Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area.

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller-Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated.

Simple sequence repeats reveal uneven distribution of genetic diversity in chloroplast genomes of Brassica oleracea L. and (n=9) wild relatives

Diversity in the chloroplast genome of 171 accessions representing the Brassica 'C' (n = 9) genome, including domesticated and wild B. oleracea and nine inter-fertile related wild species, was investigated using six chloroplast SSR (microsatellite) markers. The lack of diversity detected among 105 cultivated and wild accessions of B. oleracea contrasted starkly with that found within its wild relatives. The vast majority of B. oleracea accessions shared a single haplotype, whereas as many as six haplotypes were detected in two wild species, B. villosa Biv. and B. cretica Lam.. The SSRs proved to be highly polymorphic across haplotypes, with calculated genetic diversity values (H) of 0.23-0.87. In total, 23 different haplotypes were detected in C genome species, with an additional five haplotypes detected in B. rapa L. (A genome n = 10) and another in B. nigra L. (B genome, n = 8). The low chloroplast diversity of B. oleracea is not suggestive of multiple domestication events. The predominant B. oleracea haplotype was also common in B. incana Ten. and present in low frequencies in B. villosa, B. macrocarpa Guss, B. rupestris Raf. and B. cretica. The chloroplast SSRs reveal a wealth of diversity within wild Brassica species that will facilitate further evolutionary and phylogeographic studies of this important crop genus.

Mutational activation of niche-specific genes provides insight into regulatory networks and bacterial function in a complex environment

The genome of the plant-colonizing bacterium Pseudomonas fluorescens SBW25 harbors a subset of genes that are expressed specifically on plant surfaces. The function of these genes is central to the ecological success of SBW25, but their study poses significant challenges because no phenotype is discernable in vitro. Here, we describe a genetic strategy with general utility that combines suppressor analysis with IVET (SPyVET) and provides a means of identifying regulators of niche-specific genes. Central to this strategy are strains carrying operon fusions between plant environment-induced loci (EIL) and promoterless 'dapB. These strains are prototrophic in the plant environment but auxotrophic on laboratory minimal medium. Regulatory elements were identified by transposon mutagenesis and selection for prototrophs on minimal medium. Approximately 106 mutants were screened for each of 27 strains carrying 'dapB fusions to plant EIL and the insertion point for the transposon determined in approximately 2,000 putative regulator mutants. Regulators were functionally characterized and used to provide insight into EIL phenotypes. For one strain carrying a fusion to the cellulose-encoding wss operon, five different regulators were identified including a diguanylate cyclase, the flagella activator, FleQ, and alginate activator, AmrZ (AlgZ). Further rounds of suppressor analysis, possible by virtue of the SPyVET strategy, revealed an additional two regulators including the activator AlgR, and allowed the regulatory connections to be determined.

Assembly rules for protein networks derived from phylogenetic-statistical analysis of whole genomes

Background: We report an analysis of a protein network of functionally linked proteins, identified from a phylogenetic statistical analysis of complete eukaryotic genomes. Phylogenetic methods identify pairs of proteins that co-evolve on a phylogenetic tree, and have been shown to have a high probability of correctly identifying known functional links. Results: The eukaryotic correlated evolution network we derive displays the familiar power law scaling of connectivity. We introduce the use of explicit phylogenetic methods to reconstruct the ancestral presence or absence of proteins at the interior nodes of a phylogeny of eukaryote species. We find that the connectivity distribution of proteins at the point they arise on the tree and join the network follows a power law, as does the connectivity distribution of proteins at the time they are lost from the network. Proteins resident in the network acquire connections over time, but we find no evidence that 'preferential attachment' - the phenomenon of newly acquired connections in the network being more likely to be made to proteins with large numbers of connections - influences the network structure. We derive a 'variable rate of attachment' model in which proteins vary in their propensity to form network interactions independently of how many connections they have or of the total number of connections in the network, and show how this model can produce apparent power-law scaling without preferential attachment. Conclusion: A few simple rules can explain the topological structure and evolutionary changes to protein-interaction networks: most change is concentrated in satellite proteins of low connectivity and small phenotypic effect, and proteins differ in their propensity to form attachments. Given these rules of assembly, power law scaled networks naturally emerge from simple principles of selection, yielding protein interaction networks that retain a high-degree of robustness on short time scales and evolvability on longer evolutionary time scales.

