Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach

Microbial metropolis

Microorganisms can form tightly knit communities such as biofilms. Many others include marine snow, anaerobic digester granules, the ginger beer plant and bacterial colonies. This chapter is devoted to a survey of the main properties of these communities, with an emphasis on biofilms. We start with attachment to surfaces and the nature of adhesion. The growing community then forms within a matrix, generally of organic macromolecules. Inevitably the environment within such a matrix is different from that outside. Organisms respond by forming crowd-detection and response units; these quorum sensing systems act as switches between planktonic life and the dramatically altered conditions found inside microbial aggregates. The community then matures and changes and may even fail and disappear. Antimicrobial resistance is discussed as an example of multicellular behavior. The multicellular lifestyle has been modeled mathematically and responded to powerful molecular biological techniques. Latterly, microbial systems have been used as models for fundamental evolutionary processes, mostly because of their high rates of reproduction and the ease of genetic manipulation. The life of most microbes is a duality between the yin of the community and the yang of planktonic existence. Sadly far less research has been devoted to adaptation to free-living forms than in the opposite direction.

Role of mutation in Pseudomonas aeruginosa biofilm development

The survival of bacteria in nature is greatly enhanced by their ability to grow within surface-associated communities called biofilms. Commonly, biofilms generate proliferations of bacterial cells, called microcolonies, which are highly recalcitrant, 3-dimensional foci of bacterial growth. Microcolony growth is initiated by only a subpopulation of bacteria within biofilms, but processes responsible for this differentiation remain poorly understood. Under conditions of crowding and intense competition between bacteria within biofilms, microevolutionary processes such as mutation selection may be important for growth; however their influence on microcolony-based biofilm growth and architecture have not previously been explored. To study mutation in-situ within biofilms, we transformed Pseudomonas aeruginosa cells with a green fluorescent protein gene containing a +1 frameshift mutation. Transformed P. aeruginosa cells were non-fluorescent until a mutation causing reversion to the wildtype sequence occurs. Fluorescence-inducing mutations were observed in microcolony structures, but not in other biofilm cells, or in planktonic cultures of P. aeruginosa cells. Thus microcolonies may represent important foci for mutation and evolution within biofilms. We calculated that microcolony-specific increases in mutation frequency were at least 100-fold compared with planktonically grown cultures. We also observed that mutator phenotypes can enhance microcolony-based growth of P. aeruginosa cells. For P. aeruginosa strains defective in DNA fidelity and error repair, we found that microcolony initiation and growth was enhanced with increased mutation frequency of the organism. We suggest that microcolony-based growth can involve mutation and subsequent selection of mutants better adapted to grow on surfaces within crowded-cell environments. This model for biofilm growth is analogous to mutation selection that occurs during neoplastic progression and tumor development, and may help to explain why structural and genetic heterogeneity are characteristic features of bacterial biofilm populations.

Front instabilities and invasiveness of simulated avascular tumors

We study the interface morphology of a 2D simulation of an avascular tumor composed of identical cells growing in an homogeneous healthy tissue matrix (TM), in order to understand the origin of the morphological changes often observed during real tumor growth. We use the Glazier-Graner-Hogeweg model, which treats tumor cells as extended, deformable objects, to study the effects of two parameters: a dimensionless diffusion-limitation parameter defined as the ratio of the tumor consumption rate to the substrate transport rate, and the tumor-TM surface tension. We model TM as a nondiffusing field, neglecting the TM pressure and haptotactic repulsion acting on a real growing tumor; thus, our model is appropriate for studying tumors with highly motile cells, e.g., gliomas. We show that the diffusion-limitation parameter determines whether the growing tumor develops a smooth (noninvasive) or fingered (invasive) interface, and that the sensitivity of tumor morphology to tumor-TM surface tension increases with the size of the dimensionless diffusion-limitation parameter. For large diffusion-limitation parameters, we find a transition (missed in previous work) between dendritic structures, produced when tumor-TM surface tension is high, and seaweed-like structures, produced when tumor-TM surface tension is low. This observation leads to a direct analogy between the mathematics and dynamics of tumors and those observed in nonbiological directional solidification. Our results are also consistent with the biological observation that hypoxia promotes invasive growth of tumor cells by inducing higher levels of receptors for scatter factors that weaken cell-cell adhesion and increase cell motility. These findings suggest that tumor morphology may have value in predicting the efficiency of antiangiogenic therapy in individual patients.

3D finite element model of biofilm detachment using real biofilm structures from CLSM data

In this work, a three-dimensional model of fluid-structure interactions (FSI) in biofilm systems is developed in order to simulate biofilm detachment as a result of mechanical processes. Therein, fluid flow past the biofilm surface results in a mechanical load on the structure which in turn causes internal stresses in the biofilm matrix. When the strength of the matrix is exceeded parts of the structure are detached. The model is used to investigate the influence of several parameters related to the mechanical strength of the biofilm matrix, Young's modulus, Reynolds number, and biofilm structure on biofilm detachment. Variations in biofilm strength and flow conditions significantly influence the simulation outcome. With respect to structural properties the model is widely independent from a change of Young's modulus. A further result of this work indicates that the change of biofilm structure due to growth or other processes will significantly change the stress distribution in the biofilm and thereby the detachment rate. An increase of the mechanical load by increasing fluid flow results in a flat surface of the remaining biofilm structure. It is concluded that the change of structure during biofilm development is the key determinant in terms of the detachment behavior.

