Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on E. coli have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with E. coli. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion.

Trypanosoma cruzi: metacyclogenesis in vitro - I. Changes in the properties of metacyclic trypomastigotes maintained in the laboratory by different methods

In this work we have studied the modifications in the biological properties of Trypanosoma cruzi when the parasite is maintained for a long time in axenic culture. The studies were done with a clone from an avirulent strain (Dm30L) and a non-cloned virulent strain (EP) of T. cruzi. Both parasiteswere maintained, for at least three years, by successive triatomine/mouse alternate passage (control condition), or by serial passage in axenic medium (culture condition), or only in the mouse (mouse condition). The comparison between parasites of culture and control condition showed that metacyclogenesis capacity was reduced in the former and that the resulting metacyclics displayed an attenuatedvirulence. In order to compare the virulence of metacyclics from the urine of the insect vector, Rhodnius prolixus were infected by artificial feeding with parasites of the control or culture condition. After three triatomine/triatomine passages, there was observed an almost identical biological behavior for these parasites, hence indicating that the maintenance of T. cruzi for a long time in axenic culture affects the differentiation capacity and the virulence of the parasite. Additionally, it was demonstrated that it is possible to maintain T. cruzi exclusively through passages in the invertebrate host.

Dynamical modeling and analysis of large cellular regulatory networks.

The dynamical analysis of large biological regulatory networks requires the development of scalable methods for mathematical modeling. Following the approach initially introduced by Thomas, we formalize the interactions between the components of a network in terms of discrete variables, functions, and parameters. Model simulations result in directed graphs, called state transition graphs. We are particularly interested in reachability properties and asymptotic behaviors, which correspond to terminal strongly connected components (or "attractors") in the state transition graph. A well-known problem is the exponential increase of the size of state transition graphs with the number of network components, in particular when using the biologically realistic asynchronous updating assumption. To address this problem, we have developed several complementary methods enabling the analysis of the behavior of large and complex logical models: (i) the definition of transition priority classes to simplify the dynamics; (ii) a model reduction method preserving essential dynamical properties, (iii) a novel algorithm to compact state transition graphs and directly generate compressed representations, emphasizing relevant transient and asymptotic dynamical properties. The power of an approach combining these different methods is demonstrated by applying them to a recent multilevel logical model for the network controlling CD4+ T helper cell response to antigen presentation and to a dozen cytokines. This model accounts for the differentiation of canonical Th1 and Th2 lymphocytes, as well as of inflammatory Th17 and regulatory T cells, along with many hybrid subtypes. All these methods have been implemented into the software GINsim, which enables the definition, the analysis, and the simulation of logical regulatory graphs.

The value of selected in vitro and in silico methods to predict acute oral toxicity in a regulatory context: results from the European Project ACuteTox.

ACuteTox is a project within the 6th European Framework Programme which had as one of its goals to develop, optimise and prevalidate a non-animal testing strategy for predicting human acute oral toxicity. In its last 6 months, a challenging exercise was conducted to assess the predictive capacity of the developed testing strategies and final identification of the most promising ones. Thirty-two chemicals were tested blind in the battery of in vitro and in silico methods selected during the first phase of the project. This paper describes the classification approaches studied: single step procedures and two step tiered testing strategies. In summary, four in vitro testing strategies were proposed as best performing in terms of predictive capacity with respect to the European acute oral toxicity classification. In addition, a heuristic testing strategy is suggested that combines the prediction results gained from the neutral red uptake assay performed in 3T3 cells, with information on neurotoxicity alerts identified by the primary rat brain aggregates test method. Octanol-water partition coefficients and in silico prediction of intestinal absorption and blood-brain barrier passage are also considered. This approach allows to reduce the number of chemicals wrongly predicted as not classified (LD50>2000 mg/kg b.w.).

