MS02 - ECOP-01

Mathematical Models of Biofilm Processes

Monday, July 14 at 4:00pm

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Hermann Eberl (University of Guelph), John Ward

Description:

Bacterial biofilms are microbial depositions on immersed interfaces of surfaces that form wherever environmental conditions sustain microbial growth. Initially cells attach and then start producing extracellular polymeric substances, in which they are themselves embedded and which provide them protection from mechanical and chemical washout. Such biofilms play an important role in many natural and man made systems. For example many environmental technologies are based on biofilm processes. On the other hand, in a medical context, biofilms can be detrimental. Biofilms have been characterised as both, mechanical objects and as spatially structure bacterial populations. Most mathematical models of biofilms typically take one or the other point of view, depending on the specific process under investigation and the questions one seeks to address. In this minisymposium, several new biofilm modeling applications will be presented, utilizing a variety of biofilm modeling frameworks.

Maria Rosaria Mattei

University of Naples Federico II

"A modeling and simulation study of horizontal gene transfer in biofilms"

The global spread of Antibiotic Resistance Genes (ARGs) and Metal Resistance Genes (MRGs) represents an increasing health concern, and has been mainly attributed to antibiotics abuse and misuse. Dissemination of ARGs and MRGs is largely associated to plasmids, extra-chromosomal genetic elements. Plasmid-carried resistance is transferred to new host cells through Horizontal Gene Transfer (HGT) mechanisms, which play a crucial role in the ecological success of plasmids in bacterial communities. HGT occurs through three main mechanisms, namely conjugation, transformation and transduction, the latter referring to the case where foreign DNA is acquired by the recipient bacterium through infection by bacteriophages. In this talk, we present a biofilm model formulated as a Wanner-Gujer type free-boundary problem describing the impact of HGT on plasmid spread in biofilm communities. Nonlinear hyperbolic PDEs govern the advective transport and growth of the solid-phase components constituting the biofilm, while parabolic quasilinear PDEs model the diffusion-reaction of soluble substrates and bacteriophages. Conjugation is modelled as a mass-action kinetics process subsequent to gene expression, modelled as a nonlocal term to account for recipient-sensing mechanisms. Natural transformation is modelled as a frequency-dependent process. The presence of transducing phages is included in the model and their production is considered as a deterministic process resulting from the infection by lytic phages of bacterial cells carrying the plasmid. We investigate through numerical simulations the comparative influence of conjugation and transformation on the spread of antibiotic resistance and biofilm compartmentalisation due to differences in metabolisms and sensitivity to toxic stressors. We also show through numerical studies the impact of phage predation on bacterial communities and plasmid spread. This is joint work with Julien Vincent, Alberto Tenore and Luigi Frunzo.

Rachana Mandal

University of Guelph

"Modeling and Simulation of Biofilm Growth in a Counter-Diffusion System, Coupled with Biozone Formation in the Aqueous Phase by Chemotactic Bacteria"

In marine environments, sessile bacteria in biofilms and planktonic bacteria suspended in the aqueous medium, critically influence nutrient fluxes, particularly around plumes of marine snow that serve as moving nutrient hotspots. We develop a mathematical model on bacterial biofilm study that accounts for biomass growth, surface attachment and detachment, and chemotactic-diffusive movement of planktonic bacteria and perform a numerical simulation study. The biomass density controls the spatial expansion of biofilm, whereas biomass growth depends on the concentration of the substrates, such as carbon, an electron donor, and oxygen, an electron acceptor. Carbon, sourced from marine snow, diffuses into the domain from one boundary, while oxygen enters from the opposite boundary, establishing a counter-diffusion system. Under these conditions, chemotactic planktonic bacteria accumulate in regions with favorable growth conditions. The system is described by a one-dimensional set of four highly nonlinear partial differential equations. The flux-conservative finite volume method is used for space discretization of the transport terms corresponding to the biomass in biofilm and suspension. Later the substrate equations are discretized and numerically solved using the time-adaptive method from ‘ReacTran’ library in ‘R’. Simulation results demonstrate biofilm expansion toward the aqueous phase and the dynamic migration of suspended bacteria toward optimal nutrient zones. The interplay between chemotaxis, attachment, detachment, and counter-diffusion is shown to significantly influence biofilm maturation dynamics.

Fabiana Russo

Naples University

"Modeling biofilm growth and microbially induced corrosion in wastewater concrete pipes: a double free boundary problem"

Microbially induced corrosion (MIC) is a significant global issue impacting infrastructure, economies, and environment. In wastewater systems, MIC is primarily associated with biofilm formation on concrete sewer pipes, leading to severe degradation due to microbial metabolic activity. The proliferation of sewer biofilms occurs in both submerged and unsubmerged conditions, leading to distinct microbial communities. Commonly, these biofilms host microorganisms such as fermentation bacteria, hydrogen-producing acetogens, denitrifying bacteria, sulfate-reducing bacteria, sulfur-oxidizing bacteria, and methanogens. In particular, sulfur-oxidizing bacteria play a crucial role in corrosion, as they oxidize hydrogen sulfide from wastewater effluents, generating sulfuric acid that accelerates concrete deterioration. A one-dimensional model with double free boundaries has been developed to investigate the proliferation of biofilms and the related corrosion process in wastewater concrete pipes. The domain is composed of two free boundary regions: a biofilm that grows towards the interior cavity of the pipe, sitting on a gypsum layer formed by corrosion, which penetrates the concrete pipe. Diffusion-reaction equations govern the transport and the metabolic production or consumption of dissolved substances, such as hydrogen sulfide, oxygen, and sulfuric acid within the biofilm layer. The biofilm free boundary tracks the growth of the microbial community, regulated by microbial metabolic activity and detachment phenomena. The corrosion process is incorporated into the model through a Stefan-type condition, which drives the advancement of the gypsum free boundary into the concrete pipe, governed by microbial production of sulfuric acid. Numerical simulations have been carried out to investigate the model behavior, encompassing the development and progression of the biofilm as well as the corrosion advancement, with the aim of elucidating the key factors governing both phenomena.

Blessing Emerenini

Rochester Institute of Technology

"Modeling Biofilm Induced Corrosion Inhibition - what do we know?"

Corrosion mitigation represents a significant scientific and engineering challenge, with associated costs exceeding half a trillion dollars annually in the United States alone. Advancing corrosion prevention and control strategies is essential for enhancing the resilience and sustainability of civil infrastructure. Emerging evidence highlights the critical role of naturally occurring microbial biofilms, particularly through a phenomenon known as microbially induced corrosion inhibition (MICI), where biofilms on metal surfaces can reduce or slow corrosion processes. Developing an effective and reliable MICI-based biotechnologies requires an integrated approach, and comes with questions on sustainability. In this study, we investigate a range of modeling frameworks to identify and optimize key parameters influencing the long-term sustainability of such technologies.

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Annual Meeting for the Society for Mathematical Biology, 2025.