Substrate-limited Conditions Research Articles

Application of a backwashing strategy based on transmembrane pressure set-point in a tertiary submerged membrane bioreactor

An alternative backwashing strategy to enhance water productivity in a tertiary submerged membrane bioreactor (MBR) was assayed. This strategy is based on automatically adjustment of the backwashing frequency as a function of the membrane fouling, which is expected to increase the net permeate flux produced. The effect of the key operational parameter (transmembrane pressure set-point, TMPsp) on membrane fouling and process productivity was evaluated on a pilot-scale tertiary MBR. The system was successfully operated for over 4 months with complete sludge retention achieving a high treatment performance with a moderate liquor suspended solid concentration, as a result of carbon substrate limited conditions. The analysis of the membrane fouling at supra-critical filtrate flux of 70L/(hm2) with a specific aeration demand identical to that usual at full-scale (SADpnet=17Nm3/m3) showed that backwashing efficiency (described in terms of residual fouling resistance) was significantly affected by the selected TMPsp value. At high TMPsp, the efficiency decreased and chemical cleaning was necessary for membrane recovery. Nevertheless, moderate set-point values (30–40kPa) provided high permeate net fluxes of 65–67L/(hm2) for more than 2000h of operation, while the reversible fouling rate was not considerably influenced by TMPsp. This was also confirmed by flux steps trials.

Removal of nitrogen and phosphorus from municipal wastewater effluent using Chlorella vulgaris and its growth kinetics

Chlorella vulgaris was used for the removal of residual ammonia/ammonium ion (NH3/) and orthophosphate ion () from secondary wastewater effluent collected from a municipal wastewater treatment plant. The uptake rates for nitrogen and phosphorus were studied with different initial algal cell densities and the addition of CO2 gas for pH control and supply of inorganic carbon. Our result showed that typical NH3/ and concentrations could be readily removed within 48 h. It was found that the culture with an initial algal cell density of ∼350 mg/L and CO2 gas supply could significantly enhance both the rates of cell growth and nutrient uptake. The Monod equation well described the algal cell growth under substrate-limiting conditions, and could be used for the design and operation of photobioreactors for potential tertiary wastewater treatment.

Influence of hydrodynamics on the growth kinetics of glass-adhering Pseudomonas putida cells through a parallel plate flow chamber.

The objective of this work was to investigate the influence of hydrodynamics on the growth kinetics of surface-adhering Pseudomonas putida cells. The results showed in particular that under non substrate-limiting conditions, the early step of bacterial apparent growth rate is lower than those measured with suspended cells. Contrary to previously cited authors which explain this behavior to the different adhesive properties of the "daughter"-cells (which makes more probable the detachment of these daughter-cells), in our experimental conditions, that explanation does not hold and we show a clear dependence of growth kinetics with flow conditions, due to the formation of boundary layer concentration at low Reynolds number. These results revealed that using Monod law in the modeling of biofilm growth in fixed-biomass processes should be performed with care.

Distribution of nitrous oxide dissolved in water masses in the eastern subtropical North Pacific and its origin inferred from isotopomer analysis

N2O concentration and its isotopomer ratios were measured over a wide area from San Diego to Honolulu in the eastern subtropical North Pacific (ESNP). Waters in the study area had an N2O maximum (38.2–50.5 nmol kg−1) at 600–1000 m depth, which is similar to the profiles obtained previously in other areas in the North Pacific. We separated the seawater into five water masses (two for the surface layer, two for the middle layer, and one for the deep layer) and deduced N2O production–consumption mechanisms in each water body by use of N2O isotopomer ratios. The results showed that the mechanisms differ slightly among water masses. In the “coastal” surface layer, N2O is produced by nitrification (NH2OH oxidation). In the “open ocean” surface layer, it is produced mainly by nitrifier denitrification and to a lesser extent by nitrification under substrate-limited conditions. In both “upwelling” and “open ocean” middle layers it is produced mainly by denitrification and to a lesser extent by nitrifier denitrification. It is also partly reduced. In the deep layer, it is produced predominantly by denitrification with partial reduction. In this way, isotopomers aid elucidation of production–consumption mechanisms of N2O in the sea even though the mechanisms cannot always be ascertained.

