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BACKGROUND: In treatment of air using UV-irradiated titanium dioxide (TiO2), volatile organic compound (VOC) concentrations mostly reach zero or decrease to a miniscule amount However, when acetaldehyde (AA) is treated by photocatalysts immobilized on silica or activated carbon (AC) particles, which have a high ability to adsorb VOCs, the AA concentration decreases rapidly initially, but decreases very slowly after AA has been decomposed to a certain low concentration To overcome this problem, the performances of photocatalysts immobilized on different supporting materials were investigated RESULTS: Computer simulations clarify that the slow decrease in the AA concentration in the final stage is due to the desorption of adsorbed AA, taking a much longer time to completely decompose AA The simulations also suggest two strategies to overcome the problem: using a support with a smooth surface and low adsorption ability, and increasing the photocatalytic activity The first strategy was tested by immobilizing TiO2 on glass tubes, PET film sheets and aluminum foil sheets with low adsorption abilities The experimental results indicate that the AA concentrations for these supports decrease at lower rates than for supports with high adsorption ability, but decrease steadily toward zero The second strategy was tested by increasing the amount of immobilized-photocatalyst particles with high adsorption abilities, resulting in a shorter time for the AA concentration to reach zero CONCLUSION: For completely decomposing AA by an immobilized photocatalyst in a short period of time, the use of supporting particles with a high adsorption ability should be avoided © 2020 Society of Chemical Industry

The photocatalytic decomposition of ethylene in a spiral-type reactor was investigated to develop a method for preserving the quality of agricultural products. Ethylene was injected or discharged from an apple into a 0.016 m3 closed container and was photocatalytically decomposed in the reactor at 25 °C. The results indicated that ethylene was decomposed and became undetectable (the amount of ethylene was lower than the detection limit of 40 ppb), which is useful for preserving the quality of agricultural products over long periods of time. For the demonstration experiment, we placed an apple, a persimmon, a cucumber, a cabos (Citrus sphaerocarpa), and a banana in a 0.117 m3 closed container at 25 °C. When the air inside the container was not photocatalytically treated, the concentration of ethylene increased up to 2.7 ppm. This lowered the quality of the persimmon, cucumber, and apple significantly. In contrast, when the air inside the container was photocatalytically treated, they remained fresh for at least nine days. Methane was simultaneously generated as a byproduct. It was hypothesized that methane was the product of the photocatalytic decomposition of some unknown chemical compound released from the analyzed agricultural products; however, we were unable to identify the chemical compound. Computer simulations using experimentally determined parameter values suggested that the decomposition of ethylene begins before or as soon as agricultural products are stored in closed rooms, such as truck containers. In conclusion, the photocatalytic decomposition of ethylene using a spiral-type reactor is effective for preserving the quality of agricultural products.

Plant metabolism is characterized by a wide diversity of metabolites, with systems far more complicated than those of microorganisms. Mathematical modeling is useful for understanding dynamic behaviors of plant metabolic systems for metabolic engineering. Time-series metabolome data has great potential for estimating kinetic model parameters to construct a genome-wide metabolic network model. However, data obtained by current metabolomics techniques does not meet the requirement for constructing accurate models. In this article, we highlight novel strategies and algorithms to handle the underlying difficulties and construct dynamic in vivo models for large-scale plant metabolic systems. The coarse but efficient modeling enables the prediction of unknown mechanisms regulating plant metabolism.

In a mathematical model, estimation of parameters from time-series data of metabolic concentrations in cells is a challenging task. However, it seems that a promising approach for such estimation has not yet been established. Biochemical Systems Theory (BST) is a powerful methodology to construct a power-law type model for a given metabolic reaction system and to then characterize it efficiently. In this paper, we discuss the use of an S-system root-finding method (S-system method) to estimate parameters from time-series data of metabolite concentrations. We demonstrate that the S-system method is superior to the Newton-Raphson method in terms of the convergence region and iteration number. We also investigate the usefulness of a translocation technique and a complex-step differentiation method toward the practical application of the S-system method. The results indicate that the S-system method is useful to construct mathematical models for a variety of metabolic reaction networks.

Although the relative arrangement of a UV light source and immobilized TiO 2 is estimated to strongly affect the photocatalytic decomposition of volatile organic compounds (VOCs), no studies have been published regarding this matter. In the present study, reactor performances were compared between parallel arrangements, where UV lamps are placed in parallel to flat TiO 2 -PET sheets, and circular arrangements, where each glass tube has a UV lamp and a cylindrical TiO 2 -PET sheet closely attached to the inside surface of the tube. In the decomposition of isopropanol, acetone was released into air and decomposed after being readsorbed onto TiO 2 . In the decomposition of toluene, benzaldehyde remained on the surface and inhibited the decomposition. Parallel arrangement generated an area of low UV intensity on TiO 2 -PET sheets, leaving unconverted intermediates on the sheets. Circular arrangement made it possible to irradiate the whole surface of a TiO 2 -PET sheet with high intensity UV light and provided higher rates of VOC decomposition such that intermediates could be decomposed efficiently. To completely decompose VOCs including the intermediates, TiO 2 must be irradiated with strong UV light above a certain threshold that depends on the kind of VOC. The use of the circular arrangement is recommended for the VOC decomposition.

