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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.

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.

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.

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.

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.

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.

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

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.

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.

A numerical method for solving an axial dispersion model (two-point boundary value problem) with extremely high-order accuracy is presented. In this method, one first recasts fundamental differential equations into S-system (synergistic and saturable system) canonical form and then solves the resulting set of simultaneous first-order differential equations by the shooting method combined with a variable-order, variable-step Taylor series method. As a result, it is found that over wide ranges of systemic parameters (Peclet number, dimensionless kinetic constant, and reaction order), this method promises numerical solutions with the superhigh-order accuracy that is comparable to the machine accuracy of the computer used. The advantage of the numerical method is also discussed.

To establish a promising method for the purification of air containing volatile organic compounds, photocatalytic decompositions of gaseous acetaldehyde over TiO2 deposited on porous silica (TiO2/SiO2 catalyst) and over a platinized TiO2/SiO2 catalyst (Pt-TiO2/SiO2 catalyst) have been investigated including the capture of intermediates on the catalyst surface and regeneration of the deactivated catalyst by heating. Results of kinetic analysis show that these photocatalytic decompositions obey Langmuir-Hinshelwood kinetics. A comparison between the amounts of acetaldehyde decomposed and CO2 produced reveals that about 10 % of acetaldehyde is missing. From the observation of the photocatalyst surface before and after the reaction by FT-IR spectroscopy, we conclude that this is due to the adsorption of intermediates such as formic acid and acetic acid on the porous catalyst as well as deposition of coke-like substances. When the Pt-TiO2/SiO2 catalyst is heated to a temperature above 473 K, these substances can be removed and discharged as CO2. A series of results obtained in the present work suggests that the use of a Pt-TiO2/SiO2 catalyst will enable us to construct a multifunctional reaction process for air purification, in which volatile organic compounds are photocatalytically decomposed. The harmful intermediates formed during the reaction are partly adsorbed on the porous catalyst, remain in the reactor system, and together with deposited coke-like substances are converted into CO2 by heat treatment of the catalyst. The catalyst is thus regenerated.

A method for simultaneous treatment of an aqueous solution to photolytically sterilize microbial cells and photocatalytically decompose organic compounds was studied using an annular-flow photocatalytic reactor with a 6-W germicidal lamp (wavelength; 254 nm) as a light source. All the experiment were carried out in a batch recirculation mode. When a thin film of titanium oxide was located on the outer surface of a quartz glass tube, which was set to protect the germicidal lamp from direct contact with an aqueous solution flowing through the annulus, i.e. , when the photocatalyst was located at the inner surface of the annulus, the sterilization and decomposition slowed down. This is due to the fact that the degree of transparency of UV lights with wavelengths less 300 nm is significantly decreased by the film of titanium oxide. When the film of titanium oxide was located at the outer surface of the annulus, on the other hand, both the rates of sterilization and decomposition became higher. An experimental result using an aqueous solution containing E. coli and formaldehyde showed that the sterilization of E. coli is dependent on the circulation rate of the solution but the photocatalytic decomposition of formaldehyde is independent of it and can be approximated by a perfectly-mixed reactor model. Consequently, it was found that the annular-flow photocatalytic reactor used in the present work makes it possible to simultaneously carry out the photolytic sterilization of microbial cells and the photocatalytic decomposition of organic compounds.

The effect of electrostatic field on apparent kinetic parameters in a packed-bed immobilized enzyme reactor was investigated using a mathematical model. The relationship between the dimensionless concentration of substrate consumed in the reactor and the logarithm of the unconverted fraction of substrate at the reactor outlet was nonlinear and changed remarkably according to the magnitude of electrostatic potential and the sign of charges that carry the support and substrate. For the opposite sign of these charges, the apparent Michaelis constant was less than its intrinsic value in the region of high substrate concentration, which reflects a promoting effect on the enzyme reaction by the electrostatic attraction.