Modeling microbial products in activated sludge under feast-famine conditions

We develop an expanded unified model that integrates production and consumption of internal storage products (X(STO)) into a unified model for extracellular polymeric substances (EPS), soluble microbial products (SMP), and active and inert biomass in activated sludge. We also conducted independent experiments to find needed parameter values and to test the ability of the expanded unified model to describe all the microbial products, along with original substrate and oxygen uptake. The model simulations match all experimental measurements and provide insights into the dynamics of soluble and solid components in activated sludge exposed to dynamic feast-and-famine conditions in two batch experiments and in one cycle of a sequencing batch reactor. In particular, the model illustrates how X(STO) cycles up and down rapidly during feast and famine periods, while EPS and biomass components are relatively stable despite feast and famine. The agreement between model outputs and experimental EPS, SMP, and X(STO) data from distinctly different experiments supports that the expanded unified model properly captures the relationships among the forms of microbial products.

The sociobiology of biofilms

Biofilms are densely packed communities of microbial cells that grow on surfaces and surround themselves with secreted polymers. Many bacterial species form biofilms, and their study has revealed them to be complex and diverse. The structural and physiological complexity of biofilms has led to the idea that they are coordinated and cooperative groups, analogous to multicellular organisms. We evaluate this idea by addressing the findings of microbiologists from the perspective of sociobiology, including theories of collective behavior (self-organization) and social evolution. This yields two main conclusions. First, the appearance of organization in biofilms can emerge without active coordination. That is, biofilm properties such as phenotypic differentiation, species stratification and channel formation do not necessarily require that cells communicate with one another using specialized signaling molecules. Second, while local cooperation among bacteria may often occur, the evolution of cooperation among all cells is unlikely for most biofilms. Strong conflict can arise among multiple species and strains in a biofilm, and spontaneous mutation can generate conflict even within biofilms initiated by genetically identical cells. Biofilms will typically result from a balance between competition and cooperation, and we argue that understanding this balance is central to building a complete and predictive model of biofilm formation.

In vitro models for oral malodor

A model is a representation of some real phenomena and contains aspects or elements of the real system to be modeled. The model reflects (or duplicates) the type of behavior (or mechanisms) seen in the real system. The main characteristic of any model is the mapping of elements or parameters found in the system being studied (e.g. tongue dorsum biofilm in situ) on to the model being devised (e.g. laboratory perfusion biofilm). Such parameters include correct physico-chemical (abiotic) conditions as well as biotic conditions that occur in both model and reality. The main purpose of a model is to provide information that better explains the processes observed or thought to occur in the real system. Such models can be abstract (mental, conceptual, theoretical, mathematical or computational) or 'physical', e.g. in the form of a real disaggregated in vitro system or laboratory model. A wide range of different model systems have been used in oral biofilm research. These will be briefly reviewed with special emphasis on those models that have contributed most to knowledge in breath odor research. The different model systems used in breath odor research are compared. Finally, the requirements for developing an overall 'bad breath model' from considering the processes as a whole (real oral cavity, substrates in saliva, biotransformation by tongue microflora, odor gases in the breath) and extending this to the detection of malodor by the human nose will be outlined and discussed.

Measurements of accumulation and displacement at the single cell cluster level in Pseudomonas aeruginosa biofilms

Quantitative descriptions of biofilm growth and dynamics at the individual cell level are largely missing from the literature. To fill this gap, research was done to describe growth, accumulation and displacement patterns in developing Pseudomonas aeruginosa biofilms. A parent strain of PAO1 was labelled with either a cyan or yellow fluorescent protein. These were then grown in a flow cell biofilm together so that pockets of dividing cells could be identified and their accumulation and displacement tracked. This analysis revealed a pattern of exponential accumulation for all clusters followed by a stationary accumulation phase. A background 'carpet' layer of cells uniformly colonizing the surface exhibited zero net accumulation of bio-volume. The individual clusters were found to have a mean accumulation rate of 0.34 h(-1) with a range of 0.28-0.41 h(-1). Cluster accumulation rates were negatively correlated with cluster size; larger clusters accumulated volume at a slower rate (P < 0.001). Pockets of cells on the inside of clusters initially accumulated at a comparable rate to the cluster within which they resided, but later invariably exhibited zero to slightly negative accumulation despite continued exponential (positive) accumulation of the cluster. Expanding clusters were able to displace neighbouring cells from the surface, and larger clusters displaced smaller clusters. This work provides a more detailed quantitative experimental observation of biofilm behaviour than has been described previously.

