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.

Modelling the formation of necrotic regions in avascular tumours

The mechanisms underlying the formation of necrotic regions within avascular tumours are not well understood. In this paper, we examine the relative roles of nutrient deprivation and of cell death, from both the proliferating phase of the cell cycle via apoptosis and from the quiescent phase via necrosis, in changing the structure within multicellular tumour spheroids and particularly the accumulation of dead cell material in the centre. A mathematical model is presented and studied that accounts for nutrient diffusion, changes in cell cycling rates, the two different routes to cell death as well as active motion of cells and passive motion of the dead cell material. In studying the accumulation of dead cell matter we do not distinguish between the route by which each was formed. The resulting mathematical model is examined for a number of scenarios. Results show that in many cases the size of the necrotic core is closely correlated with low levels in nutrient concentration. However, in certain cases, particularly where the rate of necrosis is large, the resulting necrotic core can lead to regions of non-negligible nutrient concentration-dependent upon the mode of cell death.

Implementation of a Bayesian design in a dose-escalation study of an experimental agent in healthy volunteers

Bayesian decision procedures have recently been developed for dose escalation in phase I clinical trials concerning pharmacokinetic responses observed in healthy volunteers. This article describes how that general methodology was extended and evaluated for implementation in a specific phase I trial of a novel compound. At the time of writing, the study is ongoing, and it will be some time before the sponsor will wish to put the results into the public domain. This article is an account of how the study was designed in a way that should prove to be safe, accurate, and efficient whatever the true nature of the compound. The study involves the observation of two pharmacokinetic endpoints relating to the plasma concentration of the compound itself and of a metabolite as well as a safety endpoint relating to the occurrence of adverse events. Construction of the design and its evaluation via simulation are presented.

Bayesian design and conduct of phase II single-arm clinical trials with binary outcomes: a tutorial

The aim of phase II single-arm clinical trials of a new drug is to determine whether it has sufficient promising activity to warrant its further development. For the last several years Bayesian statistical methods have been proposed and used. Bayesian approaches are ideal for earlier phase trials as they take into account information that accrues during a trial. Predictive probabilities are then updated and so become more accurate as the trial progresses. Suitable priors can act as pseudo samples, which make small sample clinical trials more informative. Thus patients have better chances to receive better treatments. The goal of this paper is to provide a tutorial for statisticians who use Bayesian methods for the first time or investigators who have some statistical background. In addition, real data from three clinical trials are presented as examples to illustrate how to conduct a Bayesian approach for phase II single-arm clinical trials with binary outcomes.

Lack of myostatin results in excessive muscle growth but impaired force generation

The lack of myostatin promotes growth of skeletal muscle, and blockade of its activity has been proposed as a treatment for various muscle-wasting disorders. Here, we have examined two independent mouse lines that harbor mutations in the myostatin gene, constitutive null (Mstn(-/-)) and compact (Berlin High Line, BEH(c/c)). We report that, despite a larger muscle mass relative to age-matched wild types, there was no increase in maximum tetanic force generation, but that when expressed as a function of muscle size (specific force), muscles of myostatin-deficient mice were weaker than wild-type muscles. In addition, Mstn(-/-) muscle contracted and relaxed faster during a single twitch and had a marked increase in the number of type IIb fibers relative to wild-type controls. This change was also accompanied by a significant increase in type IIB fibers containing tubular aggregates. Moreover, the ratio of mitochondrial DNA to nuclear DNA and mitochondria number were decreased in myostatin-deficient muscle, suggesting a mitochondrial depletion. Overall, our results suggest that lack of myostatin compromises force production in association with loss of oxidative characteristics of skeletal muscle.

Antiviral effects of antisense morpholino oligomers in murine coronavirus infection models

The recent emergence of novel pathogenic human and animal coronaviruses has highlighted the need for antiviral therapies that are effective against a spectrum of these viruses. We have used several strains of murine hepatitis virus (MHV) in cell culture and in vivo in mouse models to investigate the antiviral characteristics of peptide-conjugated antisense phosphorodiamidate morpholino oligomers (P-PMOs). Ten P-PMOs directed against various target sites in the viral genome were tested in cell culture, and one of these (5TERM), which was complementary to the 5' terminus of the genomic RNA, was effective against six strains of MHV. Further studies were carried out with various arginine-rich peptides conjugated to the 5TERM PMO sequence in order to evaluate efficacy and toxicity and thereby select candidates for in vivo testing. In uninfected mice, prolonged P-PMO treatment did not result in weight loss or detectable histopathologic changes. 5TERM P-PMO treatment reduced viral titers in target organs and protected mice against virus-induced tissue damage. Prophylactic 5TERM P-PMO treatment decreased the amount of weight loss associated with infection under most experimental conditions. Treatment also prolonged survival in two lethal challenge models. In some cases of high-dose viral inoculation followed by delayed treatment, 5TERM P-PMO treatment was not protective and increased morbidity in the treated group, suggesting that P-PMO may cause toxic effects in diseased mice that were not apparent in the uninfected animals. However, the strong antiviral effect observed suggests that with further development, P-PMO may provide an effective therapeutic approach against a broad range of coronavirus infections.

