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.

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.

Comparison of the bacterial Enhancin-like proteins from Yersinia and Bacillus spp. with a baculovirus Enhancin

Enhancins are a class of metalloproteases found in some baculoviruses that enhance viral infection by degrading the peritrophic, membrane (PM) of the insect midgut. However, sequencing has revealed enhancin-like genes with 24-25% homology to viral enhancins, in the genomes of Yersinia pestis and Bacillus anthracis. AcMNPV does not encode enhancin therefore recombinant AcMNPV budded viruses (BVs) and polyhedra inclusion bodies (PIBs) were generated expressing the bacterial Enhancins. Bacterial Enhancins were found to be cytotoxic when compared to viral enhancin, however, larval bioassays suggested that the bacterial Enhancins did not enhance infection in the same way as viral Enhancin. This suggests that the bacterial Enhancins may have evolved a distinct biochemical function. (c) 2005 Elsevier Inc. All rights reserved.

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.

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.

Bergmann's rule and body size in mammals

Aim: To describe the geographical pattern of mean body size of the non-volant mammals of the Nearctic and Neotropics and evaluate the influence of five environmental variables that are likely to affect body size gradients. Location: The Western Hemisphere. Methods: We calculated mean body size (average log mass) values in 110 × 110 km cells covering the continental Nearctic and Neotropics. We also generated cell averages for mean annual temperature, range in elevation, their interaction, actual evapotranspiration, and the global vegetation index and its coefficient of variation. Associations between mean body size and environmental variables were tested with simple correlations and ordinary least squares multiple regression, complemented with spatial autocorrelation analyses and split-line regression. We evaluated the relative support for each multiple-regression model using AIC. Results: Mean body size increases to the north in the Nearctic and is negatively correlated with temperature. In contrast, across the Neotropics mammals are largest in the tropical and subtropical lowlands and smaller in the Andes, generating a positive correlation with temperature. Finally, body size and temperature are nonlinearly related in both regions, and split-line linear regression found temperature thresholds marking clear shifts in these relationships (Nearctic 10.9 °C; Neotropics 12.6 °C). The increase in body sizes with decreasing temperature is strongest in the northern Nearctic, whereas a decrease in body size in mountains dominates the body size gradients in the warmer parts of both regions. Main conclusions: We confirm previous work finding strong broad-scale Bergmann trends in cold macroclimates but not in warmer areas. For the latter regions (i.e. the southern Nearctic and the Neotropics), our analyses also suggest that both local and broad-scale patterns of mammal body size variation are influenced in part by the strong mesoscale climatic gradients existing in mountainous areas. A likely explanation is that reduced habitat sizes in mountains limit the presence of larger-sized mammals.

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.

Preparation of nanomagnetic absorbent for partition coefficient measurement

In this paper, we report a new method based on supercritical carbon dioxide (scCO(2)) to fill and distribute the porous magnetic nanoparticles with n-octanol in a homogeneous manner. The high solubility of n-octanol in scCO(2) and high diffusivity and permeability of the fluid allow efficient delivery of n-octanol into the porous magnetic nanoparticles. Thus, the n-octanol-loaded magnetic nanoparticles can be readily dispersed into aqueous buffer (pH 7.40) to form a homogenous suspension consisting of nano-sized n-octanol droplets. We refer this suspension as the n-octanol stock solution. The n-octanol stock solution is then mixed with bulk aqueous phase (pH 7.40) containing an organic compound prior to magnetic separation. The small-size of the particles and the efficient mixing enable a rapid establishment of the partition equilibrium of the organic compound between the solid supported n-octanol nano-droplets and the bulk aqueous phase. UV-vis spectrophotometry is then applied to determine the concentration of the organic compound in the aqueous phase both before and after partitioning (after magnetic separation). As a result, log D values of organic compounds of pharmaceutical interest determined by this modified method are found to be in excellent agreement with the literature data. (c) 2006 Elsevier B.V. All rights reserved.

Microbial species involved in production of 1,2-sn-diacylglycerol and effects of phosphatidylcholine on human fecal microbiota