Roles of type IV pili, flagellum-mediated motility and extracellular DNA in the formation of mature multicellular structures in Pseudomonas aeruginosa biofilms

When grown as a biofilm in laboratory flow chambers Pseudomonas aeruginosa can develop mushroom-shaped multicellular structures consisting of distinct subpopulations in the cap and stalk portions. We have previously presented evidence that formation of the cap portion of the mushroom-shaped structures in P. aeruginosa biofilms occurs via bacterial migration and depends on type IV pili (Mol Microbiol 50: 61-68). In the present study we examine additional factors involved in the formation of this multicellular substructure. While pilA mutants, lacking type IV pili, are deficient in mushroom cap formation, pilH and chpA mutants, which are inactivated in the type IV pili-linked chemosensory system, showed only minor defects in cap formation. On the contrary, fliM mutants, which are non-flagellated, and cheY mutants, which are inactivated in the flagellum-linked chemotaxis system, were largely deficient in cap formation. Experiments involving DNase treatment of developing biofilms provided evidence that extracellular DNA plays a role in cap formation. Moreover, mutants that are deficient in quorum sensing-controlled DNA release formed microcolonies upon which wild-type bacteria could not form caps. These results constitute evidence that type IV pili, flagellum-mediated motility and quorum sensing-controlled DNA release are involved in the formation of mature multicellular structures in P. aeruginosa biofilms.

Membrane-aerated biofilm reactor for the treatment of acetonitrile wastewater

A membrane-aerated biofilm reactor (MABR) was studied for the treatment of wastewater containing acetonitrile, a typical organonitrile compound. The MABR used hydrophobic hollow fiber membranes as the diffusers for bubbleless aeration as well as the carriers for biofilm growth. The objectives were to prevent the stripping-loss of acetonitrile during aeration and to achieve acetonitrile biodegradation plus nitrogen removal simultaneously in a single biolfilm on the membranes. In the MABR, oxygen and substrates were supplied to the biofilm from opposite sides, in contrast to those from the same side in conventional biofilm bioreactors. Operational factors, including surface loading rate and upflow fluid velocity in the bioreactor, on the effect of acetonitrile biodegradation performance were examined. The profiles of dissolved oxygen concentration and microbial activities and populations in the biofilm were investigated. Experimental results showed that, with the adapted microorganisms, removal of acetonitrile at approximately 98.6 and 83.3%, in terms of total organic carbon and total nitrogen, were achieved at a surface loading rate (in terms of membrane surface) of up to 11.29 g acetonitrile/ m2 x d with an upflow fluid velocity of 12 cm/s and a hydraulic retention time of 30 h. The biofilm on the membranes developed an average thickness of about 1.6 mm in the steady state and consisted of oxic/anoxic/anaerobic zones that provided different functions for acetonitrile degradation, nitrification, and denitrification. The acetonitrile-degrading bacteria in the MABR appeared to secrete more extracellular polymeric substances that enhanced the attachment and development of the biofilm on the membranes. The study demonstrated the potential of using the MABR for the treatment of organonitrile wastewater.

Analysis and IbM simulation of the stages in bacterial lag phase: basis for an updated definition

The lag phase is the initial phase of a culture that precedes exponential growth and occurs when the conditions of the culture medium differ from the pre-inoculation conditions. It is usually defined by means of cell density because the number of individuals remains approximately constant or slowly increases, and it is quantified with the lag parameter lambda. The lag phase has been studied through mathematical modelling and by means of specific experiments. In recent years, Individual-based Modelling (IbM) has provided helpful insights into lag phase studies. In this paper, the definition of lag phase is thoroughly examined. Evolution of the total biomass and the total number of bacteria during lag phase is tackled separately. The lag phase lasts until the culture reaches a maximum growth rate both in biomass and cell density. Once in the exponential phase, both rates are constant over time and equal to each other. Both evolutions are split into an initial phase and a transition phase, according to their growth rates. A population-level mathematical model is presented to describe the transitional phase in cell density. INDividual DIScrete SIMulation (INDISIM) is used to check the outcomes of this analysis. Simulations allow the separate study of the evolution of cell density and total biomass in a batch culture, they provide a depiction of different observed cases in lag evolution at the individual-cell level, and are used to test the population-level model. The results show that the geometrical lag parameter lambda is not appropriate as a universal definition for the lag phase. Moreover, the lag phase cannot be characterized by a single parameter. For the studied cases, the lag phases of both the total biomass and the population are required to fully characterize the evolution of bacterial cultures. The results presented prove once more that the lag phase is a complex process that requires a more complete definition. This will be possible only after the phenomena governing the population dynamics at an individual level of description, and occurring during the lag and exponential growth phases, are well understood.

Biofilm structure differentiation based on multi-resolution analysis

Quantitative parameters for describing the morphology of biofilms are crucial towards establishing the influence of growing conditions on biofilm structure. Parameters used in earlier studies generally fail to differentiate complex three-dimensional structures. This article presents a novel approach of defining a parameter vector based on the energy signature of multi-resolution analysis, which was applied to differentiating biofilm structures from confocal laser scanning microscopy (CLSM) biofilm images. The parameter vector distinguished differences in the spatial arrangements of synthetic images. For real CLSM images, this parameter vector detected subtle differences in biofilm structure for three sample cases: (1) two adjacent images of a CLSM stack; (2) two partial stacks from the same CLSM stack with equal numbers of images but spatially offset by one image; and (3) three complete CLSM stacks from different bacterial strains. It was also observed that filtering the noise in CLSM images enhanced the sensitivity of the differentiation using our parameter vector.

