Mathematical modeling of the action of biosensor possessing variable parameters

Electrochemical biosensor containing flat semi-permeable membrane covering enzyme-containing layer has been investigated. Mathematical modeling of the action modes of electrochemical biosensors with outer diffusion membrane was performed. Operation of the biosensor under the conditions when the permeability of the membrane and the activity of the biocatalytic layer depend on the parameters of the probe has been examined. The pH and temperature were selected as the main parameters which often affect the action of biosensors. A set of parameters was selected when the biosensor operates in kinetic and diffusion modes of action. The response time of the biosensor was shown to be sensitive to the mode of the biosensor action especially in the boundary region of the biosensor action. The linearity of the biosensor (the linear dependence of the biosensor response on the substrate concentration) in the deep diffusion mode can be increased by several magnitudes, whereas the response time increases only several times.     

Mathematical modeling of biosensor action in the region between diffusion and kinetic modes

We describe the action of electrochemical enzyme-based biosensor by applying mathematical modeling. We consider two types of biosensors: a biosensor containing a single heterogeneous enzyme layer and biosensor containing an additional protecting polymer-based layer. The initial parameters of the biosensor were selected on the basis of typical immobilized glucose oxidase-based electrochemical biosensor. A phenomenon of the accumulation of the electrochemically active product inside the biocatalytic layer was evaluated. It was shown that accumulation of the product can increase sensitivity of the biosensor no more than 2.6 times. Due to the asymmetric distribution of the electrochemically active product inside the enzyme-containing membrane and asymmetric diffusion of the substrate, it was shown that the thickness of the membrane possesses an optimal value. For the selected set of initial parameters, the optimal thickness of the enzyme-containing layer was 2.9–4.5  $\upmu $ m. Real profiles of the impact of the thickness of the membranes were evaluated. A method for the evaluation of acceptable fluctuations of the membrane diffusion parameters on biosensor response was created, and the profiles of the dependence were calculated. These dependencies can be used for development of the software for biosensor monitoring.     

Case studies with mathematical modeling of free-radical multi-component bulk/solution polymerizations: Part 2

In Part 2 of this series of two extensive overviews of multi-component polymerization case studies, we again present mathematical modeling results with experimental confirmations. Part 2 represents a refinement and expansion of the detailed and extensive mathematical model presented in Part 1 for free-radical, bulk and/or solution multi-component polymerizations. The expansion is mainly with respect to depropagation, thus making the model more fluent at elevated polymerization temperatures and, in parallel, with additional features as backbiting (with systems involving butyl acrylate). The model considers up to six monomers (unique in the literature), for either batch or semi-batch reactor modes. As the simulator database contains several monomers, initiators, solvents, chain transfer agents and inhibitors, all tested over a wide range of polymerization conditions, from data in both academic and industrial laboratories, several hundred combinations of ingredients can be modeled. The many outputs generated by the model include conversion, molecular weight, polymer composition, branching indicators, sequence length, as well as many other polymerization characteristics related to both production rate and polymer quality. Although the only literature data found to date contain a maximum of four monomers, model predictions for homo-, co-, ter- and tetra-polymerizations show reasonable agreement against the data at both regular and elevated temperatures. With these expansions, this model is directed towards becoming a complete free-radical polymerization tool for training and educational uses both in industry and academia.     

Oxidative dimerization of methane: Kinetics,mathematical modeling,and optimization with La/Ce catalysts

Kinetic features of oxidative dimerization of methane to ethane and ethylene, catalyzed by a mixture of lanthanum and cerium oxides deposited onto a magnesium oxide support, were examined. A kinetic model was proposed, and the process optimization was performed for a plug-flow reactor in the quasi-homogeneous approximation.     

Principles of rapid polymerase chain reactions: mathematical modeling and experimental verification