Film-diffusion resistance significantly reduces the decomposition of organic compounds over an immobilized photocatalyst in the vicinity. To overcome this problem, the performance of a photocatalytic system consisting of five continuous stirred-tank reactors (CSTRs) in series was investigated. Each reactor was a square-shaped container with a glass plate immobilized with a film of TiO 2 photocatalyst at the bottom. Two 4-W blacklight blue-fluorescent lamps fixed above the container provided UV light. A 10-ppm aqueous solution of 2,4-dinitrophenol (DNP) supplied continuously to the reactor was stirred by an impellor fixed to a shaft with a wind propeller at its upper end. The change in the DNP concentration in each reactor with increasing flow rate agreed with the result calculated by a mathematical model, constructed for the photocatalytic system, which included a mass-transfer coefficient expressed in terms of rotational speed. Hence, this model was used to simulate the performance of the reactor system. At sufficiently high rotational speeds, the conversion of DNP at the exit of the fifth CSTR was substantially higher than that at the exit of a single CSTR with the same liquid volume, and was close to the calculated value for a plug-flow reactor without film-diffusion resistance. At low rotational speeds, however, the DNP concentration remained remarkably high because of large film-diffusion resistance, demonstrating that the photocatalytic reaction requires sufficient liquid mixing to enhance the reaction rate. Thus, the system of five CSTRs in series is effective as a photocatalytic reactor system.

A reaction mechanism of the photocatalytic decomposition of 2,4-dinitrophenol (DNP) on TiO2 immobilized on a glass surface is investigated both theoretically and experimentally. The experimental results show that (1) the DNP concentration decreases linearly in the same manner; (2) the initial rate of decomposition increases with an increase in the initial DNP concentration, i.e., the reaction is not inhibited by DNP; and (3) product inhibition is present, but it is not as strong as that in the aqueous TiO2 suspension. To elucidate the mechanism of the photocatalytic reaction, a mathematical model is constructed by taking into consideration an electrostatic interaction between positively-charged TiO2 and negatively-charged DNP. The calculated results suggest that mixing a solution breaks down the DNP-aggregate layer formed in the neighborhood of TiO2 film and removes reactant inhibition by DNP. The results are also compared with our previous result for the DNP decomposition in an aqueous TiO2 suspension and the difference is identified.

The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC ( arameter stimation in a on- mensionalized -system with onstraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.

The aims of the present study are to propose a mathematical model for photocatalytic decomposition of 2,4-dinitrophenol (DNP) in an aqueous suspension of TiO 2 fine particles and to elucidate the reaction mechanism using this model. The following three facts were found experimentally: (i) although a reactant usually decomposes more quickly at higher concentrations, DNP decomposed more slowly; (ii) photocatalytic reaction usually obeys firstorder kinetics when the initial reactant concentration is approximately 10 g m −3 , although the DNP concentration decreased almost linearly according to zeroorder kinetics; and (iii) the resulting NO 3 ion significantly decreased the DNP decomposition rate. A mathematical model constructed by taking into consideration these findings can successfully explain the experimental data, implying that DNP molecules are highly aggregated in the neighborhood of TiO 2 particle. The DNP aggregate layer suppresses the generation of active radicals, which leads to reactant inhibition. The photocatalytic decomposition of DNP supplied from the aggregate layer of highly concentrated DNP around TiO 2 is observed by zero-order kinetics.

BACKGROUND TiO2-based heterogeneous photocatalysis is an effective way to degrade harmful refractory organic compounds. However, the rate of photocatalytic reaction is significantly decreased by film diffusion resistance and several other factors. To overcome this problem, TiO2 immobilized on a stainless steel screen is hydrophobically treated using a (γ-aminopropyl) triethoxysilane–toluene solution and the performance of the silanized TiO2 for the photocatalytic decomposition of 2,4-dinitrophenol (2,4-DNP) is investigated. RESULTS The reactant 2,4-DNP is slowly decomposed when its aqueous solution is treated using an unsilanized TiO2 screen without mixing the solution, whereas the rate of decomposition is certainly increased by use of a silanized TiO2 screen, and further increased by mixing the solution. The use of sunlight as a UV light source provides a higher rate of decomposition than does the use of an artificial UV lamp. The rate of decomposition in a well-mixed solution is less affected up to 1.5 cm in solution depth. CONCLUSIONS The use of the TiO2 screen silanized with a 2% silane–toluene solution under liquid mixing decreases film diffusion resistance and facilitates rapid decomposition of 2,4-DNP. The simultaneous use of sunlight as a UV light source and a wind-powered propeller for liquid mixing is effective. © 2013 Society of Chemical Industry

The high-throughput acquisition of metabolome data is greatly anticipated for the complete understanding of cellular metabolism in living organisms. A variety of analytical technologies have been developed to acquire large-scale metabolic profiles under different biological or environmental conditions. Time series data are useful for predicting the most likely metabolic pathways because they provide important information regarding the accumulation of metabolites, which implies causal relationships in the metabolic reaction network. Considerable effort has been undertaken to utilize these data for constructing a mathematical model merging system properties and quantitatively characterizing a whole metabolic system in toto. However, there are technical difficulties between benchmarking the provision and utilization of data. Although, hundreds of metabolites can be measured, which provide information on the metabolic reaction system, simultaneous measurement of thousands of metabolites is still challenging. In addition, it is nontrivial to logically predict the dynamic behaviors of unmeasurable metabolite concentrations without sufficient information on the metabolic reaction network. Yet, consolidating the advantages of advancements in both metabolomics and mathematical modeling remain to be accomplished. This review outlines the conceptual basis of and recent advances in technologies in both the research fields. It also highlights the potential for constructing a large-scale mathematical model by estimating model parameters from time series metabolome data in order to comprehensively understand metabolism at the systems level.