L-citrulline supplementation reverses the impaired airway relaxation in neonatal rats exposed to hyperoxia

BackgroundHyperoxia is shown to impair airway relaxation via limiting L-arginine bioavailability to nitric oxide synthase (NOS) and reducing NO production as a consequence. L-arginine can also be synthesized by L-citrulline recycling. The role of L-citrulline supplementation was investigated in the reversing of hyperoxia-induced impaired relaxation of rat tracheal smooth muscle (TSM).MethodsElectrical field stimulation (EFS, 2–20 V)-induced relaxation was measured under in vitro conditions in preconstricted tracheal preparations obtained from 12 day old rat pups exposed to room air or hyperoxia (>95% oxygen) for 7 days supplemented with L-citrulline or saline (in vitro or in vivo). The role of the L-citrulline/L-arginine cycle under basal conditions was studied by incubation of preparations in the presence of argininosuccinate synthase (ASS) inhibitor [α-methyl-D, L-aspartate, 1 mM] or argininosuccinate lyase inhibitor (ASL) succinate (1 mM) and/or NOS inhibitor [Nω-nitro-L-arginine methyl ester; 100 μM] with respect to the presence or absence of L-citrulline (2 mM).ResultsHyperoxia impaired the EFS-induced relaxation of TSM as compared to room air control (p < 0.001; 0.5 ± 0.1% at 2 V to 50.6 ± 5.7% at 20 V in hyperoxic group: 0.7 ± 0.2 at 2 V to 80.0 ± 5.6% at 20 V in room air group). Inhibition of ASS or ASL, and L-citrulline supplementation did not affect relaxation responses under basal conditions. However, inhibition of NOS significantly reduced relaxation responses (p < 0.001), which were restored to control level by L-citrulline. L-citrulline supplementation in vivo and in vitro also reversed the hyperoxia-impaired relaxation. The differences were significant (p <0.001; 0.8 ± 0.3% at 2 V to 47.1 ± 4.1% at 20 V without L-citrulline; 0.9 ± 0.3% at 2 V to 68.2 ± 4.8% at 20 V with L-citrulline). Inhibition of ASS or ASL prevented this effect of L-citrulline.ConclusionThe results indicate the presence of an L-citrulline/L-arginine cycle in the airways of rat pups. L-citrulline recycling does not play a major role under basal conditions in airways, but it has an important role under conditions of substrate limitations to NOS as a source of L-arginine, and L-citrulline supplementation reverses the impaired relaxation of airways under hyperoxic conditions.

Microbial population analysis of nutrient removal-related organisms in membrane bioreactors

Membrane bioreactors (MBR) are an important and increasingly implemented wastewater treatment technology, which are operated at low food to microorganism ratios (F/M) and retain slow-growing organisms. Enhanced biological phosphorus removal (EBPR)-related organisms grow slower than ordinary heterotrophs, but have never been studied in detail in MBRs. This study presents a comprehensive analysis of the microorganisms involved in EBPR in pilot- and full-scale MBRs, using fluorescence in situ hybridization (FISH), as well as an overall assessment of other relevant microbial groups. The results showed that polyphosphate accumulating organisms (PAOs) were present at similar levels in all studied MBRs (10% ± 6%), even those without a defined anaerobic zone. Glycogen accumulating organisms were also detected, although rarely. The FISH results correlated well with the observed P removal performance of each plant. The results from this study suggest that a defined anaerobic zone is not necessarily required for putative PAO growth in MBRs, since polyphosphate storage may provide a selective advantage in fulfilling cell maintenance requirements in substrate-limited conditions (low F/M).

Aphids alter host-plant nitrogen isotope fractionation.

