Mathematical modelling of tissue-engineered angiogenesis

We present a mathematical model for the vascularisation of a porous scaffold following implantation in vivo. The model is given as a set of coupled non-linear ordinary differential equations (ODEs) which describe the evolution in time of the amounts of the different tissue constituents inside the scaffold. Bifurcation analyses reveal how the extent of scaffold vascularisation changes as a function of the parameter values. For example, it is shown how the loss of seeded cells arising from slow infiltration of vascular tissue can be overcome using a prevascularisation strategy consisting of seeding the scaffold with vascular cells. Using certain assumptions it is shown how the system can be simplified to one which is partially tractable and for which some analysis is given. Limited comparison is also given of the model solutions with experimental data from the chick chorioallantoic membrane (CAM) assay.     

Duplication of <Emphasis Type="Italic">AP1</Emphasis> within the <Emphasis Type="Italic">Spinacia oleracea</Emphasis> L. <Emphasis Type="Italic">AP1/FUL</Emphasis> clade is followed by rapid amino acid and regulatory evolution

The AP1/FUL clade of MADS box genes have undergone multiple duplication events among angiosperm species. While initially identified as having floral meristem identity and floral organ identity function in Arabidopsis, the role of AP1 homologs does not appear to be universally conserved even among eudicots. In comparison, the role of FRUITFULL has not been extensively explored in non-model species. We report on the isolation of three AP1/FUL genes from cultivated spinach, Spinacia oleracea L. Two genes, designated SpAPETALA1-1 (SpAP1-1) and SpAPETALA1-2 (SpAP1-2), cluster as paralogous genes within the Caryophyllales AP1 clade. They are highly differentiated in the 3′, carboxyl-end encoding region of the gene following the third amphipathic alpha-helix region, while still retaining some elements of a signature AP1 carboxyl motifs. In situ hybridization studies also demonstrate that the two paralogs have evolved different temporal and spatial expression patterns, and that neither gene is expressed in the developing sepal whorl, suggesting that the AP1 floral organ identity function is not conserved in spinach. The spinach FRUITFULL homolog, SpFRUITFULL (SpFUL), has retained the conserved motif and groups with Caryophyllales FRUITFULL homologs. SpFUL is expressed in leaf as well as in floral tissue, and shows strong expression late in flower development, particularly in the tapetal layer in males, and in the endothecium layer and stigma, in the females. The combined evidence of high rates of non-synonymous substitutions and differential expression patterns supports a scenario in which the AP1 homologs in the spinach AP1/FUL gene family have experienced rapid evolution following duplication. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Biodiversity indicators in European ground waters: towards a predictive model of stygobiotic species richness

1. Estimates of species richness obtained from exhaustive field inventories over large spatial scales are expensive and time-consuming. For this reason, efficiency demands the use of indicators as 'surrogates' of species richness. Biodiversity indicators are defined herein as a limited suite of taxonomic groups the species richness of which is correlated with the species richness of all other taxonomic groups present in the survey area.
2. Species richness in ground water was assessed at different spatial scales using data collected from six regions in Europe. In total, 375 stygobiotic species were recorded across 1157 sites and 96 aquifers. The taxonomic groups collected from more than one site and with more than two species (Oligochaeta, Gastropoda, Cyclopoida, Harpacticoida, Ostracoda, Isopoda, Amphipoda, Bathynellacea and Acari) were used to develop nonparametric models to predict stygobiotic biodiversity at the aquifer scale.
3. Pair-wise correlations between taxonomic groups were low, i.e. variation in species richness of a single taxonomic group did not usually reflect variation of the other groups. In contrast, multiple regressions calculated between species richness of any combination of taxa and extra-group species richness along the six regions resulted in a number of significant relationships.
4. These results suggest that some taxonomic groups (mainly Copepoda and Amphipoda and, to a lesser extent, Oligochaeta and Gastropoda) combined in different ways across the regions, were good biodiversity indicators in European groundwater ecosystems. However, the uneven distribution of taxonomic groups prevented selection of a common set of indicators for all six regions. Faunal differences among regions are presumably related to both historical and ecological factors, including palaeogeography, palaeoecology, geology, aquifer fragmentation and isolation, and, less clearly, anthropogenic disturbance.     

Towards a model of non-equilibrium binding of metal ions in biological systems

We have used a systems biology approach to address the hitherto insoluble problem of the quantitative analysis of non-equilibrium binding of aqueous metal ions by competitive ligands in heterogeneous media. To-date, the relative proportions of different metal complexes in aqueous media has only been modelled at chemical equilibrium and there are no quantitative analyses of the approach to equilibrium. While these models have improved our understanding of how metals are used in biological systems they cannot account for the influence of kinetic factors in metal binding, transport and fate. Here we have modelled the binding of aluminium, Al(III), in blood serum by the iron transport protein transferrin (Tf) as it is widely accepted that the biological fate of this non-essential metal is not adequately described by experiments, invitro and insilico, which have consistently demonstrated that at equilibrium 90% of serum Al(III) is bound by Tf. We have coined this paradox ‘the blood-aluminium problem’ and herein applied a systems biology approach which utilised well-found assumptions to pare away the complexities of the problem such that it was defined by a comparatively simple set of computational rules and, importantly, its solution assumed significant predictive capabilities. Here we show that our novel computational model successfully described the binding of Al(III) by Tf both at equilibrium and as equilibrium for Al_Tf was approached. The model predicted significant non-equilibrium binding of Al by ligands in competition with Tf and, thereby, provided an explanation of why the distribution of Al(III) in the body cannot be adequately described by its binding and transport by Tf alone. Generically the model highlighted the significance of kinetic in addition to thermodynamic constraints in defining the fate of metal ions in biological systems.     