1,2-sn-Diacylglycerols (DAGs) are activators of protein kinase C (PKQ, which is involved in the regulation of colonic mucosal proliferation. Extracellular DAG has been shown to stimulate the growth of cancer cell lines in vitro and may therefore play an important role in tumor promotion. DAG has been detected in human fecal extracts and is thought to be of microbial origin. Hitherto, no attempts have been made to identify the predominant fecal bacterial species involved in its production. We therefore used anaerobic batch culture systems to determine whether fecal bacteria could utilize phosphatidylcholine (0.5% [wt/vol]) to produce DAG. Production was found to be dependent upon the presence of the substrate and was enhanced in the presence of high concentrations of deoxycholate (5 and 10 mM) in the growth medium. Moreover, its production increased with the pH, and large inter- and intraindividual variations were observed between cultures seeded with inocula from different individuals. Clostridia and Escherichia coli multiplied in the fermentation systems, indicating their involvement in phosphatidylcholine metabolism. On the other hand, there was a significant decrease in the number of Bifidobacterium spp. in the presence of phosphatidylcholine. Pure-culture experiments showed that 10 of the 12 strains yielding the highest DAG levels (>50 nmol/ml) were isolated from batch culture enrichments run at pH 8.5. We found that the strains capable of producing large amounts of DAG were predominantly Clostridium bifermentans (8 of 12), followed by Escherichia coli (2 of 12). Interestingly, one DAG-producing strain was Bifidobacterium infantis, which is often considered a beneficial gut microorganism. Our results have provided further evidence that fecal bacteria can produce DAG and that specific bacterial groups are involved in this process. Future strategies to reduce DAG formation in the gut should target these species.

In vitro fermentation of chitosan derivatives by mixed cultures of human faecal bacteria

Stirred, pH controlled batch cultures were carried out with faecal inocula and various chitosans to investigate the fermentation of chitosan derivatives by the human gut flora. Changes in bacterial levels and short chain fatty acids were measured over time. Low, medium and high molecular weight chitosan caused a decrease in bacteroides, bifidobacteria, clostridia and lactobacilli. A similar pattern was seen with chitosan oligosaccharide (COS). Butyrate levels also decreased. A three-stage fermentation model of the human colon was used for investigation of the metabolism of COS. In a region representing the proximal colon, clostridia decreased while lactobacilli increased. In the region representing the transverse colon, bacteroides and clostridia increased. Distally a small increase in bacteroides occurred. Butyrate levels increased. Under the highly competitive conditions of the human colon, many members of the microflora, are unable to compete for chitosans of low, medium or high molecular weight. COS were more easily utilised and when added to an in vitro colonic model led to increased production of butyrate, but some populations of potentially detrimental bacteria also increased. (c) 2005 Elsevier Ltd. All rights reserved.

In vitro evaluation of the fermentation properties of galactooligosaccharides synthesised by alpha-galactosidase from Lactobacillus reuteri

Stirred, pH-controlled anaerobic batch cultures were used to evaluate the in vitro utilisation by canine gut microflora of novel alpha-galactooligosaccharides synthesised with an enzyme extract from a canine Lactobacillus reuteri strain. Fructooligosaccharides (FOS), melibiose and raffinose were used as reference carbohydrates for the prebiotic properties of the synthesised oligosaccharide (galactosyl melibiose mixture-GMM). Addition of Lactobacillus acidophilus was used as control for the evaluation of the synbiotic properties of the oligosaccharide with L. reuteri. Populations of predominant gut bacterial groups were monitored over 48 h of batch culture by fluorescent in situ hybridisation, and short-chain fatty acid (SCFA) production was measured. GMM showed a higher increase in bifidobacteria and lactobacilli population number and size as well as a higher decrease in clostridia population number and size compared to the commercial prebiotics (FOS, melibiose, raffinose). This prebiotic effect was further increased by the addition of L. reuteri followed by a change in the SCFA production pattern compared to GMM alone or GMM with L. acidophilus. The observed change in SCFA production was in accordance with the fermentation properties of L. reuteri, suggesting that the novel synbiotic had a significant effect on the canine gut microflora fermentation.

Biodiversity of human faecal bacteria isolated from phytic acid enriched chemostat fermenters

Background: Myo-inositol hexaphosphate (IP6) or phytic acid is found mostly in cereals and legumes and is thought to possess anti-carcinogenic properties. Aim: To isolate and identify faecal bacteria capable of phytic acid metabolism and to assess the effectiveness of prebiotics (dietary oligosaccharides, metabolised by selective colonic bacteria) in preserving the integrity of phytic acid. Methods: Faecal samples from three volunteers were used in continuous culture experiments under varying conditions of pH, substrate concentration and dilution rates, seventy three different isolates cultured at steady state were then screened for phytic acid metabolism and identified through partial sequencing of their 16S rRNA genes (16S ribosomal ribonucleic acid). Utilisation of phytic acid was also assessed in a continuous culture system enriched with prebiotic fructooligosaccharides (FOS). Results: Bacteroides spp., Clostridium spp. and facultatively anaerobic bacteria generally appeared to maintain viable counts in the presence of phytic acid. Bifidobacterium spp. and Lactobacillus spp. appeared less able to maintain viable counts in the presence of phytic acid. These results were confirmed by an increase in viable counts of Bacteroides spp., Clostridium spp. and a decrease in viable counts of Bifidobacterium spp. and Lactobacillus spp. once phytic acid was introduced to a FOS enriched continuous culture. Conclusions: The phytate metabolising biodiversity from the human large intestine does not appear to encompass major bacterial genera associated with beneficial or benign health effects (e.g. Lactobacillus spp. and Bifidobacterium spp).