Mathematical Modelling of Polyamine Metabolism in Bloodstream-Form Trypanosoma brucei: An Application to Drug Target Identification

We present the first computational kinetic model of polyamine metabolism in bloodstream-form Trypanosoma brucei, the causative agent of human African trypanosomiasis. We systematically extracted the polyamine pathway from the complete metabolic network while still maintaining the predictive capability of the pathway. The kinetic model is constructed on the basis of information gleaned from the experimental biology literature and defined as a set of ordinary differential equations. We applied Michaelis-Menten kinetics featuring regulatory factors to describe enzymatic activities that are well defined. Uncharacterised enzyme kinetics were approximated and justified with available physiological properties of the system. Optimisation-based dynamic simulations were performed to train the model with experimental data and inconsistent predictions prompted an iterative procedure of model refinement. Good agreement between simulation results and measured data reported in various experimental conditions shows that the model has good applicability in spite of there being gaps in the required data. With this kinetic model, the relative importance of the individual pathway enzymes was assessed. We observed that, at low-to-moderate levels of inhibition, enzymes catalysing reactions of de novo AdoMet (MAT) and ornithine production (OrnPt) have more efficient inhibitory effect on total trypanothione content in comparison to other enzymes in the pathway. In our model, prozyme and TSHSyn (the production catalyst of total trypanothione) were also found to exhibit potent control on total trypanothione content but only when they were strongly inhibited. Different chemotherapeutic strategies against T. brucei were investigated using this model and interruption of polyamine synthesis via joint inhibition of MAT or OrnPt together with other polyamine enzymes was identified as an optimal therapeutic strategy.     

Modifying effects of ultraviolet irradiation on the development of abnormal body patterns in centrifuged insect embryos (Smittia sp., Chironomidae,Diptera)

In Smittia and other chironomid embryos, both anterior and posterior egg halves can give rise to either anterior or posterior segments. Upon various types of experimental interference, eggs may develop one of four basic body patterns: normal embryos, double cephalons, double abdomens, or inverted embryos. From a previous model of anteroposterior determination, we derive four sets of predictions for the results of combined ultraviolet irradiation and centrifugation experiments. While most of the actual results are in agreement with the predictions, some are not. Most of the discrepancies are resolved in a modified version of the model. According to the new model, anterior and posterior egg halves contain both anterior and posterior cytoplasmic determinants. These are thought to be mutually repressive, and to control an overall determination for either anterior or posterior development. Centrifugation and ultraviolet irradiation appear to affect the relative strength of anterior determinants in one or both of the egg halves, thus modifying the probabilities for the four basic body patterns to develop. Different frequencies of these patterns, which have been obtained after similar experimental treatment of different chironomid species, can be ascribed to species-specific variation in the ultraviolet sensitivity of anterior and posterior determinants.     

Modeling alcoholic fermentation of glucose/xylose mixtures by ethanologenic Escherichia coli as a function of pH

In order to understand the effect of pH on growth and ethanol production in ethanologenic Escherichia coli, we investigated the kinetic behavior of ethanologenic E. coli during alcoholic fermentation of glucose or xylose in a controlled pH environment and the fermentation of glucose, xylose, or their mixtures without pH control. Based on the Monod equation, an unstructured and unsegregated kinetic model was proposed as a function of the pH of the fermentation medium. The pH effects on cell growth, sugar consumption, and ethanol production were taken into account in the proposed model. Both cell growth and ethanol production were found to be significantly influenced by the pH of the fermentation medium. The optimal pH range for ethanol production by ethanologenic E. coli on either glucose or xylose was 6.0–6.5. The highest value of the maximum specific growth rate (μ _m) was obtained at pH 7.0. In the kinetic model of the fermentations of the sugar mixture, two inhibition terms related to glucose concentrations were included in both the cell growth and ethanol production equations because of the strong inhibitions of glucose and glucose metabolites on xylose metabolism. A good fit was found between model predictions and experimental data for both single-sugar and mixed-sugar fermentations without pH control within the experimental domain.     

