A Two-Dimensional Model of Potassium Signaling and Oscillatory Growth in a Biofilm.

Biofilms are complex communities of bacteria that exhibit a variety of collective behaviors. These behaviors improve their ability to survive in many different environments. One of these collective behaviors seen in Bacillus subtilis is the ability for starving cells to stop the growth of other cells using potassium signaling and voltage changes. This signaling produces an oscillatory growth pattern so that during periods of low growth the nutrients diffuse deeper into the biofilm and reach the nutrient-starved, interior regions of the biomass. In this paper, we develop a mathematical model to describe this oscillatory behavior, and we use this model to develop a two-dimensional simulation that reproduces many of the important features seen in the experimental data. This simulation allows us to examine the spatial patterning of the oscillatory behavior to better understand the relationships between the various regions of the biofilm. Studying the spatial components of the metabolic and voltage oscillations could allow for the development of new control techniques for biofilms with complex shapes.

A Dimensionally Reduced Model of Biofilm Growth Within a Flow Cell.

Biofilms are colonies of bacteria attached to surfaces. They play a critical role in many engineering and medical applications. Scientists study biofilm growth in flow cells but often have limited direct knowledge of the environmental conditions in the apparatus. Using fully resolved, numerical simulations to estimate conditions within a flow cell is computationally expensive. In this paper, we use asymptotic analysis to create a simulation of a biofilm system that has one growth-limiting substrate, and we show that this method runs quickly while maintaining similar accuracy to prior models. These equations can provide a better understanding of the environmental conditions in experiments and can establish the boundary conditions for further smaller-scale numerical simulations.

In Situ Biomineralization and Particle Deposition Distinctively Mediate Biofilm Susceptibility to Chlorine.

Microbial biofilms and mineral precipitation commonly co-occur in engineered water systems, such as cooling towers and water purification systems, and both decrease process performance. Microbial biofilms are extremely challenging to control and eradicate. We previously showed that in situ biomineralization and the precipitation and deposition of abiotic particles occur simultaneously in biofilms under oversaturated conditions. Both processes could potentially alter the essential properties of biofilms, including susceptibility to biocides. However, the specific interactions between mineral formation and biofilm processes remain poorly understood. Here we show that the susceptibility of biofilms to chlorination depends specifically on internal transport processes mediated by biomineralization and the accumulation of abiotic mineral deposits. Using injections of the fluorescent tracer Cy5, we show that Pseudomonas aeruginosa biofilms are more permeable to solutes after in situ calcite biomineralization and are less permeable after the deposition of abiotically precipitated calcite particles. We further show that biofilms are more susceptible to chlorine killing after biomineralization and less susceptible after particle deposition. Based on these observations, we found a strong correlation between enhanced solute transport and chlorine killing in biofilms, indicating that biomineralization and particle deposition regulate biofilm susceptibility by altering biocide penetration into the biofilm. The distinct effects of in situ biomineralization and particle deposition on biocide killing highlight the importance of understanding the mechanisms and patterns of biomineralization and scale formation to achieve successful biofilm control.

Spatial patterns of carbonate biomineralization in biofilms.

Microbially catalyzed precipitation of carbonate minerals is an important process in diverse biological, geological, and engineered systems. However, the processes that regulate carbonate biomineralization and their impacts on biofilms are largely unexplored, mainly because of the inability of current methods to directly observe biomineralization within biofilms. Here, we present a method for in situ, real-time imaging of biomineralization in biofilms and use it to show that Pseudomonas aeruginosa biofilms produce morphologically distinct carbonate deposits that substantially modify biofilm structures. The patterns of carbonate biomineralization produced in situ were substantially different from those caused by accumulation of particles produced by abiotic precipitation. Contrary to the common expectation that mineral precipitation should occur at the biofilm surface, we found that biomineralization started at the base of the biofilm. The carbonate deposits grew over time, detaching biofilm-resident cells and deforming the biofilm morphology. These findings indicate that biomineralization is a general regulator of biofilm architecture and properties.

Methods for characterizing the co-development of biofilm and habitat heterogeneity.