Shifting paradigms in Pseudomonas aeruginosa biofilm research

Biofilms formed by Pseudomonas aeruginosa have long been recognized as a challenge in clinical settings. Cystic fibrosis, endocarditis, device-related infections, and ventilator-associated pneumonia are some of the diseases that are considerably complicated by the formation of bacterial biofilms, which are resistant to most current antimicrobial therapies. Due to intense research efforts, our understanding of the molecular events involved in P. aeruginosa biofilm formation, maintenance, and antimicrobial resistance has advanced significantly. Over the years, several dogmas regarding these multicellular structures have emerged. However, more recent data reveal a remarkable complexity of P. aeruginosa biofilms and force investigators to continually re-evaluate previous findings. This chapter provides examples in which paradigms regarding P. aeruginosa biofilms have been challenged, reflecting the need to critically re-assess what is emerging in this rapidly growing field. In this process, several avenues of research have been opened that will ultimately provide the foundation for the development of preventative measures and therapeutic strategies to successfully treat P. aeruginosa biofilm infections.

Modelling the spatial dynamics of plasmid transfer and persistence

Bacterial plasmids are extra-chromosomal genetic elements that code for a wide variety of phenotypes in their bacterial hosts and are maintained in bacterial communities through both vertical and horizontal transfer. Current mathematical models of plasmid-bacteria dynamics, based almost exclusively on mass-action differential equations that describe these interactions in completely mixed environments, fail to adequately explain phenomena such as the long-term persistence of plasmids in natural and clinical bacterial communities. This failure is, at least in part, due to the absence of any spatial structure in these models, whereas most bacterial populations are spatially structured in microcolonies and biofilms. To help bridge the gap between theoretical predictions and observed patterns of plasmid spread and persistence, an individual-based lattice model (interacting particle system) that provides a predictive framework for understanding the dynamics of plasmid-bacteria interactions in spatially structured populations is presented here. To assess the accuracy and flexibility of the model, a series of experiments that monitored plasmid loss and horizontal transfer of the IncP-1beta plasmid pB10 : : rfp in Escherichia coli K12 and other bacterial populations grown on agar surfaces were performed. The model-based visual patterns of plasmid loss and spread, as well as quantitative predictions of the effects of different initial parental strain densities and incubation time on densities of transconjugants formed on a 2D grid, were in agreement with this and previously published empirical data. These results include features of spatially structured populations that are not predicted by mass-action differential equation models.

Fusarium and Candida albicans biofilms on soft contact lenses: model development, influence of lens type, and susceptibility to lens care solutions

Fungal keratitis is commonly caused by Fusarium species and less commonly by Candida species. Recent outbreaks of Fusarium keratitis were associated with contact lens wear and with ReNu with MoistureLoc contact lens care solution, and biofilm formation on contact lens/lens cases was proposed to play a role in this outbreak. However, no in vitro model for contact lens-associated fungal biofilm has been developed. In this study, we developed and characterized in vitro models of biofilm formation on various soft contact lenses using three species of Fusarium and Candida albicans. The contact lenses tested were etafilcon A, galyfilcon A, lotrafilcon A, balafilcon A, alphafilcon A, and polymacon. Our results showed that clinical isolates of Fusarium and C. albicans formed biofilms on all types of lenses tested and that the biofilm architecture varied with the lens type. Moreover, differences in hyphal content and architecture were found between the biofilms formed by these fungi. We also found that two recently isolated keratitis-associated fusaria formed robust biofilms, while the reference ATCC 36031 strain (recommended by the International Organization for Standardization guidelines for testing of disinfectants) failed to form biofilm. Furthermore, using the developed in vitro biofilm model, we showed that phylogenetically diverse planktonic fusaria and Candida were susceptible to MoistureLoc and MultiPlus. However, Fusarium biofilms exhibited reduced susceptibility against these solutions in a species- and time-dependent manner. This in vitro model should provide a better understanding of the biology and pathogenesis of lens-related fungal keratitis.

Microcolony and biofilm formation as a survival strategy for bacteria

Bacterial communities such as biofilms are widely recognized as being important for survival and persistence of bacteria in harsh environments. Mechanistic models of biofilm growth indicate that the way in which the surface is seeded can effect the morphology of simulated biofilms. Experimental studies indicate that genes which are important for chemotaxis also influence biofilm formation, perhaps by influencing aggregation on a surface. Understanding aggregation and microcolony formation could therefore help clarify factors influencing biofilm formation and illuminate how groups influence the fitness of bacteria. In this paper I develop an individual based model to examine how different behaviors involved in microcolony formation on a surface determine patterns of group sizes and link patterns to bacterial fitness.

One-dimensional mixed-culture biofilm model considering different space occupancies of particulate components

A new one-dimensional mixed-culture biofilm model was derived based on a hypothesis that each particulate component would have different space occupancy within biofilm. Contrary to conventional density-based modeling approaches, in this model the volume change of the biofilm is described with the space occupancies of the particulate components, new model parameters introduced here. The unique feature of this model is that internal pore development during biofilm growth can be predicted implicitly so that the changes of effective diffusivities of soluble components depending on internal porosity are readily implemented in the model. Simulation studies revealed that the presented biofilm model could reasonably describe several important aspects of biofilm growth phenomena. In a mixed-culture biofilm system where heterotrophs and autotrophs were involved, the overall biofilm growth pattern was governed by microbial competition depending on influent composition. In a thick heterotrophic biofilm, a simulated biomass distribution and internal porosity profile showed higher total biomass concentration, lower active cell fraction, and lower internal porosity in the bottom layers of the biofilm, which are well coincident with the experimental data reported previously. All these phenomena can be explained by the proceeding of biofilm consolidation, which happens due to the inter-conversions of the particulate components having different space-occupancy values. The presented biofilm model suggests that the space occupancy of EPS may be a key model parameter to decide the overall biofilm growth pattern by regulating the extent of biofilm consolidation.