Polymerase chain reaction (PCR) is an important diagnostic tool for the amplification of DNA. The PCR process can be treated as a problem in biochemical engineering. This study focuses on the development of a mathematical model of the polymerase chain reaction. The PCR process consists of three steps: denaturation of target DNA, annealing of sequence-specific oligonucleotide primers and the enzyme-catalyzed elongation of the annealed complex (primer:DNA:polymerase). The denaturation step separates the double strands of DNA; this model assumes denaturation is complete. The annealing step describes the formation of a primer-fragment complex followed by the attachment of the polymerase to form a ternary complex. This step is complicated by competitive annealing between primers and incomplete fragments including primer-primer reactions. The elongation step is modeled by a stochastic method. Species that compete during the elongation step are deoxynucleotide triphosphates dCTP, dATP, dTTP, dGTP, dUTP, and pyrophosphate. Thermal deamination of dCTP to form dUTP is included in the model. The probability for a species to arrive at the active site is based on its molar fraction. The number of random insertion events depends on the average processing speed of the polymerase and the elongation time of the simulation. The numerical stochastic experiment is repeated a sufficient number of times to construct a probability density distribution (PDF). The moment of the PDF and the annealing step products provide the product distribution at the end of the elongation step. The overall yield is compared to six experimental values of the yield. In all cases the comparisons are very good.     

Site-directed mutagenesis of squalene-hopene cyclase: altered substrate specificity and product distribution

BACKGROUND: Two regions of squalene-hopene cyclase (SHC) were examined to define roles for motifs posited to be responsible for initiation and termination of the enzyme-catalyzed polyolefinic cyclizations. Specifically, we first examined the triple mutant of the DDTAVV motif, a region deeply buried in the catalytic cavity and thought to be responsible for the initiation of squalene cyclization. Next, four mutants were prepared for Glu45, a residue close to the substrate entrance channel proposed to be involved in the termination of the cyclization of squalene. RESULTS: The DDTAVV motif in SHC was changed to DCTAEA, the corresponding conserved region of eukaryotic oxidosqualene cyclase (OSC), by the triple mutation of D377C/V380E/V381A; selected single mutants were also examined. The triple mutant showed no detectable cyclization of squalene, but effectively cyclized 2,3-oxidosqualene to give mono- and pentacyclic triterpene products. Of the Glu45 mutants, E45A and E45D showed reduced activity, E45Q showed slightly increased activity, and E45K was inactive. A normal yield of pentacyclic products was produced, but the ratio of hopene 2 to hopanol 3 was significantly changed in the less active mutants. CONCLUSIONS: Initiation and substrate selectivity may be determined by the interaction of the DDTAVV motif with the isopropylidene of squalene (for SHC) and of the DCTAEA motif with the epoxide of oxidosqualene (for OSC). This is the first report of a substrate switch determined by a central catalytic motif in a triterpenoid cyclase. At the termination of cyclization, the product ratio may be largely controlled by Glu45 at the entrance channel to the active site.     

Mechanism of propane oxidation–mathematical modeling

Mathematical modeling was used for the kinetics of gas-phase propane oxidation at 586, 613, and 658 K and pressures 172 and 250 torr. The reaction mechanism involving branching by decay of the peracetyl peroxy radical, and oxygen-containing products formed on decay of the RO₄ radical is discussed. Fair agreement between calculated and experimental results on the kinetics and accumulation rates of reaction products was obtained.     

Energy-efficient dehydrogenation of methanol in a membrane reactor: a mathematical modeling

A two-dimensional non-isothermal stationary mathematical model of the catalytic membrane reactor for the process of methanol dehydrogenation is described. Copper supported on the carbonaceous support was considered as a catalyst. The reaction of methanol dehydrogenation was thermodynamically conjugated with a reaction of hydrogen oxidation taking place in a shell side of the membrane reactor. The effects of various parameters on the methanol conversion and the methyl formate yield have been calculated with the developed model and discussed. Two different types of heating the gas flow were considered and compared. In the case of conjugated dehydrogenation process, the methyl formate yield reaches 77%, when the reactor outer wall was heated up to 150 °C. When the inlet gas flows in the tube and shell sides were heated up to 100 and 83 °C, correspondingly, the yield was 72%.     

Modelling synergistic action of laccase-based biosensor utilizing simultaneous substrates conversion

The response of a laccase-based amperometric biosensor that acts in a synergistic manner was modelled digitally. A mathematical model of the biosensor is based on a system of non-linear reaction diffusion equations. The modelling biosensor comprises three compartments, an enzyme layer, a dialysis membrane and an outer diffusion layer. By changing input parameters the biosensor action was analysed with a special emphasis to the influence of the species concentrations on the synergy of the simultaneous substrates conversion. The digital simulation was carried out using the finite difference technique.     

