script was developed (available upon request) to calculate the prevalence, molecular epidemiology and co-occurrence patterns of all the bacteriocin clusters in the study dataset.
Construction of the core genome phylogenetic tree
All genomes in the study dataset were annotated using the Prokka prokaryotic annotation pipeline (Seemann 2014). The annotation files were input into Roary (Page et al., 2015) and clustered using a sequence identity threshold of 90%. Genes present in every genome were selected using a core genome threshold of 100% and were aligned using Roary. FastTreeMP (Price et al., 2010) was used to construct the phylogenetic tree using generalised time-reversible model (parameters: FastTreeMP -nt -gtr). ClonalFrameML (Didelot et al., 2015) was then applied to reconstruct the phylogenetic tree adjusted for recombination. The tree was annotated using iTOL (Letunic et al., 2016) and Inkscape.
Investigation of bacteriocin cluster insertion sites
Bacteriocin cluster sequences were used as queries to BLAST against genomes in the study dataset using the custom BLAST implemented in Geneious. The matching region plus additional flanking regions were visualised using the query-centric alignment feature within the Geneious environment. Regions of DNA with different bacteriocin clusters but identical flanking genes among different isolates were identified and further investigated using the Artemis Comparison Tool (ACT) (Carver et al., 2005). Linear comparison figures were generated using Geneious, ACT and Inkscape.
RNA sequencing analyses
In the first experiment, total bacterial RNA sequencing was performed on RNA extracted from pneumococcal strain 2/2 grown at a higher incubation temperature than normal (40 vs 37°C) to induce a bacterial stress response (Kurioka et al., 2017). Pneumococci were grown in brain-heart infusion broth for 6 h and RNA extractions were performed on samples from five time points (2, 3, 4, 5 and 6 h of incubation) using the Promega Maxwell® 16 Instrument and LEV simplyRNA Cells purification kit, following the manufacturer’s protocol. Extracted RNA samples were sent to the Oxford Genomics Centre for sequencing on the Illumina platform (NCBI GEO accession number GSE103778). The sequenced forward and reverse reads were paired and mapped onto the annotated pneumococcal strain 2/2 genome using Bowtie2 (Langmead et al., 2012) with the highest sensitivity option. Differential gene expression was assessed in Geneious using the DESeq (Anders et al., 2010) method. Genes with an adjusted P value <0.05 were deemed to be differentially expressed.
In a second experiment, pneumococcal reference strains PMEN-3 (Spain9V-3) and PMEN-6 (Hungary19A-6) were grown together in brain-heart infusion broth for 6 hours. The controls were prepared by growing each strain individually in brain-heart infusion broth for 6 h. Total bacterial RNA sequencing was performed on RNA extracted from broth cultures at 2, 3, 4, 5, and 6 h after incubation using the procedures described above (NCBI GEO accession number GSE110750).
A pseudo-reference genome was constructed using Bowtie2, Velvet (Zerbino et al., 2008), and MeDuSa (Bosi et al., 2015) to sort genes into three categories: those unique to PMEN-3, those unique to PMEN-6, and those shared between the two (Supplemental Fig. 3A). The RNA sequencing reads for each individual control strain at all time points were pooled in silico. Data from all time points were combined to minimise possible variability caused by different growth rates of strains. Data from all time points sampled in the broth culture of PMEN-3 + PMEN-6 were also combined in silico and mapped to the pseudo-reference genome using Bowtie2 with the highest sensitivity option. Differential expression analyses were performed using the DESeq method by comparing sequence reads generated when strains were co-cultured to those from when strains were grown individually (Supplemental Fig. 3B).
Theoretically, the control contained double the amount of reads in comparison to the in vivo competition experiment due to being compiled in silico from two sets of samples. While this meant that the downregulation of genes could not reliably be assessed, one could have confidence that upregulated genes were differentially expressed (since expression levels must exceed that of the combined controls); however, this approach can provide only relative and not absolute values, and true fold-change ratios for the upregulated genes are most likely underestimated using this method.
Data access
Representative examples of the newly-discovered bacteriocin clusters have been deposited at GenBank under the accession numbers of MF990778-MF990796. Accession numbers for all genomes used in this study are listed in Supplemental Table 4. Raw transcriptomic sequence data used in this study is available under GEO accession numbers GSE103778 and GSE110750.
Competing interests
The authors declare that they have no competing interests.
Acknowledgements
The authors wish to acknowledge computational assistance and helpful comments on the manuscript from Dr Melissa Jansen van Rensburg.