Blood plasma model predictions for the proposed bone-seeking radiopharmaceutical [Sn]Sn(IV)-N,N′,N′-trimethylenephosphonate-poly(ethyleneimine)

In an attempt to elucidate the in vivo stability of the prospective radiopharmaceutical [^117mSn]Sn(IV)-PEI-MP, where PEI-MP stands for N,N′,N′-trimethylenephosphonate-polyethyleneimine, glass electrode potentiometry was used to determine the stability constants of the Sn⁴⁺ ion as complexed with a variety of physiological amino acids. In addition, linear free energy relationship (LFER) correlation plots were used to extrapolate the constants of the major blood plasma ligands, based on data from Cu²⁺, Pb²⁺, and Zn²⁺. In so doing, a thermodynamic model of blood plasma was established for Sn⁴⁺ from which the complexation tendencies of Sn⁴⁺ were predicted in the event of the intravenous administration of such a drug. It was found that the Sn(IV)-PEI-MP could succumb to competition by the glutamine amino acid, which forms more stable complex(es), whilst the PEI-MP gets taken up largely by Ca²⁺. Also, this study shows the value of the in vitro experiments and modeling performed for radiopharmaceutical research and for attempts to reduce the number of animal experiments.     

New in vitro colonic fermentation model for Salmonella infection in the child gut

In this study, a new in vitro continuous colonic fermentation model of Salmonella infection with immobilized child fecal microbiota and Salmonella serovar Typhimurium was developed for the proximal colon. This model was then used to test the effects of two amoxicillin concentrations (90 and 180 mg day⁻¹) on the microbial composition and metabolism of the gut microbiota and on Salmonella serovar Typhimurium during a 43-day fermentation. Addition of gel beads (2%, v/v) colonized with Salmonella serovar Typhimurium in the reactor resulted in a high and stable Salmonella concentration (log 7.5 cell number mL⁻¹) in effluent samples, and a concomitant increase of Enterobacteriaeceae, Clostridium coccoides–Eubacterium rectale and Atopobium populations and a decrease of bifidobacteria. During amoxicillin treatments, Salmonella concentrations decreased while microbial balance and activity were modified in agreement with in vivo data, with a marked decrease in C. coccoides–E. rectale and an increase in Enterobacteriaceae . After interruption of antibiotic addition, Salmonella concentration again increased to reach values comparable to that measured before antibiotic treatments, showing that our model can be used to simulate Salmonella shedding in children as observed in vivo . This in vitro model could be a useful tool for developing and testing new antimicrobials against enteropathogens.     

Neutral Models with Generalised Speciation

Hubbell’s neutral theory claims that ecological patterns such as species abundance distributions can be explained by a stochastic model based on simple assumptions. One of these assumptions, the point mutation assumption, states that every individual has the same probability to speciate. Etienne et al. have argued that other assumptions on the speciation process could be more realistic, for example, that every species has the same probability to speciate (Etienne, et al. in Oikos 116:241–258, 2007). They introduced a number of neutral community models with a different speciation process, and conjectured formulas for their stationary species abundance distribution. Here we study a generalised neutral community model, encompassing these modified models, and derive its stationary distribution, thus proving the conjectured formulas.     

A Stochastic Model of Gene Evolution with Time Dependent Pseudochaotic Mutations

We develop here a new class of stochastic models of gene evolution in which a random subset of the 64 possible trinucleotides mutates at each evolutionary time t according to some time dependent substitution probabilities. Therefore, at each time t, the numbers and the types of mutable trinucleotides are unknown. Thus, the mutation matrix changes at each time t. This pseudochaotic model developed generalizes the standard model in which all the trinucleotides mutate at each time t. It determines the occurrence probabilities at time t of trinucleotides which pseudochaotically mutate according to 3 time dependent substitution parameters associated with the 3 trinucleotide sites. The main result proves that under suitable assumptions, this pseudochaotic model converges to a uniform probability vector identical to that of the standard model. Furthermore, an application of this pseudochaotic model allows an evolutionary study of the 3 circular codes identified in both eukaryotic and prokaryotic genes. A circular code is a particular set of trinucleotides whose main property is the retrieval of the frames in genes locally, i.e., anywhere in genes and particularly without start codons, and automatically with a window of a few nucleotides. After a certain evolutionary time and with particular time dependent functions for the 3 substitution parameters, precisely an exponential decrease in the 1st and 2nd trinucleotide sites and an exponential increase in the 3rd one, this pseudochaotic model retrieves the main statistical properties of the 3 circular codes observed in genes. Furthermore, it leads to a circular code asymmetry stronger than the standard model (nonpseudochaotic) and, therefore, to a better correlation with the genes.     

The Effect of Habitat Fragmentation on Cyclic Population Dynamics: A Numerical Study

Through four spatially explicit models, we investigate how habitat fragmentation affects cyclic predator–prey population dynamics. We use a Partial Differential Equation (PDE) framework to describe the dispersal of predators and prey in a heterogeneous landscape made of high quality and low quality habitat patches, subject to increasing fragmentation through habitat separation and/or habitat loss. Our results show that habitat fragmentation decreases the amplitude of the predator–prey population cycles while average population density is not as strongly affected in general. Beyond these simple trends however, the four models show differing responses to fragmentation, indicating that when making predictions about population survival and persistence in the face of habitat fragmentation, the choice of model is important. Our results may inform conservation efforts in fragmented habitats for cyclic species such as the snowshoe hare and Canada lynx. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorised users.