Plant sap-feeding insects and blood-feeding parasites are frequently depleted in (15)N relative to their diet. Unfortunately, most fluid-feeder/host nitrogen stable-isotope studies simply report stable-isotope signatures, but few attempt to elucidate the mechanism of isotopic trophic depletion. Here we address this deficit by investigating the nitrogen stable-isotope dynamics of a fluid-feeding herbivore-host plant system: the green peach aphid, Myzus persicae, feeding on multiple brassicaceous host plants. M. persicae was consistently more than 6‰ depleted in (15)N relative to their hosts, although aphid colonized plants were 1.5‰ to 2.0‰ enriched in (15)N relative to uncolonized control plants. Isotopic depletion of aphids relative to hosts was strongly related to host nitrogen content. We tested whether the concomitant aphid (15)N depletion and host (15)N enrichment was coupled by isotopic mass balance and determined that aphid (15)N depletion and host (15)N enrichment are uncoupled processes. We hypothesized that colonized plants would have higher nitrate reductase activity than uncolonized plants because previous studies had demonstrated that high nitrate reductase activity under substrate-limiting conditions can result in increased plant δ(15)N values. Consistent with our hypothesis, nitrate reductase activity in colonized plants was twice that of uncolonized plants. This study offers two important insights that are likely applicable to understanding nitrogen dynamics in fluid-feeder/host systems. First, isotopic separation of aphid and host depends on nitrogen availability. Second, aphid colonization alters host nitrogen metabolism and subsequently host nitrogen stable-isotope signature. Notably, this work establishes a metabolic framework for future hypothesis-driven studies focused on aphid manipulation of host nitrogen metabolism.

Complex metabolic network of glycerol fermentation by Klebsiella pneumoniae and its system identification via biological robustness

The bioconversion of glycerol to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae ( K. pneumoniae) can be characterized by an intricate metabolic network of interactions among biochemical fluxes, metabolic compounds, key enzymes and genetic regulation. Since there are some uncertain factors in the fermentation, especially the transport mechanisms of substances across cell membrane, the metabolic network contains multiple possible metabolic systems. In this paper, we establish a complex metabolic network and the corresponding nonlinear hybrid dynamical system aiming to determine the most possible metabolic system. The existence, uniqueness and continuity of solutions are discussed. We quantitatively describe biological robustness and present a system identification model on the basis of robustness performance. The identification problem is decomposed into two subproblems and a procedure is constructed to solve them. Numerical results show that it is most possible that both glycerol and 1,3-PD pass the cell membrane by active transport coupling with passive diffusion under substrate-sufficient conditions, whereas, under substrate-limited conditions, glycerol passes cell membrane by active transport coupling with passive diffusion and 1,3-PD by active transport.

A Nitrospira metagenome illuminates the physiology and evolution of globally important nitrite-oxidizing bacteria

Nitrospira are barely studied and mostly uncultured nitrite-oxidizing bacteria, which are, according to molecular data, among the most diverse and widespread nitrifiers in natural ecosystems and biological wastewater treatment. Here, environmental genomics was used to reconstruct the complete genome of "Candidatus Nitrospira defluvii" from an activated sludge enrichment culture. On the basis of this first-deciphered Nitrospira genome and of experimental data, we show that Ca. N. defluvii differs dramatically from other known nitrite oxidizers in the key enzyme nitrite oxidoreductase (NXR), in the composition of the respiratory chain, and in the pathway used for autotrophic carbon fixation, suggesting multiple independent evolution of chemolithoautotrophic nitrite oxidation. Adaptations of Ca. N. defluvii to substrate-limited conditions include an unusual periplasmic NXR, which is constitutively expressed, and pathways for the transport, oxidation, and assimilation of simple organic compounds that allow a mixotrophic lifestyle. The reverse tricarboxylic acid cycle as the pathway for CO2 fixation and the lack of most classical defense mechanisms against oxidative stress suggest that Nitrospira evolved from microaerophilic or even anaerobic ancestors. Unexpectedly, comparative genomic analyses indicate functionally significant lateral gene-transfer events between the genus Nitrospira and anaerobic ammonium-oxidizing planctomycetes, which share highly similar forms of NXR and other proteins reflecting that two key processes of the nitrogen cycle are evolutionarily connected.

Identification and Characterization of a Bacterial Transport System for the Uptake of Pyruvate, Propionate, and Acetate in Corynebacterium glutamicum

The metabolism of monocarboxylic acids is of central importance for bacteria in their natural habitat as well as during biotechnological production. Although biosynthesis and degradation are well understood, the transport of such compounds is still a matter of discussion. Here we present the identification and characterization of a new transport system in Corynebacterium glutamicum with high affinity for acetate and propionate and with lower affinity for pyruvate. Biochemical analysis of this monocarboxylic acid transporter (MctC) revealed for the first time a quantitative discrimination of passive diffusion and active transport of acetate by bacterial cells. MctC is a secondary transporter and belongs to the class of sodium solute symporters, but it is driven by the electrochemical proton potential. The mctC gene is preceded by and cotranscribed with cg0952, a locus encoding a small membrane protein, and the transcription of the cg0952-mctC operon is under the control of the transcriptional regulators RamA and RamB. Both of these proteins directly bind to the promoter region of the operon; RamA is essential for expression and RamB exerts a slightly negative control on expression of the cg0952-mctC operon. mctC expression is induced in the presence of pyruvate and beneficial under substrate-limiting conditions for C. glutamicum.

