Contribution to the logistic theory of growth: temporal structure and growth potential

The analysis of a structured population according to three (juvenile, mature and senescent) cellular states is carried out within the framework of Delattre's transformation systems theory. Growth in number, with the dissymmetry of cell divisions, is determined by an autocatalysis process under the constraint of the availability of a source. Two models are presented: their dynamics results in a growth of the exponential type or of the sigmoidal type, respectively. In the sigmoidal case, the logistic equation (Richards-Nelder's function with adjunction of a lower asymptote Y not equal to 0) fits satisfactorily the simulated data of the total cell number Y. The growth potential is defined as the instantaneous capacity of autocatalysis, which is expressed in relation to the present 'mitotic resources' (source + non-senescing mature cells). The acceleration variations d2Y/dt2 are in close agreement with the growth potential gradient. The analysis is then generalized to other population structuring. As a result, the logistic equation can be interpreted in terms of a formal model of growth of a structured population submitted to autocatalysis and competition.     

Modeling operon dynamics: the tryptophan and lactose operons as paradigms

Understanding the regulation of gene control networks and their ensuing dynamics will be a critical component in the understanding of the mountain of genomic data being currently collected. This paper reviews recent mathematical modeling work on the tryptophan and lactose operons which are, respectively, the classical paradigms for repressible and inducible operons.     

Anticipating epileptic seizures: from mathematics to clinical applications

The study of dynamical changes in the neural activity preceding an epileptic seizure allows the characterization of a preictal state several minutes prior to seizure onset. This opens new perspectives for studying the mechanisms of ictogenesis as well as for possible therapeutic interventions that represent a major breakthrough. In this review we present and discuss the results from our group in this domain using nonlinear analysis of brain signals, as well as its limitation and open questions.     

New in vivo and ex vivo models for the experimental study of sheep scrapie: development and perspectives

Sheep scrapie is a prototypical transmissible spongiform encephalopathy (TSE), and the most widespread of these diseases. Experimental study of TSE infectious agents from sheep and other species essentially depends on bioassays in rodents. Transmission of natural sheep scrapie to conventional mice commonly requires one or two years. In an effort to develop laboratory models in which investigations on the sheep TSE agent would be facilitated, we have established mice and cell lines that were genetically engineered to express ovine PrP protein and examined their susceptibility to the infection. A series of transgenic mice lines (tgOv) expressing the high susceptibility allele (VRQ) of the ovine PrP gene from different constructs was expanded. Following intracerebral inoculation with natural scrapie isolates, all animals developed typical TSE neurological signs and accumulated abnormal PrP in their brain. The survival time in the highest expressing tgOv lines ranged from 2 to 7 months, depending on the isolate. It was inversely related to the brain PrP content, and essentially unchanged on further passaging. Ovine PrP transgene expression thus enhanced scrapie disease transmission from sheep to mice. Such tgOv mice may bring new opportunities for analysing the natural variation of scrapie strains and measuring infectivity. As no relevant cell culture models for agents of naturally-occurring TSE exist, we have explored various strategies in order to obtain stable cell lines that would propagate the sheep agent ex vivo without prior adaptation to rodent. In one otherwise refractory rabbit epithelial cell line, a regulable expression of ovine PrP was achieved and found to enable an efficient replication of the scrapie agent in inoculated cultures. Cells derived from sheep embryos or from tgOv mice were also used in an attempt to establish permissive cell lines derived from the nervous system. Cells engineered to express PrP proteins of a specified sequence may thus represent a promising strategy to further explore, at the cellular level, various aspects of TSE diseases.     

