Prediction of lipid accumulation-degradation in oleaginous micro-organisms growing on vegetable oils

Oleaginous micro-organisms (yeasts, moulds), in culture media having the carbon source as limited factor, degrade reserve lipids and produce new biomass, after the onset of carbon exhaustion from the medium. In this paper the process of lipid accumulation-degradation in oleaginous micro-organisms, growing on a vegatable oil was simulated. The model was integrated with 4 different methods and the parameters were optimised with the least squares method. It was found that the degradation of endocellular carbon pool is a very slow process characterised, however, by a good yield in fat-free biomass. Low values of the specific growth rates of the fat-free microbial mass, both from consumption of extra cellular and endocellular carbon pools, favourite the production of microbial lipid. The maximum of the specific rate of lipid accumulation is positively affected by the low values of the specific growth rate of the fat-free microbial mass from consumption of extra cellular carbon pool, but remained unaffected by the specific growth rate of the fat-free microbial mass from consumption of endocellular carbon pool. On the other hand, lipid production and specific rate of lipid accumulation are positively influenced by the high values of the specific rate of storage lipid formation. In conclusion, this numerical model can be used in the laboratory as pilot for planing further experimental work.     

Measurement and mathematical modelling of competition between fast- and slow-growing ordinary heterotrophic organisms in low and high substrate-loaded systems

Ordinary heterotrophic organisms (OHO) of an activated sludge wastewater treatment system showed an atypical growth behaviour when they are inoculated to batch aerobic growth tests with a high substrate-loaded condition. For example, the OHO maximum specific growth rates on readily biodegradable substrates (μ _H) increased with a high ratio of substrate concentration to OHO active biomass concentration (So/Xo), although they were assumed to be constant in a conventional microbial growth kinetic model with a single OHO population group. We, therefore, set a hypothesis in that the change of OHO maximum specific growth rates in the batch test condition is caused by turnover of fast-growing OHO population against slow-growing OHO population. And, a competitive microbial growth kinetic model of the fast- and slow-growing OHO population groups was developed and validated with model-data fitting analysis for the batch test results. The competitive microbial growth kinetic model of process selection, rather than that of kinetic selection, was capable of simulating microbial growth kinetics in high substrate-loaded dynamic systems (i.e., batch tests) and low substrate-loaded steady-state systems (i.e., continuously operated wastewater treatment systems), better than the conventional non-competitive growth kinetic model.     

A new hypothesis to explain the coexistence of n species in the presence of a single resource

This paper presents a hypothesis allowing us to explain the coexistence of several species (here micro-organisms) in competition on a single resource (called a substrate) in a chemostat. We introduce a new class of kinetics that does not only depend on the substrate concentration in the medium, but also on the biomass concentration. From the study of elementary interactions (i) between micro-organisms, (ii) between micro-organisms and their environment in which they grow and from simulations, we show that this modelling approach can be interpreted in terms of substrate diffusion phenomena. A rigorous study of this new class of models allows us to hypothesize that abiotic parameters can explain the fact that an arbitrarily large number of species can coexist in the presence of a unique substrate.     

Re-interpretation of the logistic equation for batch microbial growth in relation to Monod kinetics

Aims:  To determine the underlying substrate utilization mechanism in the logistic equation for batch microbial growth by revealing the relationship between the logistic and Monod kinetics. Also, to determine the logistic rate constant in terms of Monod kinetic constants.
Methods and Results:  The logistic equation used to describe batch microbial growth was related to the Monod kinetics and found to be first-order in terms of the substrate and biomass concentrations. The logistic equation constant was also related to the Monod kinetic constants. Similarly, the substrate utilization kinetic equations were derived by using the logistic growth equation and related to the Monod kinetics.
Conclusion:  It is revaled that the logistic growth equation is a special form of the Monod growth kinetics when substrate limitation is first-order with respect to the substrate concentration. The logistic rate constant ( k ) is directly proportional to the maximum specific growth rate constant ( μ _m) and initial substrate concentration ( S ₀) and also inversely related to the saturation constant ( K _s).
Significance and Impact of the Study:  The semi-empirical logistic equation can be used instead of Monod kinetics at low substrate concentrations to describe batch microbial growth using the relationship between the logistic rate constant and the Monod kinetic constants.     

