Maria Rosaria Mattei

Mathematical Modeling of Heavy Metal Biosorption in Multispecies Biofilms

AbstractThe biofilm matrix is a complex of secreted polymers, absorbed nutrients and metabolites, cell lysis products, and even particulate material. Being polyanionic in nature, this matrix plays a crucial role in the biosorption of metal cations. In this work, the adsorption process of heavy metals in biofilms is modeled in one space dimension. The mathematical model is a free-boundary value problem for nonlinear hyperbolic and parabolic partial differential equations. Biomass and extracellular polymeric substances (EPS) growth is governed by hyperbolic equations, and substrate evolution by parabolic equations. All equations are mutually connected. The model is general and can work for any number of microbial species, EPS, and substrates. In numerical analysis, heterotrophic–autotrophic competition for space with oxygen as common substrate is considered. The model can describe biofilm growth dynamics including spatial distribution of microbial species, substrate concentrations, EPS formation, and, in pa...

Heavy Metal Removal from Wastewaters by Biosorption: Mechanisms and Modeling

Many industrial activities result in heavy metal dispersion in the environment worldwide. Heavy metals are persistent contaminants, which get into contact with living organisms and humans creating serious environmental disorders. Metals are commonly removed from wastewaters by means of physical-chemical processes, but often microbes are also enrolled to control metal fate. When microorganisms are used as biosorbents for metal entrapment, a process called “biosorption” occurs. Biosorption efficiency is significantly influenced by many parameters such as environmental factors, the sorbing material and the metal species to be removed, and highly depends on whether microbial cultures are alive or dead. Moreover, the presence of biofilm agglomerates is of major importance for metal uptake onto extracellular polymeric substances. In this chapter, the effect of the above mentioned variables on biosorption performance was reviewed. Among the environmental factors, pH rules metal mobility and speciation. Temperature has a lower influence with an optimal value ranging between 20 and 35 °C. The co-presence of more metals usually decreases the biosorption efficiency of each single metal. Biosorption efficiency can be enhanced by using living microorganisms due to the interaction with active functional groups and the occurrence of transport phenomena into the cells. The existing mathematical modeling approaches used for heavy metal biosorption were overviewed. Several isotherms, obtained in batch conditions, are available for modeling biosorption equilibria and kinetics. In continuous systems, most of the models are used to predict the breakthrough curves. However, the modeling of complex continuous-flow reactors requires further research efforts for better incorporating the effect of the operating parameters and hydrodynamics.

Continuum and discrete approach in modeling biofilm development and structure: a review

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

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.

Sensitivity analysis for an elemental sulfur-based two-step denitrification model

A local sensitivity analysis was performed for a chemically synthesized elemental sulfur (S0)-based two-step denitrification model, accounting for nitrite (NO2-) accumulation, biomass growth and S0 hydrolysis. The sensitivity analysis was aimed at verifying the model stability, understanding the model structure and individuating the model parameters to be further optimized. The mass specific area of the sulfur particles (a*) and hydrolysis kinetic constant (k1) were identified as the dominant parameters on the model outputs, i.e. nitrate (NO3-), NO2- and sulfate (SO42-) concentrations, confirming that the microbially catalyzed S0 hydrolysis is the rate-limiting step during S0-driven denitrification. Additionally, the maximum growth rates of the denitrifying biomass on NO3- and NO2- were detected as the most sensitive kinetic parameters.

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.

Mathematical modeling of dispersal phenomenon in biofilms

A mathematical model for dispersal phenomenon in multispecies biofilm based on a continuum approach and mass conservation principles is presented. The formation of dispersed cells is modeled by considering a mass balance for the bulk liquid and the biofilm. Diffusion of these cells within the biofilm and in the bulk liquid is described using a diffusion-reaction equation. Diffusion supposes a random character of mobility. Notably, biofilm growth is modeled by a hyperbolic partial differential equation while the diffusion process of dispersed cells by a parabolic partial differential equation. The two are mutually connected but governed by different equations that are coupled by two growth rate terms. Three biological processes are discussed. The first is related to experimental observations on starvation induced dispersal [1]. The second considers diffusion of a non-lethal antibiofilm agent which induces dispersal of free cells. The third example considers dispersal induced by a self-produced biocide agent.