B. D’Acunto

Modeling multispecies biofilms including new bacterial species invasion

A mathematical model for multispecies biofilm evolution based on continuum approach and mass conservation principles is presented. The model can describe biofilm growth dynamics including spatial distribution of microbial species, substrate concentrations, attachment, and detachment, and, in particular, is able to predict the biological process of colonization of new species and transport from bulk liquid to biofilm (or vice-versa). From a mathematical point of view, a significant feature is the boundary condition related to biofilm species concentrations on the biofilm free boundary. These data, either for new or for already existing species, are not required by this model, but rather can be predicted as results. Numerical solutions for representative examples are obtained by the method of characteristics. Results indicate that colonizing bacteria diffuse into biofilm and grow only where favorable environmental conditions exist for their development.

Mathematical modeling of competition and coexistence of sulfate-reducing bacteria, acetogens, and methanogens in multispecies biofilms

AbstractThis work presents an integrated mathematical model able to simulate the physical, chemical, and biological processes prevailing in a sulfate-reducing biofilm under dynamic conditions. The model includes sulfate reduction by complete and incomplete sulfate-reducing bacteria (SRB); lactate removal by sulfate reduction and by acetogenic bacteria and acetate consumption via methanogenesis. Numerical integration based on the method of characteristics has been developed. The major problem of sulfate-reducing fixed-growth reactors is the formation of undesired bacterial species, which compete for space and substrate within the biofilm with SRB. The effect of COD/ratio on the reactor performances in terms of bacterial species distribution and substrate diffusion trends in the biofilm has been assessed. The simulation results reveal a stratification of microbial activities in biofilm reflecting the different ecological niches created by substrate gradients.

Free boundary problem for an initial cell layer in multispecies biofilm formation

Abstract The initial attached cell layer in multispecies biofilm growth is considered. The corresponding mathematical model leads to discuss a free boundary problem for a system of nonlinear hyperbolic partial differential equations, where the initial biofilm thickness is equal to zero. No assumptions on initial conditions for biomass concentrations and biofilm thickness are required. The data that the problem needs are the concentration of biomass in the bulk liquid and biomass flux from the bulk liquid. The method of characteristics is used to convert the differential system to Volterra integral equations for which an existence and uniqueness theorem is proved. Subsequently, we show that the free boundary is an increasing function of time and biomass concentrations are positive in agreement with the biological process.

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.

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.