Monod Law Research Articles

A coarse-grained resource allocation model of carbon and nitrogen metabolism in unicellular microbes.

Coarse-grained resource allocation models (C-GRAMs) are simple mathematical models of cell physiology, where large components of the macromolecular composition are abstracted into single entities. The dynamics and steady-state behaviour of such models provides insights on optimal allocation of cellular resources and have explained experimentally observed cellular growth laws, but current models do not account for the uptake of compound sources of carbon and nitrogen. Here, we formulate a C-GRAM with nitrogen and carbon pathways converging on biomass production, with parametrizations accounting for respirofermentative and purely respiratory growth. The model describes the effects of the uptake of sugars, ammonium and/or compound nutrients such as amino acids on the translational resource allocation towards proteome sectors that maximized the growth rate. It robustly recovers cellular growth laws including the Monod law and the ribosomal growth law. Furthermore, we show how the growth-maximizing balance between carbon uptake, recycling, and excretion depends on the nutrient environment. Lastly, we find a robust linear correlation between the ribosome fraction and the abundance of amino acid equivalents in the optimal cell, which supports the view that simple regulation of translational gene expression can enable cells to achieve an approximately optimal growth state.

Bridging substrate intake kinetics and bacterial growth phenotypes with flux balance analysis incorporating proteome allocation

Empirical kinetic models such as the Monod equation have been widely applied to relate the cell growth with substrate availability. The Monod equation shares a similar form with the mechanistically-based Michaelis-Menten kinetics for enzymatic processes, which has provoked long-standing and un-concluded conjectures on their relationship. In this work, we integrated proteome allocation principles into a Flux Balance Analysis (FBA) model of Escherichia coli, which quantitatively revealed potential mechanisms that underpin the phenomenological Monod parameters: the maximum specific growth rate could be dictated by the abundance of growth-controlling proteome and growth-pertinent proteome cost; more importantly, the Monod constant (Ks) was shown to relate to the Michaelis constant for substrate transport (Km,g), with the link being dependent on the cell’s metabolic strategy. Besides, the proposed model was able to predict glucose uptake rate at given external glucose concentration through the size of available proteome resource for substrate transport and its enzymatic cost, while growth rate and acetate overflow were accurately simulated for two E. coli strains. Bridging the enzymatic kinetics of substrate intake and overall growth phenotypes, this work offers a mechanistic interpretation to the empirical Monod law, and demonstrates the potential of coupling local and global cellular constrains in predictive modelling.

Reduction of adsorbed dyes content in the discharged sludge coming from an industrial textile wastewater treatment plant using aerobic activated sludge process

Dye mass balance study at full-scale industrial textile wastewater (ITW) treatment plant showed that 1.5 ton of excess waste sludge, containing 304.5 Kg of dyes, are daily produced and discharged in landfills. Therefore, this by-product of activated sludge process (ASP) presents a serious environmental problem. In this work, a laboratory and pilot scale investigations were carried out to optimize aerobic biodegradation efficiency to reduce the amount of residual adsorbed dye that will be found in the waste sludge. The resistance of acclimated biomass to the toxicity of ITW was studied in 2.5 L batch reactors using different dye to biomass (D/B) ratios of 0.102, 0.25 and 0.72 g CODS/g VSS. Results of respirometric analyses showed that acclimated activated sludge (AS) biomass is able to treat ITW at high D/B ratio of 0.72 g CODS/g VSS. Moreover, biodegradation kinetic study using Monod law showed that COD and color removal were better for the highest D/B ratio. The half saturation coefficient of heterotrophs for indigo dye (KSind) of 20.01 g/m3 showed high affinity between biomass and dye molecules. Optimization of the process at pilot-scale with different hydraulic retention time (HRT) of 2–5 days, and different sludge recycling rates (SRR) of 220–680 m3/d, showed that high HRT of 5 days and a SRR of 0.22 allowed the best dye biodegradation efficiency (95%). Application of the best conditions at full-scale reduced significantly (89%) the amount of the discharged dyes from 304.5 Kg/d to 33 Kg/d. Results were numerically validated using a mathematical model based on the activated sludge model 1 (ASM1).

Mechanistic links between cellular trade-offs, gene expression, and growth

Intracellular processes rarely work in isolation but continually interact with the rest of the cell. In microbes, for example, we now know that gene expression across the whole genome typically changes with growth rate. The mechanisms driving such global regulation, however, are not well understood. Here we consider three trade-offs that, because of limitations in levels of cellular energy, free ribosomes, and proteins, are faced by all living cells and we construct a mechanistic model that comprises these trade-offs. Our model couples gene expression with growth rate and growth rate with a growing population of cells. We show that the model recovers Monod's law for the growth of microbes and two other empirical relationships connecting growth rate to the mass fraction of ribosomes. Further, we can explain growth-related effects in dosage compensation by paralogs and predict host-circuit interactions in synthetic biology. Simulating competitions between strains, we find that the regulation of metabolic pathways may have evolved not to match expression of enzymes to levels of extracellular substrates in changing environments but rather to balance a trade-off between exploiting one type of nutrient over another. Although coarse-grained, the trade-offs that the model embodies are fundamental, and, as such, our modeling framework has potentially wide application, including in both biotechnology and medicine.

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.

Sliding mode observer for biomass estimation in a biohydrogen production process

This work deals with the problem of estimation of biomass concentration and specific growth rate in a biohydrogen production process. A photo-fermentation process with the photosynthetic bacteria Rhodobacter capsulatus is considered. The reaction dynamics is represented with a Monod law while the hydrogen production rate is modeled with a Luedeking-Piret expression. A sliding mode observer is proposed and designed, which gives an estimate of both biomass concentration and specific growth rate from measurements of the produced hydrogen volume. The proposed observer is completely robust against the growth kinetic model, and it presents a first-order reduced dynamics. Numerical simulation results are presented for a batch biohydrogen production process.

Time-varying system identification using modulating functions and spline models with application to bio-processes

Time dependent parameters are frequently encountered in many real processes which need to be monitored for process modeling, control and supervision purposes. Modulating functions methods are especially suitable for this task because they use the original continuous-time differential equations and avoid differentiation of noisy signals. Among the many versions of the method available, Pearson–Lee method offers a computationally efficient alternative. In this paper, Pearson–Lee method is generalized for non-stationary continuous-time systems and the on-line version is developed. The time dependent parameters are modeled as polynomial splines inside a moving data window and recursion formulae using shifting properties of sinusoids are formulated. The simple matrix update relations considerably reduce the number of computations required when compared with repeatedly using FFT. The method is illustrated for estimating the kinetic rates and yield factors as time-varying parameters in a fermentation process. The Monod law along with temperature dependency models were used to simulate the data. The simulation study shows that it is not necessary to assume a growth model in order to estimate the kinetic rate parameters.