Mathematical modeling of large-scale metabolic networks usually requires smoothing of metabolite time-series data to account for measurement or biological errors. Accordingly, the accuracy of smoothing curves strongly affects the subsequent estimation of model parameters. Here, an efficient parametric method is proposed for smoothing metabolite time-series data, and its performance is evaluated. To simplify parameter estimation, the method uses S-system-type equations with simple power law-type efflux terms. Iterative calculation using this method was found to readily converge, because parameters are estimated stepwise. Importantly, smoothing curves are determined so that metabolite concentrations satisfy mass balances. Furthermore, the slopes of smoothing curves are useful in estimating parameters, because they are probably close to their true behaviors regardless of errors that may be present in the actual data. Finally, calculations for each differential equation were found to converge in much less than one second if initial parameters are set at appropriate (guessed) values.

Kinetic-order sensitivity (the ratio of relative change in a dependent variable to the relative change in a kinetic order in a power-law–type differential equation) has recently become an important indicator in metabolic pathway analysis using mathematical models with parameter values determined from time-series data on cellular metabolite concentrations. Here, we discuss a potential problem in calculating kinetic-order sensitivities. When the steady-state metabolite concentration is less than unity, a slight increase in the kinetic order changes the metabolite concentration in the incorrect direction, yielding a kinetic-order sensitivity value with an incorrect sign. This is caused by a property of the power-law function ( y = X n ): when X is less than unity, y decreases for a larger positive n or for a smaller absolute value of negative n . We propose two solutions. The first is to directly calculate the kinetic-order sensitivities and then reverse the sign of the relevant value if a steady-state metabolite concentration less than unity is involved. The second involves calculation of the kinetic-order sensitivities after setting all metabolite concentrations to values greater than unity (e.g., by changing the units from mM to μM). The latter method changes the absolute values of the kinetic-order sensitivities according to the magnitude of a multiplication factor, because kinetic-order sensitivities do not have unique values. Nevertheless, since the normalized absolute values exhibit an almost identical distribution, it should not be difficult to identify which kinetic order has greater effect, although kinetic order rankings may change slightly under different calculation conditions.

Dynamic sensitivities are useful to characterize time-varying systems efficiently. In metabolic reaction systems, however, analysis using these values is not so popular. This is mainly due to the following two reasons. One is that the calculation of dynamic sensitivities requires us to derive differential equations for sensitivities from those for metabolite concentrations by partial differentiation, and it is not easy for experimentalists to perform this mathematical operation. The other is that the metabolic reaction systems are mostly described by stiff differential equations, from which it may not be easy to obtain reliable numerical solutions. We have previously developed software for calculation of dynamic sensitivities (softcads), in which one can calculate dynamic sensitivities with high accuracy by setting only differential equations for metabolite concentrations. This paper further improves the algorithm of softcads to enhance its performance. The results clearly show that regardless of the degree of stiffness, the improved softcads provides dynamic sensitivities with the super high accuracy that is comparable to the machine accuracy and also completes the calculation in a shorter time. © 2011 Curtin University of Technology and John Wiley & Sons, Ltd.

We have previously developed the software for calculation of dynamic sensitivities, SoftCADS, in which one can calculate dynamic sensitivities with high accuracy by just setting the differential equations for metabolite concentrations. However, SoftCADS did not always provide calculated values with the machine accuracy of a computer, although a Taylor series method was employed to numerically solve the differential equations. This is because numerical derivatives calculated from an approximate formula were directly used in the derivation of the differential equations for sensitivities from those for metabolite concentrations. The present work therefore attempts to further enhance the performance of SoftCADS, including not only the accuracies of the calculated values but also the calculation time. To overcome the problem, the approximate formula is expanded into a Taylor series in time and the first-term value of the series is replaced by the exact coefficient on the second term of the flux function expanded into a Taylor series in an independent or dependent variable. The result reveals that this replacement certainly provides not only numerical derivatives but also dynamic sensitivities with superhigh accuracies comparable to the machine accuracy, regardless of the degree of stiffness of the differential equations. Moreover, a comparison indicates that the improved SoftCADS shortens the calculation time of the dynamic sensitivities without reducing their accuracies, even when the simplest approximate derivative formula is used.

BACKGROUND: The authors (Chem Eng J 148, 234 (2009)) previously demonstrated the excellent performance of a photocatalytic reactor with a parallel array of nine light sources. To enhance the possibility of practical application of this reactor, the present work explores the use of a PET (polyethylene terephthalate) sheet as a new cheap material to support TiO2, as an alternative to glass tubes. A method of coating the hydrophobic PET sheet with a TiO2 film using an aqueous coating solution is investigated and the performance of the TiO2-PET sheet prepared evaluated. RESULTS: The affinity of the coating solution for the PET sheet is greatly enhanced by addition of 0.01% (w/w) nonionic surfactant (polyoxyethylene lauryl ether). A relatively uniform thin TiO2 film is formed on the entire surface of the PET sheet by applying the coating solution to the PET sheet and drying it at 100 °C. Decomposition experiments of gaseous HCHO indicate that the photocatalytic activity, although initially low, is increased with repeated use. This is because surfactant molecules added interfere initially with the decomposition of HCHO. After their decomposition, the TiO2–PET sheet decomposes HCHO at almost the same rate as does the TiO2–glass tube. CONCLUSION: The photocatalytic reactor with a parallel array of nine light sources can utilize a PET sheet as TiO2 support with a reduction in material cost. Copyright © 2011 Society of Chemical Industry

A number of recent research studies have focused on theoretical and experimental investigation of a bottleneck in a metabolic reaction network. However, there is no study on how the bottleneck affects the performance of a fermentation process when a product is highly toxic and remarkably influences the growth and death of cells. The present work therefore studies the effect of bottleneck on product concentrations under different product toxicity conditions. A generalized bottleneck model in a fed-batch fermentation is constructed including both the bottleneck and the product influences on cell growth and death. The simulation result reveals that when the toxic product strongly influences the cell growth and death, the final product concentration is hardly changed even if the bottleneck is removed, whereas it is markedly changed by the degree of product toxicity. The performance of an ethanol fermentation process is also discussed as a case example to validate this result. In conclusion, when the product is highly toxic, one cannot expect a significant increase in the final product concentration even if removing the bottleneck; rather, it may be more effective to somehow protect the cells so that they can continuously produce the product.

