Structure and shear strength of microbial biofilms as determined with confocal laser scanning microscopy and fluid dynamic gauging using a novel rotating disc biofilm reactor

The cohesive strength of microbial biofilms cultivated on a rotating disc has been measured using fluid dynamic gauging (FDG). The thickness of heterotrophic mixed culture biofilms was found to depend on substrate concentration and shear force at the biofilm surface during the cultivation. For high substrate concentrations and low shear forces the biofilm thickness increased to several 100 microm within 7 days. Low substrate concentration and higher shear forces yielded thin biofilms of about 100 microm thickness. Independent from cultivation conditions and thickness of the biofilms their cohesive strength ranged between 6.0 and 7.7 N m(-2). The ratio between cohesive strength measured with FDG and shear forces applied during biofilm cultivation have ranged from 200 to 1,100. Higher concentrations of iron in the cultivation media has a positive effect on the stability of the biofilms cultivated. By using the CLSM technique a stable base biofilm with a high amount of stained EPS glycoconjugates could be visualized after gauging. The thickness of the base biofilm was about 100 microm for all biofilms cultivated and was not removable under the applied shear conditions used during FDG.     

A study of the efficacy of ultrasonic waves in removing biofilms

doi:10.1111/j.1741‐2358.2009.00325.x
A study of the efficacy of ultrasonic waves in removing biofilms Objective: The removal of adherent biofilms was assessed using ultrasonic waves in a non‐contact mode. Materials and Methods: In in vitro experiments, Streptococcus mutans (S. mutans) biofilms were exposed to ultrasonic waves at various frequencies (280 kHz, 1 MHz, or 2 MHz), duty ratios (0–90%), and exposure times (1–3 minutes), and the optimal conditions for biofilm removal were identified. Furthermore, the effect of adding a contrast medium, such as micro bubbles (Sonazoid^®), was examined. The spatial distribution and architecture of S. mutans biofilms before and after ultrasonic wave exposure were examined via scanning electron microscopy. The biofilm removal effect was also examined in in vivo experiments, using a custom‐made oral cleaning device. Results: When a 280 kHz probe was used, the biofilm‐removing effect increased significantly compared to 1 and 2 MHz probes; more than 80% of the adherent biofilm was removed with a duty cycle of 50–90% and a 3 minutes exposure time. The maximum biofilm‐removing effect was observed with a duty cycle of 80%. Furthermore, the addition of micro bubbles enhanced this biofilm‐removing effect. In in vivo experiments, moderate biofilm removal was observed when a 280 kHz probe was used for 5 minutes. Conclusions: This study demonstrated that ultrasonic wave exposure in a non‐contact mode effectively removed adherent biofilms composed of S. mutans in vitro.     

Inhibition and eradication of Salmonella Typhimurium biofilm using P22 bacteriophage,EDTA and nisin

Abstract

P22 phage >10⁵ PFU ml^?1 could be used to inhibit Salmonella Typhimurium biofilm formation by 55–80%. Concentrations of EDTA >1.25?mM and concentrations of nisin >1,200?µg ml^?1 were also highly effective in reducing S. Typhimurium biofilm formation (≥96% and ≥95% reductions were observed, respectively). A synergistic effect was observed when EDTA and nisin were combined whereas P22 phage in combination with nisin had no synergistic impact on biofilm formation. Triple combination of P22 phage, EDTA and nisin could be also used to inhibit biofilm formation (≥93.2%) at a low phage titer (10² PFU ml^?1), and low EDTA (1.25?mM) and nisin (9.375?µg ml^?1) concentrations. A reduction of 70% in the mature biofilm was possible when 10⁷ PFU ml^?1 of P22 phage, 20?mM of EDTA and 150?μg ml^?1 of nisin were used in combination. This study revealed that it could be possible to reduce biofilm formation by S. Typhimurium by the use of P22 phage, EDTA and nisin, either alone or in combination. Although, removal of the mature biofilm was more difficult, the triple combination could be successfully used for mature biofilm of S. Typhimurium.     