Degradation product emission from historic and modern books by headspace SPME/GC-MS: evaluation of lipid oxidation and cellulose hydrolysis

Volatile organic compounds emitted from a several decade series of bound periodicals (1859–1939) printed on ground wood paper, as well as historical books dating from the 1500s to early 1800s made from cotton/linen rag, were studied using an improved headspace SPME/GC–MS method. The headspace over the naturally aging books, stored upright in glass chambers, was monitored over a 24-h period, enabling the identification of a wide range of organic compounds emanating from the whole of the book. The detection of particular straight chain aldehydes, as well as characteristic alcohols, alkenes and ketones is correlated with oxidative degradation of the C₁₈ fatty acid constituency of paper. The relative importance of hydrolytic and oxidative chemistry involved in paper aging in books published between 1560 and 1939 was examined by comparing the relative abundances of furfural (FUR) a known cellulose hydrolysis product, and straight chain aldehydes (SCA) produced from the oxidation of fatty acids in paper. The relative abundance of furfural is shown to increase across the 379-year publication time span. A comparison of relative SCA peak areas across the series of books examined reveals that SCA emission is more important in the cotton/linen rag books than in the ground wood books.     

Supercritical extraction of phloroglucinol and benzophenone derivatives from Hypericum carinatum: quantification and mathematical modeling

The aerial parts of Hypericum carinatum (Guttiferae) were extracted with supercritical carbon dioxide under constant temperature (40, 50 or 60°C) and gradual pressure increase (90, 120, 150 and 200 bar) aiming at the recovery of enriched fractions containing uliginosin B, cariphenone A and cariphenone B, compounds of pharmaceutical interest. The yields of these substances were determined by high‐performance liquid chromatography and compared with those obtained with n‐hexane maceration. The supercritical‐fluid extraction showed higher selectivity than the conventional solvent extraction method. After defining 40°C and 90 bar as the best conditions to obtain the target compounds, a mathematical model was used for the extraction process and a good correlation was achieved with the experimental data.     

FeCl3·6H2O-promoted skeleton-rearrangement of 1-substituted-3-benzazepines: substrate extension and product utilization

FeCl₃·6H₂O-promoted skeleton-rearrangement of 1-substituted-3-benzazepines was further exploited. Both 1-aryl- and 1-alkyl- or 1-alkenyl-benzazepines underwent this reaction smoothly. The rearrangement products were used to prepare a series of novel derivatives containing both tetrahydroisoquinoline (THIQ) and tetrahydropyrimidin-4(1H)-one scaffolds through a Mannich-type process.     

A mathematical model of measurement uncertainty of single substrate enzyme assays

Clinical laboratory tests provide critical information at every stage of the medical decision‐making process, and measurement of the activity levels of enzymes such as alkaline phosphatase, lactate dehydrogenase, etc. provide information regarding various body functions such as the liver and gastrointestinal tract. The uncertainty associated with these enzyme measurement processes describes the quality of the measurement process, and therefore methods to improve the quality of the measurement process require minimizing the measurement uncertainty of the enzyme assay. In this study, we develop a mathematical model of the lactate dehydrogenase measurement process, with uncertainty introduced into its parameters that represent the sources of variation in the different components and stages of the measurement process. The Monte Carlo method is then utilized to estimate the uncertainty associated with the model, and therefore the measurement process. An empirical function used to generate estimates of uncertainty for patient samples with unknown activity levels is constructed using the model. The model is then used to quantify the contributions of the individual sources of uncertainty to the net measurement uncertainty and also quantify the effect of uncertainty within the calibration process on the distribution of the measurement result. Copyright © 2014 John Wiley & Sons, Ltd.     

Atom-transfer radical polymerization of styrene with bifunctional and monofunctional initiators: Experimental and mathematical modeling results

Bulk atom transfer radical polymerization (ATRP) of styrene was carried out at 110 °C using benzal bromide as bifunctional initiator and 1-bromoethyl benzene as monofunctional initiator. CuBr/2,2′-bipyridyl was used as the ATRP catalyst. The polymerization kinetic data for styrene with both initiators was measured and compared with a mathematical model based on the method of moments and another one using Monte Carlo simulation. An empirical correlation was incorporated into the model to account for diffusion-controlled termination reactions. Both models can predict monomer conversion, polymer molecular weight averages, and polydispersity index. In addition, the Monte Carlo model can also predict the full molecular weight distribution of the polymer. Our experimental results agree with our model predictions that bifunctional initiators can produce polymers with higher molecular weights and narrower molecular weight distributions than monofunctional initiators. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2212–2224, 2007     

Experimental studies and mathematical modeling of the curing reaction of bioinspired copolymers