Fhit Interaction with Ferredoxin Reductase Triggers Generation of Reactive Oxygen Species and Apoptosis of Cancer Cells

Fhit protein is lost in most cancers, its restoration suppresses tumorigenicity, and virus-mediated FHIT gene therapy induces apoptosis and suppresses tumors in preclinical models. We have used protein cross-linking and proteomics methods to characterize a Fhit protein complex involved in triggering Fhit-mediated apoptosis. The complex includes Hsp60 and Hsp10 that mediate Fhit stability and may affect import into mitochondria, where it interacts with ferredoxin reductase, responsible for transferring electrons from NADPH to cytochrome P450 via ferredoxin. Viral-mediated Fhit restoration increases production of intracellular reactive oxygen species, followed by increased apoptosis of lung cancer cells under oxidative stress conditions; conversely, Fhit-negative cells escape apoptosis, carrying serious oxidative DNA damage that may contribute to an increased mutation rate. Characterization of Fhit interacting proteins has identified direct effectors of the Fhit-mediated apoptotic pathway that is lost in most cancers through loss of Fhit.

Complete Genome Sequence of Nitrosospira multiformis , an Ammonia-Oxidizing Bacterium from the Soil Environment

The complete genome of the ammonia-oxidizing bacterium Nitrosospira multiformis (ATCC 25196(T)) consists of a circular chromosome and three small plasmids totaling 3,234,309 bp and encoding 2,827 putative proteins. Of the 2,827 putative proteins, 2,026 proteins have predicted functions and 801 are without conserved functional domains, yet 747 of these have similarity to other predicted proteins in databases. Gene homologs from Nitrosomonas europaea and Nitrosomonas eutropha were the best match for 42% of the predicted genes in N. multiformis. The N. multiformis genome contains three nearly identical copies of amo and hao gene clusters as large repeats. The features of N. multiformis that distinguish it from N. europaea include the presence of gene clusters encoding urease and hydrogenase, a ribulose-bisphosphate carboxylase/oxygenase-encoding operon of distinctive structure and phylogeny, and a relatively small complement of genes related to Fe acquisition. Systems for synthesis of a pyoverdine-like siderophore and for acyl-homoserine lactone were unique to N. multiformis among the sequenced genomes of ammonia-oxidizing bacteria. Gene clusters encoding proteins associated with outer membrane and cell envelope functions, including transporters, porins, exopolysaccharide synthesis, capsule formation, and protein sorting/export, were abundant. Numerous sensory transduction and response regulator gene systems directed toward sensing of the extracellular environment are described. Gene clusters for glycogen, polyphosphate, and cyanophycin storage and utilization were identified, providing mechanisms for meeting energy requirements under substrate-limited conditions. The genome of N. multiformis encodes the core pathways for chemolithoautotrophy along with adaptations for surface growth and survival in soil environments.

Biodegradation dynamics of high catechol concentrations by Aspergillus awamori

The biodegradation process of high catechol concentrations by Aspergillus awamori was investigated. The values of the kinetic constants for a model of specific growth rate at different initial conditions were determined. At 1.0 g/L catechol concentration, the biodegradation process proceeded in the conditions of substrate limitation. At higher catechol concentrations (2.0 and 3.0 g/L) a presence of substrate inhibition was established. The dynamics of the specific catechol degradation rate was studied and the values of catechol and biomass concentrations, maximizing the specific catechol degradation rate, were estimated analytically. The specified ratio catechol/biomass could serve as a starting base for determination of the initial conditions for a batch process, for specifying the moment of feeding for a fed-batch process, and for monitoring and control of a continuous process by the aim of time-optimal control.

