Modelling Plasmid-Mediated Horizontal Gene Transfer in Biofilms.

In this study, we present a mathematical model for plasmid spread in a growing biofilm, formulated as a nonlocal system of partial differential equations in a 1-D free boundary domain. Plasmids are mobile genetic elements able to transfer to different phylotypes, posing a global health problem when they carry antibiotic resistance factors. We model gene transfer regulation influenced by nearby potential receptors to account for recipient-sensing. We also introduce a promotion function to account for trace metal effects on conjugation, based on literature data. The model qualitatively matches experimental results, showing that contaminants like toxic metals and antibiotics promote plasmid persistence by favoring plasmid carriers and stimulating conjugation. Even at higher contaminant concentrations inhibiting conjugation, plasmid spread persists by strongly inhibiting plasmid-free cells. The model also replicates higher plasmid density in biofilm's most active regions.

Metformin and lamotrigine sorption on a digestate amended soil in presence of trace metal contamination.

The antidiabetic drug metformin and antiepileptic drug lamotrigine are contaminants of emerging concern that have been detected in biowaste-derived amendments and in the environment, and their fate must be carefully studied. This work aimed to evaluate their sorption behaviour on soil upon digestate application. Experiments were conducted on soil and digestate-amended soil as a function of time to study kinetic processes, and at equilibrium also regarding the influence of trace metals (Pb, Ni, Cr, Co, Cu, Zn) at ratio pharmaceutical/metal 1/1, 1/10, and 1/100. Pharmaceutical desorption experiments were also conducted to assess their potential mobility to groundwater. Results revealed that digestate amendment increased metformin and lamotrigine adsorbed amounts by 210% and 240%, respectively, increasing organic matter content. Metformin adsorption kinetics were best described by Langmuir model and those of lamotrigine by Elovich and intraparticle diffusion models. Trace metals did not significantly affect the adsorption of metformin in amended soil while significantly decreased that of lamotrigine by 12-39%, with exception for Cu2+ that increased both pharmaceuticals adsorbed amounts by 5 - 8%. This study highlighted the influence of digestate amendment on pharmaceutical adsorption and fate in soil, which must be considered in the circular economy scenario of waste-to-resource.

Dynamic modelling the effects of ionic strength and ion complexation on trace metal speciation during anaerobic digestion.

Dosing trace metals into anaerobic digestors is proven to improve biogas production rate and yield by stimulating microorganisms involved in the metabolic pathways. Trace metal effects are governed by metal speciation and bioavailability. Though chemical equilibrium speciation models are well-established and widely used to understand metal speciation, the development of kinetic models considering biological and physicochemical processes has recently gained attention. This work proposes a dynamic model for metal speciation during anaerobic digestion which is based on a system of ordinary differential equations aimed to describe the kinetics of biological, precipitation/dissolution, gas transfer processes and, a system of algebraic equations to define fast ion complexation processes. The model also considers ion activity corrections to define effects of ionic strength. Results from this study shows the inaccuracy in predicting trace metal effects on anaerobic digestion by typical metal speciation models and the significance of considering non-ideal aqueous phase chemistry (ionic strength and ion pairing/complexation) to define speciation and metal labile fractions. Model results show a decrease in metal precipitation and increase in metal dissolved fraction and methane production yield with increase in ionic strength. Capability of the model to dynamically predict trace metal effects on anaerobic digestion under different conditions, like changing dosing conditions and initial iron to sulphide ratio, was also tested and verified. Dosing iron increases methane production and decreases hydrogen sulphide production. However, when iron to sulphide ratio is greater than 1, methane production decreases due to increase in dissolved iron which reaches inhibitory concentration levels.

A Mathematical Study of Metal Biosorption on Algal-Bacterial Granular Biofilms.

