Recent advances in mechanical characterisation of biofilm and their significance for material modelling

Inactivation of E. coli O157:H7, Salmonella enterica, and L. monocytogenes through semi-continuous superheated steam treatment with additional effects of enhancing initial germination rate and salinity tolerance

Superheated steam (SHS) is a powerful technology used to reduce bacteria on food surfaces while causing less damage to the underlying sublayer of food compared to conventional heating treatments. In this study, a semi-continuous SHS system was developed to inactivate foodborne pathogens within 1 s (Escherichia coli O157:H7, Salmonella enterica, and Listeria monocytogenes) on radish seed surfaces and to enhance the seeds' salinity tolerance, which is vital for adapting to arid and semi-arid regions. The temperature of the SHS was set to 200 °C and 300 °C, with flow rates of 5 m/s and 7 m/s, and treatments were cycled either once or three times. As a result, increased temperature (200 °C-300 °C) and number of treatments (1 time to 3 times) led to a significantly larger microbial reduction on the surface of radish seeds. E. coli O157:H7, S. enterica, and L. monocytogenes were reduced by 4.42, 4.73, and 3.95 log CFU/g (P < 0.05), respectively, after three SHS treatments at 300 °C and 7 m/s. However, due to the ongoing potential for recovery of residual microorganisms, further research involving combinations is essential to enhance the microbicidal effect. Water imbibition showed significantly higher values in the SHS-treated group up to 30 min, indicating faster germination rates in the SHS-treated group (71.3-81.3%) compared to the control group (52.7%) on the second day, indicating a significant enhancement in germination rate. In addition, the salinity resistance of the radish seeds increased after SHS treatment. When moisturized with 0.5% NaCl solution, more radish seeds germinated after treatment with SHS (40%) than controls (22.7%) (P < 0.05). The results of this study, the first to apply semi-continuous SHS to seeds, are expected to serve as a cornerstone for future pilot-scale investigations aiming to implement the system within the seed industry.

Challenges and current advances in in vitro biofilm characterization

Biofilms are structured communities of bacterial cells encased in a self-produced polymeric matrix, which develop over time and exhibit temporal responses to stimuli from internal biological processes or external environmental changes. They can be detrimental, threatening public health and causing economic loss, while they also play beneficial roles in ecosystem health, biotechnology processes, and industrial settings. Biofilms express extreme heterogeneity in their physical properties and structural composition, resulting in critical challenges in understanding them comprehensively. The lack of detailed knowledge of biofilms and their phenotypes has deterred significant progress in developing strategies to control their negative impacts and take advantage of their beneficial applications. A range of in vitro models and characterization tools have been developed and used to study biofilm growth and, specifically, to investigate the impact of environmental and growth factors on their development. This review article discusses the existing knowledge of biofilm properties and explains how external factors, such as flow condition, surface, interface, and host factor, may impact biofilm growth. The limitations of current tools, techniques, and in vitro models that are currently used for biofilms are also presented.

In Vitro Models of Bacterial Biofilms: Innovative Tools to Improve Understanding and Treatment of Infections

Bacterial infections are a growing concern to the health care systems. Bacteria in the human body are often found embedded in a dense 3D structure, the biofilm, which makes their eradication even more challenging. Indeed, bacteria in biofilm are protected from external hazards and are more prone to develop antibiotic resistance. Moreover, biofilms are highly heterogeneous, with properties dependent on the bacteria species, the anatomic localization, and the nutrient/flow conditions. Therefore, antibiotic screening and testing would strongly benefit from reliable in vitro models of bacterial biofilms. This review article summarizes the main features of biofilms, with particular focus on parameters affecting biofilm composition and mechanical properties. Moreover, a thorough overview of the in vitro biofilm models recently developed is presented, focusing on both traditional and advanced approaches. Static, dynamic, and microcosm models are described, and their main features, advantages, and disadvantages are compared and discussed.

Rheology of Pseudomonas fluorescens biofilms: From experiments to predictive DPD mesoscopic modeling

Bacterial biofilms mechanically behave as viscoelastic media consisting of micron-sized bacteria cross-linked to a self-produced network of extracellular polymeric substances (EPSs) embedded in water. Structural principles for numerical modeling aim at describing mesoscopic viscoelasticity without losing details on the underlying interactions existing in wide regimes of deformation under hydrodynamic stress. Here, we approach the computational challenge to model bacterial biofilms for predictive mechanics in silico under variable stress conditions. Up-to-date models are not entirely satisfactory due to the plethora of parameters required to make them functioning under the effects of stress. As guided by the structural depiction gained in a previous work with Pseudomonas fluorescens [Jara et al., Front. Microbiol. 11, 588884 (2021)], we propose a mechanical modeling by means of Dissipative Particle Dynamics (DPD), which captures the essentials of topological and compositional interactions between bacterial particles and cross-linked EPS-embedding under imposed shear. The P. fluorescens biofilms have been modeled under mechanical stress mimicking shear stresses as undergone in vitro. The predictive capacity for mechanical features in DPD-simulated biofilms has been investigated by varying the externally imposed field of shear strain at variable amplitude and frequency. The parametric map of essential biofilm ingredients has been explored by making the rheological responses to emerge among conservative mesoscopic interactions and frictional dissipation in the underlying microscale. The proposed coarse grained DPD simulation qualitatively catches the rheology of the P. fluorescens biofilm over several decades of dynamic scaling.