A simple method for measuring fungal metabolic quotient and comparing carbon use efficiency of different isolates: Application to Mediterranean leaf litter fungi

The metabolic efficiency of different microbial groups in carbon source uses and single species storage efficiency is poorly characterised and not adequately represented in most biogeochemical models. It is proposed here a simple approach for an estimation of the metabolic quotient of fungal isolates. The method is based on the values of substrate use (respiration) and growth (biomass production) obtainable for single fungal isolates in vitro using the Phenotype MicroArray? system to test the metabolic performance of fungi on different substrates. As a case study, this carbon-use efficiency method was used to compare a group of leaf litter fungi. The metabolic efforts of single fungal species were measured on 95 different substrates of different complexity. The respiration to biomass ratio showed a high reliability and the possibility of being used as a measurable property of the micro-organisms and an indicator of organism’s performance or fitness.     

Chemical reaction- and particle diffusion-based kinetic modeling of metal biosorption by a Phormidium sp.-dominated cyanobacterial mat

The present study explores the suitability of chemical reaction-based and diffusion-based kinetic models for defining the biosorption of Cu(II), Cd(II) and Pb(II) by Phormidium sp.-dominated mat. The time-course data of metal sorption by the test mat significantly (r² = 0.932-0.999) fitted to the chemical reaction-based models namely pseudo-first-order, -second-order, and the general rate law. However, these models fail to accurately describe the kinetics of metal biosorption due either to prefixed order or unjustifiable change in rate constant and reaction order with varying concentrations of metal and biomass in the solution. The diffusion-based models, namely, the intra-particle diffusion model and the external mass transfer model fitted well to the time-course metal sorption data, thus suggesting involvement of both external and intra-particle diffusion processes in sorption of test metals by mat biomass. However, the Boyd kinetic expression clearly showed that the external mass transfer is the dominant process.     

Chronic effect of erythromycin on substrate biodegradation kinetics of activated sludge

This study evaluated the chronic impact of erythromycin, a macrolide antibiotic, on microbial activities, mainly focusing on changes in process kinetics induced on substrate biodegradation and all related biochemical processes of microbial metabolism. Experiments involved two fill/draw reactors sustained at steady state at two different sludge ages of 10 and 2.0 days, fed with peptone mixture and continuous erythromycin dosing of 50 mg/L. Oxygen uptake rate profiles were generated in a series of parallel batch reactors seeded with biomass from fill/draw systems at selected periods of steady-state operation. Experimental data were evaluated by model calibration reflecting inhibitory effect on process kinetics: continuous erythromycin dosing inhibited microbial growth, reduced the rate of hydrolysis, blocked substrate storage and accelerated endogenous respiration. Adverse impact was mainly due to changes inflicted on the composition of microbial community. Interruption of erythromycin feeding resulted in partial recovery of microbial response. Sludge age affected the nature of inhibition, indicating different process kinetics for faster growing microbial community. Kinetic evaluation additionally revealed the toxic effect of erythromycin, which inactivated a fraction of biomass. Mass balance using oxygen uptake rate data also identified a stoichiometric impact, where a fraction of available substrate, although completely removed, could not be utilized in metabolic activities.     

Modelling soil organic matter levels after long-term applications of crop residues,and farmyard and green manures

A computer simulation model for long-term soil organic matter dynamics was developed and evaluated with data from long-term field trials in Belgium, Germany and The Netherlands. The model distinguishes four pools of soil organic components (including a microbial biomass pool) with different chemical properties. Transformation rates are described by (pseudo) first order kinetics. Effects of temperature and soil moisture tension were included. Simulation results were in agreement with experimental data from arable farming practices where common input rates were applied. Model calculations overestimated soil organic matter levels when green manures or exceptionally high input rates were applied. Inadequate experimental estimations of organic matter input rates and insufficient modelling of the soil preservation capacity for organic matter and biomass are likely reasons. After changes in the soil organic matter-input management it may take more than a century to reach new equilibrium levels.     

