Cellular growth in biofilms

Flow modeling and structural characterization in fungal pellets

Fungal pellets are hierarchical systems that can be found in an ample variety of applications. Modeling transport phenomena in this type of systems is a challenging but necessary task to provide knowledge-based processes that improve the outcome of their biotechnological applications. In this work, an upscaled model for total mass and momentum transport in fungal pellets is implemented and analyzed, using elements of the volume averaging and adjoint homogenization methods departing from the governing equations at the microscale in the intracellular and extracellular phases. The biomass is assumed to be composed of a non-Newtonian fluid and the organelles impervious to momentum transport are modeled as a rigid solid phase. The upscaled equations contain effective-medium coefficients, which are predicted from the solution of adjoint closure problems in a three-dimensional periodic domains representative of the microstructure. The construction of these domains was performed for Laccaria trichodermophora based on observations of actual biological structures. The upscaled model was validated with direct numerical simulations in homogeneous portions of the pellets core. It is shown that no significant differences are observed when the dolipores are open or closed to fluid flow. By comparing the predictions of the average velocity in the extracellular phase resulting from the upscaled model with those from the classical Darcy equation (i.e., assuming that the biomass is a solid phase) the contribution of the intracellular fluid phase was evidenced. This work sets the foundations for further studies dedicated to transport phenomena in this type of systems.

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.

Derivation of an Upscaled Model for Mass Transfer and Reaction for Non-Food Starch Conversion to Bioethanol

In this paper, we derive mathematical models for mass transfer and reaction taking place in first-generation bioreactors to convert non-food starch into bioethanol. Given the hierarchical nature of the system, we identified three scale levels ranging from inside bagasse fibers (the pore scale) where the reaction occurs, up to the bioreactor itself (macroscopic scale) where the various products obtained from this reaction are monitored. We derive a macroscopic model at the reactor scale by systematically upscaling the relevant information from the pore scale using the method of volume averaging. A salient feature of the model is that the effective medium coefficients involved are predicted by solving ancillary closure problems in representative unit cells of the different levels of scale. The predictions of the model in terms of CO2 production as well as cellular growth were validated with a close agreement with available experimental data. This work enhances our understanding of the relevance of transport phenomena taking place at the different scales in a bioreactor and may become an aid in design and operation applications of bioethanol production systems.

A Mixed-Culture Biofilm Model with Cross-Diffusion

We propose a deterministic continuum model for mixed-culture biofilms. A crucial aspect is that movement of one species is affected by the presence of the other. This leads to a degenerate cross-diffusion system that generalizes an earlier single-species biofilm model. Two derivations of this new model are given. One, like cellular automata biofilm models, starts from a discrete in space lattice differential equation where the spatial interaction is described by microscopic rules. The other one starts from the same continuous mass balances that are the basis of other deterministic biofilm models, but it gives up a simplifying assumption of these models that has recently been criticized as being too restrictive in terms of ecological structure. We show that both model derivations lead to the same PDE model, if corresponding closure assumptions are introduced. To investigate the role of cross-diffusion, we conduct numerical simulations of three biofilm systems: competition, allelopathy and a mixed system formed by an aerobic and an anaerobic species. In all cases, we find that accounting for cross-diffusion affects local distribution of biomass, but it does not affect overall lumped quantities such as the total amount of biomass in the system.

Anisotropic nutrient transport in three-dimensional single species bacterial biofilms

The ability for a biofilm to grow and function is critically dependent on the nutrient availability, and this in turn is dependent on the structure of the biofilm. This relationship is therefore an important factor influencing biofilm maturation. Nutrient transport in bacterial biofilms is complex; however, mathematical models that describe the transport of particles within biofilms have made three simplifying assumptions: the effective diffusion coefficient (EDC) is constant, the EDC is that of water, and/or the EDC is isotropic. Using a Monte Carlo simulation, we determined the EDC, both parallel to and perpendicular to the substratum, within 131 real, single species, three-dimensional biofilms that were constructed from confocal laser scanning microscopy images. Our study showed that diffusion within bacterial biofilms was anisotropic and depth dependent. The heterogeneous distribution of bacteria varied between and within species, reducing the rate of diffusion of particles via steric hindrance. In biofilms with low porosity, the EDCs for nutrient transport perpendicular to the substratum were significantly lower than the EDCs for nutrient transport parallel to the substratum. Here, we propose a reaction-diffusion model to describe the nutrient concentration within a bacterial biofilm that accounts for the depth dependence of the EDC.