Recent development of high-throughput analytical techniques has made it possible to qualitatively identify a number of metabolites simultaneously. Correlation and multivariate analyses such as principal component analysis have been widely used to analyse those data and evaluate correlations among the metabolic profiles. However, these analyses cannot simultaneously carry out identification of metabolic reaction networks and prediction of dynamic behaviour of metabolites in the networks. The present study, therefore, proposes a new approach consisting of a combination of statistical technique and mathematical modelling approach to identify and predict a probable metabolic reaction network from time-series data of metabolite concentrations and simultaneously construct its mathematical model. Firstly, regression functions are fitted to experimental data by the locally estimated scatter plot smoothing method. Secondly, the fitted result is analysed by the bivariate Granger causality test to determine which metabolites cause the change in other metabolite concentrations and remove less related metabolites. Thirdly, S-system equations are formed by using the remaining metabolites within the framework of biochemical systems theory. Finally, parameters including rate constants and kinetic orders are estimated by the Levenberg-Marquardt algorithm. The estimation is iterated by setting insignificant kinetic orders at zero, i.e., removing insignificant metabolites. Consequently, a reaction network structure is identified and its mathematical model is obtained. Our approach is validated using a generic inhibition and activation model and its practical application is tested using a simplified model of the glycolysis of Lactococcus lactis MG1363, for which actual time-series data of metabolite concentrations are available. The results indicate the usefulness of our approach and suggest a probable pathway for the production of lactate and acetate. The results also indicate that the approach pinpoints a probable strong inhibition of lactate on the glycolysis pathway.

The design equation for a packed-bed immobilized enzyme reactor is expressed in terms of apparent kinetic parameters and the relationship between the exit concentration of substrate consumed and the logarithm of the exit unconverted fraction of substrate is studied. Agreement of calculated values with experimental data indicate that this relationship is not linear but is convex downward. Furthermore, simulation is made to characterize the apparent kinetic parameters. The results show that with increasing flow rates of a reaction mixture, the apparent kinetic parameters decrease rapidly towards their respective intrinsic values. As the entrance substrate concentration increases, on the other hand, these values initially increase, pass through maximums, and finally decrease towards their intrinsic values. These variations are found to occur remarkably with the apparent Michaelis constant.

流通式化学反応器に対する混合拡散モデルを, Lagrange型内挿式を直接微分して導いた式により計算した選点定数を使う修正型の直交選点法によって解き, 反応器の入口, 出口における反応物濃度を基準として数値解の精度を検討した.1次反応における解析解との比較から, Peclet数と反応速度定数が大きな厳しい条件下でも, 単純に選点数を増加させることにより, 倍精度計算において10桁以上の高精度解が得られることがわかった.この結果は, 直交選点法が, Peclet数の値の大きさに応じて適切な刻み幅を選択することが必要な差分法よりも優れていることを明らかに示す.

A novel numerical method for solving two-point boundary value problems is presented. This method utilizes a recasting technique for transformation of fundamental differential equations into S-system (synergistic and saturable system) canonical form that consists of a set of simultaneous first-order differential equations, an efficient computational algorithm that was proposed to numerically solve the S-system differential equations, and the shooting method. A two-point boundary value problem associated with an immobilized enzyme reaction was investigated as a model system, and it was found that the accuracy of numerical solutions obtained by the proposed method was almost the same as the accuracy of the computer. Another advantage of the proposed method is that it enables one to write a generalized computer program for two-point boundary value problems. With such a program, the user can solve different types of two-point boundary value problems by just imputing S-system parameters that are obtained by recasting their fundamental differential equations.

直交選点法における選点定数を効率よく計算するための方法について検討した.任意の階の選点定数を同一のサブルーチンで計算できるようにするため, それらの再帰性を利用した計算アルゴリズムを提出した.これにより得られた1階, 2階の選点定数の計算値は, 前報の方法による値と同様に高精度を持つことを確認した.また, 三角関数の微分値に対する近似の精度についての検討結果より, 本アルゴリズムが高階の選点定数の計算においてもうまく動作することを確認した.1組の選点定数を計算するのに必要な時間は従来法の時間とほぼ同じであった.

A novel numerical method, based on the combined Taylor series method with a technique for rapidly selecting suitable step sizes, is given for solving two-point boundary value problems. The differential equation for an immobilized enzyme reaction is considered as a model system. Comparisons between numerical and exact solutions for the first-order reaction show that the proposed method promises superhigh-order accuracy that is almost the same as machine accuracy over wide ranges of relevant parameters. The final value of the increment or decrement used to obtain a new estimate in the Newton-Raphson iterative scheme is found to be approximately the same as the relative error of the calculated value, which means that this final value is useful to predict the accuracy of a numerical solution of the differential equation that does not provide an analytical solution. Moreover, it is shown that the selected stepsizes are suitable values that cause little loss-of-significance errors.