Dynamic logarithmic gain and its modifications can be theoretically used as a bottleneck ranking (BR) indicator in a metabolic reaction system. However, it is not sufficiently explicit whether they can be successfully used in practical applications. The present work therefore focuses on the selection of best BR indicators in both instantaneous and overall cases. A modified ethanol fermentation model is used as a case study. The results indicate that the mathematical product of dynamic logarithmic gain and desired product concentration at a given time is the best instantaneous BR indicator, whereas its value at the end time of the fermentation process is the best overall BR indicator. The former is useful for observing the time course of the desired product concentration and determining a process time to be terminated. The latter is for ranking bottleneck enzymes to determine which enzyme activity should be changed to attain a higher desired product concentration. Moreover, discussion is made on the utilization of the overall BR indicators to predict how much the final desired product concentration is increased.

Dynamic logarithmic gains (normalised time-varying sensitivities) or their products with metabolite concentrations, called an instantaneous bottleneck ranking indicator (instantaneous BR indicator), can express the time courses of bottleneck enzyme ranking. The integrated value of the instantaneous BR indicator, called an overall BR indicator, provides a ranking of bottleneck enzymes over the entire reaction period of time. Owing to the property of the logarithmic gains, these BR indicators are allowed to include both positive and negative values and in turn raise several questions on the identification of a bottleneck enzyme. To eliminate these questions, the present work studies the identification of bottleneck enzymes in four ethanol fermentation systems using suspended and immobilised cells at pH 4.5 and 5.5 as case studies. These systems consist of both intracellular reactions without cell growth (intracellular reaction systems) and those with cell growth (cell growth systems). The analyses of the intracellular reaction systems reveal that both the suspended and immobilised cell systems at pH 5.5 are not robust. In the cell growth systems, therefore, the analyses are conducted only for the suspended and immobilised cell models at pH 4.5. The enzyme glyceraldehyde 3-phosphate dehydrogenase (gapd) initially has the largest logarithmic gains under all conditions, whereas the system becomes insensitive to it over time. Interestingly, the instantaneous BR indicator for gapd is negatively large. Also, other indicators change in positive and/or negative regions. To deal with these values of different signs, all the indicators are integrated to obtain and rank the overall BR indicators in the order of the magnitudes of their absolute values. The result shows that the ranking of enzymes are completely identical to that of the final ethanol concentrations obtained by finitely increasing or decreasing the relevant enzyme activities in accordance with the signs of overall BR indicators. This result indicates that the enzymes must be ranked in the order of the magnitudes of their absolute values to determine a bottleneck enzyme. As a result, the analyses of the intracellular reaction systems reveal that the bottleneck enzyme is switched from a membrane-bound glucose transporter enzyme to phosphofructokinase when the cell-retaining condition is changed from suspension to immobilisation. In the cell growth systems, gapd is identified as the most likely bottleneck enzyme, suggesting that the gapd activity must be decreased to increase the ethanol productivity.

The present work investigates the mechanism of the photocatalytic and adsorptive treatment of an aqueous DNP (2,4-dinitrophenol) solution in an annular-flow reactor installed with a TiO 2 /AC-PET film (a polyethylene terephthalate film adhesively fixing activated carbon particles covered with a thin and porous film of titanium dioxide). Unfortunately, the experimental result indicates that it is impossible to correctly measure the time courses of product ion concentrations because they are adsorbed onto or desorbed from AC particles. Therefore, a computer simulation methodology using mathematical models is introduced in order to elucidate the treatment mechanism. Treatments of aqueous DNP solutions using the TiO 2 -PET film reveal that the diffusion of DNP from a bulk solution to a TiO 2 film is based on the gradient of DNP concentration, generated by a rapid adsorption of DNP onto AC and photocatalytic reaction, in the very neighborhood of TiO 2 film, and this diffusion increases the DNP concentration at the surface of TiO 2 film, thereby enhancing the rate of photocatalytic decomposition. Moreover, it is found that the TiO 2 /AC-PET film can lower the burden of the adsorption of DNP onto AC compared with the AC-PET film because a part of DNP molecules are photocatalytically decomposed and the percentage of this decomposition is increased at a lower linear velocity. In conclusion, the mathematical model taking into consideration a film-diffusional effect can successfully explain the complicated mechanism of the treatment of an aqueous DNP solution using the TiO 2 /AC-PET film.

This paper investigates the accuracy of a matrix method proposed by other researchers to calculate time-varying flux control coefficients (dynamic FCCs) from elasticity coefficients by means of summation and connectivity theorems in the framework of metabolic control analysis. A mathematical model for the fed-batch penicillin V fermentation process is used as a case example for discussion. Calculated results reveal that this method produces significant calculation errors because the theorems are essentially valid only in steady state, although it may provide rough time-transient behaviors of FCCs. Strictly, therefore, dynamic FCCs should be directly calculated from the differential equations for metabolite concentrations and sensitivities.

A dynamic logarithmic gain expresses the percentage change in a dependent variable or metabolite concentration in response to an infinitesimal percentage change in an independent variable or enzyme activity. This article discusses the usefulness of several bottleneck ranking (BR) indicators that are functions of the logarithmic gain, to determine the most likely bottleneck enzyme in a dynamic metabolic reaction system. Mathematical models for penicillin V and ethanol fermentations are considered as case studies. The calculated results reveal that the instantaneous BR indicator, which is a product of the dynamic logarithmic gain and the metabolite concentration, is an effective measure for instantaneous bottleneck enzyme ranking changed during the fermentation period, whereas the overall BR indicator, which is a time-averaged value of the instantaneous BR indicator, is an effective measure for bottleneck enzyme ranking throughout the entire fermentation period.

