An Exploratory Study on Spoilage Bacteria and Listeria monocytogenes in Fresh Salmon: Extending Shelf-Life Using Vacuum and Seasonings as Natural Preservatives.

A growing population increases the demand for food, but short shelf-lives and microbial hazards reduce supply and increase food waste. Fresh fish is highly perishable and may be consumed raw, such as salmon in sushi. This work aims to identify strategies to improve the shelf-life and safety of fresh salmon, using available methods (i.e., vacuum) and exploring the use of natural preservatives (i.e., seasonings). Vacuum packaging and good hygiene practices (which reduce initial flora) extended shelf-life up to 20 days. Carnobacterium maltaromaticum was dominant in vacuum packaging conditions and showed potential for inhibiting Listeria monocytogenes. For natural preservatives, L. monocytogenes required higher inhibitory concentrations in vitro when compared to the 10 spoilage bacteria isolated from fresh salmon fillets, presenting a minimum inhibitory concentration (MIC) of 0.13% for oregano essential oil (OEO), 10% for lemon juice, 50 mg mL-1 for garlic powder, and >10% for NaCl. A good bacteriostatic and bactericidal effect was observed for a mixture containing 5% NaCl, 0.002% OEO, 2.5% lemon juice, and 0.08 mg mL-1 garlic powder. Finally, using the salmon medium showed an adequate correlation with the commercial culture medium.

The transcriptional regulation of PER protein in Drosophila.

We propose an auto-activation model controlled by a negative feedback transcriptional regulator to describe the circadian rhythm in Drosophila melanogaster. The model is specific to eukaryote organisms and oscillations are induced by a two-compartment approach, the nucleus and the cytoplasm. The communication between compartments is done through diffusive coupling, simulating the protein channels connecting the interior of the nucleus with the cytoplasm. The same model without compartments has no oscillations. We calibrate the model with data from per mRNA concentration.

Fibroblast state switching orchestrates dermal maturation and wound healing.

Murine dermis contains functionally and spatially distinct fibroblast lineages that cease to proliferate in early postnatal life. Here, we propose a model in which a negative feedback loop between extracellular matrix (ECM) deposition and fibroblast proliferation determines dermal architecture. Virtual-tissue simulations of our model faithfully recapitulate dermal maturation, predicting a loss of spatial segregation of fibroblast lineages and dictating that fibroblast migration is only required for wound healing. To test this, we performed in vivo live imaging of dermal fibroblasts, which revealed that homeostatic tissue architecture is achieved without active cell migration. In contrast, both fibroblast proliferation and migration are key determinants of tissue repair following wounding. The results show that tissue-scale coordination is driven by the interdependence of cell proliferation and ECM deposition, paving the way for identifying new therapeutic strategies to enhance skin regeneration.

Intermittency in the Hodgkin-Huxley model.

We show that action potentials in the Hodgkin-Huxley neuron model result from a type I intermittency phenomenon that occurs in the proximity of a saddle-node bifurcation of limit cycles. For the Hodgkin-Huxley spatially extended model, describing propagation of action potential along axons, we show the existence of type I intermittency and a new type of chaotic intermittency, as well as space propagating regular and chaotic diffusion waves. Chaotic intermittency occurs in the transition from a turbulent regime to the resting regime of the transmembrane potential and is characterised by the existence of a sequence of action potential spikes occurring at irregular time intervals.

Directional sensing and streaming in Dictyostelium aggregation.

We merge the Kessler-Levine simple discrete model for Dictyostelium cyclic adenosine monophosphate (cAMP) production and diffusion with the Dilão-Hauser directional sensing aggregation mechanism. The resulting compound model describes all the known transient patterns that emerge during Dictyostelium aggregation, which include the spontaneous formation of cAMP self-sustained target and spiral waves and streaming. We show that the streaming patterns depend on the speed of the amoebae, on the relaxation time for the production of cAMP, on the cAMP degradation rate, and on directional sensing. Moreover, we show that different signaling centers emerge during Dictyostelium aggregation.

Bicoid mRNA diffusion as a mechanism of morphogenesis in Drosophila early development.

We show that mRNA diffusion is the main morphogenesis mechanism that consistently explains the establishment of Bicoid protein gradients in the embryo of Drosophila, contradicting the current view of protein diffusion. Moreover, we show that if diffusion for both bicoid mRNA and Bicoid protein were assumed, a steady distribution of Bicoid protein with a constant concentration along the embryo would result, contradicting observations.

Chemotherapy in heterogeneous cultures of cancer cells with interconversion.

