Dynamical analysis in growth models: Blumberg’s equation

We present a new dynamical approach to the Blumberg's equation, a family of unimodal maps. These maps are proportional to Beta(p, q) probability densities functions. Using the symmetry of the Beta(p, q) distribution and symbolic dynamics techniques, a new concept of mirror symmetry is defined for this family of maps. The kneading theory is used to analyze the effect of such symmetry in the presented models. The main result proves that two mirror symmetric unimodal maps have the same topological entropy. Different population dynamics regimes are identified, when the intrinsic growth rate is modified: extinctions, stabilities, bifurcations, chaos and Allee effect. To illustrate our results, we present a numerical analysis, where are demonstrated: monotonicity of the topological entropy with the variation of the intrinsic growth rate, existence of isentropic sets in the parameters space and mirror symmetry.

An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Taxonomy of broker's functions in virtual enterprises

Not just with the emergence but also with the growing of the electronic market, that is, the growth of online suppliers of services and products and Internet users (potential consumers), the necessary conditions to the affirmation of the agile/virtual enterprises (A/VE) as a present and future enterprise organizational model are created. In this context, it is our understanding that the broker may have an important role in its development, namely, if the broker performs functions for the A/VE with better efficacy and efficiency. In this article, we will present first a revision of the broker’s models in a structured form. We present a taxonomy of possible broker’s functions for the broker’s actuation near the A/VE and then the classification of the literature broker’s models. This classification will permit an analysis of a broker’s model and establish a mainframe for our broker’s model according to the BM_Virtual Enterprise Architecture Reference Model (BM_VEARM).

From weak Allee effect to no Allee effect in Richards’ growth models

Population dynamics have been attracting interest since many years. Among the considered models, the Richards’ equations remain one of the most popular to describe biological growth processes. On the other hand, Allee effect is currently a major focus of ecological research, which occurs when positive density dependence dominates at low densities. In this chapter, we propose the dynamical study of classes of functions based on Richards’ models describing the existence or not of Allee effect. We investigate bifurcation structures in generalized Richards’ functions and we look for the conditions in the (β, r) parameter plane for the existence of a weak Allee effect region. We show that the existence of this region is related with the existence of a dovetail structure. When the Allee limit varies, the weak Allee effect region disappears when the dovetail structure also disappears. Consequently, we deduce the transition from the weak Allee effect to no Allee effect to this family of functions. To support our analysis, we present fold and flip bifurcation curves and numerical simulations of several bifurcation diagrams.

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

Explosion birth and extinction: Double big bang bifurcations and Allee effect in Tsoularis-Wallace's growth models

This work concerns dynamics and bifurcations properties of a new class of continuous-defined one-dimensional maps: Tsoularis-Wallace's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon of extinction. To establish this result we introduce the notions of Allee's functions, Allee's effect region and Allee's bifurcation curve. Another central point of our investigation is the study of bifurcation structures for this class of functions, in a three-dimensional parameter space. We verified that under some sufficient conditions, Tsoularis-Wallace's functions have particular bifurcation structures: the big bang and the double big bang bifurcations of the so-called "box-within-a-box" type. The double big bang bifurcations are related to the existence of flip codimension-2 points. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct kinds of boxes. This work contributes to clarify the big bang bifurcation analysis for continuous maps and understand their relationship with explosion birth and extinction phenomena.

Peroxisomal beta-oxidation--a metabolic pathway with multiple functions.

Fatty acid degradation in most organisms occurs primarily via the beta-oxidation cycle. In mammals, beta-oxidation occurs in both mitochondria and peroxisomes, whereas plants and most fungi harbor the beta-oxidation cycle only in the peroxisomes. Although several of the enzymes participating in this pathway in both organelles are similar, some distinct physiological roles have been uncovered. Recent advances in the structural elucidation of numerous mammalian and yeast enzymes involved in beta-oxidation have shed light on the basis of the substrate specificity for several of them. Of particular interest is the structural organization and function of the type 1 and 2 multifunctional enzyme (MFE-1 and MFE-2), two enzymes evolutionarily distant yet catalyzing the same overall enzymatic reactions but via opposite stereochemistry. New data on the physiological roles of the various enzymes participating in beta-oxidation have been gathered through the analysis of knockout mutants in plants, yeast and animals, as well as by the use of polyhydroxyalkanoate synthesis from beta-oxidation intermediates as a tool to study carbon flux through the pathway. In plants, both forward and reverse genetics performed on the model plant Arabidopsis thaliana have revealed novel roles for beta-oxidation in the germination process that is independent of the generation of carbohydrates for growth, as well as in embryo and flower development, and the generation of the phytohormone indole-3-acetic acid and the signal molecule jasmonic acid.

