Mathematical model for NF-kappaB-driven proliferation of adult neural stem cells

Neural stem cells (NSCs) are early precursors of neuronal and glial cells. NSCs are capable of generating identical progeny through virtually unlimited numbers of cell divisions (cell proliferation), producing daughter cells committed to differentiation. Nuclear factor kappa B (NF-kappaB) is an inducible, ubiquitous transcription factor also expressed in neurones, glia and neural stem cells. Recently, several pieces of evidence have been provided for a central role of NF-kappaB in NSC proliferation control. Here, we propose a novel mathematical model for NF-kappaB-driven proliferation of NSCs. We have been able to reconstruct the molecular pathway of activation and inactivation of NF-kappaB and its influence on cell proliferation by a system of nonlinear ordinary differential equations. Then we use a combination of analytical and numerical techniques to study the model dynamics. The results obtained are illustrated by computer simulations and are, in general, in accordance with biological findings reported by several independent laboratories. The model is able to both explain and predict experimental data. Understanding of proliferation mechanisms in NSCs may provide a novel outlook in both potential use in therapeutic approaches, and basic research as well.

A role for Notch signaling in human corneal epithelial cell differentiation and proliferation

PURPOSE. To identify the role of Notch signaling in the human corneal epithelium. METHODS. Localization of Notch1, Notch2, Delta1, and Jagged1 in the human corneal epithelium was observed with the use of indirect immunofluorescence microscopy. Gene and protein expression of Notch receptors and ligands in human corneal epithelial cells was determined by RT-PCR and Western blot analysis, respectively. The effects of Notch inhibition (by {gamma}-secretase inhibition) and activation (by recombinant Jagged1) on epithelial cell proliferation (Ki67) and differentiation (CK3) were analyzed after Western blotting and immunocytochemistry. RESULTS. Immunofluorescent labeling localized Notch1 and Notch2 to suprabasal epithelial cell layers, whereas Delta1 and Jagged1 were observed throughout the corneal epithelium. Notch1, Notch2, Delta1, and Jagged1 genes and proteins were expressed in human corneal epithelial cells. {gamma}-Secretase inhibition resulted in decreased Notch1 and Notch2 expression, with an accompanying decrease in Ki67 and increased CK3 expression. The activation of Notch by Jagged1 resulted in the upregulation of active forms of Notch1 and 2 proteins (P < 0.05), with a concurrent increase in Ki67 (P < 0.05) and a decrease in CK3 (P < 0.05) expression. Interestingly, {gamma}-secretase inhibition in a three-dimensional, stratified corneal epithelium equivalent had no effect on Ki67 or CK3 expression. In contrast, Jagged1 activation resulted in decreased CK3 expression (P < 0.05), though neither Notch activation nor inhibition affected cell proliferation in the 3D tissue equivalent. CONCLUSIONS. Notch family members and ligands are expressed in the human corneal epithelium and appear to play pivotal roles in corneal epithelial cell differentiation.

A review and classification of the existing models of cyanobacteria

Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling of cyanobacteria in freshwaters is an important tool for understanding their population dynamics and predicting bloom occurrence in lakes and rivers. In this paper existing key models of cyanobacteria are reviewed, evaluated and classified. Two major groups emerge: deterministic mathematical and artificial neural network models. Mathematical models can be further subcategorized into those models concerned with impounded water bodies and those concerned with rivers. Most existing models focus on a single aspect such as the growth of transport mechanisms, but there are a few models which couple both.

Study of the lactation curve in dairy cattle on farms in Central Mexico

Accurate knowledge of lactation curves has an important relevance to management and research of dairy production systems. A number of equations have been proposed to describe the lactation curve, the most widely applied being the gamma equation. The objective of this work was to compare and evaluate candidate functions for their predictive ability in describing lactation curves from central Mexican dairy cows reared under 2 contrasting management systems. Five equations were considered: Gaines ( exponential decay), Wood ( gamma equation), Rook ( Michaelis-Menten x exponential), and 2 more mechanistic ones (Dijkstra and Pollott). A database consisting of 701 and 1283 records of cows in small-scale and intensive systems, respectively, was used in the analysis. Before analysis, the database was divided into 6 groups representing first, second, and third and higher parity cows in both systems. In all cases except second and above parity cows in small-scale systems, all models improved on the Gaines equation. The Wood equation explained much of the variation, but its parameters do not have direct biological interpretation. Although the Rook equation fitted the data well, some of the parameter estimates were not significant. The Dijkstra equation consistently gave better predictions, and its parameters were usually statistically significant and lend themselves to physiological interpretation. As such, the differences between systems and parity could be explained due to variations in theoretical initial milk production at parturition, specific rates of secretory cell proliferation and death, and rate of decay, all of which are parameters in the model. The Pollott equation, although containing the most biology, was found to be over-parameterized and resulted in nonsignificant parameter estimates. For central Mexican dairy cows, the Dijkstra equation was the best option to use in describing the lactation curve.

