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.

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 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.

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.

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.

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.