Effects of biofilm heterogeneity on the apparent mechanical properties obtained by shear rheometry

Rheometry is an experimental technique widely used to determine the mechanical properties of biofilms. However, it characterizes the bulk mechanical behavior of the whole biofilm. The effects of biofilm mechanical heterogeneity on rheometry measurements are not known. We used laboratory experiments and computer modeling to explore the effects of biofilm mechanical heterogeneity on the results obtained by rheometry. A synthetic biofilm with layered mechanical properties was studied, and a viscoelastic biofilm theory was employed using the Kelvin-Voigt model. Agar gels with different concentrations were used to prepare the layered, heterogeneous biofilm, which was characterized for mechanical properties in shear mode with a rheometer. Both experiments and simulations indicated that the biofilm properties from rheometry were strongly biased by the weakest portion of the biofilm. The simulation results using linearly stratified mechanical properties from a previous study also showed that the weaker portions of the biofilm dominated the mechanical properties in creep tests. We note that the model can be used as a predictive tool to explore the mechanical behavior of complex biofilm structures beyond those accessible to experiments. Since most biofilms display some degree of mechanical heterogeneity, our results suggest caution should be used in the interpretation of rheometry data. It does not necessarily provide the "average" mechanical properties of the entire biofilm if the mechanical properties are stratified.

Coupled CFD-DEM modelling to predict how EPS affects bacterial biofilm deformation, recovery and detachment under flow conditions

The deformation and detachment of bacterial biofilm are related to the structural and mechanical properties of the biofilm itself. Extracellular polymeric substances (EPS) play an important role on keeping the mechanical stability of biofilms. The understanding of biofilm mechanics and detachment can help to reveal biofilm survival mechanisms under fluid shear and provide insight about what flows might be needed to remove biofilm in a cleaning cycle or for a ship to remove biofilms. However, how the EPS may affect biofilm mechanics and its deformation in flow conditions remains elusive. To address this, a coupled computational fluid dynamic– discrete element method (CFD‐DEM) model was developed. The mechanisms of biofilm detachment, such as erosion and sloughing have been revealed by imposing hydrodynamic fluid flow at different velocities and loading rates. The model, which also allows adjustment of the proportion of different functional groups of microorganisms in the biofilm, enables the study of the contribution of EPS toward biofilm resistance to fluid shear stress. Furthermore, the stress–strain curves during biofilm deformation have been captured by loading and unloading fluid shear stress to study the viscoelastic properties of the biofilm. Our predicted emergent viscoelastic properties of biofilms were consistent with relevant experimental measurements.

Dynamic and mechanical evolution of an oil-water interface during bacterial biofilm formation

We present an experimental study combining particle tracking, active microrheology, and differential dynamic microscopy (DDM) to investigate the dynamics and rheology of an oil-water interface during biofilm formation by the bacteria Pseudomonas Aeruginosa PA14. The interface transitions from an active fluid dominated by the swimming motion of adsorbed bacteria at early age to an active viscoelastic system at late ages when the biofilm is established. The microrheology measurements using microscale magnetic rods indicate that the biofilm behaves as a viscoelastic solid at late age. The bacteria motility at the interface during the biofilm formation, which is characterized in the DDM measurements, evolves from diffusive motion at early age to constrained, quasi-localized motion at later age. Similarly, the mobility of passively moving colloidal spheres at the interface decreases significantly with increasing interface age and shows a dependence on sphere size after biofilm formation that is orders-of-magnitude larger than that expected in a homogeneous system in equilibrium. We attribute this anomalous size dependence to either length-scale-dependent rheology of the biofilm or widely differing effects of the bacteria activity on the motion of spheres of different sizes.

Bacterial streamers as colloidal systems: Five grand challenges

Bacteria can thrive in biofilms, which are intricately organized communities with cells encased in a self-secreted matrix of extracellular polymeric substances (EPS). Imposed hydrodynamic stresses can transform this active colloidal dispersion of bacteria and EPS into slender thread-like entities called streamers. In this perspective article, the reader is introduced to the world of such deformable 'bacteria-EPS' composites that are a subclass of the generic flow-induced colloidal structures. While bacterial streamers have been shown to form in a variety of hydrodynamic conditions (turbulent and creeping flows), its abiotic analogues have only been demonstrated in low Reynolds number (Re < 1) particle-laden polymeric flows. Streamers are relevant to a variety of situations ranging from natural formations in caves and river beds to clogging of biomedical devices and filtration membranes. A critical review of the relevant biophysical aspects of streamer formation phenomena and unique attributes of its material behavior are distilled to unveil five grand scientific challenges. The coupling between colloidal hydrodynamics, device geometry and streamer formation are highlighted.

In situ tracking of microbeads for the detection of biofilm formation

In this study, we utilize the free motion of beads incorporated in bacterial suspension to investigate the behavior of the medium surrounding the beads during biofilm formation. The use of imaging techniques such as digital image correlation enables tracking of the movement of beads, which serve as markers in the processed images. This method is applied to detect and characterize biofilm formation. The main originality of this study lies in characterizing the evolution of the typology of bead movements during biofilm formation. The aim is to identify bead behaviors that represent the start of biofilm formation. By observing inert bead movements introduced into the bacterial environment, changes in trajectory typologies are detected and appear to be related to sessile bacterial activity, bacterial hindrance, and adhesion or formation of extracellular material. We use our approach to discriminate between the presence or absence of antibiotics mixed with bacteria and to assess their effectiveness. The results highlight the potential of our approach as nondestructive tracking of biofilm dynamics over time based on optical microscope images.