Biofilm characteristics and evaluation of the sanitation procedures of thermophilic Aeribacillus pallidus E334 biofilms

The ability of Aeribacillus pallidus E334 to produce pellicle and form a biofilm was studied. Optimal biofilm formation occurred at 60 °C, pH 7.5 and 1.5% NaCl. Extra polymeric substances (EPS) were composed of proteins and eDNA (21.4 kb). E334 formed biofilm on many surfaces, but mostly preferred polypropylene and glass. Using CLSM analysis, the network-like structure of the EPS was observed. The A. pallidus biofilm had a novel eDNA content. DNaseI susceptibility (86.8% removal) of eDNA revealed its importance in mature biofilms, but the purified eDNA was resistant to DNaseI, probably due to its extended folding outside the matrix. Among 15 cleaning agents, biofilms could be removed with alkaline protease and sodium dodecyl sulphate (SDS). The removal of cells from polypropylene and biomass on glass was achieved with combined SDS/alkaline protease treatment. Strong A. pallidus biofilms could cause risks for industrial processes and abiotic surfaces must be taken into consideration in terms of sanitation procedures.     

Effective biofilm control in a membrane biofilm reactor using a quenching bacterium (Rhodococcus sp. BH4)

The biofilm thickness in membrane biofilm reactors (MBfRs) is an important factor affecting system performance because excessive biofilm formation on the membrane surface inhibits gas diffusion to the interior of the biofilm, resulting in a significant reduction in the performance of contaminant removal. This study provides innovative insights into the control of biofilm thickness in O₂-based MBfRs by using the quorum quenching (QQ) method. The study was carried out in MBfRs operated at different gas pressures and hydraulic retention times (HRTs) using QQ beads containing Rhodococcus sp. BH4 at different amounts. The highest performance was observed in reactors operated with 0.21 ml QQ bead/cm² membrane surface area, 12 HRTs and 1.40 atm. Over this period, the performance increase in chemical oxygen demand (COD) removal was 25%, while the biofilm thickness on the membrane surface was determined to be 250 μm. Moreover, acetate and equivalent oxygen flux results reached 6080 and 10 640 mg·m⁻²·d⁻¹ maximum values, respectively. The extracellular polymeric substances of the biofilm decreased significantly with the increase of gas pressure and QQ beads amount. Polymerase chain reaction denaturing gradient gel electrophoresis results showed that the microbial community in the MBfR system changed depending on operating conditions and bead amount. The results showed that the QQ method was an effective method to control the biofilm thickness in MBfR and provide insights for future research.     

In vitro and clinical evaluation of specific dentifrices for complete denture hygiene

Objectives: To study the physical properties of two experimental dentifrices for complete denture hygiene, their effect on denture biofilm removal and antimicrobial properties by means of a clinical trial. Materials and methods: The experimental dentifrices comprised two compositions. One was based on the addition of 1% chloramine T (D1) and the other on the presence of 0.01% fluorosurfactant (D2). Measurements of density, pH, consistency, rheological features and abrasiveness were conducted. Sixty complete denture wearers were randomly assigned to three groups and were instructed to brush their dentures with a specific toothbrush: (1) Water (control); (2) D1; or (3) D2. Each method was used for 21 days. Denture biofilm was disclosed by a 1% neutral red solution and quantified by means of digital photos taken from the internal surface. Microbiological assessment was conducted to quantify Candida sp. and mutans streptococci. Data were evaluated by one‐way anova and Tukey HSD, or Kruskal–Wallis (α = 0.05). Results: Both dentifrices decreased biofilm coverage when compared with the control group. D1 was the most efficacious treatment to reduce mutans streptococci, whereas D2 showed an intermediate outcome (anova , p < 0.040). No treatment influenced Candida albicans or non‐albicans species (Kruskal–Wallis, p = 0.163 and 0.746, respectively). Conclusion: It can be concluded that brushing complete dentures with the experimental dentifrices tested could be effective for the removal of denture biofilm.     

空肠弯曲杆菌生物膜形成和调控机理研究进展北大核心CSCD

空肠弯曲杆菌(Campylobacter jejuni)分泌胞外多糖和各种胞外蛋白和核酸等相互交联在一起构成生物膜,可增强其在不利环境下的生存率,尤其是对各种洗涤剂、抗生素和消毒剂的耐受力。本文从介质表面性质、温度、气体环境、以及基因的调控等多方面阐述了空肠弯曲杆菌生物膜结构及形成调控机制,同时对各种去除生物膜的实际应用做了分析和展望,为探寻生物膜的控制方法提供参考。     

Characterization of induced Staphylococcus aureus bacteriophage SAP-26 and its anti-biofilm activity with rifampicin