A generalized compartmental model to estimate the fibre mass in the ruminoreticulum: 2. Integrating digestion and passage

Models used to predict digestibility and fill of the dietary insoluble fibre (NDF) treat the ruminoreticular particulate mass as a single pool. The underlying assumption is that escape of particles follows first-order kinetics. In this paper, we proposed and evaluated a model of two ruminoreticular sequential NDF pools. The first pool is formed by buoyant particles (raft pool) and the second one by fluid dispersed particles (escapable pool) ventrally to the raft. The transference of particles between these two pools results from several processes that reduce particles buoyancy, assuming the gamma distribution. The exit of escapable pool particles from the ruminoreticulum is exponentially distributed. These concepts were evaluated by comparing ruminoreticular NDF masses as 43 and 27 means from cattle and sheep, respectively, to the same predicted variable using single- and two-pools models. Predictions of the single-pool model were based on lignin turnover and the turnover associated to the descending phase of the elimination of Yb-labelled forage particles in the faeces of sheep. Predictions of the two-pool model were obtained by estimating fractional passage rates associated to the ascending and descending phases of the same Yb excretion profiles in sheep faeces. All turnovers were scaled to the power 0.25 of body mass for interspecies comparisons. Predictions based on lignin turnover (single pool) and the two-pool model presented similar trends, accuracies and precisions. The single-pool approach based solely on the descending phase of the marker yielded biased estimates of the ruminoreticular NDF mass.     

Effect of micro-organisms on the bioavailability and biodegradation of crystalline naphthalene

Bacterial growth on crystalline naphthalene was measured and found to be related to the dissolution rate of the substrate. No evidence for enhancement of substrate availability due to bacterial influence could be detected. Using a model based on dissolution kinetics for substrate availability and Monod kinetics for bacterial growth it was possible to simulate bacterial growth on naphthalene. This model is widely applicable for growth of micro-organisms on poorly water-soluble substrates and can easily be adapted to a more complex system such as microbial growth on substrates adsorbed to matrices. Correspondence to: F. Volkering     

Kinetics of bacterial processes in natural aquatic systems based on biomass as determined by high-resolution flow cytometry

The two primary kinetic constants for describing the concentration dependency of nutrient uptake by microorganisms are shown to be maximal rate of substrate uptake and, rather than the Michaelis constant for transport, specific affinity. Of the two, the specific affinity is more important for describing natural aquatic microbial processes because it can be used independently at small substrate concentrations. Flow cytometry was used to evaluate specific affinities in natural populations of aquatic bacteria because it gives a convenient measure of biomass, which is an essential measurement in the specific-affinity approach to microbial kinetics. Total biomass, biomass in various filter fractions, and the specific affinity of the bacteria in each fraction were determined in samples from a near-arctic lake. The partial growth rate of the pelagic bacteria from the 25 micrograms/liter of dissolved amino acids present (growth rate from the amino acid fraction alone) was determined to be 0.78 per day. By measuring activity in screened and whole-system populations, the biomass of the bacteria associated with particles was computed to be 427 micrograms/liter.     

Biodegradation kinetics of select polycyclic aromatic hydrocarbon (PAH) mixtures by <Emphasis Type="Italic">Sphingomonas paucimobilis</Emphasis> EPA505

