Material modeling of biofilm mechanical properties

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.

Spatial distribution of mechanical properties in Pseudomonas aeruginosa biofilms, and their potential impacts on biofilm deformation

The mechanical properties of biofilms can be used to predict biofilm deformation under external forces, for example, under fluid flow. We used magnetic tweezers to spatially map the compliance of Pseudomonas aeruginosa biofilms at the microscale, then applied modeling to assess its effects on biofilm deformation. Biofilms were grown in capillary flow cells with Reynolds numbers (Re) ranging from 0.28 to 13.9, bulk dissolved oxygen (DO) concentrations from 1 mg/L to 8 mg/L, and bulk calcium ion (Ca²⁺ ) concentrations of 0 and 100 mg CaCl₂ /L. Higher Re numbers resulted in more uniform biofilm morphologies. The biofilm was stiffer at the center of the flow cell than near the walls. Lower bulk DO led to more stratified biofilms. Higher Ca²⁺ concentrations led to increased stiffness and more uniform mechanical properties. Using the experimental mechanical properties, fluid-structure interaction models predicted up to 64% greater deformation for heterogeneous biofilms, compared with a homogeneous biofilms with the same average properties. However, the deviation depended on the biofilm morphology and flow regime. Our results show significant spatial mechanical variability exists at the microscale, and that this variability can potentially affect biofilm deformation. The average biofilm mechanical properties, provided in many studies, should be used with caution when predicting biofilm deformation.

Strength of bacterial adhesion on nanostructured surfaces quantified by substrate morphometry

Microbial adhesion and the subsequent formation of resilient biofilms at surfaces are decisively influenced by substrate properties, such as the topography. To date, studies that quantitatively link surface topography and bacterial adhesion are scarce, as both are not straightforward to quantify. To fill this gap, surface morphometry combined with single-cell force spectroscopy was performed on surfaces with irregular topographies on the nano-scale. As surfaces, hydrophobized silicon wafers were used that were etched to exhibit surface structures in the same size range as the bacterial cell wall molecules. The surface structures were characterized by a detailed morphometric analysis based on Minkowski functionals revealing both qualitatively similar features and quantitatively different extensions. We find that as the size of the nanostructures increases, the adhesion forces decrease in a way that can be quantified by the area of the surface that is available for the tethering of cell wall molecules. In addition, we observe a bactericidal effect, which is more pronounced on substrates with taller structures but does not influence adhesion. Our results can be used for a targeted development of 3D-structured materials for/against bio-adhesion. Moreover, the morphometric analysis can serve as a future gold standard for characterizing a broad spectrum of material structures.

Effect of biofilm structural deformation on hydraulic resistance during ultrafiltration: A numerical and experimental study

Biofilm formation in membrane systems negatively impacts the filtration system performances. This study evaluated how biofilm compression driven by permeate flow increases the hydraulic resistance and leads to reduction in permeate flux. We analysed the effect of biofilm compression on hydraulic resistance and permeate flux through computational models supported by experimental data. Biofilms with homogeneous surface structure were subjected to step-wise changes in flux and transmembrane pressure during compression and relaxation tests. Biofilm thickness under applied forces was measured non-invasively in-situ using optical coherence tomography (OCT). A numerical model of poroelasticity, which couples water flow through the biofilm with biofilm mechanics, was developed to correlate the structural deformation with biofilm hydraulics (permeability and resistance). The computational model enabled extracting mechanical and hydrological parameters corresponding to the experimental data. Homogeneous biofilms under elevated compression forces experienced a significant reduction in thickness while only a slight increase in resistance was observed. This shows that hydraulic resistance of homogeneous biofilms was affected more by permeability decrease due to pore closure than by a decrease in thickness. Both viscoelastic and elastoplastic models could describe well the permanent biofilm deformation. However, for biofilms under study, a simpler elastic model could also be used due to the small irreversible deformations. The elastic moduli fitting the measured data were in agreement with other reported values for biofilm under compression. Biofilm stiffening under larger flow-driven compression forces was observed and described numerically by correlating inversely the elastic modulus with biofilm porosity. The importance of this newly developed method lies in estimation of accurate biofilm mechanical parameters to be used in numerical models for both membrane filtration system and biofouling cleaning strategies. Such model can ultimately be used to identify optimal operating conditions for membrane system subjected to biofouling.

