MS02 - ECOP-01

Mathematical Models of Biofilm Processes

Monday, July 14 at 3:50pm

SMB2025 Follow

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.

John P. Ward

Loughborough University

"An analysis of large time solutions in biofilm models of Wanner-Gujer type"

The Wanner-Gujer model has a long history in the modelling of biofilm growth, providing a framework to investigate spatio-temporal homogeneities of bacterial biofilm growth and structure in response to environmental factors. Nearly all applications of the model involve numerical solutions or a mathematical analysis (existence and uniqueness) of the time-dependent problem. However, in many applications the steady-state scenario is of most interest, as biofilms in bioreactors are required to run for several weeks or months. In this talk we present a systematic approach to the analysis of the long-time solutions of Wanner-Gujer type models, in particular travelling wave solutions (representing growth on an intermediate timescale) and steady-state solutions (in the case of material sloughing). Numerical solutions of these limiting cases enables an efficient exploration across parameter space and a means of deriving parameter sets to optimise certain desirable properties (e.g. speed of growth, biofilm thickness etc.). A few illustrative examples will be presented.

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.

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.

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.

#SMB2025 Follow

Annual Meeting for the Society for Mathematical Biology, 2025.