Many contaminated sites commonly have complex mixtures of polycyclic aromatic hydrocarbons (PAHs) whose individual microbial biodegradation may be altered in mixtures. Biodegradation kinetics for fluorene, naphthalene, 1,5-dimethylnaphthalene and 1-methylfluorene were evaluated in sole substrate, binary and ternary systems using Sphingomonas paucimobilis EPA505. The first order rate constants for fluorene, naphthalene, 1,5-dimethylnaphthalene, and 1-methylfluorene were comparable; yet Monod parameters were significantly different for the tested PAHs. S. paucimobilis completely degraded all the components in binary and ternary mixtures; however, the initial degradation rates of individual components decreased in the presence of competitive PAHs. Results from the mixture experiments indicate competitive interactions, demonstrated mathematically. The generated model appropriately predicted the biodegradation kinetics in mixtures using parameter estimates from the sole substrate experiments, validating the hypothesis of a common rate-determining step. Biodegradation kinetics in mixtures were affected by the affinity coefficients of the co-occurring PAHs and mixture composition. Experiments with equal concentrations of substrates demonstrated the effect of concentration on competitive inhibition. Ternary experiments with naphthalene, 1,5-dimethylnaphthalene and 1-methylfluorene revealed delayed degradation, where depletion of naphthalene and 1,5-dimethylnapthalene occurred rapidly only after the complete removal of 1-methylfluorene. The substrate interactions observed in mixtures require a multisubstrate model to account for simultaneous degradation of substrates. PAH contaminated sites are far more complex than even ternary mixtures; however these studies clearly demonstrate the effect that interactions can have on individual chemical kinetics. Consequently, predicting natural or enhanced degradation of PAHs cannot be based on single compound kinetics as this assumption would likely overestimate the rate of disappearance.     

Simulation of nitrogen assimilation by heterotrophic soil microbial biomass

Assimilation of N by heterotrophic soil microbial biomass is associated with decomposition of organic matter in the soil. The form of N assimilated can be either low molecular weight organic N released from the breakdown of organic matter (direct assimilation), or NH⁺₄ and NO⁻₃ from the soil inorganic N pool, into which mineralized organic N is released (mineralization immobilization turnover). The kinetics of C and N turnover in soil is quantifiable by means of computer simulation models. NCSOIL was constructed to represent the two assimilation schemes. The rate of N assimilation depends on the rate of C assimilation and microbial C/N ratio, thereby rendering it independent of the assimilation scheme. However, if any of the N forms is labeled, a different amount of labeled N assimilation will be simulated by the different schemes. Experimental data on inorganic N and ¹⁵N and on organic ¹⁵N dynamics in soils incubated with ¹⁵N added as NH⁺₄ or organic N were compared with data simulated by different model schemes. Direct assimilation could not account for the amount of ¹⁵N assimilated in any of the experimental treatments. The best fit of the model to experimental data was obtained for the mineralization immobilization turnover scheme when both NH⁺₄ and NO⁻₃ were assimilated, in proportion to their concentration in the soil.     

Kinetics of soluble microbial product formation in substrate-sufficient batch culture of activated sludge

The kinetics of soluble microbial product (SMP) formation under substrate-sufficient conditions appear to exhibit different patterns from substrate-limited cultures. However, energy spilling-associated SMP formation is not taken into account in the existing kinetic models and classification of SMP. Based on the concepts of growth yield and energy uncoupling, a kinetic model describing energy spilling-associated SMP formation in relation to the ratio of initial substrate concentration to initial biomass concentration (S ₀/X ₀) was developed for substrate-sufficient batch culture of activated sludge, and was verified by experimental data. The specific rate of energy spilling-associated SMP formation showed an increasing trend with the S ₀/X ₀ ratio up to its maximum value. The SMP productivity coefficient (α _p/e) was defined from the model on the basis of energy spilling-associated substrate consumption. Results revealed that less than 5% of energy spilling-associated substrate consumption was converted into SMP. Electronic Publication     

Predicting microbial growth dynamics in response to nutrient availability

Developing mathematical models to accurately predict microbial growth dynamics remains a key challenge in ecology, evolution, biotechnology, and public health. To reproduce and grow, microbes need to take up essential nutrients from the environment, and mathematical models classically assume that the nutrient uptake rate is a saturating function of the nutrient concentration. In nature, microbes experience different levels of nutrient availability at all environmental scales, yet parameters shaping the nutrient uptake function are commonly estimated for a single initial nutrient concentration. This hampers the models from accurately capturing microbial dynamics when the environmental conditions change. To address this problem, we conduct growth experiments for a range of micro-organisms, including human fungal pathogens, baker’s yeast, and common coliform bacteria, and uncover the following patterns. We observed that the maximal nutrient uptake rate and biomass yield were both decreasing functions of initial nutrient concentration. While a functional form for the relationship between biomass yield and initial nutrient concentration has been previously derived from first metabolic principles, here we also derive the form of the relationship between maximal nutrient uptake rate and initial nutrient concentration. Incorporating these two functions into a model of microbial growth allows for variable growth parameters and enables us to substantially improve predictions for microbial dynamics in a range of initial nutrient concentrations, compared to keeping growth parameters fixed.     