Physical structure determines compression of membrane biofilms during Gravity Driven Membrane (GDM) ultrafiltration

Increasing transmembrane pressure (TMP) can compress and increase the hydraulic resistance of membrane biofilms. The purpose of the present study is to evaluate how compression of membrane biofilms occurs and how structural rearrangement can affect hydraulic resistance. Biofilms with heterogeneous and homogeneous physical structures were grown in membrane fouling simulators (MFS) in dead-end mode for 20 days with either (i) a nutrient enriched condition with a nutrient ratio of 100:30:10 (C: N: P), (ii) a phosphorus limitation (C: N: P ratio: 100:30:0), or (iii) river water (C: N: P ratio: ca. 100:10:1). The structural and hydraulic response of membrane biofilms to (a) changes in transmembrane pressures (0.06-0.1-0.5-0.1-0.06 bar) and (b) changes in permeate flux (10-15-20-15-10 L/m²/h) were investigated. Optical coherence tomography (OCT) was used to monitor biofilm structural response, and OCT images were processed to quantify changes in the mean biofilm thickness and relative roughness. Nutrient enriched and river water biofilms had heterogeneous physical structures with greater surface roughness (Ra' > 0.2) than homogeneous P limiting biofilms (Ra' < 0.2). Compression of biofilms with rough heterogeneous structures (Ra' > 0.2) was irreversible, indicated by irreversible decrease in surface roughness, partial relaxation in mean biofilm thickness and irreversible increase in hydraulic resistance. Compression of homogeneous biofilm (Ra' < 0.2) was on the other hand reversible, indicated by full relaxation of the biofilms structure and restoration of initial hydraulic resistance. Hydraulic response (i.e., change in the specific biofilm resistance) did not correspond with the change in physical structure of heterogeneous biofilms. The presented study provides a fundamental understanding of how biofilm physical structure can affect the biofilm's response to a change in TMP, with practical relevance for the operation of GDM filtration systems.

Complex microbial systems across different levels of description

Complex biological systems offer a variety of interesting phenomena at the different physical scales. With increasing abstraction, details of the microscopic scales can often be extrapolated to average or typical macroscopic properties. However, emergent properties and cross-scale interactions can impede naïve abstractions and necessitate comprehensive investigations of these complex systems. In this review paper, we focus on microbial communities, and first, summarize a general hierarchy of relevant scales and description levels to understand these complex systems: (1) genetic networks, (2) single cells, (3) populations, and (4) emergent multi-cellular properties. Second, we employ two illustrating examples, microbial competition and biofilm formation, to elucidate how cross-scale interactions and emergent properties enrich the observed multi-cellular behavior in these systems. Finally, we conclude with pointing out the necessity of multi-scale investigations to understand complex biological systems and discuss recent investigations.

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.

The composition and compression of biofilms developed on ultrafiltration membranes determine hydraulic biofilm resistance

This study aimed at identifying how to improve the level of permeate flux stabilisation during gravity-driven membrane filtration without control of biofilm formation. The focus was therefore on understanding (i) how the different fractions of the biofilms (inorganics particles, bacterial cells, EPS matrix) influence its hydraulic resistance and (ii) how the compression of biofilms impacts its hydraulic resistance, i.e., can water head be increased to increase the level of permeate flux stabilisation. Biofilms were developed on ultrafiltration membranes at 88 and 284 cm water heads with dead-end filtration for around 50 days. A larger water head resulted in a smaller biofilm permeability (150 and 50 L m(-2) h(-1) bar(-1) for biofilms grown at 88 cm and 284 cm water head, respectively). Biofilms were mainly composed of EPS (>90% in volume). The comparison of the hydraulic resistances of biofilms to model fouling layers indicated that most of the hydraulic resistance is due to the EPS matrix. The compressibility of the biofilm was also evaluated by subjecting the biofilms to short-term (few minutes) and long-term variations of transmembrane pressures (TMP). A sudden change of TMP resulted in an instantaneous and reversible change of biofilm hydraulic resistance. A long-term change of TMP induced a slow change in the biofilm hydraulic resistance. Our results demonstrate that the response of biofilms to a TMP change has two components: an immediate variation of resistance (due to compression/relaxation) and a long-term response (linked to biofilm adaptation/growth). Our results provide relevant information about the relationship between the operating conditions in terms of TMP, the biofilm structure and composition and the resulting biofilm hydraulic resistance. These findings have practical implications for a broad range of membrane systems.