Modelling malic acid accumulation in fruits: relationships with organic acids, potassium, and temperature

Malic acid production, degradation, and storage during fruit development have been modelled. The model assumes that malic acid content is determined essentially by the conditions of its storage in the mesocarp cells, and provides a simplified representation of the mechanisms involved in the accumulation of malate in the vacuole and their regulation by thermodynamic constraints. Solving the corresponding system of equations made it possible to predict the malic acid content of the fruit as a function of organic acids, potassium concentration, and temperature. The model was applied to peach fruit, and parameters were estimated from the data of fruit development monitored over 2 years. The predictions were in good agreement with experimental data. Simulations were performed to analyse the behaviour of the model in response to variations in composition and temperature.     

Temperature Regulation of Anthocyanin Accumulation in Apple Skin

The regulation of anthocyanin accumulation in apple skin (cv.Jonathan) by temperature was studied. In the field the increasein anthocyanin in the skin before harvest coincided with decreasingtemperatures and with increasing ethylene production by thefruit. In detached apples held under continuous white light,the optimum temperatures for anthocyanin accumulation were 12°C in unripe apples and 16–24 °C in ripe apples.These effects were explained by corresponding changes in thelevel of phenylalanine ammonia-lyase (PAL), a key enzyme offlavonoid synthesis. PAL levels were higher at low than at hightemperatures and higher in ripe than in unripe apples. In intermittentlight the effects of temperature were similar but levels ofPAL and anthocyanin were lower, particularly in unripe apples.It is concluded that temperature, in conjunction with ripeningand light, is an important factor regulating anthocyanin accumulationand that its effects are mediated by effects on the level ofPAL activity. Key words: Apple, Anthocyanin, Phenylalanine ammonia-lyase     

Modelling of continuous acetonobutylic fermentation

A model of continuous acetonobutylic fermentation is proposed. This model correctly portrays the predominantly solvents formation observed at acidic extracellular pH and predominantly acids production at more neutral pH, as well as observed effects of dilution rate and feed substrate on products' concentrations. A fair agreement between experimental and theoretical predictions is achieved for a broad range of operating variables.     

cgDNA: a software package for the prediction of sequence-dependent coarse-grain free energies of B-form DNA

cgDNA is a package for the prediction of sequence-dependent configuration-space free energies for B-form DNA at the coarse-grain level of rigid bases. For a fragment of any given length and sequence, cgDNA calculates the configuration of the associated free energy minimizer, i.e. the relative positions and orientations of each base, along with a stiffness matrix, which together govern differences in free energies. The model predicts non-local (i.e. beyond base-pair step) sequence dependence of the free energy minimizer. Configurations can be input or output in either the Curves+ definition of the usual helical DNA structural variables, or as a PDB file of coordinates of base atoms. We illustrate the cgDNA package by comparing predictions of free energy minimizers from (a) the cgDNA model, (b) time-averaged atomistic molecular dynamics (or MD) simulations, and (c) NMR or X-ray experimental observation, for (i) the Dickerson–Drew dodecamer and (ii) three oligomers containing A-tracts. The cgDNA predictions are rather close to those of the MD simulations, but many orders of magnitude faster to compute. Both the cgDNA and MD predictions are in reasonable agreement with the available experimental data. Our conclusion is that cgDNA can serve as a highly efficient tool for studying structural variations in B-form DNA over a wide range of sequences.     

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 , 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].     

Effect of phenolic acids on anthocyanin content in maize roots

Supply of 0.01 to 5.0 mM salicylic, caffeic and gallic acids, either during imbibition of seeds for 24 to 48 h or during seedling growth increased anthocyanin production in maize (Zea mays L. cv. Ganga safed-2) roots. While tyrosine had no effect, phenylalanine either in the presence or absence of the phenolic acids increased anthocyanin content. Glucose in a concentration range of 1 to 20 mM and shikimic acid in 0.01 to 5.0 mM range also increased pigment level, which was higher in the presence of salicylic acid than in it.s absence. The experiments demonstrate the possibility of some indirect effects of salicylic acid and other phenolic acids on anthocyanin synthesis.     