Burkholderia Hep_Hag autotransporter (BuHA) proteins elicit a strong antibody response during experimental glanders but not human melioidosis

BACKGROUND: The bacterial biothreat agents Burkholderia mallei and Burkholderia pseudomallei are the cause of glanders and melioidosis, respectively. Genomic and epidemiological studies have shown that B. mallei is a recently emerged, host restricted clone of B. pseudomallei. RESULTS: Using bacteriophage-mediated immunoscreening we identified genes expressed in vivo during experimental equine glanders infection. A family of immunodominant antigens were identified that share protein domain architectures with hemagglutinins and invasins. These have been designated Burkholderia Hep_Hag autotransporter (BuHA) proteins. A total of 110/207 positive clones (53%) of a B. mallei expression library screened with sera from two infected horses belonged to this family. This contrasted with 6/189 positive clones (3%) of a B. pseudomallei expression library screened with serum from 21 patients with culture-proven melioidosis. CONCLUSION: Members of the BuHA proteins are found in other Gram-negative bacteria and have been shown to have important roles related to virulence. Compared with other bacterial species, the genomes of both B. mallei and B. pseudomallei contain a relative abundance of this family of proteins. The domain structures of these proteins suggest that they function as multimeric surface proteins that modulate interactions of the cell with the host and environment. Their effect on the cellular immune response to B. mallei and their potential as diagnostics for glanders requires further study.

Predicting functional gene links from phylogenetic-statistical analyses of whole genomes

An important element of the developing field of proteomics is to understand protein-protein interactions and other functional links amongst genes. Across-species correlation methods for detecting functional links work on the premise that functionally linked proteins will tend to show a common pattern of presence and absence across a range of genomes. We describe a maximum likelihood statistical model for predicting functional gene linkages. The method detects independent instances of the correlated gain or loss of pairs of proteins on phylogenetic trees, reducing the high rates of false positives observed in conventional across-species methods that do not explicitly incorporate a phylogeny. We show, in a dataset of 10,551 protein pairs, that the phylogenetic method improves by up to 35% on across-species analyses at identifying known functionally linked proteins. The method shows that protein pairs with at least two to three correlated events of gain or loss are almost certainly functionally linked. Contingent evolution, in which one gene's presence or absence depends upon the presence of another, can also be detected phylogenetically, and may identify genes whose functional significance depends upon its interaction with other genes. Incorporating phylogenetic information improves the prediction of functional linkages. The improvement derives from having a lower rate of false positives and from detecting trends that across-species analyses miss. Phylogenetic methods can easily be incorporated into the screening of large-scale bioinformatics datasets to identify sets of protein links and to characterise gene networks.

The mechanism of bacterial indigo reduction

The reduction of water-insoluble indigo by the recently isolated moderate thermophile, Clostridium isatidis, has been studied with the aim of developing a sustainable technology for industrial indigo reduction. The ability to reduce indigo was not shared with C. aurantibutyricum, C. celatum and C. papyrosolvens, but C. papyrosolvens could reduce indigo carmine (5,5-indigosulfonic acid), a soluble indigo derivative. The supernatant from cultures of C. isatidis, but not from cultures of the other bacteria tested, decreased indigo particle size to one-tenth diameter. Addition of madder powder, anthraquinone-2,6-disulfonic acid, and humic acid all stimulated indigo reduction by C. isatidis. Redox potentials of cultures of C. isatidis were about 100 mV more negative than those of C. aurantibutyricum, C. celatum and C. papyrosolvens, and reached –600 mV versus the SCE in the presence of indigo, but potentials were not consistently affected by the addition of the quinone compounds, which probably act by modifying the surface of the bacteria or indigo particles. It is concluded that C. isatidis can reduce indigo because (1) it produces an extracellular factor that decreases indigo particle size, and (2) it generates a sufficiently reducing potential.

Phylogeny of Pelargonium (Geraniaceae) based on DNA sequences from three genomes

Phylogenetic hypotheses for the largely South African genus Pelargonium L'Hér. (Geraniaceae) were derived based on DNA sequence data from nuclear, chloroplast and mitochondrial encoded regions. The datasets were unequally represented and comprised cpDNA trnL-F sequences for 152 taxa, nrDNA ITS sequences for 55 taxa, and mtDNA nad1 b/c exons for 51 taxa. Phylogenetic hypotheses derived from the separate three datasets were overall congruent. A single hypothesis synthesising the information in the three datasets was constructed following a total evidence approach and implementing dataset specific stepmatrices in order to correct for substitution biases. Pelargonium was found to consist of five main clades, some with contrasting evolutionary patterns with respect to biogeographic distributions, dispersal capacity, pollination biology and karyological diversification. The five main clades are structured in two (subgeneric) clades that correlate with chromosome size. One of these clades includes a "winter rainfall clade" containing more than 70% of all currently described Pelargonium species, and all restricted to the South African Cape winter rainfall region. Apart from (woody) shrubs and small herbaceous rosette subshrubs, this clade comprises a large "xerophytic" clade including geophytes, stem and leaf succulents, harbouring in total almost half of the genus. This clade is considered to be the result of in situ proliferation, possibly in response to late-Miocene and Pliocene aridification events. Nested within it is a radiation comprising c. 80 species from the geophytic Pelargonium section Hoarea, all characterised by the possession of (a series of) tunicate tubers.