Translation attenuation by PERK balances ER glycoprotein synthesis with lipid-linked oligosaccharide flux

Endoplasmic reticulum (ER) homeostasis requires transfer and subsequent processing of the glycan Glc3Man9GlcNAc2 (G3M9Gn2) from the lipid-linked oligosaccharide (LLO) glucose3mannose9N-acetylglucosamine2-P-P-dolichol (G3M9Gn2-P-P-Dol) to asparaginyl residues of nascent glycoprotein precursor polypeptides. However, it is unclear how the ER is protected against dysfunction from abnormal accumulation of LLO intermediates and aberrant N-glycosylation, as occurs in certain metabolic diseases. In metazoans phosphorylation of eukaryotic initiation factor 2α (eIF2α) on Ser51 by PERK (PKR-like ER kinase), which is activated by ER stress, attenuates translation initiation. We use brief glucose deprivation to simulate LLO biosynthesis disorders, and show that attenuation of polypeptide synthesis by PERK promotes extension of LLO intermediates to G3M9Gn2-P-P-Dol under these substrate-limiting conditions, as well as counteract abnormal N-glycosylation. This simple mechanism requires eIF2α Ser51 phosphorylation by PERK, and is mimicked by agents that stimulate cytoplasmic stress-responsive Ser51 kinase activity. Thus, by sensing ER stress from defective glycosylation, PERK can restore ER homeostasis by balancing polypeptide synthesis with flux through the LLO pathway.

Functional characterization of the K257R and G319E-hGALE alleles found in patients with ostensibly peripheral epimerase deficiency galactosemia

Epimerase deficiency galactosemia is an autosomal recessive condition resulting from the impairment of UDP-galactose 4′-epimerase (hGALE). Although a small number of clinically severe patients have been reported who exhibit “generalized” GALE deficiency, the vast majority exhibit an apparently benign “peripheral” form of the disorder in which enzyme impairment is restricted to the circulating red and white blood cells. Previously, preliminary data were reported suggesting that GALE deficiency is 10-fold more common among African-Americans than among non-African-Americans, and that two missense mutations, K257R and G319E, are found in at least some of these patients. We report here functional studies of these alleles involving expression of the substituted human enzymes in a null-background strain of yeast. Although under normal assay conditions both substituted proteins demonstrate enzyme activities indistinguishable from the wild-type, one (G319E) demonstrates mild impairment under conditions of substrate limitation. No impairments are evident under conditions of cofactor (NAD) limitation. These results are consistent with the apparently benign status of peripheral epimerase deficiency galactosemia, but leave open the question of why patients with these substitutions demonstrate GALE deficiency in their red blood cells. While the possibility remains that K257R and G319E may cause tissue-specific impairments not recapitulated in vitro or in yeast, an equally if not more plausible explanation suggested by interspecies sequence alignments is that both substitutions may be polymorphisms that exist in linkage disequilibrium with other, as yet unidentified causal mutations.

Disposal of chloroplasts with abnormal function into the vacuole in Arabidopsis thaliana cotyledon cells.

Autophagy is a process in which cell membrane rearrangement allows for the sequestration and degradation of part of the cytoplasm. Many protein components of the autophagic mechanism and their corresponding genes have been identified in yeast cells by molecular genetics, and this has enabled researchers to identify homologues of these genes in mammalian and plant systems. Autophagy is involved in the starvation response in which part of the cytoplasm is degraded in order to produce essential substrates to allow the cell to survive during extreme substrate-limiting conditions. However, autophagy may also be important as a quality control mechanism in normal cells. By screening Arabidopsis thaliana T-DNA insert mutants, we isolated an A. thaliana mutant that lacks the AtTIC40 gene and found that the cotyledon cells of this mutant contained undeveloped plastids. Moreover, many toluidine-stained particulate structures were found in the vacuoles of these mutant cells. The images from electron microscopy suggested that some of these particulate structures were partially degraded chloroplasts. Furthermore, oil bodies were found in the cotyledon cells of mutant and wild-type plants, which suggests that the mutant seedlings were not "starved" under the experimental conditions. These results may indicate that under nutrient-sufficient conditions, plant cells remove abnormal plastids by autophagy and that this mechanism is involved in the quality control of organelles.