Mathematical approaches to differentiation and gene regulation

We consider some mathematical issues raised by the modelling of gene networks. The expression of genes is governed by a complex set of regulations, which is often described symbolically by interaction graphs. These are finite oriented graphs where vertices are the genes involved in the biological system of interest and arrows describe their interactions: a positive (resp. negative) arrow from a gene to another represents an activation (resp. inhibition) of the expression of the latter gene by some product of the former. Once such an interaction graph has been established, there remains the difficult task to decide which dynamical properties of the gene network can be inferred from it, in the absence of precise quantitative data about their regulation. There mathematical tools, among others, can be of some help. In this paper we discuss a rule proposed by Thomas according to which the possibility for the network to have several stationary states implies the existence of a positive circuit in the corresponding interaction graph. We prove that, when properly formulated in rigorous terms, this rule becomes a theorem valid for several different types of formal models of gene networks. This result is already known for models of differential [C. Soulé, Graphic requirements for multistationarity, ComPlexUs 1 (2003) 123-133] or Boolean [E. Rémy, P. Ruet, D. Thieffry, Graphic requirements for multistability and attractive cycles in a boolean dynamical framework, 2005, Preprint] type. We show here that a stronger version of it holds in the differential setup when the decay of protein concentrations is taken into account. This allows us to verify also the validity of Thomas' rule in the context of piecewise-linear models. We then discuss open problems.     

Contribution to the study of periodic chronic myelogenous leukemia

The period (in the order of 40 to 80 days) in periodic chronic myelogenous leukemia (PCML) oscillations is quite long compared with the duration of the cell cycle of the hematopoietic stem cells from which the oscillations are presumed to originate (in the order of one or two days). Our objective is to understand the origin of these long-period oscillations using a G0 model for stem cell dynamics. We determine the local stability conditions and show under what conditions the Hopf bifurcation may occur. We interpret the role of each parameter in the loss of stability, and then examine a simpler model to try to deduce possible changes at the stem-cell level that might be responsible for the characteristics PCML.     

Role of differential adhesion in cell cluster evolution: from vasculogenesis to cancer metastasis

Cell–cell and cell–matrix adhesions are fundamental to numerous physiological processes, including angiogenesis, tumourigenesis, metastatic spreading and wound healing. We use cellular potts model to computationally predict the organisation of cells within a 3D matrix. The energy potentials regulating cell–cell (J_CC) and cell–matrix (J_MC) adhesive interactions are systematically varied to represent different, biologically relevant adhesive conditions. Chemotactically induced cell migration is also addressed. Starting from a cluster of cells, variations in relative cell adhesion alone lead to different cellular patterns such as spreading of metastatic tumours and angiogenesis. The combination of low cell–cell adhesion (high J_CC) and high heterotypic adhesion (low J_MC) favours the fragmentation of the original cluster into multiple, smaller cell clusters (metastasis). Conversely, cellular systems exhibiting high-homotypic affinity (low J_CC) preserve their original configuration, avoiding fragmentation (organogenesis). For intermediate values of J_CC and J_MC (i.e. J_CC/J_MC ～ 1), tubular and corrugated structures form. Fully developed vascular trees are assembled only in systems in which contact-inhibited chemotaxis is activated upon cell contact. Also, the rate of secretion, diffusion and sequestration of chemotactic factors, cell deformability and motility do not significantly affect these trends. Further developments of this computational model will predict the efficacy of therapeutic interventions to modulate the diseased microenvironment by directly altering cell cohesion.     

An agent-based model of sleeping sickness: simulation trials of a forest focus in southern Cameroon

An agent-based model (AMB) used to simulate the spread of Human African Trypanosomiasis is presented together with the results of simulations of a focus of the disease. This model is a completely spatialized approach taking into account a series of often overlooked parameters such as human behaviour (activity-related movements), the density and mobility of the disease vectors--tsetse flies (Glossina spp.)--and the influence of other tsetse feeding hosts (livestock and wild animal populations). The agents that represent humans and tsetse flies move in a spatially structured environment managed by specialized location agents. Existing compartmental mathematical models governed by differential equations fail to incorporate the spatial dimension of the disease transmission. Furthermore, on a small scale, transmission is unrealistically represented by entities less than one. This ABM was tested with data from one village of the Bipindi sleeping sickness focus (southern Cameroon) and with obtained realistic simulations of stable transmission involving an animal reservoir. In varying different spatial configurations, we observe that the stability of spread is linked to the spatial complexity (number of heterogeneous locations). The prevalence is very sensitive to the human densities and to the number of tsetse flies initially infected in a given location. A relatively low and durable prevalence is obtained with shortening the phase I. In addition, we discuss some upgrading possibilities, in particular the linkage to a Geographical Information System (GIS). The agent-based approach offers new ways to understanding the spread of the disease and a tool to evaluate risk and test control strategies.     