PHYTOCHROME KINASE SUBSTRATE4 modulates phytochrome-mediated control of hypocotyl growth orientation

Gravity and light are major factors shaping plant growth. Light perceived by phytochromes leads to seedling deetiolation, which includes the deviation from vertical hypocotyl growth and promotes hypocotyl phototropism. These light responses enhance survival of young seedlings during their emergence from the soil. The PHYTOCHROME KINASE SUBSTRATE (PKS) family is composed of four members in Arabidopsis (Arabidopsis thaliana): PKS1 to PKS4. Here we show that PKS4 is a negative regulator of both phytochrome A- and B-mediated inhibition of hypocotyl growth and promotion of cotyledon unfolding. Most prominently, pks4 mutants show abnormal phytochrome-modulated hypocotyl growth orientation. In dark-grown seedlings hypocotyls change from the original orientation defined by seed position to the upright orientation defined by gravity and light reduces the magnitude of this shift. In older seedlings with the hypocotyls already oriented by gravity, light promotes the deviation from vertical orientation. Based on the characterization of pks4 mutants we propose that PKS4 inhibits changes in growth orientation under red or far-red light. Our data suggest that in these light conditions PKS4 acts as an inhibitor of asymmetric growth. This hypothesis is supported by the phenotype of PKS4 overexpressers. Together with previous findings, these results indicate that the PKS family plays important functions during light-regulated tropic growth responses

Understanding the low-temperature limitations to forest growth through calibration of a forest dynamics model with tree-ring data

The sensitivity of altitudinal and latitudinal tree-line ecotones to climate change, particularly that of temperature, has received much attention. To improve our understanding of the factors affecting tree-line position, we used the spatially explicit dynamic forest model TreeMig. Although well-suited because of its landscape dynamics functions, TreeMig features a parabolic temperature growth response curve, which has recently been questioned. and the species parameters are not specifically calibrated for cold temperatures. Our main goals were to improve the theoretical basis of the temperature growth response curve in the model and develop a method for deriving that curve's parameters from tree-ring data. We replaced the parabola with an asymptotic curve, calibrated for the main species at the subalpine (Swiss Alps: Pinus cembra, Larix decidua, Picea abies) and boreal (Fennoscandia: Pinus sylvestris, Betula pubescens, P. abies) tree-lines. After fitting new parameters, the growth curve matched observed tree-ring widths better. For the subalpine species, the minimum degree-day sum allowing, growth (kDDMin) was lowered by around 100 degree-days; in the case of Larix, the maximum potential ring-width was increased to 5.19 mm. At the boreal tree-line, the kDDMin for P. sylvestris was lowered by 210 degree-days and its maximum ring-width increased to 2.943 mm; for Betula (new in the model) kDDMin was set to 325 degree-days and the maximum ring-width to 2.51 mm; the values from the only boreal sample site for Picea were similar to the subalpine ones, so the same parameters were used. However, adjusting the growth response alone did not improve the model's output concerning species' distributions and their relative importance at tree-line. Minimum winter temperature (MinWiT, mean of the coldest winter month), which controls seedling establishment in TreeMig, proved more important for determining distribution. Picea, P. sylvestris and Betula did not previously have minimum winter temperature limits, so these values were set to the 95th percentile of each species' coldest MinWiT site (respectively -7, -11, -13). In a case study for the Alps, the original and newly calibrated versions of TreeMig were compared with biomass data from the National Forest Inventor), (NFI). Both models gave similar, reasonably realistic results. In conclusion, this method of deriving temperature responses from tree-rings works well. However, regeneration and its underlying factors seem more important for controlling species' distributions than previously thought. More research on regeneration ecology, especially at the upper limit of forests. is needed to improve predictions of tree-line responses to climate change further.