Accuracies of the numerical solution of a two-point boundary value problem by the orthogonal collocation method are examined. The collocation constants for first and second derivatives are calculated by the matrix operation method (Method 1) and the method based on Lagrange’s interpolation formula (Method 2). Comparison of the calculated results shows that Method 1 produces marked loss-of-significance errors with increasing number of collocation points, N. These values are used to solve the two-point boundary value problem concerning an immobilized enzyme reaction, and then to calculate the effectiveness factor. These numerical solutions are compared with those of the previously proposed method that provides a numerical solution whose accuracy is almost the same as machine accuracy. It is found that Method 1 provides a numerical solution of significantly low accuracy under the condition of steep concentration gradient and this is never improved, even if N is increased, while Method 2 gives highly accurate values by simply increasing N. These tendencies are shown to depend strongly on the accuracies of the collocation constants.

The current model for the tricarboxylic acid cycle in Dictyostelium discoideum is based on extensive experimental studies of enzyme kinetics in vitro and of metabolite fluxes measured in vivo. In the previous papers (Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22912-22918; 22919-22925; 22926-22933; 22934-22943) of this series we have carried out extensive analyses of the current model within the framework of biochemical systems theory with a view toward understanding the behavior of the integrated system. The model was found to be ill determined with respect to at least three of its features. In this paper we propose a minimal modification in the model that is consistent with previous experimental data but also includes recycling of amino acids for protein synthesis, one of the neglected features identified as important in the previous analysis. We again perform an analysis within the framework of biochemical systems theory to determine the systemic consequences of this change. The results show that the robustness of the modified model, as determined by the parameter sensitivities, is improved by 2 orders of magnitude over that of the previous model. Analysis of the dynamics shows that the turnover times for the pools of alanine, glutamate, and aspartate are reduced by 2 orders of magnitude and made more physiologically realistic. The distribution of flux is no longer rigidly fixed, and problems previously centered on the metabolism of pyruvate have been partially alleviated. Continued discrepancies lead us to question the degree to which kinetic data obtained with purified enzymes in vitro faithfully reflect the kinetic behavior of the integrated enzyme system in vivo. We must continue to re-examine the manner in which the kinetics of reactions in vivo are represented and to reassess the physical conditions that prevail in vitro and in vivo. Results in this paper direct our attention toward specific aspects of the system where these efforts should be focused. Thus, a minimal modification of the previous model has led to several improvements that make it more representative of the tricarboxylic acid cycle in D. discoideum, and the analysis in this paper leads to further predictions for improving the model.

When kinetic models of complex biochemical systems are reconstructed from knowledge of the component reactions that have been characterized in vitro, or when values must be assumed for some of the parameters, errors are invariably encountered, and, as a consequence, the resulting model is frequently internally inconsistent. The simplest and most basic manifestations of such logical inconsistency are the failure of the model to exhibit a steady state or to yield a steady state that is in agreement with the actual steady state of the integrated system, or to yield a steady state that is dynamically stable. Models that are consistent may nonetheless be lacking in robustness, which is manifested as a pathological sensitivity to small changes in the values of their parameters. In this paper, we examine the current model of the tricarboxylic acid cycle in Dictyostelium discoideum (see Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22912-22918) with regard to these basic indicators of model quality. This may be viewed as a preliminary analysis; the object is to determine whether or not the model is reasonable and worthy of a more refined analysis and, if not, to diagnose the areas in need of modification before further analysis is undertaken. The results demonstrate that the current model of the tricarboxylic acid cycle is self-consistent and possesses a steady state that is in agreement with experimental evidence. However, the results also suggest that this model is not very robust. The high sensitivities of parameters influencing pyruvate metabolism indicate that the experimental characterization of these reactions might be fruitfully re-examined. These high sensitivities lead us to predict that this model of the tricarboxylic acid cycle should be accurate only over a very narrow range in variation of the independent variables. This is verified by the results presented in the following paper (Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22926-22933).

