Half-saturation Constant Research Articles

Modeling ethanol production through gas fermentation: a biothermodynamics and mass transfer-based hybrid model for microbial growth in a large-scale bubble column bioreactor

BackgroundEthanol production through fermentation of gas mixtures containing CO, CO2 and H2 has just started operating at commercial scale. However, quantitative schemes for understanding and predicting productivities, yields, mass transfer rates, gas flow profiles and detailed energy requirements have been lacking in literature; such are invaluable tools for process improvements and better systems design. The present study describes the construction of a hybrid model for simulating ethanol production inside a 700 m3 bubble column bioreactor fed with gas of two possible compositions, i.e., pure CO and a 3:1 mixture of H2 and CO2.ResultsEstimations made using the thermodynamics-based black-box model of microbial reactions on substrate threshold concentrations, biomass yields, as well as CO and H2 maximum specific uptake rates agreed reasonably well with data and observations reported in literature. According to the bioreactor simulation, there is a strong dependency of process performance on mass transfer rates. When mass transfer coefficients were estimated using a model developed from oxygen transfer to water, ethanol productivity reached 5.1 g L−1 h−1; when the H2/CO2 mixture is fed to the bioreactor, productivity of CO fermentation was 19% lower. Gas utilization reached 23 and 17% for H2/CO2 and CO fermentations, respectively. If mass transfer coefficients were 100% higher than those estimated, ethanol productivity and gas utilization may reach 9.4 g L−1 h−1 and 38% when feeding the H2/CO2 mixture at the same process conditions. The largest energetic requirements for a complete manufacturing plant were identified for gas compression and ethanol distillation, being higher for CO fermentation due to the production of CO2.ConclusionsThe thermodynamics-based black-box model of microbial reactions may be used to quantitatively assess and consolidate the diversity of reported data on CO, CO2 and H2 threshold concentrations, biomass yields, maximum substrate uptake rates, and half-saturation constants for CO and H2 for syngas fermentations by acetogenic bacteria. The maximization of ethanol productivity in the bioreactor may come with a cost: low gas utilization. Exploiting the model flexibility, multi-objective optimizations of bioreactor performance might reveal how process conditions and configurations could be adjusted to guide further process development.

Characterizing the biofilm stoichiometry and kinetics on the media in situ based on pulse-flow respirometer coupling with a new breathing reactor

Biofilm based systems and the hybrid between activated sludge and biofilms have been popularly applied for wastewater treatment. Unlike the suspended biomass, the biofilm concentration and kinetics on the media cannot be easily measured. In this study, a novel and easy-to-use approach has been developed based on pulse-flow respirometer to characterize the biofilm stoichiometry and kinetics in situ. With the new designed breathing reactor, the mutual interference between the magnetic stirring and biofilm media that happened in the conventional breathing reactor was solved. Moreover, Microsoft Excel based programs had been developed to fit the oxygen uptake rate curves with dynamic nonlinear regression. With this new approach, the yield coefficient, maximum oxidation capacity, and half-saturation constant of substrate for the heterotrophic biofilms in a fix bed reactor were determined to be 0.46 g-VSS/g-COD, 67.0 mg-COD/(h·L-media), and 4.4 mg-COD/L, respectively. Those parameters for biofilm ammonia oxidizers from a moving bed biofilm reactor were determined to be 0.17 g-VSS/g-N, 18.6 mg-N/(h·L-media), and 1.2 mg-N/L, respectively, and they were 0.11 g-VSS/g-N, 20.9 mg-N/(h·L-media), and 0.98 mg-N/L for nitrite oxidizers in the same biofilms. This study also found that the maximum specific substrate utilization rate for detached biofilms increased by 3.2 times, indicating that maintaining biofilm integrity was very important in the kinetic tests. Using this approach, the biofilm kinetics on the media can be regularly measured for treatment optimization.

Membrane Activity and Channel Formation of the Adenylate Cyclase Toxin (CyaA) of Bordetella pertussis in Lipid Bilayer Membranes.