A multiscale mathematical model describing the metals biosorption on algal-bacterial photogranules within a sequencing batch reactor (SBR) is presented. The model is based on systems of partial differential equations (PDEs) derived from mass conservation principles on a spherical free boundary domain with radial symmetry. Hyperbolic PDEs account for the dynamics of sessile species and their free sorption sites, where metals are adsorbed. Parabolic PDEs govern the diffusion, conversion and adsorption of nutrients and metals. The dual effect of metals on photogranule ecology is also modelled: metal stimulates the production of EPS by sessile species and negatively affects the metabolic activities of microbial species. Accordingly, a stimulation term for EPS production and an inhibition term for metal are included in all microbial kinetics. The formation and evolution of the granule domain are governed by an ordinary differential equation with a vanishing initial value, accounting for microbial growth, attachment and detachment phenomena. The model is completed with systems of impulsive differential equations describing the evolution of dissolved substrates, metals, and planktonic and detached biomasses within the granular-based SBR. The model is integrated numerically to examine the role of the microbial species and EPS in the adsorption process, and the effect of metal concentration and adsorption properties of biofilm components on the metal removal. Numerical results show an accurate description of the photogranules evolution and ecology and confirm the applicability of algal-bacterial photogranule technology for metal-rich wastewater treatment.

A mechanistic mathematical model for photo fermentative hydrogen and polyhydroxybutyrate production.

An original mathematical model describing the photo fermentation process is proposed. The model represents the first attempt to describe the photo fermentative hydrogen production and polyhydroxybutyrate accumulation, simultaneously. The mathematical model is derived from mass balance principles and consists of a system of ordinary differential equations describing the biomass growth, the nitrogen and the substrate degradation, the hydrogen and other catabolites production, and the polyhydroxybutyrate accumulation in photo fermentation systems. Moreover, the model takes into account important inhibiting phenomena, such as the self-shading and the substrate inhibition, which can occur during the evolution of the process. The calibration was performed using a real experimental data set and it was supported by the results of a sensitivity analysis study. The results showed that the most sensitive parameters for both hydrogen and PHB production were the hydrogen yield on substrate, the catabolites yield on substrate, and the biomass yield. Successively, a different experimental data set was used to validate the model. Performance indicators showed that the model could efficiently be used to simulate the photo fermentative hydrogen and polyhydroxybutyrate production by Rhodopseudomonas palustris. For instance, the index of agreement of 0.95 was observed for the validated hydrogen production trend. Moreover, the model well predicted the maximum PHB accumulation in bacterial cells. Indeed, the predicted and observed accumulated PHB were 4.5 and 4.8%, respectively. Further numerical simulations demonstrated the model consistency in describing process inhibiting phenomena. Numerical simulations showed that the acetate and nitrogen inhibition phenomena take place when concentrations are higher than 12.44 g L-1 and lower than 4.76 mg L-1, respectively. Finally, the potential long term hydrogen production from accumulated polyhydroxybutyrate in bacterial cells was studied via a fast-slow analysis technique.

A transient biological fouling model for constant flux microfiltration.

Microfiltration is a widely used engineering technology for fresh water production and water treatment. The major concern in many applications is the formation of a biological fouling layer leading to increased hydraulic resistance and flux decline during membrane operations. The growth of bacteria constituting such a biological layer implicates the formation of a multispecies biofilm and the consequent increase of operational costs for reactor management and cleaning procedures. To predict the biofouling evolution, a mono-dimensional continuous free boundary model describing biofilm dynamics and EPS production in different operational phases of microfiltration systems has been well studied. The biofouling growth is governed by a system of hyperbolic PDEs. Substrate dynamics are modeled through parabolic equations accounting for diffusive and advective fluxes generated during the filtration process. The free boundary evolution depends on both microbial growth and detachment processes. What is not addressed is the interplay between biofilm dynamics, filtration, and water recovery. In this study, filtration and biofilm growth modeling principles have been coupled for the definition of an original mathematical model able to reproduce biofouling evolution in membrane systems. The model has been solved numerically to simulate biologically relevant conditions, and to investigate the hydraulic behavior of the membrane. It has been calibrated and validated using lab-scale data. Numerical results accurately predicted the pressure drop occurring in the microfiltration system. A calibrated model can give information for optimization protocols as well as fouling prevention strategies.