Simultaneous Removal of Volatile Organic Compounds (VOCs) and Nitrogen: Batch Test

A batch test was conducted to investigate the effect of the chemical oxygen demand, (COD)/N ratio, nitrate, nitrite and temperature, on the microbial degradation of volatile organic compounds (VOCs), and the denitrification capability using VOCs-acclimatized and un-acclimatized cultures. The nitrite reduction rates differed with each reactor, as follows: 15.418 NO2-N mg MLVSS g−1 h−1 in the benzene and methanol (BM) reactor, 27.463 NO2-N mg MLVSS g−1 h−1 in the toluene and methanol (TM) reactor and 44.358 NO2-N mg MLVSS g−1 h−1 in the methanol (M) reactor. According to the COD/N ratio, the nitrate reduction rates of the BM and TM reactors acclimatized by VOCs changed in the ranges of 29.4–33.41 NO3-N mg MLVSS g−1 day−1 and 56.4–65.9 NO3-N mg MLVSS g−1 day−1, respectively. Thus, benzene was not effectively utilized as a carbon source. Conversely, toluene was utilized as a carbon source by the denitrifiers under substrate limited conditions. The specific denitrification rates were also greater in the TM reactor than those for both the substrate limited and unlimited conditions in the BM reactor.

Analyses of microbial activity in biomass-recycle reactors using denaturing gradient gel electrophoresis of 16S rDNA and 16S rRNA PCR products.

The relationship between mixed microbial community structure and physiology when grown under substrate-limited conditions was investigated using continuous-flow bioreactors with 100% biomass recycle. Community structure was analyzed by denaturing gradient gel electrophoresis (DGGE) of the PCR and RT-PCR amplified V3 region of 16S rDNA and 16S rRNA templates, respectively. Comparisons were made of communities exposed to different types of transient conditions (e.g., long- and short-term starvation, increasing nutrients). With progressively more stringent substrate limitation over time, the specific content of community RNA declined by more than 10-fold and closely followed the decline in specific growth rate. In contrast, the DNA content was variable (up to 3-fold differences) and did not follow the same trend. Cluster analysis of the presence or absence of individual bands indicated that the fingerprints generated by the two templates were different, and community response was first observed in the rRNA fraction. However, both the rDNA and rRNA fingerprints provided a picture of temporal population dynamics. Dice similarity coefficients gave a quantitative measure of the differences and changes between the communities. In comparison, standard cultivation techniques yielded only a quarter of the phylotypes detected by DGGE, but included the most dominant population based on rRNA. Nucleotide-sequence analyses of the almost complete 16S rRNA genes of these isolates place them in the same group of organisms that is typically cultivated from environmental samples: alpha, beta, and gamma Proteobacteria and the high GC and the low GC Gram-positive divisions.

Interaction between catabolism and anabolism in the oxidative assimilation of dissolved organic carbon

Catabolism is tightly coupled to anabolism in substrate-limited cultures. However, the dissolved organic carbon (DOC) distribution between catabolism and anabolism has been hardly studied. Based on a balanced DOC reaction, the DOC distribution between catabolism and anabolism was defined using a ratio of the DOC channeled into CO2 (\(S_{CO_2 } \)) to that DOC converted to biomass (Sg). A \(S_{CO_2 } \)/Sg-dependent growth yield model was proposed for substrate-limited cultures and was verified using the literature data obtained in the oxidative assimilation processes of different types of organic substrates. The model showed that the growth yield (Ys) was proportional to anabolic activity, but was inversely related to catabolic activity. Results indicated that both Ys and \(S_{CO_2 } \)/Sg varied markedly with the free energy of oxidation of the organic substrate. Further, the observed phenomena were closely associated with maintenance metabolism under substrate-limited conditions.

Model of dissolved organic carbon distribution for substrate-sufficient continuous culture.

The growth yields (Yobs) are greater under substrate-limited conditions than those under substrate-sufficient conditions in continuous cultures. This indicates that the excess substrate should cause uncoupling between anabolism and catabolism. It appears that the excess substrate could determine metabolic pathways of microorganisms, which further control dissolved organic carbon (DOC) distribution under substrate-sufficient conditions. However, how to quantitatively describe the DOC distribution remains unclear in substrate-sufficient continuous culture. Based on a balanced DOC reaction, a DOC distribution model was developed in relation to residual substrate concentration for substrate-sufficient continuous cultures. Results showed that a considerable portion of the DOC consumed was directly oxidized to carbon dioxide through energy spilling under substrate-sufficient conditions. The proposed model for the first time quantified the DOC distribution between nongrowth-associated and growth-associated metabolisms of cells. The proposed model was verified with literature data very well.