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

Discontinuous Galerkin methods for the Multi-dimensional Vlasov-Poisson problem

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

Dynamics of experimental populations of native and introduced blowflies (Diptera: Calliphoridae): mathematical modelling and the transition from asymptotic equilibrium to bounded oscillations

The equilibrium dynamics of native and introduced blowflies is modelled using a density-dependent model of population growth that takes into account important features of the life-history in these flies. A theoretical analysis indicates that the product of maximum fecundity and survival is the primary determinant of the dynamics. Cochliomyia macellaria, a blowfly native to the Americas and the introduced Chrysomya megacephala and Chrysomya putoria, differ in their dynamics in that the first species shows a damping oscillatory behavior leading to a one-point equilibrium, whereas in the last two species population numbers show a two-point limit cycle. Simulations showed that variation in fecundity has a marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations and aperiodic behavior. Variation in survival has much less influence on the dynamics.

Reliability of serological methods for detection of leishmaniasis in portuguese domestic and wild reservoirs

A direct agglutination test (DAT) and an immunofluorescence technique (IFAT) were compared for detection of Leishmania infantum infection in 43 dogs and five foxes from Alto-Douro and Arrábida, two known endemic areas in Portugal. In four dogs with proved canine leishmaniasis, both DAT and IFAT showed positive readings (titres >1:320 and >1:128). Of 34 samples collected from apparently healthy dogs, ten were positive by both serological tests and eight were serologically positive by one test or the other. Three foxes out of five captured in this area, scored titres indicative of leishmaniasis in both DAT and IFAT. The concordance between DAT and IFAT in all collected samples (48) was 81.25%. Considering these and previous studies in the adjacent Mediterranean areas, the seroprevalence of L. infantum infection in the canine and vulpine populations appear to be of high magnitude.

Direct Determination of mechanical properties in shallow formations by (ultra) sonic methods

For several decades mechanical properties of shallow formations (soil) obtained by sonic to ultrasonic wave testing were reported to be greater than those based on mechanical tests. The present article relying on a statistical analysis of more than 300 tests shows that elastic moduli of the soil can indeed be obtained from (ultra)sonic tests and that they are identical to those resulting from mechanical tests.

Comparison between Two Methods for Diagnosis of Trichinellosis: Trichinoscopy and Artificial Digestion

Two direct methods for the diagnosis of trichinellosis were compared: trichinoscopy and artificial digestion. Muscles from 17 wistar rats, orally infected with 500 Trichinella spiralis encysted larvae were examined. From each of the following muscles: diaphragm, tongue, masseters, intercostals, triceps brachialis and cuadriceps femoralis, 648,440 larvae from 1 g samples were recovered. The linear correlation between trichinoscopy and artificial digestion was very high and significant (r=0.94, p< 0.0001), showing that both methods for the detection of muscular larvae did not differ significantly. In both methods, significant differences were found in the distribution of larvae per gramme of muscle

A two-compartment mathematical model of neuroglial metabolism using [1-(11)C] acetate.

The purpose of this study was to develop a two-compartment metabolic model of brain metabolism to assess oxidative metabolism from [1-(11)C] acetate radiotracer experiments, using an approach previously applied in (13)C magnetic resonance spectroscopy (MRS), and compared with an one-tissue compartment model previously used in brain [1-(11)C] acetate studies. Compared with (13)C MRS studies, (11)C radiotracer measurements provide a single uptake curve representing the sum of all labeled metabolites, without chemical differentiation, but with higher temporal resolution. The reliability of the adjusted metabolic fluxes was analyzed with Monte-Carlo simulations using synthetic (11)C uptake curves, based on a typical arterial input function and previously published values of the neuroglial fluxes V(tca)(g), V(x), V(nt), and V(tca)(n) measured in dynamic (13)C MRS experiments. Assuming V(x)(g)=10 × V(tca)(g) and V(x)(n)=V(tca)(n), it was possible to assess the composite glial tricarboxylic acid (TCA) cycle flux V(gt)(g) (V(gt)(g)=V(x)(g) × V(tca)(g)/(V(x)(g)+V(tca)(g))) and the neurotransmission flux V(nt) from (11)C tissue-activity curves obtained within 30 minutes in the rat cortex with a beta-probe after a bolus infusion of [1-(11)C] acetate (n=9), resulting in V(gt)(g)=0.136±0.042 and V(nt)=0.170±0.103 μmol/g per minute (mean±s.d. of the group), in good agreement with (13)C MRS measurements.