The Gram-negative bacterium Bordetella pertussis is the cause of whooping cough. One of its pathogenicity factors is the adenylate cyclase toxin (CyaA) secreted by a Type I export system. The 1706 amino acid long CyaA (177 kDa) belongs to the continuously increasing family of repeat in toxin (RTX) toxins because it contains in its C-terminal half a high number of nine-residue tandem repeats. The protein exhibits cytotoxic and hemolytic activities that target primarily myeloid phagocytic cells expressing the αMβ2 integrin receptor (CD11b/CD18). CyaA represents an exception among RTX cytolysins because the first 400 amino acids from its N-terminal end possess a calmodulin-activated adenylate cyclase (AC) activity. The entry of the AC into target cells is not dependent on the receptor-mediated endocytosis pathway and penetrates directly across the cytoplasmic membrane of a variety of epithelial and immune effector cells. The hemolytic activity of CyaA is rather low, which may have to do with its rather low induced permeability change of target cells and its low conductance in lipid bilayer membranes. CyaA forms highly cation-selective channels in lipid bilayers that show a strong dependence on aqueous pH. The pore-forming activity of CyaA but not its single channel conductance is highly dependent on Ca2+ concentration with a half saturation constant of about 2 to 4 mM.

A steady-state modeling approach for simulation of antimicrobial peptide-cell membrane interaction

Antimicrobial Peptides (AMPs) are host defense molecules that initiate microbial death by binding to the membrane. On membrane binding, AMPs undergo changes in conformation and aggregation state to enable killing action. Depending on the AMP and cell membrane characteristics, the nature of binding can be aggregating or non-aggregating, with high/low cooperativity, at single or multiple sites with high/low affinity leading to a unique killing action that needs to be studied individually. In the present study, a steady-state model that simulates AMP-membrane interaction was developed and was used to predict the mechanism of AMP binding. The predictions obtained from the model were validated with experimentally deciphered values available in literature. The model was further used to predict the mechanism for a set of designed AMPs with high sequence similarity to Myeloid Antimicrobial Peptide (MAP) family. Depending on the predicted mechanism, a unique half saturation constant and steepness of response (Hill coefficient) was obtained which was further validated with available data from literature. The model could reliably predict the mechanism, the half saturation constant and the Hill coefficient values. Further based on the analysis, it was observed that aggregation and oligomerization result in drastic killing action in a short range of peptide concentration owing to high Hill coefficient values. Mechanisms such as monomers binding at multiple sites with/without cooperativity result in antimicrobial activity at low half saturation constant though the killing action may not be steep. Thus, the methodology developed here can be used to develop hypothesis for studying AMP-membrane interaction mechanisms.

Kinetic evaluation of a partially packed upflow anaerobic fixed film reactor treating low-strength synthetic rubber wastewater

A bench-scale model of a partially packed upflow anaerobic fixed film (UAF) reactor was set up and operated at five different hydraulic retention times (HRTs) of (17, 14, 10, 8, and 5) days. The reactor was fed with synthetic rubber wastewater consisting of a chemical oxygen demand (COD) concentration of 6355–6735 mg/L. The results were analyzed using the Monod model, the Modified Stover-Kincannon models, and the Grau Second-Order Model. The Grau Second-Order model was found to best fit the experimental data. The biokinetic constant values, namely the growth yield coefficient (Y) and the endogenous coefficient (Kd) were 0.027 g VSS/g COD and 0.1705 d−1, respectively. The half-saturation constant (Ks) and maximum substrate utilization rate (K) returned values of 84.1 mg/L and 0.371 d−1, respectively, whereas the maximum specific growth rate of the microorganism (μmax) was 0.011 d−1. The constants, Umax and KB, of the Stover-Kincannon model produced values of 6.57 g/L/d and 6.31 g/L/d, respectively. Meanwhile, the average second-order substrate removal rate, ks(2), was 105 d−1. These models gave high correlation coefficients with the value of R2 = 80–99% and these indicated that these models can be used in designing UAF reactor consequently predicting the behaviour of the reactor.