Muscle hypertrophy driven by myostatin blockade does not require stem/precursor-cell activity

Myostatin, a member of the TGF-beta family, has been identified as a powerful inhibitor of muscle growth. Absence or blockade of myostatin induces massive skeletal muscle hypertrophy that is widely attributed to proliferation of the population of muscle fiber-associated satellite cells that have been identified as the principle source of new muscle tissue during growth and regeneration. Postnatal blockade of myostatin has been proposed as a basis for therapeutic strategies to combat muscle loss in genetic and acquired myopathies. But this approach, according to the accepted mechanism, would raise the threat of premature exhaustion of the pool of satellite cells and eventual failure of muscle regeneration. Here, we show that hypertrophy in the absence of myostatin involves little or no input from satellite cells. Hypertrophic fibers contain no more myonuclei or satellite cells and myostatin had no significant effect on satellite cell proliferation in vitro, while expression of myostatin receptors dropped to the limits of detectability in postnatal satellite cells. Moreover, hypertrophy of dystrophic muscle arising from myostatin blockade was achieved without any apparent enhancement of contribution of myonuclei from satellite cells. These findings contradict the accepted model of myostatin-based control of size of postnatal muscle and reorient fundamental investigations away from the mechanisms that control satellite cell proliferation and toward those that increase myonuclear domain, by modulating synthesis and turnover of structural muscle fiber proteins. It predicts too that any benefits of myostatin blockade in chronic myopathies are unlikely to impose any extra stress on the satellite cells.

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.

Oestrogenic activity of p-hydroxybenzoic acid (common metabolite of paraben esters) and methylparaben in human breast cancer cell lines

This paper addresses the question of whether p-hydroxybenzoic acid, the common metabolite of parabens, possesses oestrogenic activity in human breast cancer cell lines. The alkyl esters of p-hydroxybenzoic acid (parabens) are used widely as preservatives in consumer products to which the human population is exposed and have been shown previously to possess oestrogenic activity and to be present in human breast tumour tissue, which is an oestrogen-responsive tissue. Recent work has shown p-hydroxybenzoic acid to give an oestrogenic response in the rodent uterotrophic assay. We report here that p-hydroxybenzoic acid possesses oestrogenic activity in a panel of assays in human breast cancer cell lines. p-Hydroxybenzoic acid was able to displace [H-3]oestradiol from cytosolic oestrogen receptor of MCF7 human breast cancer cells by 54% at 5 x 10(6)-fold molar excess and by 99% at 10(7)-fold molar excess. It was able to increase the expression of a stably integrated oestrogen responsive reporter gene (ERE-CAT) at a concentration of 5 x 10(-4) M in MCF7 cells after 24 h and 7 days, which could be inhibited by the anti-oestrogen ICI 182 780 (Faslodex, fulvestrant). Proliferation of two human breast cancer cell lines (MCF7, ZR-75-1) could be increased by 10(-5) M p-hydroxybenzoic acid. Following on from previous studies showing a decrease in oestrogenic activity of parabens with shortening of the linear alkyl chain length, this study has compared the oestrogenic activity of p-hydroxybenzoic acid where the alkyl grouping is no longer present with methylparaben, which has the shortest alkyl group. Intrinsic oestrogenic activity of p-hydroxybenzoic acid was similar to that of methylparaben in terms of relative binding to the oestrogen receptor but its oestrogenic activity on gene expression and cell proliferation was lower than that of methylparaben. It can be concluded that removal of the ester group from parabens does not abrogate its oestrogenic activity and that p-hydroxybenzoic acid can give oestrogenic responses in human breast cancer cells. Copyright (C) 2005 John Wiley & Sons, Ltd.