The fossil bat assemblage of Sima del Elefante Lower Red Unit (Atapuerca,Spain): First results and contribution to the palaeoenvironmental approach to the site

The fossil bat assemblage from the Lower Red Unit of Sima del Elefante (TELRU) in Atapuerca (Burgos, Spain) has been exhaustively analysed for the first time. Bat fossil assemblages are of particular relevance to palaeoenvironmental approaches to sites. Here we integrate our new data on the chiropteran fauna with the data provided previously by other authors on the basis of the small-vertebrate assemblages and the palynology of the site. Our results are consistent with the earlier results in that they indicate a generally warmer climate than at present in the area and stable environmental conditions throughout the major part of the TELRU sequence. However, fossil bat assemblages sometimes lead to problems when they are used in landscape reconstruction. These problems are discussed here and should be taken into account in future works.     

Kinetics of zooplankton in an aquatic continuum: from the Marne River and reservoir to the Seine estuary

A study was carried out within a 700-km river sector, including three types of ecosystems (a reservoir, a river and its estuary) to characterise the major features of zooplankton communities in the Seine Basin. In rivers, zooplankton biomass becomes significant only when the growth rate of the organisms is higher than the dilution rate (4-5th orders rivers, according to River Continuum Concept). Upstream, short residence times favour the development of small species (Rotifers) with low individual body weight and biomass. Conversely, larger species (microcrustaceans) develop more downstream, where increased residence time leads to autochthonous production (Riverine Productivity Model). Such a pattern is greatly modified by human impact. Zooplankton input from the Marne reservoir represents one type of disruption in the general upstream-downstream trend (according to the Serial Discontinuity Concept). This reservoir is a source of microcrustaceans; they rapidly disappear mainly through fish predation, and therefore have little impact on the river phytoplankton. Discontinuities, such as confluences, have a relatively small effect on the stock of zooplankton with regard to the water release from the reservoir, but they persist more downstream, because they have the same lotic origin. A few microhabitats with macrophytes play a small role for this canalised river, but they can modify locally the plankton community structure and composition. As a whole, the flux of zooplankton rises exponentially, whereas discharge increases linearly from upstream (4th order) to downstream (8th order). In the canalised sectors, Dreissena larvae build up an important biomass, adding to that of the zooplankton sensu stricto. Especially abundant in the downstream sector of the Marne and Seine Rivers, the larvae show a widespread colonisation of the benthic substrates by the adult Dreissena. One of the largest mussel colonies in the middle estuary can contribute to a rapid decrease of zooplankton. Estuary ecosystems form a transitional zone between freshwater and seawater, with zooplankton dynamics closely linked to the particular conditions on this part of the river system.     

A new protein from human plasma lipoproteins: isolation and partial characterization of apolipoprotein G]

A new apolipoprotein has been identified in VHDL1 and in HDL. This protein is immunologically distinct from already isolated apoproteins. It was isolated by column chromatography on hydroxylapatite. In polyacrylamide gel electrophoresis, its mobility is very close to that of apo D. The amino acid composition differs from those of the well characterized polypeptides of the human plasma lipoproteins. It contains glucosamine. The apparent molecular weight is 72 000 +/- 2 000 in the presence and absence of reducing agent. According to the ABCDEF nomenclature, this protein can be named apolipoprotein G (apo G). It is present in a lipoprotein distinct from the lipoproteins A and D among the VHDL1 : this new lipoprotein can be named lipoprotein G (LPG).