Cryptochrome, phytochrome, and anthocyanin production

Anthocyanin production in cabbage (Brassica oleracea L.) and tomato (Lycopersicon esculentum Mill.) seedlings exposed to prolonged irradiations was studied under conditions that allowed discrimination, within certain limits, between the contribution of cryptochrome and phytochrome in the photoregulation of the response. The results of the study provide confirming evidence for the involvement of cryptochrome and direct evidence for a significant contribution of cryptochrome to the fluence rate dependence of the response to blue. The results provide some preliminary, direct indication for an interaction between cryptochrome and phytochrome in the photoregulation of anthocyanin production in seedlings exposed to the prolonged irradiations required for a high level of expression of the response. The type and degree of interaction between the two photoreceptors vary significantly, depending on the species and experimental conditions.     

An unstructured kinetic model for the improvement of triterpenes production by Ganoderma lucidum G0119 based on nitrogen source effect

The kinetics of cell growth and triterpenes production for liquid submerged fermentation of the medicinal mushroom Ganoderma lucidum were investigated. A kinetic model was developed based on the Logistic and Luedeking-Piret equations for cell growth, substrate consumption and triterpene formation. The kinetic parameters of the model were optimized by specifically designed Runge-Kutta genetic algorithms. The mathematical model simulated the experimental data well and was capable of explaining the behavior of triterpenes production. The predictions of the kinetics from this model are very good both for normal fermentation kinetics under nitrogen limitation as well as for predictions of transitions to sluggish fermentations. The resulting model is very useful for scaling up liquid submerged fermentation of the mushroom G. lucidum and its application to the industrial production of triterpene.     

Predicting Liquid–Vapour Equilibria for Water Using an ab-initio Potential from Histogram Reweighting Monte Carlo Simulations

Abstract

The coexisting densities for an ab-initio model for water have been calculated using grand canonical Monte Carlo simulations with the histogram reweighting technique. Although good agreement with experimental data is found for the radial distribution function at room temperature, the predicted critical density and temperature are well below both the experimental value as well as predictions from semi-empirical potentials. Improvement in the repulsive part of the ab-initio potential is suggested as a way to obtain better agreement with experiment.     

A combined phenolic extraction and fermentation reactor engineering model for multiphase red wine fermentation

Red wine production begins with a simultaneous fermentation and solid-phase extraction process. Red wine color and mouthfeel is the result of the extraction of phenolics from grape skins and seeds during fermentation, where extraction is a strong function of temperature and ethanol concentration. During fermentation, grape solids form a porous “cap” at the top of the fermentor, resulting in a heterogeneous fermentation system with significant temperature and concentration gradients. In this work, we present a spatial, time-variant reactor engineering model for phenolic extraction during red wine fermentation, incorporating fermentation kinetics, mass transfer, heat transfer, compressible fluid flow, and phenolic extraction kinetics. The temperature and ethanol concentration profiles predicted by this model allow for the calculation of phenolic extraction rates over the course of fermentation. Phenolic extraction predictions were validated against prior experimental data to good agreement and compared to a well-mixed model's predictions to show the utility of a spatial model over well-mixed models.     

The Role of Cell Contraction and Adhesion in Dictyostelium Motility

The crawling motion of Dictyostelium discoideum on substrata involves a number of coordinated events including cell contractions and cell protrusions. The mechanical forces exerted on the substratum during these contractions have recently been quantified using traction force experiments. Based on the results from these experiments, we present a biomechanical model of the contraction phase of Dictyostelium discoideum motility with an emphasis on the adhesive properties of the cell-substratum contact. Our model assumes that the cell contracts at a constant rate and is bound to the substratum by adhesive bridges that are modeled as elastic springs. These bridges are established at a spatially uniform rate while detachment occurs at a spatially varying, load-dependent rate. Using Monte Carlo simulations and assuming a rigid substratum, we find that the cell speed depends only weakly on the detachment kinetics of the cell-substratum interface, in agreement with experimental data. By varying the parameters that control the adhesive and contractile properties of the cell, we are able to make testable predictions. We also extend our model to include a flexible substrate and show that our model is able to produce substratum deformations and force patterns that are quantitatively and qualitatively in agreement with experimental data.