A three-dimensional computer model analysis of three hypothetical biofilm detachment mechanisms

Three hypothetical mechanisms of detachment were incorporated into a three-dimensional computer model of biofilm development. The model integrated processes of substrate utilization, substrate diffusion, growth, cell advection, and detachment in a cellular automata framework. The purpose of this investigation was to characterize each of the mechanisms with respect to four criteria: the resulting biofilm structure, the existence of a steady state, the propensity for sloughing events, and the dynamics during starvation. The three detachment mechanisms analyzed represented various physical and biological influences hypothesized to affect biofilm detachment. The first invoked the concept of fluid shear removing biomass that protrudes far above the surface and is therefore subjected to relatively large drag forces. The second pathway linked detachment to changes in the local availability of a nutrient. The third pathway simulated an erosive process in which individual cells are lost from the surface of a biofilm cell cluster. The detachment mechanisms demonstrated diverse behaviors with respect to the four analysis criteria. The height-dependant mechanism produced flat, steady state biofilms that lacked sloughing events. Detachment based on substrate limitation produced significant sloughing events. The resulting biofilm structures included distinct, hollow clusters separated by channels. The erosion mechanism produced neither a non-zero steady state nor sloughing events. A mechanism combining all three-detachment mechanisms produced mushroom-like structures. The dynamics of biofilm decay during starvation were distinct for each detachment mechanism. These results show that detachment is a critical determinant of biofilm structure and of the dynamics of biofilm accumulation and loss.

Multiple roles of biosurfactants in structural biofilm development by Pseudomonas aeruginosa

Recent studies have indicated that biosurfactants produced by Pseudomonas aeruginosa play a role both in maintaining channels between multicellular structures in biofilms and in dispersal of cells from biofilms. Through the use of flow cell technology and enhanced confocal laser scanning microscopy, we have obtained results which suggest that the biosurfactants produced by P. aeruginosa play additional roles in structural biofilm development. We present genetic evidence that during biofilm development by P. aeruginosa, biosurfactants promote microcolony formation in the initial phase and facilitate migration-dependent structural development in the later phase. P. aeruginosa rhlA mutants, deficient in synthesis of biosurfactants, were not capable of forming microcolonies in the initial phase of biofilm formation. Experiments involving two-color-coded mixed-strain biofilms showed that P. aeruginosa rhlA mutants were defective in migration-dependent development of mushroom-shaped multicellular structures in the later phase of biofilm formation. Experiments involving three-color-coded mixed-strain P. aeruginosa biofilms demonstrated that the wild-type and rhlA and pilA mutant strains formed distinct subpopulations on top of each other dependent on their ability to migrate and produce biosurfactants.

A Multidimensional Multispecies Continuum Model for Heterogeneous Biofilm Development

We propose a multidimensional continuum model for heterogeneous growth of biofilm systems with multiple species and multiple substrates. The new model provides a deterministic framework for the study of the interactions between several spe1cies and their effects on biofilm heterogeneity. It consists of a system of partial differential equations derived on the basis of conservation laws and reaction kinetics. The derivation and key assumptions are presented. The assumptions used are a combination of those used in the established one dimensional model, due to Wanner and Gujer, and for the viscous fluid model, of Dockery and Klapper. The work of Wanner and Gujer in particular has been extensively used through the years, and thus this new model is an extension to several spatial dimensions of an already proven working model. The model equations are solved using numerical techniques, for purposes of simulation and verification. The new model is applied to two different biofilm systems in several spatial dimensions, one of which is equivalent to a system originally studied by Wanner and Gujer. Dimensionless formulations for these two systems are given, and numerical simulation results with varying initial conditions are presented.

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.

Tracer measurements reveal experimental evidence of biofilm consolidation

The ability to simultaneously measure both biofilm thickness and the mass transfer coefficient of an inert tracer through it provides a powerful method to study biofilm development. In this communication previously published data has been collated to interpret global trends in biofilm structure during the transition towards steady-state. It appears that sudden changes in biofilm structure (directly related to the rate of change of biofilm mass transfer resistance) may occur following transitions in rate of biomass production. These observations are consistent with the concept of consolidation, recently introduced into spatially structured biofilm mathematical models to account for structural realignment of the biofilm under dynamic conditions.