Preliminary X-ray diffraction analysis of YcdB from Escherichia coli: a novel haem-containing and Tat-secreted periplasmic protein with a potential role in iron transport

YcdB is a periplasmic haem-containing protein from Escherichia coli that has a potential role in iron transport. It is currently the only reported haem-containing Tat-secreted substrate. Here, the overexpression, purification, crystallization and structure determination at 2.0 angstrom resolution are reported for the apo form of the protein. The apo-YcdB structure resembles those of members of the haem-dependent peroxidase family and thus confirms that YcdB is also a member of this family. Haem-soaking experiments with preformed apo-YcdB crystals have been optimized to successfully generate haem-containing YcdB crystals that diffract to 2.9 angstrom. Completion of model building and structure refinement are under way.

Fas ligand-induced apoptosis is regulated by nitric oxide through the inhibition of fas receptor clustering and the nitrosylation of protein kinase Cepsilon

Apoptosis induced by the death-inducing ligand FasL (CD95L) is a major mechanism of cell death. Trophoblast cells express the Fas receptor yet survive in an environment that is rich in the ligand. We report that basal nitric oxide (NO) production is responsible for the resistance of trophoblasts to FasL-induced apoptosis. In this study we demonstrate that basal NO production resulted in the inhibition of receptor clustering following ligand binding. In addition NO also protected cells through the selective nitrosylation, and inhibition, of protein kinase Cepsilon (PKCepsilon) but not PKCalpha. In the absence of NO production PKCepsilon interacted with, and phosphorylated, the anti-apoptotic protein cFLIP. The interaction is predominantly with the short form of cFLIP and its phosphorylation reduces its recruitment to the death-inducing signaling complex (DISC) that is formed following binding of a death-inducing ligand to its receptor. Inhibition of cFLIP recruitment to the DISC leads to increased activation of caspase 8 and subsequently to apoptosis. Inhibition of PKCepsilon using siRNA significantly reversed the sensitivity to apoptosis induced by inhibition of NO synthesis suggesting that NO-mediated inhibition of PKCepsilon plays an important role in the regulation of Fas-induced apoptosis.

Cell entry by enveloped viruses: redox considerations for HIV and SARS-coronavirus

For enveloped viruses, genome entry into the target cell involves two major steps: virion binding to the cell-surface receptor and fusion of the virion and cell membranes. Virus-cell membrane fusion is mediated by the virus envelope complex, and its fusogenicity is the result of an active virus-cell interaction process that induces conformation changes within the envelope. For some viruses, such as influenza, exposure to an acidic milieu within the cell during the early steps of infection triggers the necessary structural changes. However, for other pathogens which are not exposed to such environmental stress, activation of fusogenicity can result from precise thiol/disulfide rearrangements mediated by either an endogenous redox autocatalytic isomerase or a cell-associated oxidoreductase. Study of the activation of HIV envelope fusogenicity has revealed new knowledge about how redox changes within a viral envelope trigger fusion. We discuss these findings and their implication for anti-HIV therapy. In addition, to compare and contrast the situation outlined for HIV with an enveloped virus that can fuse with the cell plasma membrane independent of the redox status of its envelope protein, we review parallel data obtained on SARS coronavirus entry.

Diversification of a large genus in a continental biodiversity hotspot: temporal and spatial origin of Muraltia (Polygalaceae) in the Cape of South Africa

Phylogenetic relationships in the largely South African genus Muraltia (Polygalaceae) are assessed based on DNA sequence data (nuclear ribosomal ITS, plastid atpB-rbcL spacer, trnL intron, and trnL-F spacer) for 73 of the 117 currently recognized species in the genus. The previously recognised subgenus Muraltia is monophyletic, but the South African endemic genus Nylandtia is embedded in Muraltia subgenus Psiloclada. Subgenus Muraltia is found to be sister to subgenus Psiloclada. Estimates show the beginning of diversification of the two subgenera in the early Miocene (Psiloclada, 19.3+/-3.4 Ma; Muraltia, 21.0+/-3.5 Ma) pre-dating the establishment of the Benguela current (intermittent in the middle to late Oligocene and markedly intensifying in the late Miocene), and summer-dry climate in the Cape region. However, the later increase in species numbers is contemporaneous with these climatic phenomena. Results of dispersal-vicariance analyses indicate that major clades in Muraltia diversified from the southwestern and northwestern Cape, where most of the species are found today.

An evaluation of the costs of making specific secondary metabolites: does the yield penalty incurred by host plant resistance to insects due to competition for resources?