Divergent functions of three Candida albicans zinc-cluster transcription factors (CTA4, ASG1 and CTF1) complementing pleiotropic drug resistance in Saccharomyces cerevisiae.

One of the mediators of pleiotropic drug resistance in Saccharomyces cerevisiae is the ABC-transporter gene PDR5. This gene is regulated by at least two transcription factors with Zn(2)-Cys(6) finger DNA-binding motifs, Pdr1p and Pdr3p. In this work, we searched for functional homologues of these transcription factors in Candida albicans. A C. albicans gene library was screened in a S. cerevisiae mutant lacking PDR1 and PDR3 and clones resistant to azole antifungals were isolated. From these clones, three genes responsible for azole resistance were identified. These genes (CTA4, ASG1 and CTF1) encode proteins with Zn(2)-Cys(6)-type zinc finger motifs in their N-terminal domains. The C. albicans genes expressed in S. cerevisiae could activate the transcription of a PDR5-lacZ reporter system and this reporter activity was PDRE-dependent. They could also confer resistance to azoles in a S. cerevisiae strain lacking PDR1, PDR3 and PDR5, suggesting that CTA4-, ASG1- and CTF1-dependent azole resistance can be caused by genes other than PDR5 in S. cerevisiae. Deletion of CTA4, ASG1 and CTF1 in C. albicans had no effect on fluconazole susceptibility and did not alter the expression of the ABC-transporter genes CDR1 and CDR2 or the major facilitator gene MDR1, which encode multidrug transporters known as mediators of azole resistance in C. albicans. However, additional phenotypic screening tests on the C. albicans mutants revealed that the presence of ASG1 was necessary to sustain growth on non-fermentative carbon sources (sodium acetate, acetic acid, ethanol). In conclusion, C. albicans possesses functional homologues of the S. cerevisiae Pdr1p and Pdr3p transcription factors; however, their properties in C. albicans have been rewired to other functions.

Effects of corticosterone on innate and humoral immune functions and oxidative stress in barn owl nestlings.

The costs of coping with stressful situations are traded-off against other functions such as immune responses. This trade-off may explain why corticosterone secretion reduces immune reactions. Corticosterone differentially affects various immunity components. However, which component is suppressed varies between studies. It remains unclear whether the trade-off in energy, nutrition, autoimmunity or oxidative stress accounts for differential immunosuppression. In this study, we investigated whether corticosterone differentially affects the constitutive innate and humoral acquired immunity. We used barn owl nestlings, implanting 50% with a corticosterone-releasing pellet and the other 50% with a placebo pellet. To measure the effect on humoral immunity we vaccinated 50% of the corticosterone-nestlings and 50% of the placebo-nestlings with the antigens 'Tetravac' and the other 50% were injected with PBS. To assess the costs of elevated corticosterone, we measured body mass and resistance to oxidative stress. Administration of corticosterone increased corticosterone levels whereas vaccination induced the production of antibodies. Corticosterone reduced the production of antibodies, but it did not significantly affect the constitutive innate immunity. Corticosterone reduced body growth and resistance to oxidative stress. Under stressful conditions barn owl nestlings seem to keep the constitutive innate immunity, whereas elevated corticosterone levels negatively affected inducible immune responses. We found evidence that mounting a humoral immune reaction is not costly in terms of growth, but reduces the resistance to oxidative stress independently of corticosterone administration. We suggest that humoral immunity is suppressed because the risk of immunopathologies may be disproportionately high when mounting an antibody response under stressful situations.

Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates

We prove two-sided inequalities between the integral moduli of smoothness of a function on R d[superscript] / T d[superscript] and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is given by the equivalence results for functions satisfying certain regular conditions. Applications include a quantitative form of the Riemann-Lebesgue lemma as well as several other questions in approximation theory and the theory of function spaces.