Biological filtration limits carbon availability and affects downstream biofilm formation and community structure

Carbon removal strategies have gained popularity in the mitigation of biofouling in water reuse processes, but current biofilm-monitoring practices based on organic-carbon concentrations may not provide an accurate representation of the in situ biofilm problem. This study evaluated a submerged microtiter plate assay for direct and rapid monitoring of biofilm formation by subjecting the plates to a continuous flow of either secondary effluent (SE) or biofilter-treated secondary effluent (BF). This method was very robust, based on a high correlation (R(2) = 0.92) between the biomass (given by the A(600) in the microtiter plate assay) and the biovolume (determined from independent biofilms developed on glass slides under identical conditions) measurements, and revealed that the biomasses in BF biofilms were consistently lower than those in SE biofilms. The influence of the organic-carbon content on the biofilm community composition and succession was further evaluated using molecular tools. Terminal restriction fragment length polymorphism analysis of 16S rRNA genes revealed a group of pioneer colonizers, possibly represented by Sphingomonadaceae and Caulobacter organisms, to be common in both SE and BF biofilms. However, differences in organic-carbon availabilities in the two water samples eventually led to the selection of distinct biofilm communities. Alphaproteobacterial populations were confirmed by fluorescence in situ hybridization to be enriched in SE biofilms, while Betaproteobacteria were dominant in BF biofilms. Cloning analyses further demonstrated that microorganisms adapted for survival under low-substrate conditions (e.g., Aquabacterium, Caulobacter, and Legionella) were preferentially selected in the BF biofilm, suggesting that carbon limitation strategies may not achieve adequate biofouling control in the long run.

Three-dimensional biofilm model with individual cells and continuum EPS matrix

An innovative type of biofilm model is derived by combining an individual description of microbial particles with a continuum representation of the biofilm matrix. This hybrid model retains the advantages of each approach, while providing a more realistic description of the temporal development of biofilm structure in two or three spatial dimensions. The general model derivation takes into account any possible number of soluble components. These are substrates and metabolic products, which diffuse and react in the biofilm within individual microbial cells. The cells grow, divide, and produce extracellular polymeric substances (EPS) in a multispecies model setting. The EPS matrix is described by a continuum representation as incompressible viscous fluid, which can expand and retract due to generation and consumption processes. The cells move due to a pushing mechanism between cells in colonies and by an advective mechanism supported by the EPS dynamics. Detachment of both cells and EPS follows a continuum approach, whereas cells attach in discrete events. Two case studies are presented for model illustration. Biofilm consolidation is explained by shrinking due to EPS and cell degradation processes. This mechanism describes formation of a denser layer of cells in the biofilm depth and occurrence of an irregularly shaped biofilm surface under nutrient limiting conditions. Micro-colony formation is investigated by growth of autotrophic microbial colonies in an EPS matrix produced by heterotrophic cells. Size and shape of colonies of ammonia and nitrite-oxidizing bacteria (NOB) are comparatively studied in a standard biofilm and in biofilms aerated from a membrane side.

Multidimensional modelling to investigate interspecies hydrogen transfer in anaerobic biofilms

Anaerobic digestion is a multistep process, mediated by a functionally and phylogenetically diverse microbial population. One of the crucial steps is oxidation of organic acids, with electron transfer via hydrogen or formate from acetogenic bacteria to methanogens. This syntrophic microbiological process is strongly restricted by a thermodynamic limitation on the allowable hydrogen or formate concentration. In order to study this process in more detail, we developed an individual-based biofilm model which enables to describe the processes at a microbial resolution. The biochemical model is the ADM1, implemented in a multidimensional domain. With this model, we evaluated three important issues for the syntrophic relationship: (i) Is there a fundamental difference in using hydrogen or formate as electron carrier? (ii) Does a thermodynamic-based inhibition function produced substantially different results from an empirical function? and; (iii) Does the physical co-location of acetogens and methanogens follow directly from a general model. Hydrogen or formate as electron carrier had no substantial impact on model results. Standard inhibition functions or thermodynamic inhibition function gave similar results at larger substrate field grid sizes (> 10 microm), but at smaller grid sizes, the thermodynamic-based function reduced the number of cells with long interspecies distances (> 2.5 microm). Therefore, a very fine grid resolution is needed to reflect differences between the thermodynamic function, and a more generic inhibition form. The co-location of syntrophic bacteria was well predicted without a need to assume a microbiological based mechanism (e.g., through chemotaxis) of biofilm formation.

Role of cohesion in the material description of biofilms

Biofilm structure plays an important role in biofilm function and control. It is thus important to determine the extent to which mechanics may determine structure in biofilms. We consider a generic qualitative constitutive description of biofilm incorporating as assumptions a small number of fundamental physical properties of biofilm viscoelasticity and cohesion. Implications of cohesive energy on biofilm structure are then explored. Steady solutions and energy minima are studied and it is demonstrated that cohesion energy leads naturally to a free surface film state. It is found that in many circumstances, biofilms could be subject to heterogeneity formation via spinodal decomposition. Such material heterogeneity may have important implications for structural stability in biofilms both on short and long time scales.

Effect of wall growth on the kinetic modeling of nitrite oxidation in a CSTR

A simple kinetic model was developed for describing nitrite oxidation by autotrophic aerobic nitrifiers in a continuous stirred tank reactor (CSTR), in which mixed (suspended and attached) growth conditions prevail. The CSTR system was operated under conditions of constant nitrite feed concentration and varying volumetric flow rates. Experimental data from steady-state conditions in the CSTR system and from batch experiments were used for the determination of the model's kinetic parameters. Model predictions were verified against experimental data obtained under transient operating conditions, when volumetric flow rate and nitrite feed concentration disturbances were imposed on the CSTR. The presented kinetic modeling procedure is quite simple and general and therefore can also be applied to other mixed growth biological systems.