The presumption that the synthesis of 'defence' compounds in plants must incur some 'trade-off' or penalty in terms of annual crop yields has been used to explain observed inverse correlations between resistance to herbivores and rates of growth or photosynthesis. An analysis of the cost of making secondary compounds suggests that this accounts for only a small part of the overall carbon budget of annual crop plants. Even the highest reported amounts of secondary metabolites found in different crop species (flavonoids, allylisothiocyanates, hydroxamic acids, 2-tridecanone) represent a carbon demand that can be satisfied by less than an hour's photosynthesis. Similar considerations apply to secondary compounds containing nitrogen or sulphur, which are unlikely to represent a major investment compared to the cost of making proteins, the major demand for these elements. Decreases in growth and photosynthesis in response to stress are more likely the result of programmed down-regulation. Observed correlations between yield and low contents of unpalatable or toxic compounds may be the result of parallel selection during the refinement of crop species by humans.

Effect of heparin and fractionated heparin on trophoblast invasion

BACKGROUND: Heparin can significantly reduce pregnancy complications in women with certain thrombophilias, such as antiphospholipid syndrome. Recent reports suggest that heparin may act by mechanisms other than anticoagulation. However, the effect of heparin on trophoblast biology in the absence of thrombophilia has not been extensively investigated. Therefore, this study aimed to evaluate trophoblast invasion, using an established cell line and primary extravillous trophoblasts (EVTs), following exposure to heparin and fractionated heparin. METHODS: An EVT cell line (SGHPL-4) was used to study invasion in the presence of hepatocyte growth factor (HGF) and varying concentrations of fractionated and unfractionated heparin. These experiments were repeated using first trimester primary EVTs. RESULTS: Both forms of heparin significantly reduced HGF-induced invasion in the SGHPL-4 cell line. This suppression of invasion appeared to be dose-dependent for fractionated heparin. In primary EVT cells, fractionated heparin also demonstrated significant suppression of invasion. CONCLUSIONS: Heparin has the potential to reduce trophoblast invasion in cell lines and first trimester EVT cells. This article highlights the need for further evaluation of these medications in vitro and in vivo, especially when used in the absence of thrombophilic disorders.

Genetic characterization of tick-borne flaviviruses: new insights into evolution, pathogenetic determinants and taxonomy

Here, we analyze the complete coding sequences of all recognized tick-borne flavivirus species, including Gadgets Gully, Royal Farm and Karshi virus, seabird-associated flaviviruses, Kadam virus and previously uncharacterized isolates of Kyasanur Forest disease virus and Omsk hemorrhagic fever virus. Significant taxonomic improvements are proposed, e.g. the identification of three major groups (mammalian, seabird and Kadam tick-borne flavivirus groups), the creation of a new species (Karshi virus) and the assignment of Tick-borne encephalitis and Louping ill viruses to a unique species (Tick-borne encephalitis virus) including four viral types (i.e. Western Tick-borne encephalitis virus, Eastern Tick-borne encephalitis virus, Turkish sheep Tick-borne encephalitis virus and Louping ill Tick-borne encephalitis virus). The analyses also suggest a complex relationship between viruses infecting birds and those infecting mammals. Ticks that feed on both categories of vertebrates may constitute the evolutionary bridge between the three distinct identified lineages.

Origin and evolution of 3'UTR of flaviviruses: long direct repeats as a basis for the formation of secondary structures and their significance for virus transmission

The 3' untranslated regions (3'UTRs) of flaviviruses are reviewed and analyzed in relation to short sequences conserved as direct repeats (DRs). Previously, alignments of the 3'UTRs have been constructed for three of the four recognized flavivirus groups, namely mosquito-borne, tick-borne, and nonclassified flaviviruses (MBFV, TBFV, and NCFV, respectively). This revealed (1) six long repeat sequences (LRSs) in the 3'UTR and open-reading frame (ORF) of the TBFV, (2) duplication of the 3'UTR of the NCFV by intramolecular recombination, and (3) the possibility of a common origin for all DRs within the MBFV. We have now extended this analysis and review it in the context of all previous published analyses. This has been achieved by constructing a robust alignment between all flaviviruses using the published DRs and secondary RNA structures as "anchors" to reveal additional homologies along the 3'UTR. This approach identified nucleotide regions within the MBFV, NKV (no-known vector viruses), and NCFV 3'UTRs that are homologous to different LRSs in the TBFV 3'UTR and ORF. The analysis revealed that some of the DRs and secondary RNA structures described individually within each flavivirus group share common evolutionary origins. The 3'UTR of flaviviruses, and possibly the ORF, therefore probably evolved through multiple duplication of an RNA domain, homologous to the LRS previously identified only in the TBFV. The short DRs in all virus groups appear to represent the evolutionary remnants of these domains rather than resulting from new duplications. The relevance of these flavivirus DRs to evolution, diversity, 3'UTR enhancer function, and virus transmission is reviewed.