Lytic bacteriophages (phages) have been investigated as treatments for bacterial infectious diseases. An induced phage, SAP-26, was isolated from a clinical isolate of Staphylococcus aureus. It belongs to the family Siphoviridae and its genome consists of double-stranded 41,207 bp DNA coding for 63 open reading frames. The phage SAP-26 showed a wide spectrum of lytic activity against both methicillin-resistant S. aureus and methicillin-susceptible S.aureus. Furthermore, combined treatment with a phage and antimicrobial agents showed a strong biofilm removal effect which induced structural changes in the biofilm matrix and a substantial decrease in the number of bacteria. Such a broad host range in S. aureus and biofilm removal activity of the phage SAP-26 suggests the possibility of its use as a therapeutic phage in combination with appropriate antimicrobial agent(s). Among the three antimicrobial agents combined with phage, the combination of rifampicin showed the best biofilm removal effect. To the authors' knowledge, this study showed for the first time that S. aureus biofilm could be efficiently eradicated with the mixture of phage and an antimicrobial agent, especially rifampicin.     

“Escherichia coli‐milk” biofilm removal from stainless steel surfaces: Synergism between ultrasonic waves and enzymes

Three different methods to standardize biofilm removal for in situ sanitary control of closed surfaces in the food industry have been developed and compared, i.e. sonication, enzymatic treatment and a combined treatment which involved the application of ultrasound to enzyme preparations. The biofilm studied was an Escherichia coli model biofilm, made with milk on stainless steel sheets. Plate counting and epifluorescence microscopy were used to assess the efficiency of each treatment. The results are expressed in percentages, 100% denoting total removal, obtained with a flat ultrasonic transducer (T1) developed and presented in a previous study. The application of ultrasound by a patented curved transducer, T2 (10 s, 40 kHz), specifically devised for closed surfaces, was not sufficient to completely remove the biofilm (30 ± 7%). This biofilm was dislodged by two proteolytic enzyme preparations tested by immersion, viz. a 15‐min application of protease (84±1%) and a 30‐min trypsin application (95±8%). Using a combined treatment, the results showed a synergism between ultrasonic waves and proteolytic or glycolytic enzyme preparations, with removal of a significant amount of biofilm, i.e. 61–96% depending on the conditions tested, i.e. two to three times greater compared to sonication alone (30%). This application was in agreement with an industrial control, i.e. a good reproducible recovery of the biofilm in 10 s compared with 30 or 15 min with the enzyme alone.     

A putative LysR-type transcriptional regulator inhibits biofilm synthesis in Pseudomonas aeruginosa

Biofilm formation is an important virulence factor which is controlled by complex regulatory circuits in Pseudomonas aeruginosa. In this work, a biofilm hyper-producing strain, P2-7, was selected from a collection of transposon insertion mutants in which the PA2121 gene was disrupted. PA2121 was predicted as a putative LysR-type regulator. Analyses showed that it was involved in early biofilm formation, mature biofilm development, and colony morphology. Quantitative measurements revealed that PA2121 repressed biosynthesis of extracellular polysaccharides (alginate, psl and pel). Furthermore, it was observed that PA2121 was self-regulated, highly expressed in the early phase of biofilm development, and subject to the negative regulation by a biofilm synthesis regulator SrpA that binds directly to the PA2121 gene promoter. Collectively, this study proposes that PA2121 is a novel biofilm synthesis repressor (BsrA) in P. aeruginosa.     

Prevention of Staphylococcus aureus biofilm formation and reduction in established biofilm density using a combination of phage K and modified derivatives

Aims: To investigate the ability of a mixture of phage K and six of its modified derivatives to prevent biofilm formation by Staphylococcus aureus and also to reduce the established biofilm density. Methods and Results: The bioluminescence‐producing Staph. aureus Xen29 strain was used in the study, and incubation of this strain in static microtitre plates at 37°C for 48 h confirmed its strong biofilm‐forming capacity. Subsequently, removal of established biofilms of Staph. aureus Xen29 with the high‐titre phage combination was investigated over time periods of 24 h, 48 h and 72 h. Results suggested that these biofilms were eliminated in a time‐dependant manner, with biofilm biomass reduction significantly greater after 72 h than after 24–48 h. In addition, initial challenge of Staph. aureus Xen29 with the phage cocktail resulted in the complete inhibition of biofilm formation over a 48‐h period with no appearance of phage resistance. Conclusions: In general, our findings demonstrate the potential use of a modified phage combination for the prevention and successful treatment of Staph. aureus biofilms, which are implicated in several antibiotic‐resistant infections. Significance and Impact of the Study: This study highlights the first use of phage K for the successful removal and prevention of biofilms of Staph. aureus.     