Predicting random level and seasonality of hotel prices. A structural equation growth curve approach

This article examines the effect on price of different characteristics of holiday hotels in the sun-and-beach segment, under the hedonic function perspective. Monthly prices of the majority of hotels in the Spanish continental Mediterranean coast are gathered from May to October 1999 from the tour operator catalogues. Hedonic functions are specified as random-effect models and parametrized as structural equation models with two latent variables, a random peak season price and a random width of seasonal fluctuations. Characteristics of the hotel and the region where they are located are used as predictors of both latent variables. Besides hotel category, region, distance to the beach, availability of parking place and room equipment have an effect on peak price and also on seasonality. 3- star hotels have the highest seasonality and hotels located in the southern regions the lowest, which could be explained by a warmer climate in autumn

Genetic investigation of the functions of c-Myc and N-Myc in Hematopoietic stem cells

Résumé : c-Myc, le premier facteur de transcription de la famille Myc a été découvert il y a maintenant trente ans. Il reste à l'heure actuelle parmi les plus puissants proto-oncogènes connus. c-Myc est dérégulé dans plus de 50% des cancers, où il promeut la prolifération, la croissance cellulaire, et la néoangiogenèse. Myc peut aussi influencer de nombreuses autres fonctions de par sa capacité à activer ou à réprimer la transcription de nombreux gènes, et à agir globalement sur le génome à travers des modifications épigénétiques de la chromatine. La famille d'oncogènes Myc comprend, chez les mammifères, trois protéines structurellement proches: c-Myc, N-Myc et L-Myc. Ces protéines ont les mêmes proprietés biochimiques, exercent les mêmes fonctions mais sont le plus souvent exprimées de façon mutuellement exclusive. Myc a été récemment identifié comme un facteur clef dans la maintenance des cellules souches embryonnaires et adultes ainsi que dans la réacquisition des proprietés des cellules souches. Nous avons précédemment démontré que l'élimination de c-Myc provoque une accumulation de cellules souches hématopoïétiques (CSH) suite à un défaut de différenciation lié à la niche. Les CSH sont responsables de la production de tous les éléments cellulaires du sang pour toute la vie de l'individu et sont définies par leur capacité à s'auto-renouveler tout en produisant des précurseurs hématopoïétiques. Afin de mieux comprendre la fonction de Myc dans les CSH, nous avons choisi de combiner l'utilisation de modèles de souris génétiquement modifiées à une caractérisation systématique des schémas d'expression de c-Myc, N-Myc et L-Myc dans tout le système hématopoïétique. Nous avons ainsi découvert que les CSH les plus immatures expriment des quantités équivalentes de transcrits de c-myc et N-myc. Si les CSH déficientes en N-myc seulement ont une capacité d'auto-renouvellement à long-terme réduite, l'invalidation combinée des gènes c-myc et N-myc conduit à une pan-cytopénie suivie d'une mort rapide de l'animal, pour cause d'apoptose de tous les types cellulaires hématopoïétiques. En particulier, les CSH en cours d'auto-renouvelemment, mais pas les CSH quiescentes, accumulent du Granzyme B (GrB), une molécule fortement cytotoxique qui provoque une mort cellulaire rapide. Ces données ont ainsi mis au jour un nouveau mécanisme dont dépend la survie des CSH, à savoir la répression du GrB, une enzyme typiquement utilisée par le système immunitaire inné pour éliminer les tumeurs et les cellules infectées par des virus. Dans le but d'évaluer l'étendue de la redondance entre c-Myc et N-Myc dans les CSH, nous avons d'une part examiné des souris dans lesquelles les séquences codantes de c-myc sont remplacées par celles de N-myc (NCR) et d'autre part nous avons géneré une série allèlique de myc en éliminant de façon combinatoire un ou plusieurs allèles de c-myc et/ou de N-myc. Alors que l'analyse des souris NCR suggère que c-Myc et N-Myc sont qualitativement redondants, la série allélique indique que les efficiences avec lesquelles ces deux protéines influencent des procédés essentiels à la maintenance des CSH sont différentes. En conclusion, nos données génétiques montrent que l'activité générale de MYC, fournie par c-Myc et N-Myc, contrôle plusieurs aspects cruciaux de la fonction des CSH, notamment l'auto-renouvellement, la survie et la différenciation. Abstract : c-Myc, the first Myc transcription factor was discovered 30 years ago and is to date one of the most potent proto-oncogenes described. It is found to be misregulated in over 50% of all cancers, where it drives proliferation, cell growth and neo-angiogenesis. Myc can also influence a variety of other functions, owing to its ability to activate and repress transcription of many target genes and to globally regulate the genome via epigenetic modifications of the chromatin. The Myc family of oncogenes consists of three closely related proteins in mammals: c-Myc, N-Myc and L-Myc. These proteins share the same biochemical properties, exert mostly the same functions, but are most often expressed in mutually exclusive patterns. Myc is now emerging as a key factor in maintenance of embryonic and adult stem cells as well as in reacquisition of stem cell properties, including induced reprogramming. We previously showed that c-Myc deficiency can cause the accumulation of hematopoietic stem cells (HSCs) due to a niche dependent differentiation defect. HSCs are responsible for life-long replenishment of all blood cell types, and are defined by their ability to self-renew while concomitantly giving rise to more commited progenitors. To gain further insight into the function of Myc in HSCs, in this study we combine the use of genetically-modified mouse models with the systematic characterization of c-myc, N-myc and L-myc transcription patterns throughout the hematopoietic system. Interestingly, the most immature HSCs express not only c-myc, but also about equal amounts of N-myc transcripts. Although conditional deletion of N-myc alone in the bone marrow does not affect steady-state hematopoiesis, N-myc null HSCs show impaired long-term self-renewal capacity. Strikingly, combined deficiency of c-Myc and N-Myc results in pan-cytopenia and rapid lethality, due to the apoptosis of most hematopoietic cell types. In particular, self-renewing HSCs, but not quiescent HSCs or progenitor cell types rapidly up-regulate and accumulate the potent cytotoxic molecule GranzymeB (GrB), causing their rapid cell death. These data uncover a novel pathway on which HSC survival depends on, namely repression of GrB, a molecule typically used by the innate immune system to eliminate tumor and virus infected cells. To evaluate the extent of redundancy between c-Myc and N-Myc in HSCs, we examined mice in which c-myc coding sequences are replaced by that of N-myc (NCR) and also generated an allelic series of myc, by combinatorially deleting one or several c-myc and/or N-myc alleles. While the analysis of NCR mice suggests that c-Myc and N-Myc are qualitatively functionally redundant, our allelic series indicates that the efficiencies with which these two proteins affect crucial HSC maintenance processes are likely to be distinct. Collectively, our genetic data show that general "MYC" activity delivered by c-Myc and N-Myc controls crucial aspects of HSC function, including self-renewal, survival and niche dependent differentiation.