Dimeric Eg5 maintains processivity through alternating-site catalysis with rate-limiting ATP hydrolysis

Eg5/KSP is a homotetrameric, Kinesin-5 family member whose ability to cross-link microtubules has associated it with mitotic spindle assembly and dynamics for chromosome segregation. Transient-state kinetic methodologies have been used to dissect the mechanochemical cycle of a dimeric motor, Eg5-513, to better understand the cooperative interactions that modulate processive stepping. Microtubule association, ADP release, and ATP binding are all fast steps in the pathway. However, the acid-quench analysis of the kinetics of ATP hydrolysis with substrate in excess of motor was unable to resolve a burst of product formation during the first turnover event. In addition, the kinetics of P(i) release and ATP-promoted microtubule-Eg5 dissociation were observed to be no faster than the rate of ATP hydrolysis. In combination the data suggest that dimeric Eg5 is the first kinesin motor identified to have a rate-limiting ATP hydrolysis step. Furthermore, several lines of evidence implicate alternating-site catalysis as the molecular mechanism underlying dimeric Eg5 processivity. Both mantATP binding and mantADP release transients are biphasic. Analysis of ATP hydrolysis through single turnover assays indicates a surprising substrate concentration dependence, where the observed rate is reduced by half when substrate concentration is sufficiently high to require both motor domains of the dimer to participate in the reaction.     

Kinetic study of the velum formation by Saccharomyces cerevisiae (beticus ssp.) during the biological aging of wines

The main objetive of this work was to evaluate and model the biofilm growth of the Saccharomyces cerevisiae (beticus ssp.) yeast during the biological aging of some types of wines. Thus, we have study how the biofilm growth, the glycerine is consumed and the acetaldehyde is produced, and how this phenomena are affected by the media ethanol concentration (0–17%, v/v), under experimental conditions similar to the industrial ones. In consequence, the growth of the S. cerevisiae (beticus ssp.) biofilm on the surface of the liquid was studied and kinetically modelled. Growth curves were fitted by using general kinetic models that include biomass and substrate inhibition factors. The alcohol content of the medium for the fastest growth rate of biofilm was found to be 4.3%, v/v. The proposed kinetic models for biomass growth, glycerine consumption and acetaldehyde formation fit well with the experimental data.The growth kinetics of S. cerevisiae beticus ssp. in biofilm phase presents a typical discontinuous microbial growth profile (with lag, exponential and stationary phases). The glycerine consumption is directly related to the substrate concentrations (ethanol and glycerine). Finally, the rate of acetaldehyde formation suggests a model associated with the rate of microbial growth, which is modified by a substrate-dependent factor. The suggested model can be used for optimization and control processes of biological aging of wines.     

Diffusion and reaction within porous packing media: a phenomenological model

A phenomenological model has been developed to describe biomass distribution and substrate depletion in porous diatomaceous earth (DE) pellets colonized by Pseudomonas aeruginosa. The essential features of the model are diffusion, attachment and detachment to/from pore walls of the biomass, diffusion of substrate within the pellet, and external mass transfer of both substrate and biomass in the bulk fluid of a packed bed containing the pellets. A bench-scale reactor filled with DE pellets was inoculated with P. aeruginosa and operated in plug flow without recycle using a feed containing glucose as the limiting nutrient. Steady-state effluent glucose concentrations were measured at various residence times, and biomass distribution within the pellet was measured at the lowest residence time. In the model, microorganism/substrate kinetics and mass transfer characteristics were predicted from the literature. Only the attachment and detachment parameters were treated as unknowns, and were determined by fitting biomass distribution data within the pellets to the mathematical model. The rate-limiting step in substrate conversion was determined to be internal mass transfer resistance; external mass transfer resistance and microbial kinetic limitations were found to be nearly negligible. Only the outer 5% of the pellets contributed to substrate conversion. (c) 1993 Wiley & Sons, Inc.