Application of photorespirometry to unravel algal kinetic parameters of nitrogen consumption in complex media

Photorespirometry is a quick method to assess the effect of several variables on algal growth performances in complex media such as wastewater. In this work, respirometry was applied to derive kinetic parameters of nitrogen exploitation. Oxygen production was found to be related to the internal nitrogen quota, suggesting that the Droop model is more appropriate to describe these systems. The protocol was optimized to minimize the internal N quota in the biomass used for the respirometric tests, so that the half-saturation constant of nutrient uptake could be simply derived. This parameter resulted similar (about 14 mgN L−1) for different nitrogen species (nitrate, ammonium, peptone and urea). The maximum uptake rate cannot be measured with respirometric tests, due to the different stoichiometry of nitrogen species, that affects the yield on oxygen production, but was measured through batch experiments. The preference of microalgae between nitrate and ammonium was ascertained in both batch and continuous reactors. In a continuous system, nitrate is partially removed even when ammonium is present, as a possible result of acclimation phenomena. Finally, mass balances were applied on the continuous systems to derive the value of minimum internal nitrogen quota, that resulted comparable when nitrate or ammonium was supplied.

Di-n-octyl phthalate degradation by a halotolerant bacterial consortium LF and its application in soil

ABSTRACT Di-n-octyl phthalate (DOP), a plasticizer used in many different industrial products, is a frequently observed pollutant in the environment. Biodegradation by microorganisms is considered to be a realistic choice for the remediation of DOP contamination. In the present research, the halotolerant bacterial consortium (LF) enriched in our previous research was used to degrade DOP. It was found that the optimal conditions for LF to degrade DOP was temperature 30oC, pH 6.0, inoculum size >5%, and salt content <3%. LF could degrade a high concentration of DOP (2000 mg/L) with the removal efficiency of 96.33%. Substrate inhibition analyses indicated that the inhibition constant, maximum specific degradation rate and half-saturation constant were 2544.6 mg/L, 0.7 d−1 and 59.1 mg/L, respectively. Based on the analysis of the gas chromatography-mass spectrometry (GC-MS), the biodegradation pathway for DOP by LF was proposed. Furthermore, LF could degrade DOP in soil (100 mg/kg) with the highest removal efficiency of 89.3%. This study is the first report on DOP biodegradation by bacterial consortium. These results suggest that LF can be used to remediate DOP-contaminated environment.

Biological purification of acidic Fenton effluent by a fungal consortium without pre-neutralization upon base addition: Microbial screening and performance

Great progresses have been made to carry out Fenton oxidation under neutral or alkaline pH in which, nevertheless, organic acids and other acidic intermediates usually result in acidic Fenton effluent. To eliminate the classical neutralization step prior to biological treatment, acid-tolerant microbes were here screened and used for purification of acidic Fenton effluent to achieve pH increase and further COD (chemical oxygen demand) removal. The bacterial and fungal community diversity was analyzed before and after screening for acid-tolerant microbes. After screening the bacterial diversity sharply decreased while the fungal diversity at the genus level became richer, mainly including Phialemoniopsis (relative abundance 38.69%), Vanrija (20.08%), Hypocreaceae (18.44%) and Candida (14.74%). Acidic pH and residual H2O2 are the features of Fenton effluent; hence, effects of pH and H2O2 on the screened acid-tolerant microbes were investigated in the aspects of growth rate and oxygen uptake rate. The kinetic parameters, including YH–biomass yield coefficient; Kd–biomass decay coefficient; μm–specific maximum COD removal rate; Ks–half saturation constant for COD removal, of the acid-tolerant microbes using 1/5 YM (yeast extract and malt extract culture medium) as substrate at 25 °C were measured by respirometric methodology. In BAC (biological activated carbon) inoculated with acid-tolerant microbes to treat actual Fenton effluent, the average COD removal efficiency was 72% at HRT (hydraulic retention time) of 3 h and the effluent pH was above 6 after removing the dissolved CO2 by air stripping. This study will provide a basis for developing a new combined process including Fenton and biological oxidation without pH adjustment.

