A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

Energetics of rare earth manganese perovskites A1-xA ' xMnO3 (A = La, Nd, Y and A ' = Sr, La) systems

High temperature reaction calorimetry using molten lead berate as solvent has been used to study the thermochemistry of NdMnO3, YMnO3, La1-xSrxMnO3 (with 0 < x < 0.5), and Ln(0.5)Ca(0.5)MnO(3) (with Ln = La, Nd, Y), The enthalpies of formation of these multicomponent oxides from their binary constituents have been calculated from the measured enthalpy of drop solution, The energetic stability of the perovskite depends on the size of the A cation, The enthalpy of formation of YMnO3 (smallest A cation) is more endothermic than those of NdMnO3 and LaMnO3. The energetics of the perovskite also depends on the oxidation state of the B site's ions. In the La1-xSrxMnO3 system, the energetic stability of the structure increases with the Mn4+/Mn3+ ratio, The new values of the enthalpies of oxidations, with reliable standard entropies, were used to plot the phase stability diagram of the lanthanum-manganese-oxygen system in the temperature range 300-1100 K, The LaMnO3/MnO phase boundary evaluated in this study agrees with the one published by Atsumi et nl. calculated from thermogravimetric and conductivity measurements.

On Systems Thinking, Systems Biology, and the in Silico Plant

The recent summary report of a Department of Energy Workshop on Plant Systems Biology (P.V. Minorsky [2003] Plant Physiol 132: 404-409) offered a welcomed advocacy for systems analysis as essential in understanding plant development, growth, and production. The goal of the Workshop was to consider methods for relating the results of molecular research to real-world challenges in plant production for increased food supplies, alternative energy sources, and environmental improvement. The rather surprising feature of this report, however, was that the Workshop largely overlooked the rich history of plant systems analysis extending over nearly 40 years (Sinclair and Seligman, 1996) that has considered exactly those challenges targeted by the Workshop. Past systems research has explored and incorporated biochemical and physiological knowledge into plant simulation models from a number of perspectives. The research has resulted in considerable understanding and insight about how to simulate plant systems and the relative contribution of various factors in influencing plant production. These past activities have contributed directly to research focused on solving the problems of increasing biomass production and crop yields. These modeling approaches are also now providing an avenue to enhance integration of molecular genetic technologies in plant improvement (Hammer et al., 2002).

Reactivity of Cationic Terminal Borylene Complexes: Novel Mechanisms for Insertion and Metathesis Chemistry Involving Strongly Lewis Acidic Ligand Systems

The reactions of terminal borylene complexes of the type [CpFe(CO)(2)(BNR2)](+) (R = `Pr, Cy) with heteroallenes have been investigated by quantum-chemical methods, in an attempt to explain the experimentally observed product distributions. Reaction with dicyclohexylcarbodiimide (CyNCNCy) gives a bis-insertion product, in which 1 equiv of carbodiimide is assimilated into each of the Fe=B and B=N double bonds to form a spirocyclic boronium system. In contrast, isocyanates (R'NCO, R' = Ph, 2,6-wXy1, CY; XYl = C6H3Me2) react to give isonitrile complexes of the type [CpFe(CO)(2)(CNR')]+, via a net oxygen abstraction (or formal metathesis) process. Both carbodiimide and socyanate substrates are shown to prefer initial attack at the Fe=B bond rather than the B=N bond of the borylene complex. Further mechanistic studies reveal that the carbodiimide reaction ultimately leads to the bis-insertion compounds [CpFe(CO)(2)C(NCy)(2)B(NCY)(2)CNR2](+), rather than to the isonitrile system [CpFe(CO)(2)(CNCy)](+), on the basis of both thermodynamic (product stability) and kinetic considerations (barrier heights). The mechanism of the initial carbodiimide insertion process is unusual in that it involves coordination of the substrate at the (borylene) ligand followed by migration of the metal fragment, rather than a more conventional process: i.e., coordination of the unsaturated substrate at the metal followed by ligand migration. In the case of isocyanate substrates, metathesis products are competitive with those from the insertion pathway. Direct, single-step metathesis reactivity to give products containing a coordinated isonitrile ligand (i.e. [CpFe(CO)(2)(CNR')](+)) is facile if initial coordination of the isocyanate at boron occurs via the oxygen donor (which is kinetically favored); insertion chemistry is feasible when the isocyanate attacks initially via the nitrogen atom. However, even in the latter case, further reaction of the monoinsertion product so formed with excess isocyanate offers a number of facile (low energetic barrier) routes which also generate ['CpFe(CO)(2)(CNR')](+), rather than the bis-insertion product [CpFe(CO)(2)C(NR')(O)B(NR')(O)CNR2](+) (i.e., the direct analogue of the observed products in the carbodiimide reaction).

