Modelling mechanical characteristics of microbial biofilms by network theory

Modeling Inelastic Responses Using Constrained Reactive Mixtures

This study reviews the progression of our research, from modeling growth theories for cartilage tissue engineering, to the formulation of constrained reactive mixture theories to model inelastic responses in any solid material, such as theories for damage mechanics, viscoelasticity, plasticity, and elasto-plastic damage. In this framework, multiple solid generations α can co-exist at any given time in the mixture. The oldest generation is denoted by α = s and is called the master generation, whose reference configuration X s is observable. The solid generations α are all constrained to share the same velocity v s , but may have distinct reference configurations X α . An important element of this formulation is that the time-invariant mapping F α s = ∂ X α / ∂ X s between these reference configurations is a function of state, whose mathematical formulation is postulated by constitutive assumption. Thus, reference configurations X α are not observable ( α ≠ s ) . This formulation employs only observable state variables, such as the deformation gradient F s of the master generation and the referential mass concentrations ρ r α of each generation, in contrast to classical formulations of inelastic responses which rely on internal state variable theory, requiring evolution equations for those hidden variables. In constrained reactive mixtures, the evolution of the mass concentrations is governed by the axiom of mass balance, using constitutive models for the mass supply densities ρ ˆ r α . Classical and constrained reactive mixture approaches share considerable mathematical analogies, as they both introduce a multiplicative decomposition of the deformation gradient, also requiring evolution equations to track some of the state variables. However, they also differ at a fundamental level, since one adopts only observable state variables while the other introduces hidden state variables. In summary, this review presents an alternative foundational approach to the modeling of inelastic responses in solids, grounded in the classical framework of mixture theory.

Rheological characterisation of alginate-like exopolymer gels crosslinked with calcium

Bacterial alginate-like exopolymers (ALE) gels have been used in this work as a model for the extracellular polymeric matrix of biofilms. Aim was to relate the mechanical properties and strength of this matrix that make biofilms as persistent to cleaning as they are, to the complex cohesive molecular interactions involved. Mechanical properties of the gels as a function of CaCO₃ concentration were investigated using dynamic and static rheology. Gels with relatively low CaCO₃ concentrations, between 100 μmol and 300 μmol per g ALE, were found to exhibit similar viscoelastic behaviour as real biofilms, with elastic moduli between 50 Pa and 100 Pa and dissipation factors between 0.2 and 0.3. Increasing CaCO₃ concentrations resulted in an increase of the elastic modulus up to 250 Pa, accompanied by an increase in brittleness. At a CaCO₃ concentration of 1250 μmol per g ALE this trend stopped, probably due to disturbance of the continuous ALE network by precipitation of salts. Therefore, overdosing of Ca salts can be an adequate approach for the removal of biofouling. All gels exhibited permanent strain hardening under medium strain, and their mechanical properties showed dependency on their strain history. Even after application of an oscillatory strain with 200% amplitude that caused the gel structure to collapse, the gels recovered 65 to 90% of their original shear modulus, for the major part within the first 20 s. Recovery was slightly less for gels with high CaCO₃ concentration. In creep tests fitted with a Burgers model with multiple Kelvin elements at least three different interactions in the ALE gels could be distinguished with characteristic retardation times in the range of 10, 100 and 1000 s. Further identification of the mechanisms underlying the gel mechanics will allow the development of targeted strategies to undermine the mechanical strength of biofouling and aid the cleaning process.

A Microscopically Motivated Model for Particle Penetration into Swollen Biological Networks

Biological gels (bio-gels) are hydrated polymer networks that serve diverse biological functions, which often lead to intentional or unintentional exposure to particulate matter. In this work, we derive a microscopically motivated framework that enables the investigation of penetration mechanisms into bio-gels. We distinguish between two types of mechanisms: spontaneous (unforced) penetration and forced penetration. Using experimental data available in the literature, we exploit the proposed model to characterize and compare between the microstructures of respiratory, intestinal, and cervicovaginal mucus and two types of biofilms. Next, we investigate the forced penetration process of spherical and ellipsoidal particles into a locally quadrilateral network. The proposed framework can be used to improve and complement the analysis of experimental findings in vitro, ex vivo, and in vivo. Additionally, the insights from this work pave the way towards enhanced designs of nano-medicines and allow the assessment of risk factors related to the nano-pollutants exposure.

Challenges of biofilm control and utilization: lessons from mathematical modelling

This article reviews modern applications of mathematical descriptions of biofilm formation. The focus is on theoretically obtained results which have implications for areas including the medical sector, food industry and wastewater treatment. Examples are given as to how models have contributed to the overall knowledge on biofilms and how they are used to predict biofilm behaviour. We conclude that the use of mathematical models of biofilms has demonstrated over the years the ability to significantly contribute to the vast field of biofilm research. Among other things, they have been used to test various hypotheses on the nature of interspecies interactions, viability of biofilm treatment methods or forces behind observed biofilm pattern formations. Mathematical models can also play a key role in future biofilm research. Many models nowadays are analysed through computer simulations and continue to improve along with computational capabilities. We predict that models will keep on providing answers to important challenges involving biofilm formation. However, further strengthening of the ties between various disciplines is necessary to fully use the tools of collective knowledge in tackling the biofilm phenomenon.