Influential sources of uncertainty in glyphosate biochemical degradation in soil

Reactive transport models are important numerical tools to support decision making in many fields, such as herbicide use regulation. Though, models may be affected by multiple sources of uncertainty. Therefore, uncertainty and sensitivity analyses should become the practice to assess the confidence of such models. Here, the uncertainty in steady-state concentrations of glyphosate (GLP) and its metabolite aminomethylphosphonic acid (AMPA) was assessed using a reaction network that accounts for GLP and AMPA biotic and abiotic degradation pathways in soil including biological oxidation or hydrolysis in aerobic conditions via metabolic or cometabolic reactions. The mathematical framework is based on Michealis–Menten–Monod kinetic equations, which allow to account for microbial strategies to biodegrade contaminants. Chemical oxidation is assumed to occur independently from environmental conditions and resulted in a reduction of GLP concentration up to 15% when it was accounted for. The wide spectrum of interconnected catabolic reactions, each occurring at a different rate, as well as uncertainties in kinetic parameters estimation, suggest variability in modelling outcomes, which were addressed by means of a sensitivity analysis. In particular, the tested reaction network was mainly driven by GLP oxidation to AMPA; increasing the corresponding rate constant or decreasing the half-saturation constant resulted in a substantial decrease of GLP concentration but to an increase in AMPA concentration. Identification of the conditions responsible for GLP degradation to non-toxic metabolites, as well as for AMPA production and degradation, can allow to forecast unexpected consequences of GLP use and to design optimal land management and bioremediation plans.

Properties of main phytoplankton species of the Black Sea, determining the change in their dominance in annual dynamics

Using mathematical model, we tested three hypotheses of bloom regulation mechanisms for dominant phytoplankton species in the northeastern Black Sea. The model is based on the concept of intracellular regulation using the Droop equation, and values of the model constants that satisfy the conditions of domination are found. The bloom of the small-cell diatom Pseudo-nitzschia pseudodelicatissima is due to higher specific growth rates than other species in early spring. The half-saturation constants and minimum quotas for mineral nutrition elements (nitrogen and phosphorus) are also relatively high. In late spring and early summer, the bloom of coccolithophore Emiliania huxleyi is usually recorded. Prerequisites are a low half-saturation constant for nitrogen uptake and minimum quota for this nutrient. The third mechanism gains strength in the summer with the deepening of seasonal thermocline and the dominance of large-cell diatoms. It was shown that for the supremacy of large diatom Proboscia alata, it is necessary to have low half-saturation constants for the phosphorus uptake and minimum quotas for this nutrient.

Harvesting in tri-trophic food chain stabilises the chaotic dynamics-conclusion drawn from Hastings and Powell model

The paper explores a tri-trophic food chain model with harvesting in the species. The curiosity of this paper is to observe chaotic dynamics and its control. We perform the local stability analysis of the equilibrium points. The Hopf bifurcation analysis and global stability around the interior equilibrium point are also performed. Our numerical simulations reveal that the three species food chain model induces chaos from period-doubling, limit cycle and stable focus for increasing values of half saturation constant. We conclude that chaotic dynamics can be controlled by the harvesting parameter. We apply basic tools of non-linear dynamics such as Poincare section and Lyapunov exponent to identify chaotic behaviour of the system.

Harvesting in tri-trophic food chain stabilises the chaotic dynamics-conclusion drawn from Hastings and Powell model

The paper explores a tri-trophic food chain model with harvesting in the species. The curiosity of this paper is to observe chaotic dynamics and its control. We perform the local stability analysis of the equilibrium points. The Hopf bifurcation analysis and global stability around the interior equilibrium point are also performed. Our numerical simulations reveal that the three species food chain model induces chaos from period-doubling, limit cycle and stable focus for increasing values of half saturation constant. We conclude that chaotic dynamics can be controlled by the harvesting parameter. We apply basic tools of non-linear dynamics such as Poincare section and Lyapunov exponent to identify chaotic behaviour of the system.