Effect of predation on the mechanical properties and detachment of MABR biofilms

The membrane-aerated biofilm reactor (MABR) is an emerging wastewater treatment technology that uses O₂-supplying membranes as a biofilm support. Because O₂ is supplied from the biofilm base instead of the bulk liquid, MABR biofilms have distinct microbial community structures and behavior. Past research showed that protozoan predation in MABR biofilms can greatly increase biofilm porosity, producing a void layer at the base of the biofilm. We hypothesized that this void layer could weaken the biofilm and promote sloughing, and investigated this with heterotrophic MABR biofilms. A rheometer was used to measure biofilm mechanical strength, and MABR flow cells were used to explore detachment. MABRs supplied with cycloheximide, a protozoan inhibitor, were used as controls. Predation increased the internal void ratio from 6 ± 7% to 50 ± 16%. The storage modulus was 1,780 ± 1,180 Pa with predation condition, compared to 9,800 ± 4,290 Pa for the control. Similarly, the loss modulus was 1,580 ± 729 Pa with predation and 363 ± 189 Pa for the control. When subjected to an increased flow, the biofilm loss was 44 ± 24% for the flow cell with predation, while only 7 ± 9% for the control. This research shows that predation can have an important impact on biofilm porosity in MABRs, reducing the mechanical strength and increasing detachment. Understanding this phenomenon can help develop more effective biofilm control strategies in MABRs.

Chelate chemistry governs ion-specific stiffening of Bacillus subtilis B-1 and Azotobacter vinelandii biofilms

Unwanted formation of bacterial biofilms can cause problems in both the medical sector and industrial settings. However, removing them from surfaces remains an ongoing challenge since biofilm bacteria efficiently protect themselves from external influences such as mechanical shear forces by embedding themselves into a matrix of extracellular polymeric substances. Here, we discuss microscopic principles, which are responsible for alterations in the viscoelastic properties of biofilms upon contact with metal ions. We suggest that it is a combination of mainly two parameters, that decides if biofilm stiffening occurs or not: the ion size and the detailed configuration of polyanionic macromolecules from the biofilm matrix. Our results provide new insights in the molecular mechanisms that govern the mechanical properties of biofilms. Also, they indicate that hydrogels comprising purified biopolymers can serve as suitable model systems to reproduce certain aspects of biofilm mechanics - provided that the correct biopolymer is chosen.

Genetic Control of Radical Cross-linking in a Semisynthetic Hydrogel

Enhancing materials with the qualities of living systems, including sensing, computation, and adaptation, is an important challenge in designing next-generation technologies. Living materials address this challenge by incorporating live cells as actuating components that control material function. For abiotic materials, this requires new methods that couple genetic and metabolic processes to material properties. Toward this goal, we demonstrate that extracellular electron transfer (EET) from Shewanella oneidensis can be leveraged to control radical cross-linking of a methacrylate-functionalized hyaluronic acid hydrogel. Cross-linking rates and hydrogel mechanics, specifically storage modulus, were dependent on various chemical and biological factors, including S. oneidensis genotype. Bacteria remained viable and metabolically active in the networks for a least 1 week, while cell tracking revealed that EET genes also encode control over hydrogel microstructure. Moreover, construction of an inducible gene circuit allowed transcriptional control of storage modulus and cross-linking rate via the tailored expression of a key electron transfer protein, MtrC. Finally, we quantitatively modeled hydrogel stiffness as a function of steady-state mtrC expression and generalized this result by demonstrating the strong relationship between relative gene expression and material properties. This general mechanism for radical cross-linking provides a foundation for programming the form and function of synthetic materials through genetic control over extracellular electron transfer.

Environmental-Stress-Induced Increased Softness of Electroactive Biofilms, Determined with a Torsional Quartz Crystal Microbalance

Electroactive biofilms are intensely studied not only for energy conversion and electrosynthesis, but also as sensing systems. The electrical current produced by the layer is largely proportional to the rate of metabolism and therefore decreases when the biofilm experiences adverse environmental conditions. Acoustic measurements may complement this approach. The layer's softness can be inferred from shifts of resonance frequency and resonance bandwidth of a quartz crystal microbalance (QCM) contacting these layers. The layer's softness responds to the environment. Both negative potentials of the electrode (the equivalent of "suffocation") and lack of nutrient supply (the equivalent of "starvation") were studied. For comprehensive analysis, torsional resonators operating on three different modes of vibration are suited best. Such data can be fitted with a viscoelastic model, leading to a quantitative estimate of the shear modulus. On a more empirical level, one might also use the ratio of the shift in bandwidth to the negative shift in frequency as an indicator of stress. For ease of operation, one might even replace the torsional resonators with thickness-shear resonators.

Arrested fungal biofilms as low-modulus structural bio-composites: Water holds the key

Biofilms are self-assembling structures consisting of rigid microbial cells embedded in a soft biopolymeric extracellular matrix (ECM), and have been commonly viewed as being detrimental to health and equipment. In this work, we show that biofilms formed by a non-pathogenic fungus Neurospora discreta, are fungal bio-composites (FBCs) that can be directed to self-organize through active stresses to achieve specific properties. We induced active stresses by systematically varying the agitation rate during the growth of FBCs. By growing FBCs that are strong enough to be conventionally tensile loaded, we find that as agitation rate increases, the elongation strain at which the FBCs break, increases linearly, and their elastic modulus correspondingly decreases. Using results from microstructural imaging and thermogravimetry, we rationalize that agitation increases the production of ECM, which concomitantly increases the water content of agitated FBCs up to 250% more than un-agitated FBCs. Water held in the nanopores of the ECM acts a plasticizer and controls the ductility of FBCs in close analogy with polyelectrolyte complexes. This paradigm shift in viewing biofilms as bio-composites opens up the possibility for their use as sustainable, biodegradable, low-modulus structural materials.