Multiscale modelling of the start-up process of anammox-based granular reactors.

This work proposes a mathematical model on partial nitritation/anammox (PN/A) granular bioreactors, with a particular interest in the start-up phase. The formation and growth of granular biofilms is modelled by a spherical free boundary problem with radial symmetry and vanishing initial value. Hyperbolic PDEs describe the advective transport and growth of sessile species inhabiting the granules. Parabolic PDEs describe the diffusive transport and conversion of soluble substrates, and the invasion process mediated by planktonic species. Attachment and detachment phenomena are modelled as continuous and deterministic fluxes at the biofilm-bulk liquid interface. The dynamics of planktonic species and substrates within the bulk liquid are modelled through ODEs. A simulation study is performed to describe the start-up process of PN/A granular systems and the development of anammox granules. The aim is to investigate the role that the invasion process of anaerobic ammonia-oxidizing (anammox) bacteria plays in the formation of anammox granules and explore how it affects the microbial species distribution of anaerobic ammonia-oxidizing, aerobic ammonia-oxidizing, nitrite-oxidizing and heterotrophic bacteria. Moreover, the model is used to study the role of two key parameters in the start-up process: the anammox inoculum size and the inoculum addition time. Numerical results confirm that the model can be used to simulate the start-up process of PN/A granular systems and to predict the evolution of anammox granular biofilms, including the ecology and the microbial composition. In conclusion, after being calibrated, the proposed model could provide quantitatively reliable results and support the start-up procedures of full-scale PN/A granular reactors.

Modelling the effect of SMP production and external carbon addition on S-driven autotrophic denitrification.

The aim of this study was to develop a mathematical model to assess the effect of soluble microbial products production and external carbon source addition on the performance of a sulfur-driven autotrophic denitrification (SdAD) process. During SdAD, the growth of autotrophic biomass (AUT) was accompanied by the proliferation of heterotrophic biomass mainly consisting of heterotrophic denitrifiers (HD) and sulfate-reducing bacteria (SRB), which are able to grow on both the SMP derived from the microbial activities and on an external carbon source. The process was supposed to occur in a sequencing batch reactor to investigate the effects of the COD injection on both heterotrophic species and to enhance the production and consumption of SMP. The mathematical model was built on mass balance considerations and consists of a system of nonlinear impulsive differential equations, which have been solved numerically. Different simulation scenarios have been investigated by varying the main operational parameters: cycle duration, day of COD injection and quantity of COD injected. For cycle durations of more than 15 days and a COD injection after the half-cycle duration, SdAD represents the prevailing process and the SRB represent the main heterotrophic family. For shorter cycle duration and COD injections earlier than the middle of the cycle, the same performance can be achieved increasing the quantity of COD added, which results in an increased activity of HD. In all the performed simulation even in the case of COD addition, AUT remain the prevailing microbial family in the reactor.

Mathematical modeling of metal recovery from E-waste using a dark-fermentation-leaching process.

In this work, an original mathematical model for metals leaching from electronic waste in a dark fermentation process is proposed. The kinetic model consists of a system of non-linear ordinary differential equations, accounting for the main biological, chemical, and physical processes occurring in the fermentation of soluble biodegradable substrates and in the dissolution process of metals. Ad-hoc experimental activities were carried out for model calibration purposes, and all experimental data were derived from specific lab-scale tests. The calibration was achieved by varying kinetic and stoichiometric parameters to match the simulation results to experimental data. Cumulative hydrogen production, glucose, organic acids, and leached metal concentrations were obtained from analytical procedures and used for the calibration. The results confirmed the high accuracy of the model in describing biohydrogen production, organic acids accumulation, and metals leaching during the biological degradation process. Thus, the mathematical model represents a useful and reliable tool for the design of strategies for valuable metals recovery from waste or mineral materials. Moreover, further numerical simulations were carried out to analyze the interactions between the fermentation and the leaching processes and to maximize the efficiency of metals recovery due to the fermentation by-products.