Responses of C-, N- and P-acquiring hydrolases to P and N fertilizers in a subtropical Chinese fir plantation depend on soil depth

Large amounts of carbon (C), nitrogen (N) and phosphorus (P) in soil are stored in forms that are not bioavailable unless they are modified by hydrolytic enzymes. The activity of hydrolases is affected directly and indirectly by fertilizers treated, but the effects depend on soil depth. We collected soil core (0–80 cm depth) from fertilized and unfertilized (control) plots in a subtropical Chinese fir plantation. The soil with fertilizers had been treated for five years with either N (50 kg N ha−1 yr−1), P (50 kg P ha−1 yr−1) or N and P together. The kinetics of three hydrolases (β-1,4-glucosidase (βGluc), β-1,4-N-acetylglucosaminidase (NAG) and acid phosphatase (Phos)) were measured, and their potential activities (Vmax), half-saturation constants (Km), and enzyme efficiencies (Vmax/Km) were calculated for 0–10 cm, 10–20 cm, 20–40 cm, 40–60 cm, and 60–80 cm soil depth increments. The effect of depth on enzyme kinetics was greater than fertilizers treated. Smaller soil organic carbon (SOC) contents were related to the stable efficiencies of NAG and Phos from 0 to 60 cm in the control plots. In general, decreases in SOC content with depth triggered the production of enzymes with low Km (i.e. high substrate affinity). The minimum and maximum decreases in the Km of βGluc, NAG and Phos were 0%, 22% and 64% in the top 20 cm and 30%, 54% and 79% at 80 cm depth, respectively, compared to 0–10 cm soil depth. Nitrogen fertilizer downregulated NAG production without changing Km with soil depth, leading to decreased Vmax and Vmax/Km compared to the control. Responses of Phos to P and NP fertilizers depended on soil organic matter (SOM) and available P contents. Relative to the control, the Phos Vmax decreased in the top 10 cm, increased between 10 and 40 cm, and lack of difference between 40 and 80 cm in the P- and NP-treated soils. The Vmax and Vmax/Km of βGluc increased by P fertilizers between 60 and 80 cm compared to the control, indicating microbial mobilization of P from SOM to meet energy and C requirements in nutrient-poor subsoil. We conclude that limitations in microbial activity caused by decreases in SOM with depth with N and P fertilizers Chinese fir plantations are offset by the production of more efficient enzymes. However, longer term management to build SOM in tree plantations is required to prevent further soil degradation and loss of productivity.

Ammonia Oxidizing Bacteria (AOB) kinetic parameters estimated using the actual maximum ammonia oxidation rate

The objective of this paper was to define a new and reliable approach to the Ammonia Oxidizing Bacteria kinetic parameters estimation process. The proposed approach is based on the use of the information provided by a continuous on-line differential titrimeter developed for the estimation of the Actual Maximum Ammonia Oxidation Rate. The instrument was tested in a 200000 p.e. WRRF (Water Resources Recovery Facility) treating urban and industrial (textile) sewage wastewater and truck-transported liquid wastes in the Tuscan textile district (Italy). Maximum Ammonia Oxidation Rate was used as an innovative data series for maximum specific growth rate (μmaxAOB) and decay coefficient (bAOB) estimation. Titrimetric tests were conducted under non-limiting condition for oxygen and substrate and half-saturation constant of ammonia (KNH) was calibrated referring to the effluent quality of the WRRF. The proposed procedure allows to define a new kinetic parameters data set for AOB biomass (μmaxAOB = 0.72 d−1, bAOB = 0.25 d−1, KNH = 0.4 mg N–NH4+ L−1). The new data set was used to produce a new model that allows to improve the accuracy of the description of the process efficiency of the WRRF when compared with a model using kinetic parameters estimated through conventional methods.

Microbial degradation kinetics and molecular mechanism of 2,6-dichloro-4-nitrophenol by a Cupriavidus strain