Recently, the interconversion between differentiated and stem-like cancer cells has been observed. Here, we model the in vitro growth of heterogeneous cell cultures in the presence of interconversion from differentiated cancer cells to cancer stem cells (CSCs), showing that, by targeting only CSC with cytotoxic agents, it is not always possible to eradicate cancer. We have determined the kinetic conditions under which cytotoxic agents in in vitro heterogeneous cultures of cancer cells eradicate cancer. In particular, we have shown that the chemotherapeutic elimination of in vitro cultures of heterogeneous cancer cells is effective only if it targets all cancer cell types, and if the induced death rates for the different subpopulations of cancer cell types are large enough. The quantitative results of the model are compared and validated with experimental data.

The regulation of gene expression in eukaryotes: bistability and oscillations in repressilator models.

To model the regulation of gene expression in eukaryotes by transcriptional activators and repressors, we introduce delays in conjugation with the mass action law. Delays are associated with the time gap between the mRNA transcription in the nucleoplasm and the protein synthesis in the cytoplasm. After re-parameterisation of the m-repressilator model with the Hill cooperative parameter n, for n=1, the m-repressilator is deducible from the mass action law and, in the limit n→∞, it is a Boolean type model. With this embedding and with delays, if m is odd and n>1, we show that there is always a choice of parameters for which the m-repressilator model has sustained oscillations (limit cycles), implying that the 1-repressilator is the simplest genetic mechanism leading to sustained oscillations in eukaryotes. If m is even and n>1, there is always a choice of parameters for which the m-repressilator model has bistability.

Chemotaxis with directional sensing during Dictyostelium aggregation.

We show that the chemotactic movements of colonies of the starving amoeba Dictyostelium discoideum are driven by a force that depends on both the direction of propagation (directional sensing) of reaction-diffusion chemotactic waves and on the gradient of the concentration of the chemoattractant, solving the chemotactic wave paradox. It is shown that the directional sensing of amoebae is due to the sensitivity of the cells to the time variation of the concentration of the chemoattractant combined with its spatial gradient. It is also shown that chemotaxis exclusively driven by local concentration gradient leads to unstable local motion, preventing cells from aggregation. These findings show that the formation of mounds, which initiate multicellularity in Dictyostelium discoideum, is caused by the sensitivity of the amoebae due to three factors, namely, to the direction of propagation of the chemoattractant, to its spatial gradient, and to the emergence of cAMP "emitting centres", responsible for the local accumulation of the amoebae.

Calibration and validation of a genetic regulatory network model describing the production of the protein Hunchback in Drosophila early development.

We fit the parameters of a differential equations model describing the production of gap-gene proteins Hunchback and Knirps along the antero-posterior axis of the embryo of Drosophila. As initial data for the differential equations model, we take the antero-posterior distribution of the proteins Bicoid, Hunchback and Tailless at the beginning of cleavage cycle 14. We calibrate and validate the model with experimental data using single- and multi-objective evolutionary optimization techniques. In the multi-objective optimization technique, we compute the associated Pareto fronts. We analyze the cross regulation mechanism between the gap-genes protein pair Hunchback-Knirps and we show that the posterior distribution of Hunchback follow the experimental data if Hunchback is negatively regulated by the Huckebein protein. This approach enables to us predict the posterior localization on the embryo of the protein Huckebein, and to validate with the experimental data the genetic regulatory network responsible for the antero-posterior distribution of the gap-gene protein Hunchback. We discuss the importance of Pareto multi-objective optimization techniques in the calibration and validation of biological models.

A software tool to model genetic regulatory networks. Applications to the modeling of threshold phenomena and of spatial patterning in Drosophila.

We present a general methodology in order to build mathematical models of genetic regulatory networks. This approach is based on the mass action law and on the Jacob and Monod operon model. The mathematical models are built symbolically by the Mathematica software package GeneticNetworks. This package accepts as input the interaction graphs of the transcriptional activators and repressors of a biological process and, as output, gives the mathematical model in the form of a system of ordinary differential equations. All the relevant biological parameters are chosen automatically by the software. Within this framework, we show that concentration dependent threshold effects in biology emerge from the catalytic properties of genes and its associated conservation laws. We apply this methodology to the segment patterning in Drosophila early development and we calibrate the genetic transcriptional network responsible for the patterning of the gap gene proteins Hunchback and Knirps, along the antero-posterior axis of the Drosophila embryo. In this approach, the zygotically produced proteins Hunchback and Knirps do not diffuse along the antero-posterior axis of the embryo of Drosophila, developing a spatial pattern due to concentration dependent thresholds. This shows that patterning at the gap genes stage can be explained by the concentration gradients along the embryo of the transcriptional regulators.

mRNA diffusion explains protein gradients in Drosophila early development.