Targeting the cell cycle machinery for the treatment of cardiovascular disease

Cardiovascular disease represents a major clinical problem affecting a significant proportion of the world's population and remains the main cause of death in the UK. The majority of therapies currently available for the treatment of cardiovascular disease do not cure the problem but merely treat the symptoms. Furthermore, many cardioactive drugs have serious side effects and have narrow therapeutic windows that can limit their usefulness in the clinic. Thus, the development of more selective and highly effective therapeutic strategies that could cure specific cardiovascular diseases would be of enormous benefit both to the patient and to those countries where healthcare systems are responsible for an increasing number of patients. In this review, we discuss the evidence that suggests that targeting the cell cycle machinery in cardiovascular cells provides a novel strategy for the treatment of certain cardiovascular diseases. Those cell cycle molecules that are important for regulating terminal differentiation of cardiac myocytes and whether they can be targeted to reinitiate cell division and myocardial repair will be discussed as will the molecules that control vascular smooth muscle cell (VSMC) and endothelial cell proliferation in disorders such as atherosclerosis and restenosis. The main approaches currently used to target the cell cycle machinery in cardiovascular disease have employed gene therapy techniques. We will overview the different methods and routes of gene delivery to the cardiovascular system and describe possible future drug therapies for these disorders. Although the majority of the published data comes from animal studies, there are several instances where potential therapies have moved into the clinical setting with promising results.

A study on intelligent building models

Mathematical models devoted to different aspects of building studies and brought about a significant shift in the way we view buildings. From this background a new definition of building has emerged known as intelligent building that requires integration of a variety of computer-based complex systems. Research relevant to intelligent continues to grow at a much faster pace. This paper is a review of different mathematical models described in literature, which make use of different mathematical methodologies, and are intended for intelligent building studies without complex mathematical details. Models are discussed under a wide classification. Mathematical abstract level of the applied models is detailed and integrated with its literature. The goal of this paper is to present a comprehensive account of the achievements and status of mathematical models in intelligent building research. and to suggest future directions in models.

Modelling oil absorption during post-frying cooling - II: solution of the mathematical model, model testing and simulations

The mathematical models that describe the immersion-frying period and the post-frying cooling period of an infinite slab or an infinite cylinder were solved and tested. Results were successfully compared with those found in the literature or obtained experimentally, and were discussed in terms of the hypotheses and simplifications made. The models were used as the basis of a sensitivity analysis. Simulations showed that a decrease in slab thickness and core heat capacity resulted in faster crust development. On the other hand, an increase in oil temperature and boiling heat transfer coefficient between the oil and the surface of the food accelerated crust formation. The model for oil absorption during cooling was analysed using the tested post-frying cooling equation to determine the moment in which a positive pressure driving force, allowing oil suction within the pore, originated. It was found that as crust layer thickness, pore radius and ambient temperature decreased so did the time needed to start the absorption. On the other hand, as the effective convective heat transfer coefficient between the air and the surface of the slab increased the required cooling time decreased. In addition, it was found that the time needed to allow oil absorption during cooling was extremely sensitive to pore radius, indicating the importance of an accurate pore size determination in future studies.

Modelling the interdependence between the stoichiometry of receptor oligomerization and ligand binding for a coexisting dimer/tetramer receptor system

Many G protein-coupled receptors have been shown to exist as oligomers, but the oligomerization state and the effects of this on receptor function are unclear. For some G protein-coupled receptors, in ligand binding assays, different radioligands provide different maximal binding capacities. Here we have developed mathematical models for co-expressed dimeric and tetrameric species of receptors. We have considered models where the dimers and tetramers are in equilibrium and where they do not interconvert and we have also considered the potential influence of the ligands on the degree of oligomerization. By analogy with agonist efficacy, we have considered ligands that promote, inhibit or have no effect on oligomerization. Cell surface receptor expression and the intrinsic capacity of receptors to oligomerize are quantitative parameters of the equations. The models can account for differences in the maximal binding capacities of radioligands in different preparations of receptors and provide a conceptual framework for simulation and data fitting in complex oligomeric receptor situations.

Markov models of aging: theory and practice

We review and structure some of the mathematical and statistical models that have been developed over the past half century to grapple with theoretical and experimental questions about the stochastic development of aging over the life course. We suggest that the mathematical models are in large part addressing the problem of partitioning the randomness in aging: How does aging vary between individuals, and within an individual over the lifecourse? How much of the variation is inherently related to some qualities of the individual, and how much is entirely random? How much of the randomness is cumulative, and how much is merely short-term flutter? We propose that recent lines of statistical inquiry in survival analysis could usefully grapple with these questions, all the more so if they were more explicitly linked to the relevant mathematical and biological models of aging. To this end, we describe points of contact among the various lines of mathematical and statistical research. We suggest some directions for future work, including the exploration of information-theoretic measures for evaluating components of stochastic models as the basis for analyzing experiments and anchoring theoretical discussions of aging.