Functional group surface modifications for enhancing the formation and performance of exoelectrogenic biofilms on the anode of a bioelectrochemical system

Various new energy technologies have been developed to reduce reliance on fossil fuels. The bioelectrochemical system (BES), an integrated microbial-electrochemical energy conversion process, is projected to be a sustainable and environmentally friendly energy technology. However, low power density is still one of the main limiting factors restricting the practical application of BESs. To enhance power output, functional group modification on anode surfaces has been primarily developed to improve the bioelectrochemical performances of BESs in terms of startup, power density, chemical oxygen demand (COD) removal and coulombic efficiency (CE). This modification could change the anode surface characteristics: roughness, hydrophobicity, biocompatibility, chemical bonding and electrochemically active surface area. This will facilitate bacterial adhesion, biofilm formation and extracellular electron transfer (EET). Additionally, some antibacterial functional groups are applied on air cathodes in order to suppress aerobic biofilms and enhance cathodic oxygen reduction reactions (ORRs). Various modification strategies such as: soaking, heat treatment and plasma modification have been reported to introduce functional groups typically as O-, N- and S-containing groups. In this review, the effects of anode functional groups on electroactive bacteria through the whole biofilm formation process are summarized. In addition, the application of those modification technologies to improve bioelectricity generation, resource recovery, bioelectrochemical analysis and the production of value-added chemicals and biofuels is also discussed. Accordingly, this review aims to help scientists select the most appropriate functional groups and up-to-date methods to improve biofilm formation.

Testing Anti-Biofilm Polymeric Surfaces: Where to Start?

Present day awareness of biofilm colonization on polymeric surfaces has prompted the scientific community to develop an ever-increasing number of new materials with anti-biofilm features. However, compared to the large amount of work put into discovering potent biofilm inhibitors, only a small number of papers deal with their validation, a critical step in the translation of research into practical applications. This is due to the lack of standardized testing methods and/or of well-controlled in vivo studies that show biofilm prevention on polymeric surfaces; furthermore, there has been little correlation with the reduced incidence of material deterioration. Here an overview of the most common methods for studying biofilms and for testing the anti-biofilm properties of new surfaces is provided.

Nondestructive characterization of soft materials and biofilms by measurement of guided elastic wave propagation using optical coherence elastography

Biofilms are soft multicomponent biological materials composed of microbial communities attached to surfaces. Despite the crucial relevance of biofilms to diverse industrial, medical, and environmental applications, the mechanical properties of biofilms are understudied. Moreover, most of the available techniques for the characterization of biofilm mechanical properties are destructive. Here, we detail a model-based approach developed to characterize the viscoelastic properties of soft materials and bacterial biofilms based on experimental data obtained using the nondestructive dynamic optical coherence elastography (OCE) technique. The model predicted the frequency- and geometry-dependent propagation velocities of elastic waves in a soft viscoelastic plate supported by a rigid substratum. Our numerical calculations suggest that the dispersion curves of guided waves recorded in thin soft plates by the dynamic OCE technique are dominated by guided waves, whose phase velocities depend on the viscoelastic properties and plate thickness. The numerical model was validated against experimental measurements in agarose phantom samples with different thicknesses and concentrations. The model was then used to interpret guided wave dispersion curves obtained by the OCE technique in bacterial biofilms developed in a rotating annular reactor, which allowed the quantitative characterization of biofilm shear modulus and viscosity. This study is the first to employ measurements of elastic wave propagation to characterize biofilms, and it provides a novel framework combining a theoretical model and an experimental approach for studying the relationship between the biofilm internal physical structure and mechanical properties.

Determination of mechanical properties of biofilms by modelling the deformation measured using optical coherence tomography

The advantage of using non-invasive imaging such as optical coherence tomography (OCT) to asses material properties from deformed biofilm geometries can be compromised by the assumptions made on fluid forces acting on the biofilm. This study developed a method for the determination of elastic properties of biofilms by modelling the biofilm deformation recorded by OCT imaging with poroelastic fluid-structure interaction computations. Two-dimensional biofilm geometries were extracted from OCT scans of non-deformed and deformed structures as a result of hydrodynamic loading. The biofilm geometries were implemented in a model coupling fluid dynamics with elastic solid mechanics and Darcy flow in the biofilm. The simulation results were compared with real deformed geometries and a fitting procedure allowed estimation of the Young's modulus in given flow conditions. The present method considerably improves the estimation of elastic moduli of biofilms grown in mini-fluidic rectangular channels. This superior prediction is based on the relaxation of several simplifying assumptions made in past studies: shear stress is not anymore taken constant over the biofilm surface, total stress including also pressure is accounted for, any biofilm shape can be used in the determinations, and non-linear behavior of mechanical properties can be estimated. Biofilm elastic moduli between 70 and 700 Pa were obtained and biofilm hardening at large applied stress due to increasing flow velocity was quantified. The work performed here opens the way for in-situ determination of other mechanical properties (e.g., viscoelastic properties, relaxation times, plastic yields) and provides data for modelling biofilm deformation and detachment with eventual applications in biofilm control and removal strategies.