Anatase titanium dioxide (TiO 2 ) in particle sizes of roughly 0.5–20 μm was prepared from amorphous TiO 2 in an aqueous H 2 O 2 solution by heating at 90 °C for 9 h and directly deposited on a PET film. On the other hand, granular activated carbon (AC) particles in sizes of 1–2 mm in diameter were adhesively deposited on a PET film, and their surfaces were also coated with TiO 2 . The resulting three preparations (TiO 2 -, AC-, and TiO 2 /AC-PET films) were set up in an annular-flow reactor to treat aqueous solutions of 2,4-dinitrophenol (DNP) in a batch-recirculation mode. The rate of DNP adsorption onto the TiO 2 /AC-PET film without UV irradiation was almost the same as that onto the AC-PET film, indicating that the attraction of DNP to AC was not lowered in the presence of TiO 2 film. Observation of SEM photographs suggests that this result is attributed to the porous structure of the thin TiO 2 film covering AC particles. The rate of DNP removal by the TiO 2 -AC PET film under UV irradiation was 2.9 times higher than that by the TiO 2 -PET film under UV irradiation, and was 1.1 times higher than the rate of DNP adsorption onto the AC-PET film. The rate of DNP removal by the AC-PET film decreased by 40% after six runs, while that by the TiO 2 /AC-PET film decreased by 22%. Durable experiments using the TiO 2 /AC-PET and AC-PET films clarified that the lifetime of the TiO 2 /AC-PET film is at least two times longer than that of the AC-PET film. This result suggests that DNP molecules are photocatalytically decomposed when passing through the porous TiO 2 -PET film, which lessens a burden of DNP adsorption on AC. Moreover, the DNP treatments in the batch-recirculation flow system suggested that the TiO 2 /AC-PET film saturated with DNP can be successfully regenerated at 60 °C.

Dynamic sensitivity analysis has become an important tool to successfully characterize all sorts of biological systems. However, when the analysis is carried out on large scale systems, it becomes imperative to employ a highly accurate computational method in order to obtain reliable values. Furthermore, the preliminary laborious mathematical operations required by current software before the computation of dynamic sensitivities makes it inconvenient for a significant number of unacquainted users. To satisfy these needs, the present work investigates a newly developed algorithm consisting of a combination of Taylor series method that can directly execute Taylor expansions for simultaneous non-linear-differential equations and a simple but highly-accurate numerical differentiation method based on finite-difference formulas. Applications to three examples of biochemical systems indicate that the proposed method makes it possible to compute the dynamic sensitivity values with highly-reliable accuracies and also allows to readily compute them by setting up only the differential equations for metabolite concentrations in the computer program. Also, it is found that the Padé approximation introduced in the Taylor series method shortens the computation time greatly because it stabilizes the computation so that it allows us to use larger stepsizes in the numerical integration. Consequently, the calculated results suggest that the proposed computational method, in addition to being user-friendly, makes it possible to perform dynamic sensitivity analysis in large-scale metabolic reaction systems both efficiently and reliably.

This work investigates photocatalytic decompositions of HCHO in air over thin films of titanium oxide prepared on inside surfaces of glass tubes by the following two methods: Method I (the inside surface of a glass tube was covered with an aqueous H2O2 solution containing amorphous titanium oxide, followed by calcination at 500 °C to convert amorphous titanium oxide to anatase one) and Method II (the inside surface of a glass tube was covered with an aqueous H2O2 solution containing anatase titanium oxide, followed by heating at 100 °C). All the experiments were conducted in a photocatalytic reactor with a parallel array of nine light sources. It is found that there is no remarkable difference between the permeabilities of UV light through glass tube walls coated with the photocatalyst films, although the photocatalyst film prepared by Method I is more transparent than that by Method II. As previously observed with the photocatalyst film prepared by Method I, therefore, the photocatalyst film by Method II is found to increase the rate of decomposition of HCHO as a result of action of the UV light emitted from the light source in a given glass tube on the photocatalyst films that coat adjacent glass tubes. Observation by SEM reveals that the photocatalyst film prepared by Method I has a very smooth surface, whereas that by Method II has a rugged one. This is because anatase titanium oxide particles prepared by Method II possesses much larger crystal sizes and is therefore estimated to have a very large specific surface area. As a result, the photocatalytic reactor equipped with the photocatalyst glass tubes prepared by Method II is found to rapidly decompose HCHO especially in the region of its high concentration and also even when the humidity is very high. Kinetic analyses indicate that the photocatalytic decompositions of HCHO on the titanium oxide films prepared by the two methods obey Langmuir–Hinshelwood type kinetics. It is also found that the rate constant for Method II is 53 times larger than that for Method I, implying that the higher activity for Method II is due to its larger specific surface area.