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.

Modeling of Mesoscale Variability in Biofilm Shear Behavior

Formation of bacterial colonies as biofilm on the surface/interface of various objects has the potential to impact not only human health and disease but also energy and environmental considerations. Biofilms can be regarded as soft materials, and comprehension of their shear response to external forces is a key element to the fundamental understanding. A mesoscale model has been presented in this article based on digitization of a biofilm microstructure. Its response under externally applied shear load is analyzed. Strain stiffening type behavior is readily observed under high strain loads due to the unfolding of chains within soft polymeric substrate. Sustained shear loading of the biofilm network results in strain localization along the diagonal direction. Rupture of the soft polymeric matrix can potentially reduce the intercellular interaction between the bacterial cells. Evolution of stiffness within the biofilm network under shear reveals two regimes: a) initial increase in stiffness due to strain stiffening of polymer matrix, and b) eventual reduction in stiffness because of tear in polymeric substrate.

Nanoindentation and finite element modelling of chitosan-alginate multilayer coated hydrogels

Composite soft materials are used as compounds for determining the effects of mechanical cues on cell behavior and cell encapsulation and for controlling drug release. The appropriate composite soft materials are conventionally prepared by selective deposition of polymers at the surface of an ionic hydrogel. In the present study we address the impact of a mechanically stratified two-layer structure of these materials on their overall mechanical characterization by applying a combination of nanoindentation, confocal microscopy and finite element modelling. We prepare covalent cross-linked hydrogels based on acrylamide (AAM) and including an anionic group, and impregnate them using a multilayer deposition strategy of alternating exposure to cationic chitosan and anionic alginate. The thickness of the chitosan-alginate layer on the hydrogels was determined to be 0.4 ± 0.05 μm for 4 bilayers, and 0.7 ± 0.1 μm for the 8 bilayer deposition procedure employing a fluorescently labelled chitosan and confocal microscopy. The force-indentation data for the AAM gels were highly reproducible, whereas 77% and 50% of the force-indentation data were reproducible following the 4 and 8 bilayer deposition. The main trends in the reproducible force-distance data were found to yield an apparent increased Young's modulus after the deposition. Finite element modelling showed that adaption of a homogeneous Young's modulus for the specimens with deposited layers yields approximately three times too low stiffness compared to the estimate of the mechanical properties of the outer part in the two-layered mechanical model. The thickness of the multilayer region determined by confocal microscopy was used in the model. This study shows that the mechanical layered property needs to be included in the interpretation of the nanoindentation data when there is a significant mechanical contrast.

Direct Comparison of Physical Properties of Bacillus subtilis NCIB 3610 and B-1 Biofilms

Many bacteria form surface-attached communities known as biofilms. Due to the extreme resistance of these bacterial biofilms to antibiotics and mechanical stresses, biofilms are of growing interest not only in microbiology but also in medicine and industry. Previous studies have determined the extracellular polymeric substances present in the matrix of biofilms formed by Bacillus subtilis NCIB 3610. However, studies on the physical properties of biofilms formed by this strain are just emerging. In particular, quantitative data on the contributions of biofilm matrix biopolymers to these physical properties are lacking. Here, we quantitatively investigated three physical properties of B. subtilis NCIB 3610 biofilms: the surface roughness and stiffness and the bulk viscoelasticity of these biofilms. We show how specific biomolecules constituting the biofilm matrix formed by this strain contribute to those biofilm properties. In particular, we demonstrate that the surface roughness and surface elasticity of 1-day-old NCIB 3610 biofilms are strongly affected by the surface layer protein BslA. For a second strain,B. subtilis B-1, which forms biofilms containing mainly γ-polyglutamate, we found significantly different physical biofilm properties that are also differently affected by the commonly used antibacterial agent ethanol. We show that B-1 biofilms are protected from ethanol-induced changes in the biofilm's stiffness and that this protective effect can be transferred to NCIB 3610 biofilms by the sole addition of γ-polyglutamate to growing NCIB 3610 biofilms. Together, our results demonstrate the importance of specific biofilm matrix components for the distinct physical properties of B. subtilis biofilms.

Multicomponent model of deformation and detachment of a biofilm under fluid flow

A novel biofilm model is described which systemically couples bacteria, extracellular polymeric substances (EPS) and solvent phases in biofilm. This enables the study of contributions of rheology of individual phases to deformation of biofilm in response to fluid flow as well as interactions between different phases. The model, which is based on first and second laws of thermodynamics, is derived using an energetic variational approach and phase-field method. Phase-field coupling is used to model structural changes of a biofilm. A newly developed unconditionally energy-stable numerical splitting scheme is implemented for computing the numerical solution of the model efficiently. Model simulations predict biofilm cohesive failure for the flow velocity between [Formula: see text] and [Formula: see text] m s(-1) which is consistent with experiments. Simulations predict biofilm deformation resulting in the formation of streamers for EPS exhibiting a viscous-dominated mechanical response and the viscosity of EPS being less than [Formula: see text]. Higher EPS viscosity provides biofilm with greater resistance to deformation and to removal by the flow. Moreover, simulations show that higher EPS elasticity yields the formation of streamers with complex geometries that are more prone to detachment. These model predictions are shown to be in qualitative agreement with experimental observations.