Multi-layer composite mechanical modeling for the inhomogeneous biofilm mechanical behavior

Experiments showed that bacterial biofilms are heterogeneous, for example, the density, the diffusion coefficient, and mechanical properties of the biofilm are different along the biofilm thickness. In this paper, we establish a multi-layer composite model to describe the biofilm mechanical inhomogeneity based on unified multiple-component cellular automaton (UMCCA) model. By using our model, we develop finite element simulation procedure for biofilm tension experiment. The failure limit and biofilm extension displacement obtained from our model agree well with experimental measurements. This method provides an alternative theory to study the mechanical inhomogeneity in biological materials.

Response of Simulated Drinking Water Biofilm Mechanical and Structural Properties to Long-Term Disinfectant Exposure

Mechanical and structural properties of biofilms influence the accumulation and release of pathogens in drinking water distribution systems (DWDS). Thus, understanding how long-term residual disinfectants exposure affects biofilm mechanical and structural properties is a necessary aspect for pathogen risk assessment and control. In this study, elastic modulus and structure of groundwater biofilms was monitored by atomic force microscopy (AFM) and optical coherence tomography (OCT) during three months of exposure to monochloramine or free chlorine. After the first month of disinfectant exposure, the mean stiffness of monochloramine- or free-chlorine-treated biofilms was 4 to 9 times higher than those before treatment. Meanwhile, the biofilm thickness decreased from 120 ± 8 μm to 93 ± 6-107 ± 11 μm. The increased surface stiffness and decreased biofilm thickness within the first month of disinfectant exposure was presumably due to the consumption of biomass. However, by the second to third month during disinfectant exposure, the biofilm mean stiffness showed a 2- to 4-fold decrease, and the biofilm thickness increased to 110 ± 7-129 ± 8 μm, suggesting that the biofilms adapted to disinfectant exposure. After three months of the disinfectant exposure process, the disinfected biofilms showed 2-5 times higher mean stiffness (as determined by AFM) and 6-13-fold higher ratios of protein over polysaccharide, as determined by differential staining and confocal laser scanning microscopy (CLSM), than the nondisinfected groundwater biofilms. However, the disinfected biofilms and nondisinfected biofilms showed statistically similar thicknesses (t test, p > 0.05), suggesting that long-term disinfection may not significantly remove net biomass. This study showed how biofilm mechanical and structural properties vary in response to a complex DWDS environment, which will contribute to further research on the risk assessment and control of biofilm-associated-pathogens in DWDS.

Differential growth of wrinkled biofilms

Biofilms are antibiotic-resistant bacterial aggregates that grow on moist surfaces and can trigger hospital-acquired infections. They provide a classical example in biology where the dynamics of cellular communities may be observed and studied. Gene expression regulates cell division and differentiation, which affect the biofilm architecture. Mechanical and chemical processes shape the resulting structure. We gain insight into the interplay between cellular and mechanical processes during biofilm development on air-agar interfaces by means of a hybrid model. Cellular behavior is governed by stochastic rules informed by a cascade of concentration fields for nutrients, waste, and autoinducers. Cellular differentiation and death alter the structure and the mechanical properties of the biofilm, which is deformed according to Föppl-Von Kármán equations informed by cellular processes and the interaction with the substratum. Stiffness gradients due to growth and swelling produce wrinkle branching. We are able to reproduce wrinkled structures often formed by biofilms on air-agar interfaces, as well as spatial distributions of differentiated cells commonly observed with B. subtilis.