Polymer curing is a complex process that significantly delineate the final properties of the synthetized material. In this work, the photo-induced crosslinking reaction of synthetic “bio-inspired” copolymers based on thymine and ionic groups was studied by gel permeation chromatography and UV absorption spectroscopy. A mathematical model for the curing process based on statistical techniques and coupled to the kinetics of crosslinking was developed. The model allows to predict both, the evolution of the crosslinking degree as a function of curing time and the gel times as a function of the molecular structure of the copolymer and the curing conditions. The theoretical values showed a very good agreement with the UV–Vis and GPC spectroscopy experimental results for all the copolymers studied. A better knowledge of the curing kinetics of thymine-based biopolymers will enable to develop materials with pre-specified properties and to improve their applications.     

Optimization of beta-carotene production from synthetic medium by Blakeslea trispora: a mathematical modeling

The effect of inoculum, pH, carbon and nitrogen source, natural oils, fatty acids, antioxidant, and precursors on beta-carotene production by Blakeslea trispora in shake-flask culture was investigated. The highest concentration of beta-carotene was obtained in the medium (pH 7.0) inoculated with one loop of each culture. Sucrose, glycerol, cornmeal, soy protein acid hydrolysate, and distiller's solubles did not improve the production of beta-carotene. By contrast, glucose, corn steep liquor, antioxidant, olive oil, soybean oil, cottonseed oil, oleic and linoleic acids, and kerosene significantly increased the beta-carotene production. A central composite design was employed to determine the maximum beta-carotene production at optimum values for the process variables (linoleic acid, kerosene, and antioxidant). The fit of the model was found to be good. Linoleic acid, kerosene, and antioxidant had a strong linear effect on beta-carotene production. The concentration of beta-carotene was significantly affected by linoleic acid-kerosene and linoleic acid-antioxidant interactions as well as by the negative quadratic effects of these variables. The interaction between kerosene and antioxidant had no significant linear effect. The maximum beta-carotene concentration (2.88 g/L) was obtained at concentrations of 17.15 g/L of linoleic acid, 39.25 g/L of kerosene, and 9.04 g/L of antioxidant.     

Crystallization of poly(vinyl alcohol) during solvent removal: Infrared characterization and mathematical modeling

Crystallization of semicrystalline polymer films during drying has a significant effect on the rate of solvent removal. Understanding and controlling the crystallization kinetics is important in controlling residual solvent levels and drying kinetics. The degree of crystallinity of the poly(vinyl alcohol) films during multicomponent drying was investigated using Fourier transform infrared spectroscopy (FTIR). The 1141 cm^?1 band is sensitive to the degree of crystallinity of the polymer and the growth of intensity of this band was monitored as drying progressed. The results from the FTIR studies were comparable to the results obtained from differential scanning calorimetry. Studies were conducted to test the effect of initial solvent composition (water–methanol mixture), drying temperature, and polymer molecular weight on the rate of crystallization and the final crystallinity of the films. An increase in initial methanol composition increased the crystallization rate but did not affect the final degree of crystallinity. An increase in drying temperature and decrease in polymer molecular weight increased the rate of crystallization as well as the final degree of crystallinity. Based on the experimental data, rate constants for crystallization kinetics were extracted from our previously developed model based on free volume theory. The experimental data and the simulation results showed good agreement. The ability of the free volume theory to illustrate the crystallization behavior validated the model and improved its capability. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 930–935, 2007     

Potential oscillations in galvanostatic electrooxidation of formic acid on platinum: a mathematical modeling and simulation

We have modeled temporal potential oscillations during the electrooxidation of formic acid on platinum on the basis of the experimental results obtained by time-resolved surface-enhanced infrared absorption spectroscopy (J. Phys. Chem. B 2005, 109, 23509). The model was constructed within the framework of the so-called dual-path mechanism; a direct path via a reactive intermediate and an indirect path via strongly bonded CO formed by dehydration of formic acid. The model differs from earlier ones in the intermediate in the direct path. The reactive intermediate in this model is formate, and the oxidation of formate to CO2 is rate-determining. The reaction rate of the latter process is represented by a second-order rate equation. Simulations using this model well reproduce the experimentally observed oscillation patterns and the temporal changes in the coverages of the adsorbed formate and CO. Most properties of the voltammetric behavior of formic acid, including the potential dependence of adsorbate coverages and a negative differential resistance, are also reproduced.