Biohythane production from food waste in a two-stage process: assessing the energy recovery potential.

ABSTRACTBiohythane (hydrogen + methane) production in a two stage dark fermentation (DF) and anaerobic digestion (AD) process from food waste (FW) has been studied. This paper investigated the effect of operation temperature, i.e. mesophilic (34 °C) and thermophilic (55 °C) , on biohythane yield and total energy recovery carried out at the initial culture pH 5.5 and pH 7, respectively for DF and AD batch tests. The mesophilic DF tests gave a higher hydrogen yield of 53.5 (±4) mL H2/g VS added compared to thermophilic DF tests, i.e. 37.6 (±1) mL H2/g VS added. However, higher methane yields, i.e. 307.5 (± 10) mL CH4/g VS, were obtained at thermophilic AD tests compared to mesophilic AD, i.e. 276.5 (±4.3) mL CH4/g VS. The total energy recovery from thermophilic DF + AD was higher (11.4 MJ/kg VS) than the mesophilic (10.4 MJ/kg VS) combined process. Interestingly, the analysis of kinetic parameters of mesophilic tests, determined from the Modified Gompertz equation, showed that mesophilic DF had faster H2 production kinetics, which can be attributed to a faster adaptation of the heat-shocked inoculum used in the tests to the incubation temperature. However, thermophilic AD tests exhibited faster kinetics for methane production.

A general framework to model the fate of trace elements in anaerobic digestion environments.

Due to the multiplicity of biogeochemical processes taking place in anaerobic digestion (AD) systems and limitations of the available analytical techniques, assessing the bioavailability of trace elements (TEs) is challenging. Determination of TE speciation can be facilitated by developing a mathematical model able to consider the physicochemical processes affecting TEs dynamics. A modeling framework based on anaerobic digestion model no 1 (ADM1) has been proposed to predict the biogeochemical fate TEs in AD environments. In particular, the model considers the TE adsorption-desorption reactions with biomass, inerts and mineral precipitates, as well as TE precipitation/dissolution, complexation reactions and biodegradation processes. The developed model was integrated numerically, and numerical simulations have been run to investigate the model behavior. The simulation scenarios predicted the effect of (i) organic matter concentration, (ii) initial TEs concentrations, (iii) initial Ca-Mg concentrations, (iv) initial EDTA concentration, and (v) change in TE binding site density, on cumulative methane production and TE speciation. Finally, experimental data from a real case continuous AD system have been compared to the model predictions. The results prove that this modelling framework can be applied to various AD operations and may also serve as a basis to develop a model-predictive TE dosing strategy.

A comprehensive review of mathematical models of photo fermentation.

This work aims at analyzing and comparing the different modeling approaches used to date to simulate, design and control photo fermentation processes for hydrogen production and/or wastewater treatment. The study is directed to researchers who approach the problem of photo fermentation mathematical modeling. It is a useful tool to address future research in this specific field in order to overcome the difficulty of modeling a complex, not totally elucidate process. We report a preliminary identification of the environmental and biological parameters, included in the models, which affect photo fermentation. Based on model features, we distinguish three different approaches, i.e. kinetic, parametric and non-ideal reactors. We explore the characteristics of each approach, reporting and comparing the obtained results and underlining the differences between models, together with the advantages and the limitations of each of them. The analysis of the approaches indicates that Kinetic models are useful to describe the process from a biochemical point of view, without considering bio-reactor hydrodynamics and the spatial variations that Parametric Models can be utilized to study the influence and the interactions between the operational conditions. They do not take into account the biochemical process mechanism and the influence of reactor hydrodynamics. Quite the opposite, non-ideal reactors models focus on the reactor configuration. Otherwise, the biochemical description of purple non-sulfur bacteria activities is usually simplified. This review indicates that there still is a lack of models that fully describe photo fermentation processes.