2,6-Dichloro-4-nitrophenol (2,6-DCNP) is an emerging chlorinated nitroaromatic pollutant, and its fate in the environment is an important question. However, microorganisms with the ability to utilize 2,6-DCNP have not been reported. In this study, Cupriavidus sp. CNP-8 having been previously reported to degrade various halogenated nitrophenols, was verified to be also capable of degrading 2,6-DCNP. Biodegradation kinetics assay showed that it degraded 2,6-DCNP with the specific growth rate of 0.124 h−1, half saturation constant of 0.038 mM and inhibition constant of 0.42 mM. Real-time quantitative PCR analyses indicated that the hnp gene cluster was involved in the catabolism of 2,6-DCNP. The hnpA and hnpB gene products were purified to homogeneity by Ni-NTA chromatography. Enzymatic assays showed that HnpAB, a FAD-dependent two-component monooxygenase, converted 2,6-DCNP to 6-chlorohydroxyquinol with a Km of 3.9 ± 1.4 μM and a kcat/Km of 0.12 ± 0.04 μΜ−1 min−1. As the oxygenase component encoding gene, hnpA is necessary for CNP-8 to grow on 2,6-DCNP by gene knockout and complementation. The phylogenetic analysis showed that the hnp cluster originated from the cluster involved in the catabolism of chlorophenols rather than nitrophenols. To our knowledge, CNP-8 is the first bacterium with the ability to utilize 2,6-DCNP, and this study fills a gap in the microbial degradation mechanism of this pollutant at the molecular, biochemical and genetic levels. Moreover, strain CNP-8 could degrade three chlorinated nitrophenols rapidly from the synthetic wastewater, indicating its potential in the bioremediation of chlorinated nitrophenols polluted environments.

Characterisation of Pseudomonas stutzeri T13 for aerobic denitrification: Stoichiometry and reaction kinetics

The mechanism of total nitrogen (TN) removal at aerobic condition in wastewater treatment plants (WWTPs) has been one of the most popular research fields. However, the role of aerobic denitrification in TN removal was unclear because of the lack of stoichiometric coefficients and kinetic constants of aerobic denitrification bacterium. Thus, this study aimed to investigate the stoichiometry and kinetics of aerobic denitrification by using Pseudomonas stutzeri T13 as a model aerobic denitrification bacterium. Results indicated that strain T13 obtained the maximum yield coefficient (0.1098 mol biomass-N/mol COD) when using NH4+-N as the sole nitrogen source. This value decreased slightly (0.1077 mol biomass-N/mol COD) during aerobic denitrification, but was still higher than that of conventional denitrification. The half-saturation constants for ammonium, nitrate and nitrite (KNH4+, KNO3- and KNO2-) of strain T13 were fitted based on the experimental data and were 2.72, 18.33 and 209.07 mg/L, respectively. The validity of the stoichiometric coefficients and kinetic constants was tested at two extra conditions and perfect fitting results were obtained. To our knowledge, this is the first time to report the stoichiometric coefficients and kinetic constants of aerobic denitrification. These parameters will be useful in modelling nitrogen removal performance in systems inoculated with aerobic denitrification bacterium. Moreover, this study could provide an experimental basis for further clarifying the mechanism of aerobic denitrification from a quantitative perspective.

Specific affinity and relative abundance of methanogens in acclimated anaerobic sludge treating low-strength wastewater.

Kinetic parameters affecting effluent water quality including half saturation constant (Ks), maximum specific growth rate (μmax), and specific affinity ([Formula: see text], defined as μmax/Ks) were investigated using three types of anaerobic sludge (raw anaerobic digestion sludge referred to as unacclimated sludge, unacclimated sludge after endogenous decay, and sludge acclimated to low-strength wastewater in an anaerobic membrane bioreactor (AnMBR) for 360 days). Long-term acclimation to low-strength wastewater resulted in sludge with high specific affinity (1.6 × 10-3 L/mg COD/day for acclimated sludge compared to 4.1 × 10-4 L/mg COD/day for unacclimated sludge). The μmax values for unacclimated sludge and acclimated sludge were 0.08 and 0.07 day-1, respectively. The Ks values for unacclimated sludge and acclimated sludge were 194 ± 81 mg COD/L and 45 ± 13 mg COD/L, respectively. Although the Ks of unacclimated sludge after endogenous decay increased to 772 ± 74 mg COD/L, μmax increased to 0.35 day-1 as well, resulting in no statistically significant difference of [Formula: see text] between the two types of unacclimated sludge. Overall, [Formula: see text] is a better indicator than μmax or Ks alone for determining effluent water quality, as effluent substrate concentration is approximately inversely proportional to the specific affinity. 16S rRNA sequencing data analysis indicated a high abundance (85.8% of total archaea) of Methanosaeta in the microbial community after long-term acclimation. High [Formula: see text] associated with the enrichment of Methanosaeta appears to ensure successful anaerobic treatment of low-strength wastewater.