Optical method for long-term and large-scale monitoring of spatial biofilm development

A method was developed that allows biofilm monitoring on the square centimeter scale over extended periods of time. The method is based on image acquisition using a desktop scanner and subsequent image analysis. It was shown that results from grey level analysis are highly correlated with physical properties of the biofilm like average biomass and biofilm thickness. The scanner method was applied to monitor overall biofilm growth, detachment, and surface roughness during two 3 and 4 week long experiments. Two significantly different growth dynamics during the biofilm development could be identified, depending on the biofilm history. Surface roughness on transects in flow direction was always higher than on transects perpendicular to the flow, reflecting the anisotropic characteristics of biofilms growing in a flow field.

A general description of detachment for multidimensional modelling of biofilms

A general method for describing biomass detachment in multidimensional biofilm modelling is introduced. Biomass losses from processes acting on the entire surface of the biofilm, such as erosion, are modelled using a continuous detachment speed function F(det). Discrete detachment events, i.e. sloughing, are implicitly derived from simulations. The method is flexible to allow F(det) to take several forms, including expressions dependent on any state variables such as the local biofilm density. This methodology for biomass detachment was integrated with multidimensional (2D and 3D) particle-based multispecies biofilm models by using a novel application of the level set method. Application of the method is illustrated by trends in the dynamics of biofilms structure and activity derived from simulations performed on a simple model considering uniform biomass (case study I) and a model discriminating biomass composition in heterotrophic active mass, extracellular polymeric substances (EPS) and inert mass (case study II). Results from case study I demonstrate the effect of applied detachment forces as a fundamental factor influencing steady-state biofilm activity and structure. Trends from experimental observations reported in literature were correctly described. For example, simulation results indicated that biomass sloughing is reduced when erosion forces are increased. Case study II illustrates the application of the detachment methodology to systems with non-uniform biomass composition. Simulations carried out at different bulk concentrations of substrate show changes in biofilm structure (in terms of shape, density and spatial distribution of biomass components) and activity (in terms of oxygen and substrate consumption) as a consequence of either oxygen-limited or substrate-limited growth.

Formation of aerobic granules and conversion processes in an aerobic granular sludge reactor at moderate and low temperatures

Temperature changes can influence biological processes considerably. To investigate the effect of temperature changes on the conversion processes and the stability of aerobic granular sludge, an aerobic granular sludge sequencing batch reactor (GSBR) was exposed to short-term and long-term temperature changes. Start-up at 8 degrees C resulted in irregular granules that aggregated as soon as aeration was stopped, which caused severe biomass washout and instable operation. The presence of COD during the aerobic phase is considered to be the major reason for this granule instability. Start-up at 20 degrees C and lowering the temperature to 15 degrees C and 8 degrees C did not have any effect on granule stability and biomass could be easily retained in the system. The temperature dependency of nitrification was lower for aerobic granules than usually found for activated sludge. Due to decreased activity in the outer layers of granules at lower temperatures, the oxygen penetration depth could increase, which resulted in a larger aerobic biomass volume, compensating the decreased activity of individual organisms. Consequently the denitrifying capacity of the granules decreased at reduced temperatures, resulting in an overall poorer nitrogen removal capacity. The overall conclusion that can be drawn from the experiments at low temperatures is that start-up in practice should take place preferentially during warm summer periods, while decreased temperatures during winter periods should not be a problem for granule stability and COD and phosphate removal in a granular sludge system. Nitrogen removal efficiencies should be optimized by changes in reactor operation or cycle time during this season.

Spatial organization of dual-species bacterial aggregates on leaf surfaces

The spatial organization of cells within bacterial aggregates on leaf surfaces was determined for pair-wise mixtures of three different bacterial species commonly found on leaves, Pseudomonas syringae, Pantoea agglomerans, and Pseudomonas fluorescens. Cells were coinoculated onto bean plants and allowed to grow under moist conditions, and the resulting aggregates were examined in situ by epifluorescence microscopy. Each bacterial strain could be localized because it expressed either the green or the cyan fluorescent protein constitutively, and the viability of individual cells was assessed by propidium iodide staining. Each pair of bacterial strains that was coinoculated onto leaves formed mixed aggregates. The degree of segregation of cells in mixed aggregates differed between the different coinoculated pairs of strains and was higher in mixtures of P. fluorescens A506 and P. agglomerans 299R and mixtures of P. syringae B728a and P. agglomerans 299R than in mixtures of two isogenic strains of P. agglomerans 299R. The fractions of the total cell population that were dead in mixed and monospecific aggregates of a gfp-marked strain of P. agglomerans 299R and a cfp-marked strain of P. agglomerans 299R, or of P. fluorescens A506 and P. agglomerans 299R, were similar. However, the proportion of dead cells in mixed aggregates of P. syringae B728a and P. agglomerans 299R was significantly higher (13.2% +/- 8.2%) than that in monospecific aggregates of these two strains (1.6% +/- 0.7%), and it increased over time. While dead cells in such mixed aggregates were preferentially found at the interface between clusters of cells of these strains, cells of these two strains located at the interface did not exhibit equal probabilities of mortality. After 9 days of incubation, about 77% of the P. agglomerans 299R cells located at the interface were dead, while only about 24% of the P. syringae B728a cells were dead. The relevance of our results to understanding bacterial interactions on leaf surfaces and the implications for biological control of pathogenic and other deleterious microorganisms is discussed.