Towards standardized mechanical characterization of microbial biofilms: analysis and critical review

Developing reliable anti-biofilm strategies or efficient biofilm-based bioprocesses strongly depends on having a clear understanding of the mechanisms underlying biofilm development, and knowledge of the relevant mechanical parameters describing microbial biofilm behavior. Many varied mechanical testing methods are available to assess these parameters. The mechanical properties thus identified can then be used to compare protocols such as antibiotic screening. However, the lack of standardization in both mechanical testing and the associated identification methods for a given microbiological goal remains a blind spot in the biofilm community. The pursuit of standardization is problematic, as biofilms are living structures, i.e., both complex and dynamic. Here, we review the main available methods for characterizing the mechanical properties of biofilms through the lens of the relationship linking experimental testing to the identification of mechanical parameters. We propose guidelines for characterizing biofilms according to microbiological objectives that will help the reader choose an appropriate test and a relevant identification method for measuring any given mechanical parameter. The use of a common methodology for the mechanical characterization of biofilms will enable reliable analysis and comparison of microbiological protocols needed for improvement of engineering process and screening.

New insights into MagPI: a promising tool to determine the adhesive capacity of biofilm on the mesoscale

The adhesiveness and stability of ubiquitously distributed biofilms is a significant issue in many areas such as ecology, biotechnology and medicine. The magnetic particle induction (MagPI) system allows precise determinations of biofilm adhesiveness at high temporal and spatial resolution on the mesoscale. This paper concerns several technical aspects to further improve the performance of this powerful experimental approach and enhance the range of MagPI applications. First, several electromagnets were built to demonstrate the influence of material and geometry with special regard to core remanence and magnetic strength. Secondly, the driving force to lift up the particles was evaluated and it was shown that both the magnetic field strength and the magnetic field gradient are decisive in the physics of the MagPI approach. The intricate combination of these two quantities was demonstrated with separate experiments that add permanent magnets to the MagPI system.

Use of torsional resonators to monitor electroactive biofilms

Whereas the study of interfaces and thin films with the quartz crystal microbalance (QCM) is well established, biofilms have proven to be a difficult subject for the QCM. The main problem is that the shear wave emanating from the resonator surface does not usually reach to the top of the sample. This problem can be solved with torsional resonators. These have a resonance frequency in the range of tens of kHz, which is much below the frequency of the thickness-shear QCMs. The depth of penetration of the shear wave is correspondingly larger. Data acquisition and data analysis can proceed in analogy to the conventional thickness-shear QCM. Torsional resonators may also be operated as electrochemical QCMs (EQCMs), meaning that a DC electrical potential may be applied to the active electrode and that shifts of frequency and bandwidth may be acquired in parallel to the electrical current. Here we report on the formation of mixed-culture biofilms dominated by the microorganism Geobacter anodireducens. The viscoelastic analysis evidences an increase in rigidity as the films grows. Potential sweeps on electroactive biofilms reveal a softening under negative potentials, that is, under conditions, where the layer's metabolism was slowed down by insufficient oxidative activity of the substrate. For comparison, biofilms were monitored in parallel with a conventional thickness-shear QCM.

On-demand release of Candida albicans biofilms from urinary catheters by mechanical surface deformation

Candida albicans is a leading cause of catheter-associated urinary tract infections and elimination of these biofilm-based infections without antifungal agents would constitute a significant medical advance. A novel urinary catheter prototype that utilizes on-demand surface deformation is effective at eliminating bacterial biofilms and here the broader applicability of this prototype to remove fungal biofilms has been demonstrated. C. albicans biofilms were debonded from prototypes by selectively inflating four additional intralumens surrounding the main lumen of the catheters to provide the necessary surface strain to remove the adhered biofilm. Deformable catheters eliminated significantly more biofilm than the controls (>90% eliminated vs 10% control; p < 0.001). Mechanical testing revealed that fungal biofilms have an elastic modulus of 45 ± 6.7 kPa with a fracture energy of 0.4-2 J m^-2. This study underscores the potential of mechanical disruption as a materials design strategy to combat fungal device-associated infections.

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.

Advances in the microrheology of complex fluids

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.

Mechanical properties of the superficial biofilm layer determine the architecture of biofilms

Cells in biofilms sense and interact with their environment through the extracellular matrix. The physicochemical properties of the matrix, particularly at the biofilm-environment interface, determine how cells respond to changing conditions. In this study we describe the application of atomic force microscopy and confocal imaging to probe in situ the mechanical properties of these interfacial regions and to elucidate how key matrix components can contribute to the physical sensing by the cells. We describe how the Young's modulus of microcolonies differs according to the size and morphology of microcolonies, as well as the flow rate. The Young's modulus increased as a function of microcolony diameter, which was correlated with the production of the polysaccharide Psl at later stages of maturation for hemispherical or mushroom shaped microcolonies. The Young's modulus of the periphery of the biofilm colony was however independent of the hydrodynamic shear. The morphology of the microcolonies also influenced interfacial or peripheral stiffness. Microcolonies with a diffuse morphology had a lower Young's modulus than isolated, circular ones and this phenomenon was due to a deficiency of Psl. In this way, changes in the specific polysaccharide components imbue the biofilm with distinct physical properties that may modulate the way in which bacteria perceive or respond to their environment. Further, the physical properties of the polysaccharides are closely linked to the specific architectures formed by the developing biofilm.