The performance of the miniaturized photocatalytic air purifier including a continuous adsorption/desorption unit with a zeolite particles-loaded honeycomb rotor was investigated in the photocatalytic purification of 1 m3 air containing toluene at concentrations of 3–11 mg m−3 (about 1–3 ppmv). While operating the continuous adsorption/desorption unit only, and for desorption temperatures controlled within the range of 90–120 and 130–160 °C, the unit took approximately 10 min to reduce the toluene concentration in a 1 m3 room, to a value of almost zero. Almost the same time courses of toluene concentrations were obtained when the photocatalytic reactor was switched on. This result clearly shows that the rapid decrease in the toluene concentration in the 1 m3 room is mainly due to the adsorption of toluene onto the zeolite rotor. When the reactor was switched off, the concentration of toluene desorbed into the 0.022 m3 reactor box increased rapidly and then levelled off in 10 min. On the other hand when the reactor was switched on, the toluene concentration in the reactor box increased rapidly, passing through a maximum in 10–150 min, and then decreasing to a value near zero, leading to the toluene concentration in the 1 m3 room becoming negligible. The apparent rates of decomposition determined from the decreasing toluene concentration in the reactor box were 10-fold smaller than the intrinsic rate constant in the Langmuir–Hinshelwood equation, which would suggest that the desorption process of toluene from the rotor is the rate-limiting. All the decomposition experiments were performed using the same zeolite rotor and photocatalytic reactor over a six month period; and the runs were repeated more than one hundred times. Nevertheless, there was no distinct decrease in decomposition activity of the photocatalyst or any significant loss in ability for the zeolite rotor to adsorb toluene could be seen, indicating that these materials can perform constantly over a long period of time. However, as the rotor will sooner or later become saturated with toluene, it may become necessary to introduce a regeneration procedure in order to periodically remove toluene from the rotor.

In fermentation processes, it is important to identify the bottleneck enzyme in a given metabolic reaction network, because increasing its activity would lead to an enhancement in the productivity of a desired metabolite. To efficiently identify the bottleneck enzyme, the present work discusses a systematic approach using dynamic logarithmic gains, i.e., percentage changes in the concentration of the desired metabolite in the response to an infinitesimal percentage change in enzyme activities, as an indicator. A penicillin V fed-batch fermentation model proposed by other researchers was used as an example of application. The calculated results showed that not only the time courses of the dynamic logarithmic gains but also the ranking of the magnitudes of their values is changed with time, implying that the bottleneck enzyme is changed with time in this fermentation process. To determine the bottleneck enzyme from such time-transient behaviors, the dynamic logarithmic gains were integrated over the entire ...

A mathematical model has been constructed for the removal of gaseous HCHO at a very low concentration level in a closed room by use of an air purifier that consists of a photocatalytic reactor combined with a continuous adsorption and desorption concentrator and the performance of the air purifier has been evaluated by computer simulation. The calculated result for the time course of the HCHO concentration in a 10 m3 closed room shows that the mathematical model can satisfactorily describe the time-transient behavior of the experimental values. The computer simulation for the treatment of HCHO in an actual dwelling house with the continuous release of HCHO from the building materials indicates that the air purifier can steadily keep the HCHO concentration below the WHO guideline (

Metabolite concentrations in cells are governed by enzyme kinetics in the metabolic reaction system. One can analyze how these concentrations depend on system variables such as enzyme activities by computing system sensitivities, which generally vary with time. Dynamic sensitivities, i.e., time-varying sensitivities, reflect the time-dependent response of the metabolic reaction network to perturbations. Unfortunately, dynamic sensitivity profiles are not commonly used in the analysis of metabolic reaction systems. In the present study, we demonstrate the use of dynamic logarithmic gains, i.e., normalized time-varying sensitivities, to gain insights into the dynamic behavior of metabolic networks. A biosynthetic reaction model of aromatic amino acids proposed by other researchers is used as a case study. The model system is analyzed using the dynamic logarithmic gains in parallel with simulations of the time-transient behavior of metabolite concentrations and metabolic fluxes. The result indicates that the influences of independent variables are most pronounced just after perturbations and the effects of perturbations on metabolite concentration at early times can be larger than those at steady state. These findings suggest that it is important to perform dynamic sensitivity analysis in addition to steady-state analysis. Furthermore, the rankings of the bottleneck ranking indicators, defined as the product of dynamic logarithmic gain and metabolite concentration, for three desired amino acids reveal that the degree of bottleneck for each enzyme changes with time. In conclusion, the dynamic logarithmic gains are not only useful for analyzing metabolic reaction systems but also can offer additional insights on the transient behavior of the system over steady state sensitivities, leading to a proper design of metabolic systems., Mathematical Biosciences, 269, ISSN:0025-5564, ISSN:1879-3134

Stability and sensitivity analyses of biological systems require the ad hoc writing of computer code, which is highly dependent on the particular model and burdensome for large systems. We propose a very accurate strategy to overcome this challenge. Its core concept is the conversion of the model into the format of biochemical systems theory (BST), which greatly facilitates the computation of sensitivities. First, the steady state of interest is determined by integrating the model equations toward the steady state and then using a Newton-Raphson method to fine-tune the result. The second step of conversion into the BST format requires several instances of numerical differentiation. The accuracy of this task is ensured by the use of a complex-variable Taylor scheme for all differentiation steps. The proposed strategy is implemented in a new software program, COSMOS, which automates the stability and sensitivity analysis of essentially arbitrary ODE models in a quick, yet highly accurate manner. The methods underlying the process are theoretically analyzed and illustrated with four representative examples: a simple metabolic reaction model; a model of aspartate-derived amino acid biosynthesis; a TCA-cycle model; and a modified TCA-cycle model. COSMOS has been deposited to https://github.com/BioprocessdesignLab/COSMOS.