We propose a new model describing the production and the establishment of the stable gradient of the Bicoid protein along the antero-posterior axis of the embryo of Drosophila. In this model, we consider that bicoid mRNA diffuses along the antero-posterior axis of the embryo and the protein is produced in the ribosomes localized near the syncytial nuclei. Bicoid protein stays localized near the syncytial nuclei as observed in experiments. We calibrate the parameters of the mathematical model with experimental data taken during the cleavage stages 11-14 of the developing embryo of Drosophila. We obtain good agreement between the experimental and the model gradients, with relative errors in the range 5-8%. The inferred diffusion coefficient of bicoid mRNA is in the range 4.6 x 10(-12)-1.5 x 10(-11)m(2)s(-1), in agreement with the theoretical predictions and experimental measurements for the diffusion of macromolecules in the cytoplasm. We show that the model based on the mRNA diffusion hypothesis is consistent with the known observational data, supporting the recent experimental findings of the gradient of bicoid mRNA in Drosophila [Spirov et al. (2009). Development 136, 605-614].

Antiphase and in-phase synchronization of nonlinear oscillators: the Huygens's clocks system.

We introduce an interaction mechanism between oscillators leading to exact antiphase and in-phase synchronization. This mechanism is applied to the coupling between two nonlinear oscillators with a limit cycle in phase space, leading to a simple justification of the antiphase synchronization as observed in Huygens's pendulum clocks experiment. If the two coupled nonlinear oscillators reach the antiphase or the in-phase synchronized oscillatory state, the period of oscillation is different from the eigenperiods of the uncoupled oscillators.

Modeling segmental patterning in Drosophila: Maternal and gap genes.

We propose a new mathematical model describing the establishment of maternal and gap proteins segmental patterning along the antero-posterior axis of the Drosophila early embryo. This model is based on experimental data and, without recurring to pre-defined activation thresholds, predicts qualitatively and quantitatively the expression patterns of the maternal and gap proteins, as well as the expression patterns of proteins resulting from mRNA ectopic expression and from some loss-of-function mutations. We conclude that the gap genes segmental patterning and consequent spatial organization of the embryo is determined by three main factors: (1) the initial positioning of the maternal bicoid and torso mRNA inside the egg, and subsequent diffusion of the corresponding proteins; (2) the structure of the genetic regulatory network; (3) the role of conservation laws in the establishment of steady and non-uniform spatial distributions of non-diffusing proteins.

A simple framework to describe the regulation of gene expression in prokaryotes.

Based on the bimolecular mass action law and the derived mass conservation laws, we propose a mathematical framework in order to describe the regulation of gene expression in prokaryotes. It is shown that the derived models have all the qualitative properties of the activation and inhibition regulatory mechanisms observed in experiments. The basic construction considers genes as templates for protein production, where regulation processes result from activators or repressors connecting to DNA binding sites. All the parameters in the models have a straightforward biological meaning. After describing the general properties of the basic mechanisms of positive and negative gene regulation, we apply this framework to the self-regulation of the trp operon and to the genetic switch involved in the regulation of the lac operon. One of the consequences of this approach is the existence of conserved quantities depending on the initial conditions that tune bifurcations of fixed points. This leads naturally to a simple explanation of threshold effects as observed in some experiments.

Modelling butterfly wing eyespot patterns.

Eyespots are concentric motifs with contrasting colours on butterfly wings. Eyespots have intra- and interspecific visual signalling functions with adaptive and selective roles. We propose a reaction-diffusion model that accounts for eyespot development. The model considers two diffusive morphogens and three non-diffusive pigment precursors. The first morphogen is produced in the focus and determines the differentiation of the first eyespot ring. A second morphogen is then produced, modifying the chromatic properties of the wing background pigment precursor, inducing the differentiation of a second ring. The model simulates the general structural organization of eyespots, their phenotypic plasticity and seasonal variability, and predicts effects from microsurgical manipulations on pupal wings as reported in the literature.

Harvesting in a resource dependent age structured Leslie type population model.

We analyse the effect of harvesting in a resource dependent age structured population model, deriving the conditions for the existence of a stable steady state as a function of fertility coefficients, harvesting mortality and carrying capacity of the resources. Under the effect of proportional harvest, we give a sufficient condition for a population to extinguish, and we show that the magnitude of proportional harvest depends on the resources available to the population. We show that the harvesting yield can be periodic, quasi-periodic or chaotic, depending on the dynamics of the harvested population. For populations with large fertility numbers, small harvesting mortality leads to abrupt extinction, but larger harvesting mortality leads to controlled population numbers by avoiding over consumption of resources. Harvesting can be a strategy in order to stabilise periodic or quasi-periodic oscillations in the number of individuals of a population.