Self-assembly and bioactivity of a polymer/peptide conjugate containing the RGD cell adhesion motif and PEG

The self-assembly and bioactivity of the peptide–polymer conjugate DGRFFF–PEG3000 containing the RGD cell adhesion motif has been examined, in aqueous solution. The conjugate is designed to be amphiphilic by incorporation of three hydrophobic phenylalanine residues as well as the RGD unit and a short poly(ethylene glycol) (PEG) chain of molar mass 3000 kg mol-1. Above a critical aggregation concentration, determined by fluorescence measurements, signals of b-sheet structure are revealed by spectroscopic measurements, as well as X-ray diffraction. At high concentration, a self-assembled fibril nanostructure is revealed by electron microscopy. The fibrils are observed despite PEG crystallization which occurs on drying. This suggests that DGRFFF has an aggregation tendency that is sufficiently strong not to be prevented by PEG crystallization. The adhesion, viability and proliferation of human corneal fibroblasts was examined for films of the conjugate on tissue culture plates (TCPs) as well as low attachment plates. On TCP, DGRFFF–PEG3000 films prepared at sufficiently low concentration are viable, and cell proliferation is observed. However, on low attachment surfaces, neither cell adhesion nor proliferation was observed, indicating that the RGD motif was not available to enhance cell adhesion. This was ascribed to the core–shell architecture of the self-assembled fibrils with a peptide core surrounded by a PEG shell which hinders access to the RGD unit.

Alanine-rich amphiphilic peptide containing the RGD cell adhesion motif: a coating material for human fibroblast attachment and culture

We studied the self-assembly of peptide A6RGD (A: alanine, R: arginine, G: glycine, D: aspartic acid) in water, and the use of A6RGD substrates as coatings to promote the attachment of human cornea stromal fibroblasts (hCSFs). The self-assembled motif of A6RGD was shown to depend on the peptide concentration in water, where both vesicle and fibril formation were observed. Oligomers were detected for 0.7 wt% A6RGD, which evolved into short peptide fibres at 1.0 wt% A6RGD, while a co-existence of vesicles and long peptide fibres was revealed for 2–15 wt% A6RGD. A6RGD vesicle walls were shown to have a multilayer structure built out of highly interdigitated A6 units, while A6RGD fibres were based on β-sheet assemblies. Changes in the self-assembly motif with concentration were reflected in the cell culture assay results. Films dried from 0.1–1.0 wt% A6RGD solutions allowed hCSFs to attach and significantly enhanced cell proliferation relative to the control. In contrast, films dried from 2.5 wt% A6RGD solutions were toxic to hCSFs.

Synbiotic approach restores intestinal homeostasis and prolongs survival in leukaemia mice with cachexia

Cancer cachexia is a multifactorial syndrome that includes muscle wasting and inflammation. As gut microbes influence host immunity and metabolism, we investigated the role of the gut microbiota in the therapeutic management of cancer and associated cachexia. A community-wide analysis of the caecal microbiome in two mouse models of cancer cachexia (acute leukaemia or subcutaneous transplantation of colon cancer cells) identified common microbial signatures, including decreased Lactobacillus spp. and increased Enterobacteriaceae and Parabacteroides goldsteinii/ASF 519. Building on this information, we administered a synbiotic containing inulin-type fructans and live Lactobacillus reuteri 100-23 to leukaemic mice. This treatment restored the Lactobacillus population and reduced the Enterobacteriaceae levels. It also reduced hepatic cancer cell proliferation, muscle wasting and morbidity, and prolonged survival. Administration of the synbiotic was associated with restoration of the expression of antimicrobial proteins controlling intestinal barrier function and gut immunity markers, but did not impact the portal metabolomics imprinting of energy demand. In summary, this study provided evidence that the development of cancer outside the gut can impact intestinal homeostasis and the gut microbial ecosystem and that a synbiotic intervention, by targeting some alterations of the gut microbiota, confers benefits to the host, prolonging survival and reducing cancer proliferation and cachexia.