A framework for multidimensional modelling of activity and structure of multispecies biofilms

Concepts from previous biofilm models were integrated to create a framework for the implementation of multidimensional (2D and 3D) multispecies biofilm models. The framework is here described at three levels: (i) mathematical representation of the processes involved in biofilm formation, (ii) numerical implementation into a computer program (freely available from our website http://www.biofilms.bt.tudelft.nl/frameworkMaterial) and (iii) using the program for the creation of biofilm models with multiple bacterial and solute species. An improved version of the individual-based modelling (IbM) that allows structured biomass was used. In this approach biomass composition may be discriminated into any number of particulate species, including extracellular polymeric substances (EPS) for which specific functionality was included. Detachment is also included, described as occurring at the biofilm surface with variable local rates derived from functions of state variables. The application of this modelling framework to a multispecies system with structured biomass is illustrated in a case study where the competition between an organism capable of accumulating polyhydroxybutyrate (PHB, an internal storage compound) and an EPS-producing organism in a two-species biofilm is analysed. Results illustrate that biofilms enriched in PHB-producing organisms may be obtained by supplying substrate intermittently in feast/famine cycles.

Relationship between size and mass transfer resistance in aerobic granules

AIMS

To investigate the size effect of aerobic granules on mass transfer efficiency by introducing the effective factor and the modified Thiele modulus.

METHODS AND RESULTS

Batch experiments of aerobic granules with different sizes were conducted to study the size effect of granules on mass transfer resistance. Results showed that both specific substrate removal and biomass growth rates were size dependent, i.e. reduced rates were observed at big sizes. It was found that the diffusion resistance described by the effective factor and the Thiele modulus increased with the increase of the size of aerobic granules.

CONCLUSIONS

The effective factor should be controlled at values higher than 0.44 and the Thiele modulus lower than 1.05 for efficient mass transfer in aerobic granules.

SIGNIFICANCE AND IMPACT OF THE STUDY

Based on the coupled effective factor and Thiele modulus, an operation guidance including granule radius, kinetics of biomass and environmental conditions could be proposed for stable aerobic granulation.

Modeling biofilm and floc diffusion processes based on analytical solution of reaction-diffusion equations

Biofilm modeling is often considered as a complex mathematical subject. This paper evaluates simple equations to describe the basic processes in a biofilm system with the main aim to show several interesting applications. To avoid mathematical complexity the simulations are carried out in a simple spreadsheet. Frequently, only the solution for zero-order reaction kinetics of the reaction-diffusion equation is used (better known as half-order kinetics). A weighted average of the analytical solutions for zero- and first-order reactions is proposed as basic and useful model to describe steady-state (in biofilm composition) biofilm reactors. This approach is compared with several modeling approaches, such as the simple solution for zero-order reaction and more complex ones (i) direct numerical solution for the diffusion equations, (ii) 1-D AQUASIM and (iii) 2-D modeling. The systems evaluated are single and multiple species biofilms. It is shown that for describing conversions in biofilm reactors, the zero-order solution is generally sufficient; however, for design purposes large deviations of the correct solution can occur. Additionally, the role of diffusion in flocculated and granular sludge systems is discussed. The relation between the measured (apparent) substrate affinity constant and diffusion processes is outlined.

Simultaneous COD, nitrogen, and phosphate removal by aerobic granular sludge

Aerobic granular sludge technology offers a possibility to design compact wastewater treatment plants based on simultaneous chemical oxygen demand (COD), nitrogen and phosphate removal in one sequencing batch reactor. In earlier studies, it was shown that aerobic granules, cultivated with an aerobic pulse-feeding pattern, were not stable at low dissolved oxygen concentrations. Selection for slow-growing organisms such as phosphate-accumulating organisms (PAO) was shown to be a measure for improved granule stability, particularly at low oxygen concentrations. Moreover, this allows long feeding periods needed for economically feasible full-scale applications. Simultaneous nutrient removal was possible, because of heterotrophic growth inside the granules (denitrifying PAO). At low oxygen saturation (20%) high removal efficiencies were obtained; 100% COD removal, 94% phosphate (P-) removal and 94% total nitrogen (N-) removal (with 100% ammonium removal). Experimental results strongly suggest that P-removal occurs partly by (biologically induced) precipitation. Monitoring the laboratory scale reactors for a long period showed that N-removal efficiency highly depends on the diameter of the granules.

Detachment and diffusive-convective transport in an evolving heterogeneous two-dimensional biofilm hybrid model

Under the hypothesis of correlation between biofilm survival and nutrient availability, by considering fluid drag forces and mortality due to nutrient depletion, a biofilm detachment/breaking condition is derived. The mechanisms leading to biofilm detachment/breaking are discussed. We construct and describe a hybrid model for a heterogeneous biofilm attached to walls in a channel where liquid is flowing. The model is called hybrid because it couples conservation equations with a cellular automaton. The biofilm layer is viewed as a porous medium with variable porosity, tortuosity, and permeability. The model is solved using asymptotic and finite differences methods. Results for porosity, nutrient distribution, and average surface location are presented. The model is capable of reproducing biofilm heterogeneity as well as the typical surface fingering (mushroomlike structure).