Flux balance analysis of biological systems: applications and challenges

Systems level modelling and simulations of biological processes are proving to be invaluable in obtaining a quantitative and dynamic perspective of various aspects of cellular function. In particular, constraint-based analyses of metabolic networks have gained considerable popularity for simulating cellular metabolism, of which flux balance analysis (FBA), is most widely used. Unlike mechanistic simulations that depend on accurate kinetic data, which are scarcely available, FBA is based on the principle of conservation of mass in a network, which utilizes the stoichiometric matrix and a biologically relevant objective function to identify optimal reaction flux distributions. FBA has been used to analyse genome-scale reconstructions of several organisms; it has also been used to analyse the effect of perturbations, such as gene deletions or drug inhibitions in silico. This article reviews the usefulness of FBA as a tool for gaining biological insights, advances in methodology enabling integration of regulatory information and thermodynamic constraints, and finally addresses the challenges that lie ahead. Various use scenarios and biological insights obtained from FBA, and applications in fields such metabolic engineering and drug target identification, are also discussed. Genome-scale constraint-based models have an immense potential for building and testing hypotheses, as well as to guide experimentation.

Energetics of the condensed ternary fuel-oxidizer systems

the heats of reaction of an oxygen-balanced ternary fuel-oxidizer system have been shown to be linearly related to the total oxidizing valences (P0) of the composition. Because calculation of P0 is simple, the method is found to help in evaluating the energetics of such systems. The accuracy of the method when applied to various ternary systems has been discussed.

Reaction of Hexachlorocyclotriphosphazene with Sodium p-Cresoxide

The reaction of hexachlorocyclotriphosphazene (N3P3Cl6) with sodium p-cresoxide proceeds by a predominantly nongeminal pathway. The presence of geminal isomers at the bis- and tris-stages of substitution in tiny quantities (< 5%) has also been observed. All the chloro(p-cresoxy)cyclotriphosphazenes and their dimethylamino derivatives have been characterized by 1H-, 13C{1H}-, and 31P{1H}-NMR spectroscopy. The reaction of N3P3Cl6 with sodium phenoxide has been reinvestigated. The relative yields of the products at various stages of substitution and their isomeric compositions are almost the same for both phenoxy and p-cresoxy systems. Possible mechanisms to explain the observed isomeric compositions are discussed. A through-space interaction involving oxygen-2p and phosphorus-3d orbitals is invoked to explain the greater yield of the cis isomer of N3P3Cl4(OAr)2 than that of its trans isomer.

Protein cross-linking with oxidative enzymes and transglutaminase : Effects in meat protein systems

The effects of tyrosinase, laccase and transglutaminase (TG) were studied in different meat protein systems. The study was focused on the effects of the enzymes on the gel formation properties of myofibrils, and on the textural and water-holding properties of the heated meat systems. The cross-linking efficiency of a novel Trichoderma reesei tyrosinase was compared to that of the commercial Agaricus bisporus tyrosinase. Trichoderma tyrosinase was found to be superior compared to the Agaricus enzyme in its protein cross-linking efficiency and in the incorporation of a small molecule into a complex proteinaceous substrate. Tyrosinase, laccase and TG all polymerised myofibrillar proteins, but laccase was also found to cause protein fragmentation. A positive connection between covalent cross-link and gel formation was observed with tyrosinase and TG. Laccase was able to increase the gel formation only slightly. With an excessive laccase dosage the gel formation declined due to protein fragmentation. Tyrosinase, laccase and TG had different effects on the texture and water-holding of the heated chicken breast meat homogenates. Tyrosinase improved the firmness of the homogenate gels free of phosphate and with a low amount of meat. TG improved the firmness of all studied homogenates. Laccase weakened the gel firmness of the low-meat, low-salt and low-salt/phosphate homogenates and maintained the firmness on the control level in the homogenate free of phosphate. Tyrosinase was the only enzyme capable of reducing the weight loss in the homogenates containing a low amount of meat and a low amount of NaCl. TG was the only enzyme that could positively affect the firmness of the homogenate gel containing both low NaCl and phosphate amounts. In pilot scale the test products were made of coarsely ground chicken breast fillet with a moderate amount of salt. Increasining the amount of meat, salt and TG contents favoured the development of firmness of the test products. The evaporation loss decreased slightly along with increasing TG and NaCl amounts in the experimental conditions used, indicating a positive interaction between these two factors. In this work it was shown that tyrosinase, laccase and TG affected the same myofibrillar proteins, i.e. myosin and troponin T. However, these enzymes had distinguishable effects on the gel formation of a myofibril system as well as on the textural and water-holding properties of the finely ground meat homogenates, reflecting distinctions at least in the reaction mechanisms and target amino acid availability in the protein substrates for these enzymes.