Background Progress in systems biology offers sophisticated approaches toward a comprehensive understanding of biological systems. Yet, computational analyses are held back due to difficulties in determining suitable model parameter values from experimental data which naturally are subject to biological fluctuations. The data may also be corrupted by experimental uncertainties and sometimes do not contain all information regarding variables that cannot be measured for technical reasons. Results We show here a streamlined approach for the construction of a coarse model that allows us to set up dynamic models with minimal input information. The approach uses a hybrid between a pure mass action system and a generalized mass action (GMA) system in the framework of biochemical systems theory (BST) with rate constants of 1, normal kinetic orders of 1, and -0.5 and 0.5 for inhibitory and activating effects, named Unity (U)-system. The U-system model does not necessarily fit all data well but is often sufficient for predicting metabolic behavior of metabolites which cannot be simultaneously measured, identifying inconsistencies between experimental data and the assumed underlying pathway structure, as well as predicting system responses to a modification of gene or enzyme. The U-system approach was validated with small, generic systems and implemented to model a large-scale metabolic reaction network of a higher plant, Arabidopsis. The dynamic behaviors obtained by predictive simulations agreed with actually available metabolomic time-series data, identified probable errors in the experimental datasets, and estimated probable behavior of unmeasurable metabolites in a qualitative manner. The model could also predict metabolic responses of Arabidopsis with altered network structures due to genetic modification. Conclusions The U-system approach can effectively predict metabolic behaviors and responses based on structures of an alleged metabolic reaction network. Thus, it can be a useful first-line tool of data analysis, model diagnostics and aid the design of next-step experiments.

A continuous-flow recirculation mode, generally called a recycle mode, is known to be practically meaningless except when the reactant is separated from the product at the reactor exit or when the reaction is autocatalytic, because when simply circulating a small amount of the fluid containing a reactant, the reactant concentration in this mode is lowered due to mixing of the fluid at the reactor entrance, leading to a decrease in the conversion at the reactor exit. This mode may, however, be meaningful in photocatalytic reactions with very large film-diffusional resistance. To indicate the validity of this estimation, therefore, characteristics of a continuous-flow recirculation reactor have been investigated both theoretically and experimentally. As a result, it is found that by increasing the circulation flow rate the conversion and productivity in this reactor is higher than that in a continuous-flow reactor because the film-diffusional resistance is remarkably reduced. Copyright © 2006 Society of Chemical Industry

To develop a high-performance photocatalytic reactor for purification of indoor air, the photocatalytic decomposition of gaseous HCHO at a very low concentration is investigated both theoretically and experimentally. In this second paper, a photocatalytic reactor with a parallel array of nine light sources, designed on the basis of the experimental result in the first paper, is applied to the air containing HCHO at an indoor concentration level and the reactor performance is discussed. The experimental result indicates that this photocatalytic reactor can rapidly decompose HCHO toward zero concentration. The reason for this high reactor performance is explained by a mathematical model that takes into consideration a film-diffusional resistance in the neighborhood of the photocatalyst as follows: (1) the reaction field is irradiated with a high light intensity because the distance between the light source and photocatalyst surface is only 6 mm; (2) the rate of decomposition is increased by the UV light that permeates through a glass tube; (3) the film-diffusional resistance is remarkably reduced because of a high linear velocity (709 m min −1 ).

We recently found that photocatalytic reactions produce H2O2 at a concentration level of ppm (parts per million) from water. For some reason, however, other researchers have paid little attention to the formation of H2O2 in this reaction. Of course, one of the reasons is due to low sensitivities of the conventional methods employed to measure the H2O2 concentration. However, we suppose that there is another reason which makes it difficult to measure it. To elucidate this reason, therefore, an effect of linear liquid velocity on the photocatalytic formation of H2O2 from water is experimentally investigated, and an explanation for the experimental result is made using a mathematical model that takes into consideration the formation and decomposition of H2O2 and its diffusion through a film in the neighborhood of the photocatalyst surface into a bulk liquid. This effect is also discussed on the formation of H2O2 from an aqueous solution of formic acid. As a result, it is concluded that the diffusion film is ...

Three kinds of metals (Pd, Cu, and Pt) have been photodeposited either individually or simultaneously on a transparent thin film of titanium dioxide (TiO2) that covers the inside surface of a Pyrex glass tube and the photocatalytic activities of these preparations have been investigated based on the oxidative decompositions of 2,4-dinitrophenol (DNP), formaldehyde (HCHO), and trichloroethylene (TCE) dissolved in aqueous solutions. The initial rate of DNP decomposition by Pd/TiO2 is 2.5 times higher than that by TiO2. Similarly, the initial rate of HCHO decomposition by Pd/TiO2 is increased by 5.1 times. Such remarkable enhancements in the photocatalytic decompositions are also obtained with Pd–Cu/TiO2 and Pd–Cu–Pt/TiO2. Furthermore, Pd/TiO2 is effective to promote the photocatalytic decomposition of TCE. This is different from the experimental result that was recently reported by other researchers, who used Pd/TiO 2 particles in the form of aqueous slurries. Microscopic observations of the metals deposited on the TiO2 films reveal that the morphologies of the metal-photodepositing TiO2 preparations are remarkably different from that of the TiO2 film; each metal possesses its own coating pattern. A series of the photocatalytic reaction experiments indicate that the photocatalytic activities of the metal-depositing TiO 2 preparations are superior to that of the TiO2 film and are highly stable. © 2003 Elsevier B.V. All rights reserved.

To characterize the formation of H2O2 in photocatalytic reactions, HCHO and HCOOH have been photocatalytically decomposed by use of TiO2 and Pd/TiO2 under irradiation with the UV light emitted from a blacklight blue fluorescent lamp (BL) or germicidal lamp (GL). An enzymatic method has been introduced to accurately measure the H2O2 concentration. The photocatalyst irradiated with the UV light emitted from the GL produces H2O2 from water at a larger rate and amount. Deposition of Pd on TiO2 increases the rate and amount of the formation of H2O2 from water. In the absence of the photocatalyst, no HCOOH is decomposed under irradiations with both the UV lights from the BL and GL, whereas the decomposition becomes possible in the presence of the photocatalyst. H2O2 is formed in parallel with the photocatalytic decomposition of HCOOH. In the presence of the photocatalyst, the concentration of the H2O2 formed during the decomposition of HCHO is smaller than that formed from water alone. In contrast, this relatio...