Dynamics of bacterial communities and substrate conversion during olive-mill waste dark fermentation: Prediction of the metabolic routes for hydrogen production.

The aim of this work was to study the biological catalysts and possible substrate conversion routes in mesophilic dark fermentation reactors aimed at producing H2 from olive mill wastewater. Bacillus and Clostridium were the most abundant phylotypes during the rapid stage of H2 production. Chemical analyses combined with predictive functional profiling of the bacterial communities indicated that the lactate fermentation was the main H2-producing route. In fact, during the fermentation process, lactate and acetate were consumed, while H2 and butyrate were being produced. The fermentation process was rich in genes that encode enzymes for lactate generation from pyruvate. Lactate conversion to butyrate through the generation of pyruvate produced H2 through the recycling of electron carriers via the pyruvate ferredoxin oxydoreductase pathway. Overall, these findings showed the synergy among lactate-, acetate- and H2-producing bacteria, which complex interactions determine the H2 production routes in the bioreactors.

Calibration and validation of an activated sludge model for membrane bioreactor wastewater treatment plants.

A mathematical model to simulate the biological processes occurring in a membrane bioreactor (MBR) is presented. The model accounts for different MBR technical features by introducing specific permeability parameters for the applied membrane system. The model considers for the heterotrophic storage process and the formation of soluble microbial products. The introduction of an inhibition coefficient influencing the anoxic kinetics enables the model to simulate the particular operating conditions of the plant, such as a high or low dissolved oxygen concentration in the denitrification tank. The model was applied at the MBR wastewater treatment plant of Vila Nova do Ceira (Portugal) which uses a classic pre-denitrification cycle. Data for calibration and validation were sampled at the same wastewater treatment plant. Calibration was achieved by varying the kinetic parameters of the model to match the simulation results to the experimental data. The values of the kinetic parameters were similar to those found in the literature. The validation was performed by two different methodologies to analyse the model response to diverse operating conditions, and to evaluate the resilience of the MBR. Calibration and validation results were evaluated with mean average error, root mean square error and fractional mean bias as performance indexes. In most cases, these indexes confirmed the high accuracy of the model. Overall, the results of the calibration and validation steps enriched the proposed model by providing an effective biological description of the processes characterizing the MBR. Thus, the model is a reliable tool for the management and designing of MBR.

Investigation of architecture development and phosphate distribution in Chlorella biofilm by complementary microscopy techniques.

Microalgae biofilms may play an important role in the mitigation and prevention of eutrophication caused by domestic, agricultural and industrial wastewater effluents. Despite their potential, the biofilm development and role in nutrient removal are not well understood. Its clarification requires comprehensive studies of the complex three-dimensional architecture of the biofilm. In this study, we established a multimodal imaging approach to provide key information regarding architecture development and nutrient distribution in the biofilm of two green algae organisms: Chlorella pyrenoidosa and Chlorella vulgaris. Helium ion microscopy (HIM), scanning electron microscopy coupled with energy dispersive X-ray analysis (SEM-EDX) and time-of-flight secondary ion mass spectrometry (ToF-SIMS) were employed for i) elucidation of spatial arrangement, ii) elemental mapping and iii) 3D chemical imaging of the biofilm. The fine structure of the algal biofilm was resolved by HIM, the evidence of the accumulation of phosphate in hot spots was provided by SEM-EDX and the localization of phosphate oxides granules throughout the whole sample was clarified by ToF-SIMS. The reported results shed light on the phosphorus distribution during Chlorella's biofilm formation and highlight the potential of such correlative approach to solve fundamental question in algal biotechnology research.

ADM1 based mathematical model of trace element complexation in anaerobic digestion processes.