Applying the digital image correlation method to estimate the mechanical properties of bacterial biofilms subjected to a wall shear stress

A digital image correlation (DIC) method was applied to characterize the mechanical behavior of Pseudomonas aeruginosa biofilms in response to wall shear stress using digital video micrographs taken from biofilm flow cells. The appearance of the biofilm in the transmitted light photomicrographs presented a natural texture which was highly conducive to random encoding for DIC. The displacement fields were calculated for two biofilm specimens. The DIC method concurred with previous analysis showing that biofilms exhibit viscoelastic behavior, but had the advantage over simple length measurements of longitudinal strain that it could precisely measure local strains in length (x) and width (y) within biofilm clusters with a 2 μm resolution as a function of time and wall shear stress. It was concluded that DIC was more accurate at measuring elastic moduli than simple length measurements, but that time-lapse 3D images would enable even more accurate estimates to be performed.     

Candida albicans biofilm formation on soft denture liners and efficacy of cleaning protocols

doi: 10.1111/j.1741‐2358.2011.00485.x
Candida albicans biofilm formation on soft denture liners and efficacy of cleaning protocols Objective: The aim of this study was to investigate Candida albicans biofilm formation on denture liners and to analyse the efficacy of cleaning protocols. Material and methods: Specimens were prepared from four silicone‐based soft denture liners. After artificial ageing and surface free energy determination, specimens were incubated with saliva (2 h) and Candida albicans ATCC 10231 for either short‐ (2.5 h) or long‐term (24 h) biofilm formation. Adherent cells were determined either after incubation of specimens with Candida albicans or after treatment with different denture cleaning protocols. Statistical analysis was performed using one‐way anova and the Games–Howell test (α = 0.05). Results: For both short‐ and long‐term biofilm formation, similar amounts of Candida albicans cells were found on the surface of the different liners (p = 0.295 and 0.178, respectively). For both short‐ and long‐term biofilm formation, the highest cleaning efficacy was observed for sodium hypochlorite (NaOCl; p < 0.01). The efficacy of the chemical denture cleaner in removing long‐term Candida albicans biofilms was significantly lower than the efficacy of removal by brushing (p < 0.001). Conclusion: Different silicone‐based soft denture liners yield similar Candida albicans biofilm formation on their surface. The highest efficacy for the removal of Candida albicans biofilms was identified for NaOCl. Chemical denture cleaners appear to have rather low efficacy to remove mature Candida albicans biofilms.     

In vitro antibiofilm and anti‐adhesion effects of magnesium oxide nanoparticles against antibiotic resistant bacteria

The aim of the current investigation was to determine the antibacterial and antibiofilm potential of MgO nanoparticles (NPs) against antibiotic‐resistant clinical strains of bacteria. MgO NPs were synthesized by a wet chemical method and further characterized by scanning electron microscopy and energy dispersive X‐ray. Antibacterial activity was determined by broth microdilution and agar diffusion methods. The Bradford method was used to assess cellular protein leakage as a result of loss of membrane integrity. Microtiter plate assay following crystal violet staining was employed to determine the effect of MgO NPs on biofilm formation and removal of established biofilms. MIC values ranged between 125 and 500 μg/mL. Moreover, treatment with MgO NPs accelerated rate of membrane disruption, measured as a function of leakage of cellular proteins. Leakage of cellular protein content was greater among gram‐negative bacteria. Cell adherence assay indicated 25.3–49.8% inhibition of bacterial attachment to plastic surfaces. According to a static biofilm method, MgO NPs reduced biofilm formation potential from 31% to 82.9% in a time‐dependent manner. Moreover, NPs also significantly reduced the biomass of 48, 72, 96 and 120 hr old biofilms (P < 0.05). Cytotoxicity experiments using a neutral red assay revealed that MgO NPs are non‐toxic to HeLa cells at concentrations of 15–120 μg/mL. These data provide in vitro scientific evidence that MgO NPs are effective and safe antibiofilm agents that inhibit adhesion, biofilm formation and removal of established biofilms of multidrug‐resistant bacteria.