A novel air-purification system, consisting of the photocatalytic reactor with a parallel array of blacklight blue fluorescent lamps and the continuous adsorption and desorption apparatus with a cylindrical ceramic-paper honeycomb rotor retaining activated carbon or zeolite fine particles, was constructed and the performance of this system was investigated for treatment of gaseous HCHO at a concentration level of ppbv ( mg m −3 ) in a 10 m 3 highly tight closed room. With the zeolite rotor, it was very difficult to desorb the adsorbed HCHO by exposing the rotor to heated air and then to photocatalytically decompose the desorbed HCHO. In contrast, the activated carbon rotor provided an excellent performance. With this rotor, the indoor HCHO concentration was reduced to the neighborhood of the WHO guideline (0.1 mg m −3 ) in 10 min and to an almost zero value in 90 min . Needless to say, this surprisingly high performance is owing to the cooperative work by the activated carbon rotor to adsorb the indoor HCHO and the photocatalytic reactor to rapidly decompose the HCHO desorbed by heating the rotor. This system offers several other advantages. The adsorption rotor can be used semi-permanently because it is continuously regenerated. In addition, the HCHO adsorbed on the activated carbon rotor is readily released at a desorption temperature of 120°C. Under such a low temperature condition, little loss in the photocatalytic activity was caused.

A synergistic effect of photocatalysis and ozonation on the decomposition of formic acid dissolving in an aqueous solution has been studied. In the photocatalysis over a thin film of titanium oxide immobilized on the inner surface of a glass tube, a 6 W blacklight blue fluorescent lamp (wavelength: 300–400 nm) was used as a light source. The initial decomposition rates followed a Langmuir–Hinshelwood type and the hydrogen peroxide generated during the photocatalytic reaction played an important role in the decomposition of formic acid. In the ozonation, a 6 W low-pressure mercury lamp (wavelength: 185 nm) was used to produce ozone by irradiation of the air with UV. When this air was circulated in a closed system with a water-holding glass container, the ozone concentrations in the air and water reached 0.350 g m −3 air and 0.037 g m −3 liquid, respectively, at maximum. The decomposition rate of formic acid by ozone was higher for a lower liquid temperature and a higher pH value. For comparison, the Langmuir–Hinshelwood type was also used to analyze both the experimental values obtained in the ozonation alone and in the combination of photocatalysis and ozonation. A relationship between the reaction rate and reactant concentration was calculated using the kinetic parameters determined from the experimental values in each reaction system. As a result, the decomposition rate of formic acid by the combination of photocatalysis and ozonation was found to be 31% higher at maximum than the sum of the decomposition rates when formic acid was individually decomposed by the two methods, which indicates the presence of a synergistic effect of the photocatalysis and ozonation. This effect may be explained by the promoted production of hydroxyl radicals by ozone over titanium oxide.

The analysis of immobilized enzyme reactions leads to a two-point boundary value problem that requires numerical solutions based on root-finding methods. The standard Newton-Raphson (N-R) algorithm is adequate if the root-finding is initiated close to the true solution; in other cases, large numbers of iterations may be needed before the algorithm converges. An alternative is a root-finding method based on the theory of S-systems. This method turns out to be much more robust and efficient than the N-R algorithm. It converges quadratically, with fewer iterations, and in a wider range of relevant initial values. An investigation of a simpler algebraic equation with a similar mathematical structure demonstrates that the rate of convergence in the S-system method is not very sensitive to the distance between the root and initial value, whereas convergence of the N-R algorithm slows down drastically with increasing distance.

A variable-order, variable-step Taylor-series method in Cartesian space is discussed which makes it possible to solve simultaneous first-order differential equations expressed in GMA-system canonical form with a super high-order accuracy that is comparable to the machine accuracy of the computer. In this method, the stepsize for each differential equation is calculated from the formula derived by setting the ratio of the appropriate two terms of the first few Taylor-series terms at unity, and a minimum value of them is then used as the initial value of the stepsize at each step of the integration and is halved if several criterions are satisfied. Also, when each dependent variable takes a value near zero, the integration is carried out with a very small stepsize. The Taylor-series method constructed here is first applied to the Lotka-Volterra equation to confirm the validity of the calculation algorithm and it is found that the calculated values completely agree with those by the conventional method in which the Taylor-series solution in logarithmic space is used. Second, the differential equation with a solution of cos(t) is solved and the relative error is found to instantaneously increase when the dependent variables take a value near zero and becomes equal to zero or almost zero in the other region. Finally, the differential equation for a two-body problem is solved and it is shown that the accuracies of the calculated values are kept at high levels even after integration over 625 cycles. In conclusion, the Taylor-series method constructed in Cartesian space is considered to have high applicability to simultaneous differential equations and provides high accuracies for the calculated values.

The performance of a photocatalytic reactor system with a parallel array of four 6 W blacklight blue fluorescent lamps (wavelength: 300–400 nm) was investigated, based on the decomposition of formic acid in an aqueous solution. An aqueous solution of formic acid (7.8–22.0 gm−3) was recirculated between the photocatalytic reactor and perfectly-mixed flow container. The results show that the UV-light that penetrated through the wall of a glass tube and then passed through the flowing liquid solution accelerated the photocatalytic reaction occurring on the neighboring glass tubes, which greatly contributed to an increase in the reactor activity. This confirms that the arrangement of several light sources in parallel which uses effectively a three-dimensional space can lead to increased reactor activity and an increase in decomposition rates. A significant reduction in the reaction rate due to a film-diffusional resistance in the vicinity of the titanium dioxide film was observed. © 2002 Society of Chemical Industry