The influence of flow cell geometry related shear stresses on the distribution, structure and susceptibility of Pseudomonas aeruginosa 01 biofilms

The effects of non-uniform hydrodynamic conditions resulting from flow cell geometry (square and rectangular cross-section) on Pseudomonas aeruginosa 01 (PAO1) biofilm formation, location, and structure were investigated for nominally similar flow conditions using a combination of confocal scanning laser microscope (CSLM) and computational fluid dynamics (CFD). The thickness and surface coverage of PAO1 biofilms were observed to vary depending on the location in the flow cell and thus also the local wall shear stress. The biofilm structure in a 5:1 (width to height) aspect ratio rectangular flow cell was observed to consist mainly of a layer of bacterial cells with thicker biofilm formation observed in the flow cell corners. For square cross-section (1:1 aspect ratio) flow cells, generally thicker and more uniform surface coverage biofilms were observed. Mushroom shaped structures with hollow centers and wall breaks, indicative of 'seeding' dispersal structures, were found exclusively in the square cross-section tubes. Exposure of PAO1 biofilms grown in the flow cells to gentamicin revealed a difference in susceptibility. Biofilms grown in the rectangular flow cell overall exhibited a greater susceptibility to gentamicin compared to those grown in square flow cells. However, even within a given flow cell, differences in susceptibility were observed depending on location. This study demonstrates that the spanwise shear stress distribution within the flow cells has an important impact on the location of colonization and structure of the resultant biofilm. These differences in biofilm structure have a significant impact on the susceptibility of the biofilms grown within flow channels. The impact of flow modification due to flow cell geometry should be considered when designing flow cells for laboratory investigation of bacterial biofilms.

Computational pore network modeling of the influence of biofilm permeability on bioclogging in porous media

For many years, controversy has surrounded the use of biofilm models to describe the distribution of microbial biomass in natural or artificial porous media. This use is often advocated on the basis of the relative mathematical simplicity of the biofilm concept, and of the widespread availability of analytical solutions or numerical implementations. However, microscopic observations consistently point to a patchy, rather than homogeneous, distribution of microorganisms at the pore scale in many porous media of interest, even under conditions of severe bioclogging. Also, bioclogging models involving biofilms tend to underpredict the extent of permeability reductions in all be the coarse-textured materials. In this context, computer simulations described in the present article show that some of the limitations of biofilm models to describe the bioclogging of porous media are linked to the common constitutive assumption that biofilms are impermeable, that is, that nutrient transport occurs through the biofilms only by molecular diffusion. When this restriction is alleviated and liquid flow is allowed in the biofilms, the level of bioclogging achievable by a given biomass is very significantly increased and is comparable to that observed in experiments. In addition, the distribution of microorganisms becomes patchy and exhibits a self-organized periodic pattern with pores either entirely filled with biomass or without any biomass at all, again similar to published microscopic observations. These results suggest that biofilm models should not be ruled out a priori for the quantitative description of bioclogging in porous media, as long as biofilms are allowed to be permeable.

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.

Particle-based multidimensional multispecies biofilm model

In this paper we describe a spatially multidimensional (two-dimensional [2-D] and three-dimensional [3-D]) particle-based approach for modeling the dynamics of multispecies biofilms growing on multiple substrates. The model is based on diffusion-reaction mass balances for chemical species coupled with microbial growth and spreading of biomass represented by hard spherical particles. Effectively, this is a scaled-up version of a previously proposed individual-based biofilm model. Predictions of this new particle-based model were quantitatively compared with those obtained with an established one-dimensional (1-D) multispecies model for equivalent problems. A nitrifying biofilm containing aerobic ammonium and nitrite oxidizers, anaerobic ammonium oxidizers, and inert biomass was chosen as an example. The 2-D and 3-D models generally gave the same results. If only the average flux of nutrients needs to be known, 2-D and 1-D models are very similar. However, the behavior of intermediates, which are produced and consumed in different locations within the biofilm, is better described in 2-D and 3-D models because of the multidirectional concentration gradients. The predictions of 2-D or 3-D models are also different from those of 1-D models for slowly growing or minority species in the biofilm. This aspect is related to the mechanism of biomass spreading or advection implemented in the models and should receive more attention in future experimental studies.

Calculation of effective diffusivities for biofilms and tissues

In this study we describe a scheme for numerically calculating the effective diffusivity of cellular systems such as biofilms and tissues. This work extends previous studies in which we developed the macroscale representations of the transport equations for cellular systems based on the subcellular-scale transport and reaction processes. A finite-difference model is used to predict the effective diffusivity of a cellular system on the basis of the subcellular-scale geometry and transport parameters. The effective diffusivity is predicted for a complex three-dimensional structure that is based on laboratory observations of a biofilm, and these numerical predictions are compared with predictions from a simple analytical solution and with experimental data. Our results indicate that, under many practical circumstances, the simple analytical solution can be used to provide reasonable estimates of the effective diffusivity.