The development of biofilm architecture

We extend the one-dimensional polymer solution theory of bacterial biofilm growth described by Winstanley et al. (2011 Proc. R. Soc. A467, 1449-1467 (doi:10.1098/rspa.2010.0327)) to deal with the problem of the growth of a patch of biofilm in more than one lateral dimension. The extension is non-trivial, as it requires consideration of the rheology of the polymer phase. We use a novel asymptotic technique to reduce the model to a free-boundary problem governed by the equations of Stokes flow with non-standard boundary conditions. We then consider the stability of laterally uniform biofilm growth, and show that the model predicts spatial instability; this is confirmed by a direct numerical solution of the governing equations. The instability results in cusp formation at the biofilm surface and provides an explanation for the common observation of patterned biofilm architectures.

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.

Effect of Particulate Contaminants on the Development of Biofilms at Air/Water Interfaces

The development of biofilms at air/water or oil/water interfaces has important ramifications on several applications, but it has received less attention than biofilm formation on solid surfaces. A key difference between the growth of biofilms on solid surfaces versus liquid interfaces is the range of complicated boundary conditions the liquid interface can create that may affect bacteria, as they adsorb onto and grow on the interface. This situation is exacerbated by the existence of complex interfaces in which interfacially adsorbed components can even more greatly affect interfacial boundary conditions. In this work, we present evidence as to how particle-laden interfaces impact biofilm growth at an air/water interface. We find that particles can enhance the rate of growth and final strength of biofilms at liquid interfaces by providing sites of increased adhesive strength for bacteria. The increased adhesion stems from creating localized areas of hydrophobicity that protrude in the water phase and provide sites where bacteria preferentially adhere. This mechanism is found to be primarily controlled by particle composition, with particle size providing a secondary effect. This increased adhesion through interfacial conditions creates biofilms with properties similar to those observed when adhesion is increased through biological means. Because of the generally understood ubiquity of increased bacteria attachment to hydrophobic surfaces, this result has general applicability to pellicle formation for many pellicle-forming bacteria.

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.

Biofilm Cohesive Strength as a Basis for Biofilm Recalcitrance: Are Bacterial Biofilms Overdesigned?

Bacterial biofilms are highly resistant to common antibacterial treatments, and several physiological explanations have been offered to explain the recalcitrant nature of bacterial biofilms. Herein, a biophysical aspect of biofilm recalcitrance is being reported on. While engineering structures are often overdesigned with a factor of safety (FOS) usually under 10, experimental measurements of biofilm cohesive strength suggest that the FOS is on the order of thousands. In other words, bacterial biofilms appear to be designed to withstand extreme forces rather than typical or average loads. In scenarios requiring the removal or control of unwanted biofilms, this emphasizes the importance of considering strategies for structurally weakening the biofilms in conjunction with bacterial inactivation.

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.

Quantifying cell adhesion through impingement of a controlled microjet

The impingement of a submerged, liquid jet onto a cell-covered surface allows assessing cell attachment on surfaces in a straightforward and quantitative manner and in real time, yielding valuable information on cell adhesion. However, this approach is insufficiently characterized for reliable and routine use. In this work, we both model and measure the shear stress exerted by the jet on the impingement surface in the micrometer-domain, and subsequently correlate this to jet-induced cell detachment. The measured and numerically calculated shear stress data are in good agreement with each other, and with previously published values. Real-time monitoring of the cell detachment reveals the creation of a circular cell-free area upon jet impingement, with two successive detachment regimes: 1), a dynamic regime, during which the cell-free area grows as a function of both the maximum shear stress exerted by the jet and the jet diameter; followed by 2), a stationary regime, with no further evolution of the cell-free area. For the latter regime, which is relevant for cell adhesion strength assessment, a relationship between the jet Reynolds number, the cell-free area, and the cell adhesion strength is proposed. To illustrate the capability of the technique, the adhesion strength of HeLa cervical cancer cells is determined ((34 ± 14) N/m(2)). Real-time visualization of cell detachment in the dynamic regime shows that cells detach either cell-by-cell or by collectively (for which intact parts of the monolayer detach as cell sheets). This process is dictated by the cell monolayer density, with a typical threshold of (1.8 ± 0.2) × 10(9) cells/m(2), above which the collective behavior is mostly observed. The jet impingement method presents great promises for the field of tissue engineering, as the influence of both the shear stress and the surface characteristics on cell adhesion can be systematically studied.

Artificial biofilms establish the role of matrix interactions in staphylococcal biofilm assembly and disassembly

We demonstrate that the microstructural and mechanical properties of bacterial biofilms can be created through colloidal self-assembly of cells and polymers, and thereby link the complex material properties of biofilms to well understood colloidal and polymeric behaviors. This finding is applied to soften and disassemble staphylococcal biofilms through pH changes. Bacterial biofilms are viscoelastic, structured communities of cells encapsulated in an extracellular polymeric substance (EPS) comprised of polysaccharides, proteins, and DNA. Although the identity and abundance of EPS macromolecules are known, how these matrix materials interact with themselves and bacterial cells to generate biofilm morphology and mechanics is not understood. Here, we find that the colloidal self-assembly of Staphylococcus epidermidis RP62A cells and polysaccharides into viscoelastic biofilms is driven by thermodynamic phase instability of EPS. pH conditions that induce phase instability of chitosan produce artificial S. epidermidis biofilms whose mechanics match natural S. epidermidis biofilms. Furthermore, pH-induced solubilization of the matrix triggers disassembly in both artificial and natural S. epidermidis biofilms. This pH-induced disassembly occurs in biofilms formed by five additional staphylococcal strains, including three clinical isolates. Our findings suggest that colloidal self-assembly of cells and matrix polymers produces biofilm viscoelasticity and that biofilm control strategies can exploit this mechanism.