Glucose-dependent insulinotropic polypeptide (GIP) and its receptor (GIPR): cellular localization, lesion-affected expression, and impaired regenerative axonal growth.

Glucose-dependent insulinotropic polypeptide (GIP) was initially described to be rapidly regulated by endocrine cells in response to nutrient ingestion, with stimulatory effects on insulin synthesis and release. Previously, we demonstrated a significant up-regulation of GIP mRNA in the rat subiculum after fornix injury. To gain more insight into the lesion-induced expression of GIP and its receptor (GIPR), expression profiles of the mRNAs were studied after rat sciatic nerve crush injury in 1) affected lumbar dorsal root ganglia (DRG), 2) spinal cord segments, and 3) proximal and distal nerve fragments by means of quantitative RT-PCR. Our results clearly identified lesion-induced as well as tissue type-specific mRNA regulation of GIP and its receptor. Furthermore, comprehensive immunohistochemical stainings not only confirmed and exceeded the previous observation of neuronal GIP expression but also revealed corresponding GIPR expression, implying putative modulatory functions of GIP/GIPR signaling in adult neurons. In complement, we also observed expression of GIP and its receptor in myelinating Schwann cells and oligodendrocytes. Polarized localization of GIPR in the abaxonal Schwann cell membranes, plasma membrane-associated GIPR expression of satellite cells, and ependymal GIPR expression strongly suggests complex cell type-specific functions of GIP and GIPR in the adult nervous system that are presumably mediated by autocrine and paracrine interactions, respectively. Notably, in vivo analyses with GIPR-deficient mice suggest a critical role of GIP/GIPR signal transduction in promoting spontaneous recovery after nerve crush, insofar as traumatic injury of GIPR-deficient mouse sciatic nerve revealed impaired axonal regeneration compared with wild-type mice.