In this study, a new model based on anaerobic digestion model no.1 (ADM1) approach has been proposed to simulate trace elements (TEs) complexation, precipitation and their effect on the anaerobic batch methane production. TEs complexation reactions with VFAs and EDTA have been incorporated in an extended ADM1 model which considers TE precipitation/dissolution reactions as well as biodegradation processes. The kinetic model tracks the dynamics of 90 state variables which constitute the components of the proposed anaerobic digestion (AD) model. The incorporation of the complexation reactions required the definition of new inorganic components (EDTA species) and new complexation process rates in the ADM1 framework. The charge balance was modified accordingly to consider the effects of the additional components. The new model is able to predict: a) the effect of TE-EDTA/VFA complexation on methane production, and b) the effect of the initial calcium and magnesium concentrations on process performance.

Nutrient removal efficiency of green algal strains at high phosphate concentrations.

The effects of autotrophic and mixotrophic conditions on microalgae growth and nutrient removal efficiency from synthetic wastewater by different microalgae were investigated. Although several studies have demonstrated the suitability of microalgae technologies for ammonia-rich wastewater treatment, only a few have been used for treatment of phosphate-rich industrial wastewaters. In this work, six microalgae were cultivated in batch mode in a growth medium with a high phosphate concentration (0.74 Mm PO4 3--P) and different carbon sources (ammonium acetate and sodium bicarbonate) without CO2 supplementation or pH adjustment. Their potential for nutrient removal and biomass generation was estimated. The biomass growth in the reactors was modeled and the data aligned to the Verhulst model with R2 > 0.93 in all cases. Chlorella pyrenoidosa ACUF_808 showed the highest final biomass productivity of 106.21 and 75.71 mg·L-1·d-1 in media with inorganic and organic carbon sources, respectively. The highest phosphorus removal efficiency was 32% with Chlorella vulgaris ACUF_809, while the nitrate removal efficiency in all reactors exceeded 93%. The coupled cultivation of the novel isolated strains of C. pyrenoidosa and C. vulgaris under mixotrophic conditions supplemented with ammonium acetate might be a promising solution for simultaneous nitrate and phosphate removal from phosphorus-rich wastewaters.

ADM1 based mathematical model of trace element precipitation/dissolution in anaerobic digestion processes.

Due to the complex biogeochemistry of trace elements (TEs, e.g. Fe, Ni and Co) in anaerobic digestion processes, their role and fate is poorly understood. Challenging, time consuming and low detection limits of analytical procedures necessitate recruitment of mathematical models. A dynamic mathematical model based on anaerobic digestion model no.1 (ADM1) has been proposed to simulate the effect of TEs. New chemical equilibrium association/dissociation and precipitation/dissolution reactions have been implemented to determine TE bioavailability and their effect on anaerobic digestion. The model considers interactions with inorganic carbonate (HCO3- and CO32-), phosphate (PO43-, HPO42-, H2PO4-) and sulfide (HS- and S2-). The effect of deficiency, activation, inhibition and toxicity of TEs on the biochemical processes has been modelled based on a dose-response type inhibition function. The new model can predict: the dynamics of TEs (among carbonate, sulfide and phosphate); the starvation of TEs; and the effect of initial sulfur-phosphorus ratio in an in-silico batch anaerobic system.

Elemental sulfur-based autotrophic denitrification and denitritation: microbially catalyzed sulfur hydrolysis and nitrogen conversions.

The hydrolysis of elemental sulfur (S0) coupled to S0-based denitrification and denitritation was investigated in batch bioassays by microbiological and modeling approaches. In the denitrification experiments, the highest obtained NO3--N removal rate was 20.9 mg/l·d. In the experiments with the biomass enriched on NO2-, a NO2--N removal rate of 10.7 mg/l·d was achieved even at a NO2--N concentration as high as 240 mg/l. The Helicobacteraceae family was only observed in the biofilm attached onto the chemically-synthesized S0 particles with a relative abundance up to 37.1%, suggesting it was the hydrolytic biomass capable of S0 solubilization in the novel surface-based model. S0-driven denitrification was modeled as a two-step process in order to explicitly account for the sequential reduction of NO3- to NO2- and then to N2 by denitrifying bacteria.