     

Utilisation of a packed-bed biofilm reactor for the determination of the potential of biofilm accumulation in water systems

Abstract

An experimental system has been developed that allows the monitoring of biofilm development on supports exposed to water of different characteristics. The system consists of a series of packed-bed reactors filled with glass beads, and by periodically removing biofilm attached to these beads for off-line analyses this provides a means for monitoring biofilm development. Despite its reduced dimensions (6.9 cm long and 1.58 cm in diameter), the experimental system used has a sampling surface of 90.3 cm² (including only the surface of the glass beads). This allows reproducible and representative samples to be taken from different water systems, providing a reliable and economic method for evaluating in situ the formation of biofilms from different environments. The set-up of the entire experimental system was constructed to meet the demands of field experiments in a well-defined hydrodynamic environment and to allow easy removal of samples for biomass quantification and microscopic observation. Data obtained using this device can be used as an indicator of the risk of biofilm formation in different water systems. This indicator, “the biofilm accumulation potential”, represents an effective and representative tool for the monitoring of biofilm development in an integrated antifouling strategy, in order to help keep biofouling, scaling and microbial risks under control. According to the experiments with the packed-bed reactors used with a high flow regime, the ratio TCN/HPC could provide an indication of the state of the biofilm, and lower ratios could indicate a higher biofilm accumulation potential.     

Biofilms: strategies for metal corrosion inhibition employing microorganisms

Corrosion causes dramatic economic loss. Currently widely used corrosion control strategies have disadvantages of being expensive, subject to environmental restrictions, and sometimes inefficient. Studies show that microbial corrosion inhibition is actually a common phenomenon. The present review summarizes recent progress in this novel strategy: corrosion control using beneficial bacteria biofilms. The possible mechanisms may involve: (1) removal of corrosive agents (such as oxygen) by bacterial physiological activities (e.g., aerobic respiration), (2) growth inhibition of corrosion-causing bacteria by antimicrobials generated within biofilms [e.g., sulfate-reducing bacteria (SRB) corrosion inhibition by gramicidin S-producing Bacillus brevis biofilm], (3) generation of protective layer by biofilms (e.g., Bacillus licheniformis biofilm produces on aluminum surface a sticky protective layer of γ-polyglutamate). Successful utilization of this novel strategy relies on advances in study at the interface of corrosion engineering and biofilm biology.     

Extracellular DNA in Helicobacter pylori biofilm: a backstairs rumour

Aims: This study detected and characterized the extracellular DNA (eDNA) in the biofilm extracellular polymeric substance (EPS) matrix of Helicobacter pylori and investigated the role of such component in the biofilm development. Methods and Results: Extracellular DNA was purified and characterized in a 2‐day‐old mature biofilm developed by the reference strain H. pylori ATCC 43629, the clinical isolate H. pylori SDB60 and the environmental strain H. pylori MDC1. Subsequently, the role of eDNA in the H. pylori biofilm was evaluated by adding DNase I during biofilm formation and on mature biofilms. Extracellular DNA was detected in the 2‐day‐old EPS biofilm matrix of all analysed H. pylori strains. The DNA fingerprintings, performed by RAPD analysis, on eDNA and intracellular DNA (iDNA), showed some remarkable differences. The data obtained by microtitre biofilm assay as well as colony forming unit count and CLSM (confocal laser scanning microscopy) qualitative analysis did not show any significant differences between the DNase I‐treated biofilms and the corresponding not treated controls both in formation and on mature biofilms. Conclusions: In this study, we provide evidence that eDNA is a component of the EPS matrix of H. pylori biofilm. The different profiles of eDNA and iDNA indicate that lysed cells are not the primary source of eDNA release, suggesting that other active mechanisms might be involved in this process. Moreover, the biomass assay suggests that eDNA may not be the main component of biofilm matrix, suggesting that it could be primarily involved in other mechanisms such as recombination processes, via transformation, contributing to the wide genomic variability of this micro‐organism defined as a ‘quasi‐species’. Significance and Impact of the Study: The presence of eDNA in H. pylori biofilm can contribute to the active dynamic exchange of information aimed to reach the best condition for the bacterial survival in the host and in the environment.     