Biomechanical Analysis of Infectious Biofilms

The removal of infectious biofilms from tissues or implanted devices and their transmission through fluid transport systems depends in part of the mechanical properties of their polymeric matrix. Linking the various physical and chemical microscopic interactions to macroscopic deformation and failure modes promises to unveil design principles for novel therapeutic strategies targeting biofilm eradication, and provide a predictive capability to accelerate the development of devices, water lines, etc, that minimise microbial dispersal. Here, our current understanding of biofilm mechanics is appraised from the perspective of biophysics , with an emphasis on constitutive modelling that has been highly successful in soft matter. Fitting rheometric data to viscoelastic models has quantified linear and nonlinear stress relaxation mechanisms, how they vary between species and environments, and how candidate chemical treatments alter the mechanical response. The rich interplay between growth, mechanics and hydrodynamics is just becoming amenable to computational modelling and promises to provide unprecedented characterisation of infectious biofilms in their native state.

A novel technique using potassium permanganate and reflectance confocal microscopy to image biofilm extracellular polymeric matrix reveals non-eDNA networks in Pseudomonas aeruginosa biofilms

Biofilms are etiologically important in the development of chronic medical and dental infections. The biofilm extracellular polymeric substance (EPS) determines biofilm structure and allows bacteria in biofilms to adapt to changes in mechanical loads such as fluid shear. However, EPS components are difficult to visualize microscopically because of their low density and molecular complexity. Here, we tested potassium permanganate, KMnO4, for use as a non-specific EPS contrast-enhancing stain using confocal laser scanning microscopy in reflectance mode. We demonstrate that KMnO4 reacted with EPS components of various strains of Pseudomonas, Staphylococcus and Streptococcus, yielding brown MnO2 precipitate deposition on the EPS, which was quantifiable using data from the laser reflection detector. Furthermore, the MnO2 signal could be quantified in combination with fluorescent nucleic acid staining. COMSTAT image analysis indicated that KMnO4 staining increased the estimated biovolume over that determined by nucleic acid staining alone for all strains tested, and revealed non-eDNA EPS networks in Pseudomonas aeruginosa biofilm. In vitro and in vivo testing indicated that KMnO4 reacted with poly-N-acetylglucosamine and Pseudomonas Pel polysaccharide, but did not react strongly with DNA or alginate. KMnO4 staining may have application as a research tool and for diagnostic potential for biofilms in clinical samples.

Soft robotic concepts in catheter design: an on-demand fouling-release urinary catheter

Infectious biofilms are problematic in many healthcare-related devices and are especially challenging and ubiquitous in urinary catheters. This report presents an on-demand fouling-release methodology to mechanically disrupt and remove biofilms, and proposes this method for the active removal of infectious biofilms from the previously inaccessible main drainage lumen of urinary catheters. Mature Proteus mirabilis crystalline biofilms detach from silicone elastomer substrates upon application of strain to the substrate, and increasing the strain rate increases biofilm detachment. The study presents a quantitative relationship between applied strain rate and biofilm debonding through an analysis of biofilm segment length and the driving force for debonding. Based on this mechanism, hydraulic and pneumatic elastomer actuation is used to achieve surface strain selectively within the lumen of prototypes of sections of a fouling-release urinary catheter. Proof-of-concept prototypes of sections of active, fouling-release catheters are constructed using techniques typical to soft robotics including 3D printing and replica molding, and those prototypes demonstrate release of mature P. mirabilis crystalline biofilms (e.g., ≈90%) from strained surfaces. These results provide a basis for the development of a new urinary catheter technology in which infectious biofilms are effectively managed through new methods that are entirely complementary to existing approaches.

On the mechanics of bacterial biofilms on non-dissolvable surgical sutures: a laser scanning confocal microscopy-based finite element study

Biofilms are bacterial communities encapsulated within a self-secreted extracellular polymeric substance and are responsible for a wide range of chronic medical device related infections. Understanding and addressing the conditions that lead to the attachment and detachment of biofilms from biomedical surfaces (orthopaedic implants, sutures, intravenous catheters, cardio-vascular stents) has the potential to identify areas of the device that might be more prone to infection and predict how and when biofilms might dislodge. In this study, an integrated software methodology was devised to create image-based microscopic finite element models of real biofilm colonies of Staphylococcus aureus attached to a fragment of surgical suture. The goal was to predict how deformation of the suture may lead to the potential detachment of biofilm colonies by solving the equations of continuum mechanics using the finite element method for various loading cases. Tension, torsion and bending of the biomaterial structure were simulated, demonstrating that small strains in the suture can produce surface shear stresses sufficient to trigger the sliding of biofilms over the suture surface. Applications of this technique to other medical devices are discussed.