Prey–predator–scavenger model with Monod–Haldane type functional response

In this paper, we have developed a prey, predator and scavenger interaction dynamical model. The positivity, boundedness and stability conditions of our proposed system have been derived. Hopf bifurcation analysis has been done theoretically with respect to half saturation constant in the absence of direct measure of inhibitory effects $$(\phi _1)$$ . Also, we have numerically studied Hopf bifurcation with respect to direct effects of inhibitory effects $$(\phi _2)$$ related to Monod–Haldane type functional response, carrying capacity of prey $$(\gamma )$$ , death rate of scavenger $$(\mu )$$ , conservation rate of prey $$(\alpha )$$ and harvesting rate of predator $$(\eta )$$ . It is observed that the intra-species competition can lead our proposed system towards stability. It is also found that the harvesting of predator can control the chaotic dynamics of our proposed system. The increase of death rate of scavenger species can be stabilized our proposed system. Finally, some numerical simulation results have been presented for better understanding the dynamics of our proposed model.

Continuous Cultivation as a Method to Assess the Maximum Specific Growth Rate of Photosynthetic Organisms.

Modeling the growth of photosynthetic organisms is challenging, due to the complex role of light, which can be limiting because of self-shading, or photoinhibiting in the case of high intensities. A case of particular interest is represented by nitrogen-fixing cyanobacteria, whose growth is controlled not only by the light intensity, but also by the availability of atmospheric nitrogen in the liquid medium. The determination of the maximum specific growth rate is often affected by many variables that, in batch growth systems, may change significantly. On the other hand, in a continuous system, once the steady state is reached the values of all the process variables remain constant, including the biomass concentration and the specific light supply rate. In this work, the diazotrophic cyanobacterium Anabaena PCC 7122 was cultivated in continuous photobioreactors, to investigate the role of nitrogen, light and residence time on growth kinetics, and to retrieve the value of the maximum specific growth rate of this organism. In addition, the kinetic parameters for temperature and the half saturation constant for nitrogen (3 mg L−1) were measured by respirometric tests. Based on the results of continuous experiments, the specific maintenance rate was found to depend on the light intensity supplied to the reactor, ranging between 0.5 and 0.8 d−1. All these parameters were used to develop a kinetic model able to describe the biomass growth in autotrophic conditions. The maximum specific growth rate could hence be determined by applying the kinetic model in the material balances of the continuous photobioreactor, and resulted equal to 8.22 ± 0.69 d−1.

Competitor and substrate sizes and diffusion together define enzymatic depolymerization and microbial substrate uptake rates

Diffusion limitations of extracellular enzymes and soluble monomers have been recognized as important mechanisms controlling soil organic matter (SOM) dynamics. Here we combine diffusion limitation with the geometric sizes of extracellular enzymes, polymer particles, monomers, and bacterial cells to derive testable relationships of SOM kinetic parameters, including (1) maximum reaction rates and (2) binding half saturation constants (also known as substrate affinity parameters). We integrate the relevant mechanisms with the Equilibrium Chemistry Approximation (ECA) kinetics, which has been shown to reasonably represent these complex competitive interactions in soils, and then evaluate the reverse and forward Michaelis-Menten kinetics approximations under different conditions. We found: (1) due to the size contrast between larger organic polymer particles and smaller enzyme molecules, depolymerization is limited by the abundance of enzyme binding sites supplied by polymer particles, making the reverse Michaelis-Menten kinetics a better approximation to the ECA kinetics for depolymerization, and (2) due to the size contrast between larger microbial cells and smaller monomer molecules, monomer uptake is limited by accessible microbial cell transporters, making the forward Michaelis-Menten kinetics a better approximation to ECA kinetics for microbial monomer substrate uptake. These results may explain conflicting applications in the literature associated with using reverse and forward Michaelis-Menten kinetics to represent SOM dynamics. Further, the size contrast between litter particles and extracellular enzymes suggests that litter fragmentation by soil fauna and fungi is an important process to be included in models of organic matter decomposition and challenges soil enzyme assays to accurately measure enzyme abundances in order to properly derive the kinetic parameters.