The ability of an antimicrobial agent to penetrate a biofilm is not correlated with its killing or removal efficiency

The penetration ability of 12 antimicrobial agents, including antibiotics and biocides, was determined against biofilms of B. cereus and P. fluorescens using a colony biofilm assay. The surfactants benzalkonium chloride (BAC) and cetyltrimethyl ammonium bromide (CTAB), and the antibiotics ciprofloxacin and streptomycin were of interest due to their distinct activities. Erythromycin and CTAB were retarded by the presence of biofilms, whereas ciprofloxacin and BAC were not. The removal and killing efficacies of these four agents was additionally evaluated against biofilms formed in microtiter plates. The most efficient biocide was CTAB for both bacterial biofilms. Ciprofloxacin was the best antibiotic although none of the selected antimicrobial agents led to total biofilm removal and/or killing. Comparative analysis of the results obtained with colony biofilms and microtiter plate biofilms show that although extracellular polymeric substances and the biofilm structure are considered a determining factor in biofilm resistance, the ability of an antimicrobial agent to penetrate a biofilm is not correlated with its killing or removal efficiency. Also, the results reinforce the role of an appropriate antimicrobial selection as a key step in the design of disinfection processes for biofilm control.     

Permeability of a growing biofilm in a porous media fluid flow analyzed by magnetic resonance displacement‐relaxation correlations

Biofilm growth in porous media is difficult to study non‐invasively due to the opaqueness and heterogeneity of the systems. Magnetic resonance is utilized to non‐invasively study water dynamics within porous media. Displacement‐relaxation correlation experiments were performed on fluid flow during biofilm growth in a model porous media of mono‐dispersed polystyrene beads. The spin–spin T₂ magnetic relaxation distinguishes between the biofilm phase and bulk fluid phase due to water–biopolymer interactions present in the biofilm, and the flow dynamics are measured using PGSE NMR experiments. By correlating these two measurements, the effects of biofilm growth on the fluid dynamics can be separated into a detailed analysis of both the biofilm phase and the fluid phase simultaneously within the same experiment. Within the displacement resolution of these experiments, no convective flow was measured through the biomass. An increased amount of longitudinal hydrodynamic dispersion indicates increased hydrodynamic mixing due to fluid channeling caused by biofilm growth. The effect of different biofilm growth conditions was measured by varying the strength of the bacterial growth medium. Biotechnol. Bioeng. 2013; 110: 1366–1375. © 2012 Wiley Periodicals, Inc.     

In situ effective diffusion coefficient profiles in live biofilms using pulsed‐field gradient nuclear magnetic resonance

Diffusive mass transfer in biofilms is characterized by the effective diffusion coefficient. It is well documented that the effective diffusion coefficient can vary by location in a biofilm. The current literature is dominated by effective diffusion coefficient measurements for distinct cell clusters and stratified biofilms showing this spatial variation. Regardless of whether distinct cell clusters or surface‐averaging methods are used, position‐dependent measurements of the effective diffusion coefficient are currently: (1) invasive to the biofilm, (2) performed under unnatural conditions, (3) lethal to cells, and/or (4) spatially restricted to only certain regions of the biofilm. Invasive measurements can lead to inaccurate results and prohibit further (time‐dependent) measurements which are important for the mathematical modeling of biofilms. In this study our goals were to: (1) measure the effective diffusion coefficient for water in live biofilms, (2) monitor how the effective diffusion coefficient changes over time under growth conditions, and (3) correlate the effective diffusion coefficient with depth in the biofilm. We measured in situ two‐dimensional effective diffusion coefficient maps within Shewanella oneidensis MR‐1 biofilms using pulsed‐field gradient nuclear magnetic resonance methods, and used them to calculate surface‐averaged relative effective diffusion coefficient (D_rs) profiles. We found that (1) D_rs decreased from the top of the biofilm to the bottom, (2) D_rs profiles differed for biofilms of different ages, (3) D_rs profiles changed over time and generally decreased with time, (4) all the biofilms showed very similar D_rs profiles near the top of the biofilm, and (5) the D_rs profile near the bottom of the biofilm was different for each biofilm. Practically, our results demonstrate that advanced biofilm models should use a variable effective diffusivity which changes with time and location in the biofilm. Biotechnol. Bioeng. 2010;106: 928–937. © 2010 Wiley Periodicals, Inc.