Live-streaming: Time-lapse video evidence of novel streamer formation mechanism and varying viscosity

Time-lapse videos of growing biofilms were analyzed using a background subtraction method, which removed camouflaging effects from the heterogeneous field of view to reveal evidence of streamer formation from optically dense biofilm segments. In addition, quantitative measurements of biofilm velocity and optical density, combined with mathematical modeling, demonstrated that streamer formation occurred from mature, high-viscosity biofilms. We propose a streamer formation mechanism by sudden partial detachment, as opposed to continuous elongation as observed in other microfluidic studies. Additionally, streamer formation occurred in straight microchannels, as opposed to serpentine or pseudo-porous channels, as previously reported.

Surface indentation and fluid intake generated by the polymer matrix of Bacillus subtilis biofilms

Bacterial biofilms are highly structured, surface associated bacteria colonies held together by a cell-generated polymer network known as EPS (extracellular polymeric substance). This polymer network assists in adhesion to surfaces and generates spreading forces as colonies grow over time. In the laboratory and in nature, biofilms often grow at the interface between air and an elastic, semi-permeable nutrient source. As this type of biofilm increases in volume, an accommodating compression of its substrate may arise, potentially driven by the osmotic pressure exerted by the EPS against the substrate surface. Here we study Bacillus subtilis biofilm force generation by measuring the magnitude and rate of deformation imposed by colonies against the agar-nutrient slabs on which they grow. We find that the elastic stress stored in deformed agar is orders of magnitude larger than the drag stress associated with pulling fluid through the agar matrix. The stress exerted by the biofilm is nearly the same as the osmotic pressure generated by the EPS, and mutant colonies incapable of producing EPS exert much lower levels of stress. The fluid flow rate into B. subtilis biofilms suggest that EPS generated pressure provides some metabolic benefit as colonies expand in volume. These results reveal that long-term biofouling and colony expansion may be tied to the hydraulic permeability and elasticity of the surfaces that biofilms colonize.

Selected metal ions protect Bacillus subtilis biofilms from erosion

Many problems caused by bacterial biofilms can be traced back to their high resilience towards chemical perturbations and their extraordinary sturdiness towards mechanical forces. However, the molecular mechanisms that link the mechanical properties of a biofilm with the ability of bacteria to survive in different chemical environments remain enigmatic. Here, we study the erosion stability of Bacillus subtilis (B. subtilis) biofilms in the presence of different chemical environments. We find that these biofilms can utilize the absorption of certain metal ions such as Cu(2+), Zn(2+), Fe(2+), Fe(3+) and Al(3+) into the biofilm matrix to avoid erosion by shear forces. Interestingly, many of these metal ions are toxic for planktonic B. subtilis bacteria. However, their toxic activity is suppressed when the ions are absorbed into the biofilm matrix. Our experiments clearly demonstrate that the biofilm matrix has to fulfill a dual function, i.e. regulating both the mechanical properties of the biofilm and providing a selective barrier towards toxic chemicals.

Material properties of biofilms-a review of methods for understanding permeability and mechanics

Microorganisms can form biofilms, which are multicellular communities surrounded by a hydrated extracellular matrix of polymers. Central properties of the biofilm are governed by this extracellular matrix, which provides mechanical stability to the 3D biofilm structure, regulates the ability of the biofilm to adhere to surfaces, and determines the ability of the biofilm to adsorb gases, solutes, and foreign cells. Despite their critical relevance for understanding and eliminating of biofilms, the materials properties of the extracellular matrix are understudied. Here, we offer the reader a guide to current technologies that can be utilized to specifically assess the permeability and mechanical properties of the biofilm matrix and its interacting components. In particular, we highlight technological advances in instrumentation and interactions between multiple disciplines that have broadened the spectrum of methods available to conduct these studies. We review pioneering work that furthers our understanding of the material properties of biofilms.

Mechanical properties of a mature biofilm from a wastewater system: from microscale to macroscale level

A fundamental understanding of biofilm mechanical stability is critical in order to describe detachment and develop biofouling control strategies. It is thus important to characterise the elastic deformation and flow behaviour of the biofilm under different modes of applied force. In this study, the mechanical properties of a mature wastewater biofilm were investigated with methods including macroscale compression and microscale indentation using atomic force microscopy (AFM). The mature biofilm was found to be mechanically isotropic at the macroscale level as its mechanical properties did not depend on the scales and modes of loading. However, the biofilm showed a tendency for mechanical inhomogeneity at the microscale level as indentation progressed deeper into the matrix. Moreover, it was observed that the adhesion force had a significant influence on the elastic properties of the biofilm at the surface, subjected to microscale tensile loading. These results are expected to inform a damage-based model for biofilm detachment.

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.

Biophysics of biofilm infection

This article examines a likely basis of the tenacity of biofilm infections that has received relatively little attention: the resistance of biofilms to mechanical clearance. One way that a biofilm infection persists is by withstanding the flow of fluid or other mechanical forces that work to wash or sweep microorganisms out of the body. The fundamental criterion for mechanical persistence is that the biofilm failure strength exceeds the external applied stress. Mechanical failure of the biofilm and release of planktonic microbial cells is also important in vivo because it can result in dissemination of infection. The fundamental criterion for detachment and dissemination is that the applied stress exceeds the biofilm failure strength. The apparent contradiction for a biofilm to both persist and disseminate is resolved by recognizing that biofilm material properties are inherently heterogeneous. There are also mechanical aspects to the ways that infectious biofilms evade leukocyte phagocytosis. The possibility of alternative therapies for treating biofilm infections that work by reducing biofilm cohesion could (1) allow prevailing hydrodynamic shear to remove biofilm, (2) increase the efficacy of designed interventions for removing biofilms, (3) enable phagocytic engulfment of softened biofilm aggregates, and (4) improve phagocyte mobility and access to biofilm.