The examination of model robustness in the previous paper (Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22919-22925 led to the suggestion that the current model for the tricarboxylic acid cycle in Dictyostelium discoideum is ill-determined with respect to one or more of the features reflecting pyruvate metabolism. This conclusion is further supported here by results of steady state and dynamic analyses. The tricarboxylic acid cycle, according to the current model, is poised on a knife's edge with its behavior rigidly determined; any alteration of the system's components leads to nonviable behavior, as exemplified by explosive accumulation of pyruvate and loss of steady state in response to a minute change in the level of malate dehydrogenase. With the additional results in this paper, we are able to refine the diagnosis of the problem and suggest three different areas of the current model that might profitably be re-examined by experiment. These include the kinetics of the reactions at the malate branch point, the turnover times for the alanine, glutamate, and aspartate pools in vivo, and the dynamic mass balances for the cofactor NAD. We also suggest a minimal modification in the current model that could alleviate or circumvent some of these problems.

Enzyme systems within living cells have recently been shown to be highly ordered structures that violate classic assumptions of the Michaelis-Menten formalism, which originally was developed for the characterization of isolated reactions in vitro. This evidence suggests that a thorough examination of alternative kinetic formalisms for integrated biochemical systems is in order. The purpose of this series of papers is to assess the utility of an alternative power-law formalism by carrying out a detailed comparative analysis of a relatively large, representative system--the tricarboxylic acid cycle of Dictyostelium discoideum. This system was chosen because considerable experimental information already has been synthesized into a detailed kinetic model of the intact system. In this first paper, we set the stage for subsequent analysis within the framework of the power-law formalism: we review the underlying theory, emphasizing recent developments, formulate the model in terms that are convenient for the analysis to follow, and develop the system representation in both the Michaelis-Menten and power-law forms. In the second paper (Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22919-22925), these alternative representations are shown to be internally consistent and locally equivalent. The third paper (Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22926-22933) provides a complete analysis of the steady state behavior and also treats the dynamic behavior of the model.

拡散抵抗および静電場が影響する固定化酵素反応において, Sb/υ～Sbプロット曲線の接線の式に基づき, みかけの速度パラメーターV appm, K appmに対する式を誘導した.これらの式の妥当性は, みかけのMichaelis定数K appmに対する式を, 表面固定化酵素反応に対して他の研究者が提出した2つの近似式と比較することにより検証した.計算結果から, 基質濃度のV appm, K appmへの効果が表面および細孔内固定化酵素の両系で基本的に異なることがわかった.

充填層型固定化酵素反応器のみかけの速度パラメーターVmapp, Kmappへ及ぼす多孔性担体内の不均一活性分布の影響を理論的に検討した.Vmapp, Kmappは活性分布の型に関わらず外部拡散抵抗の増加とともに増大した.また, 反応器入口基質濃度への依存性も小さくなり, ほぼ一定となった.拡散抵抗や静電場の場合と同様に, 不均一酵素活性分布はKmappに大きな影響を及ぼした.

To determine the usefulness of equations previously proposed for the apparent maximum reaction rate and apparent Michaelis constant of an immobilized enzyme, starch hydrolysis by glucoamylase immobilized on a porous ceramic support was considered as a model system. Initial reaction rates, v0, were measured for a wide range of initial starch concentrations, Sb0, to make a nonlinear plot of Sb0/v0 versus Sb0, and the apparent kinetic parameters were determined from the slopes and intercepts of tangents to the nonlinear plot at given values of Sb0. The equations were found to accurately express the diffusional effect on the kinetic parameters.

A response to the comments by Lortie and Andre is given, and the usefulness of their methodology is considered. The need for simplification should be reconsidered in light of the remarkably improved ability of modern personal computers to perform numerical calculations.

セラミックモノリスに固定化したβ-アミラーゼと枝切り酵素 (プルラナーゼまたはイソアミラーゼ) による可溶性澱粉の加水分解反応を, pH 4.8.40℃において回分式反応器および流通式反応器を用いて行った.回分式反応は3個の固定化酵素モノリスをセットしたバスケット撹拌翼を使い, 外部拡散効果の無視できる条件下で反応液を撹拌することによって行った.まずマルトース収率の向上をはかるためセラミックモノリスへの効率のよい酵素固定化法を検討した.次にマルトース濃度の経時変化データに対して先の論文で検討した遊離の2酵素反応に対する反応速度式と細孔内拡散現象を組み合わせたモデル式を適用し, その適合性を調べた.流通式反応は固定化酵素モノリス10個を積み重ねた反応器を用いて行い, 5～100kg・m-3の濃度の澱粉を基質とする連続的なマルトース生産を検討した.その結果本固定化酵素モノリス反応器では効率よくマルトース生産が行われることが明らかになった.