Specificity of protein - Nucleic acid interaction and the biochemical evolution

The water soluble carbodiimide mediated condensation of dipeptides of the general form Gly-X was carried out in the presence of mono- and poly-nucleotides. The observed yield of the tetrapeptide was found to be higher for peptide-nucleotide system of higher interaction specificity following mainly the anticodon-amino acid relationship (Basu, H.S. & Podder, S.K., 1981, Ind. J. Biochem. Biophys.,19, 251-253). The yield of the condensation product of L-peptide was more because of its higher interaction specificity. The extent of the racemization during the condensation of Gly-L-Phe, Gly-L-Tyr and Gly-D-Phe was found to be dependent on the specificity of the interaction -the higher the specificity, the lesser the racemization. The product formed was shown to have a catalytic effect on the condensation reaction. These data thus provide a mechanism showing how the specific interaction between amino acids/dipeptides and nucleic acids could lead to the formation of the lsquoprimitiversquo translation machinery.

An oxygenase from guinea-pig liver which catalyses sulphoxidation

A mono-oxygenase catalysing the conversion of 2-ethyl-4-thioisonicotinamide (ethionamide) into its sulphoxide was purified from guinea-pig liver homogenates. The enzyme required stoicheiometric amounts of oxygen and NADPH for the sulphoxidation reaction. The purified protein is homogeneous by electrophoretic, antigenic and chromatographic criteria. The enzyme has mol.wt. 85000 and it contains 1g-atom of iron and 1mol of FAD per mol, but not cytochrome P-450. The enzyme shows maximal activity at pH7.4 in a number of different buffer systems and the Km values calculated for the substrate and NADPH are 6.5×10-5m and 2.8×10-5m respectively. The activation energy of the reaction was calculated to be 36kJ/mol. Under optimal conditions, the molecular activity of the enzyme (mol of substrate oxidized/min per mol of enzyme) is calculated to be 2.1. The oxygenase belongs to the class of general drug-metabolizing enzymes and it may act on different compounds which can undergo sulphoxidation. The mechanism of sulphoxidation was shown to be mediated by superoxide anions.

Ionic Liquids and Microwaves in Promotion of Organic Synthesis : Friedel-Crafts reaction, deuterolabelling and O-Demethylation

The use of ionic liquids in chemical research has gained considerable interest and activity in recent years. Due to their unique and varied physicochemical properties, in comparison to molecular solvents, the potential applications for ionic liquids are enormous. The use of microwave irradiation, as a powerful dielectric heating technique, in synthetic organic chemistry has been known since 1986. Since then, it has gained significant recognition for its research and application in both academia and industry. The use of either ionic liquids or microwave irradiation in synthetic organic chemistry has been known to afford improved, alternative or complimentary selectivities, in comparison to traditional processes. In this study, the use of ionic liquids as solvents, co-solvents and catalytic media was explored in Friedel-Crafts, deuterolabelling and O-demethylation reactions. Alternative methods for the production of a variety of aromatic ketones using the Friedel-Crafts acylation methodology were investigated using ionic liquid catalyst or ionic liquid acidic additive systems. The disclosed methods, i.e. metal bistriflamides and chloroindate ionic liquids systems, possessed good catalytic activity in the synthesis of typical benzophenones. These catalytic systems were also recyclable. Microwave irradiation was found to be useful in the synthesis of various polyhydroxydeoxybenzoins and arylpropanones as synthetic precursors to naturally occurring or potentially bioactive compounds. Under optimized condition, the reaction occurred in only four minutes using systems such as [bmim][NTf2]/HNTf2 and [bmim][BF4]/BF3·OEt2. Naturally occurring polyphenols, such as isoflavones, can possess various types of biological or pharmacological activity. In particular, some are noted for their beneficial effects on human health. Isotopically labelled analogues of polyphenols are valuable as analytical standards in the quantification of these compounds from biological matrices. A new strategy for deuterolabelling of polyphenols was developed using ionic liquids as co-solvents and 35% DCl/D2O, as a cheap deuterium source, under microwave irradiation. Under these conditions, perdeuterated compounds were achieved in short reaction times, in high isotopic purity and in excellent yields. An O-demethylation reaction was developed, using an ionic liquid reaction medium with BBr3 for the deprotection of a variety methyl protected polyphenolic compounds, such as isoflavons and lignans. This deprotection procedure was found to be very practical as the reaction occurred under mild reaction conditions and in short reaction times. The isolation and purification steps were particularly straightforward and high yielding, in comparison to traditional methods.

Prediction of Intrinsic kinetics in diffusion disguised immobilized enzyme systems

When immobilized enzyme kinetics are disguised by inter- and intraparticle diffusion effects, an approximate mathematical procedure is indicated whereby experimental data obtained in the limiting ranges of first- and zeroth-order Michaelis-Menten kinetics could be used for the prediction of the kinetic constants.

Conversion of (+/-)-synephrine into p-hydroxyphenylacetaldehyde by Arthrobacter synephrinum: A novel enzymic reaction

A partically purified enzyme from Arthrobacter synephrinum was found to catalyse the conversion of (+/-)-synphrine into p-hydroxyphrenylacetaldehyde and methylamine. The enzyme is highly specific for synephrine and is distinctly different from monoamine oxidase.