Biofilm growth: a multi-scale and coupled fluid-structure interaction and mass transport approach

In this paper, we propose a novel approach for modelling biofilm growth. It is based on a finite element method and includes both fluid-structure interaction (FSI) as well as scalar transport effects. Due to the different time-scales of the involved phenomena, the growth of the biofilm structure is coupled with the FSI and mass transport through a multi-scale approach in time. In each hydrodynamic time step, first the non-linear FSI problem is solved followed by the scalar transport equations, using the information on velocities and deformations obtained in the FSI step. After a steady state solution is reached, information on mass fluxes and stresses are passed to the growth model. At this point, the growth is calculated for a biological time step larger than the hydrodynamic one and based on the mass flux through the interface and on normal and shear stresses on it. This type of approach can significantly contribute to the understanding of biofilm development in fluid flows, since the influence of hydrodynamic conditions and availability of nutrients is well known to have effects on biofilm development. Therefore, for the purpose of understanding biofilm macro-scale dynamics, it is essential to adopt a modeling approach, which takes into account all the relevant aspects, like fluid flow, structure deformation, mass transport and their effect on biofilm growth and erosion. First numerical examples demonstrate the suitability of the proposed model to catch the main features of a growing biofilm structure.

A novel methodology providing insights into removal of biofilm-mimicking hydrogel from lateral morphological features of the root canal during irrigation procedures

AIM

To introduce and characterize a reproducible hydrogel as a suitable biofilm mimic in endodontic research. To monitor and visualize the removal of hydrogel from a simulated lateral canal and isthmus for the following: I) Ultrasonic-Activated Irrigation (UAI) with water, ii) UAI with NaOCl and iii) NaOCl without UAI.

METHODOLOGY

A rheometer was used to characterize the viscoelastic properties and cohesive strength of the hydrogel for suitability as a biofilm mimic. The removal rate of the hydrogel from a simulated lateral canal or isthmus was measured by high-speed imaging operating at frame rates from 50 to 30,000 fps.

RESULTS

The hydrogel demonstrated viscoelastic behaviour with mechanical properties comparable to real biofilms. UAI enhanced the cleaning effect of NaOCl in isthmi (P < 0.001) and both NaOCl and water in lateral canals (P < 0.001). A greater depth of cleaning was achieved from an isthmus (P = 0.009) than from a lateral canal with UAI and also at a faster rate for the first 20 s. NaOCl without UAI resulted in a greater depth of hydrogel removal from a lateral canal than an isthmus (P < 0.001). The effect of UAI was reduced when stable bubbles were formed and trapped in the lateral canal. Different removal characteristics were observed in the isthmus and the lateral canal, with initial highly unstable behaviour followed by slower viscous removal inside the isthmus.

CONCLUSIONS

The biofilm-mimicking hydrogel is reproducible, homogenous and can be easily applied and modified. Visualization of its removal from lateral canal anatomy provides insights into the cleaning mechanisms of UAI for a biofilm-like material. Initial results showed that UAI improves hydrogel removal from the accessory canal anatomy, but the creation of stable bubbles on the hydrogel-liquid interface may reduce the cleaning rate.

Modeling of biofilm systems: a review

The modeling of biochemical processes in biofilms is more complex compared to those in suspended biomass due to the existence of substrate gradients. The diffusion and reaction of substrates within the biofilms were simulated in 1D models in the 1970s. The quality of these simulation results was later improved by consideration of mass transfer at the bulk/biofilm interface and detachment of biomass from the surface. Furthermore, modeling of species distribution along the axis perpendicular to the substratum helped to simulate productivity and long-term behavior in multispecies biofilms. Multidimensional models that were able to give a realistic prediction of the surface structure of biofilms were published in the 1990s. The 2D or 3D representation of the distribution of the species in a matrix of extracellular polymeric substances (EPS) helped predict the behavior of multispecies biofilm systems. The influence of shear forces on such 2D or 3D biofilm structures was included by solving the Navier-Stokes equation for the liquid phase above the biofilm. More recently, the interaction between the fluid and biofilm structures was addressed more seriously by no longer considering the biofilm structures as being rigid. The latter approach opened a new door, enabling one to describe biofilms as viscoelastic systems that are not only able to grow and produce but also be deformed or even dislodged if external forces are applied.

Modelling mechanical characteristics of microbial biofilms by network theory

In this contribution, we present a constitutive model to describe the mechanical behaviour of microbial biofilms based on classical approaches in the continuum theory of polymer networks. Although the model is particularly developed for the well-studied biofilms formed by mucoid Pseudomonas aeruginosa strains, it could easily be adapted to other biofilms. The basic assumption behind the model is that the network of extracellular polymeric substances can be described as a superposition of worm-like chain networks, each connected by transient junctions of a certain lifetime. Several models that were applied to biofilms previously are included in the presented approach as special cases, and for small shear strains, the governing equations are those of four parallel Maxwell elements. Rheological data given in the literature are very adequately captured by the proposed model, and the simulated response for a series of compression tests at large strains is in good qualitative agreement with reported experimental behavior.