Bacterial iron homeostasis

Iron is essential to virtually all organisms, but poses problems of toxicity and poor solubility. Bacteria have evolved various mechanisms to counter the problems imposed by their iron dependence, allowing them to achieve effective iron homeostasis under a range of iron regimes. Highly efficient iron acquisition systems are used to scavenge iron from the environment under iron-restricted conditions. In many cases, this involves the secretion and internalisation of extracellular ferric chelators called siderophores. Ferrous iron can also be directly imported by the G protein-like transporter, FcoB. For pathogens, host-iron complexes (transferrin, lactoferrin, haem, haemoglobin) are directly used as iron sources. Bacterial iron storage proteins (ferritin, bacterioferritin) provide intracellular iron reserves for use when external supplies are restricted, and iron detoxification proteins (Dps) are employed to protect the chromosome from iron-induced free radical damage. There is evidence that bacteria control their iron requirements in response to iron availability by downregulating the expression of iron proteins during iron-restricted growth. And finally, the expression of the iron homeostatic machinery is subject to iron-dependent global control ensuring that iron acquisition, storage and consumption are geared to iron availability and that intracellular levels of free iron do not reach toxic levels. (C) 2003 Federation of European Microbiological Societies. Published by Elsevier Science B.V. All rights reserved.

Chromosomal mapping of ANTP class homeobox genes in amphioxus: piecing together ancestral genomes

Homeobox genes encode DNA-binding proteins, many of which are implicated in the control of embryonic development. Evolutionarily, most homeobox genes fall into two related clades: the ANTP and the PRD classes. Some genes in ANTP class, notably Hox, ParaHox, and NK genes, have an intriguing arrangement into physical clusters. To investigate the evolutionary history of these gene clusters, we examined homeobox gene chromosomal locations in the cephalochordate amphioxus, Branchiostoma floridae. We deduce that 22 amphioxus ANTP class homeobox genes localize in just three chromosomes. One contains the Hox cluster plus AmphiEn, AmphiMnx, and AmphiDll. The ParaHox cluster resides in another chromosome, whereas a third chromosome contains the NK type homeobox genes, including AmphiMsx and ArnphiTlx. By comparative analysis we infer that clustering of ANTP class homeobox genes evolved just once, during a series of extensive cis-duplication events of genes early in animal evolution. A trans-duplication event occurred later to yield the Hox and ParaHox gene clusters on different chromosomes. The results obtained have implications for understanding the origin of homeobox gene clustering, the diversification of the ANTP class of homeobox genes, and the evolution of animal genomes.

The poliovirus 2C cis-acting replication element-mediated uridylylation of VPg is not required for synthesis of negative-sense genomes

Nucleotides in the terminal loop of the poliovirus 2C cis-acting replication element (2C(CRE)), a 61 nt structured RNA, function as the template for the addition of two uridylate (U) residues to the viral protein VPg. This uridylylation reaction leads to the formation of VPgpUpU, which is used by the viral RNA polymerase as a nucleotide-peptide primer for genome replication. Although VPg primes both positive- and negative-strand replication, the specific requirement for 2C(CRE)-mediated uridylylation for one or both events has not been demonstrated. We have used a cell-free in vitro translation and replication reaction to demonstrate that 2C(CRE) is not required for the initiation of the negative-sense strand, which is synthesized in the absence of 2C(CRE)-mediated VPgpUpU formation. We propose that the 3' poly(A) tail could serve as the template for the formation of a VPg-poly(U) primer that functions in the initiation of negative-sense strands.

Analysis of the sulfate-reducing bacterial and methanogenic archaeal populations in contrasting Antarctic sediments

The distribution and activity of communities of sulfate-reducing bacteria (SRB) and methanogenic archaea in two contrasting Antarctic sediments were investigated. Methanogenesis dominated in freshwater Lake Heywood, while sulfate reduction dominated in marine Shallow Bay. Slurry experiments indicated that 90% of the methanogenesis in Lake Heywood was acetoclastic. This finding was supported by the limited diversity of clones detected in a Lake Heywood archaeal clone library, in which most clones were closely related to the obligate acetate-utilizing Methanosaeta concilii. The Shallow Bay archaeal clone library contained clones related to the C-1-utilizing Methanolobus and Methanococcoides and the H-2-utilizing Methanogenium. Oligonucleotide probing of RNA extracted directly from sediment indicated that archaea represented 34% of the total prokaryotic signal in Lake Heywood and that Methanosaeta was a major component (13.2%) of this signal. Archaea represented only 0.2% of the total prokaryotic signal in RNA extracted from Shallow Bay sediments. In the Shallow Bay bacterial clone library, 10.3% of the clones were SRB-like, related to Desulfotalea/Desulforhopalus, Desulfofaba, Desulfosarcina, and Desulfobacter as well as to the sulfur and metal oxidizers comprising the Desulfuromonas cluster. Oligonucleotide probes for specific SRB clusters indicated that SRB represented 14.7% of the total prokaryotic signal, with Desulfotalea/Desulforhopalus being the dominant SRB group (10.7% of the total prokaryotic signal) in the Shallow Bay sediments; these results support previous results obtained for Arctic sediments. Methanosaeta and Desulfotalea/Desulforhopalus appear to be important in Lake Heywood and Shallow Bay, respectively, and may be globally important in permanently low-temperature sediments.