Biofilms are surface-attached microbial communities that have complex structures and produce significant spatial heterogeneities. Biofilm development is strongly regulated by the surrounding flow and nutritional environment. Biofilm growth also increases the heterogeneity of the local microenvironment by generating complex flow fields and solute transport patterns. To investigate the development of heterogeneity in biofilms and interactions between biofilms and their local micro-habitat, we grew mono-species biofilms of Pseudomonas aeruginosa and dual-species biofilms of P. aeruginosa and Escherichia coli under nutritional gradients in a microfluidic flow cell. We provide detailed protocols for creating nutrient gradients within the flow cell and for growing and visualizing biofilm development under these conditions. We also present protocols for a series of optical methods to quantify spatial patterns in biofilm structure, flow distributions over biofilms, and mass transport around and within biofilm colonies. These methods support comprehensive investigations of the co-development of biofilm and habitat heterogeneity.

Modeling the impact of interspecies competition on performance of a microbial fuel cell.

Previous models of biofilms growing in a microbial fuel cell (MFC) have primarily focused on modeling a single growth mechanism: growth via a conductive biofilm matrix, or growth utilizing diffusible electron shuttles or mediators. In this work, we implement both flavors of models in order to explore the competition for space and nutrients in a MFC biofilm populated by both species types. We find that the optimal growth conditions are for bacteria that utilize conductive EPS provided a minimal energy used to create the EPS matrix. Mediator-utilizing bacteria do have favorable niche regions, most notably close to the anode and where exposed to the bulk inflow, where oxidized mediator is readily available.

The extracellular matrix protects Pseudomonas aeruginosa biofilms by limiting the penetration of tobramycin.

Biofilm cells are less susceptible to antimicrobials than their planktonic counterparts. While this phenomenon is multifactorial, the ability of the matrix to reduce antibiotic penetration into the biofilm is thought to be of limited importance studies suggest that antibiotics move fairly rapidly through biofilms. In this study, we monitored the transport of two clinically relevant antibiotics, tobramycin and ciprofloxacin, into non-mucoid Pseudomonas aeruginosa biofilms. To our surprise, we found that the positively charged antibiotic tobramycin is sequestered to the biofilm periphery, while the neutral antibiotic ciprofloxacin readily penetrated. We provide evidence that tobramycin in the biofilm periphery both stimulated a localized stress response and killed bacteria in these regions but not in the underlying biofilm. Although it is unclear which matrix component binds tobramycin, its penetration was increased by the addition of cations in a dose-dependent manner, which led to increased biofilm death. These data suggest that ionic interactions of tobramycin with the biofilm matrix limit its penetration. We propose that tobramycin sequestration at the biofilm periphery is an important mechanism in protecting metabolically active cells that lie just below the zone of sequestration.

A novel prospective three-dimensional analysis of nasolabial fold augmentation.

BACKGROUND: There are many products approved for aesthetic soft tissue augmentation. Despite this abundance, there is limited objective data regarding safety, longevity, and complication rates. Instead, most reports rely on subjective measures to report volume changes and outcomes, making product comparison difficult. OBJECTIVES: The authors developed and validated a mathematical model to prospectively calculate and analyze three-dimensional (3D) volumetric changes associated with nasolabial fold augmentation based on human acellular dermis. METHODS: Seven consecutive patients were included in this prospective review. The patients underwent nasolabial fold treatment with BellaDerm (Musculoskeletal Transplant Foundation, Edison, NJ), administered by a single surgeon. 3D photographs were obtained and analyzed with a novel mathematical model to determine absolute volumetric changes and objective longevity. RESULTS: Mean preoperative nasolabial fold volume was 0.17 mL. The mean one-, three-, and six-month postoperative fill volumes were 0.35, 0.19, and 0.07 mL, respectively. Fill volumes and contour changes returned to baseline by 24 weeks postoperatively in the majority of patients. CONCLUSIONS: The mathematical model utilized in this study provided prospective and objective data regarding longevity and volumetric changes associated with nasolabial fold augmentation. The analysis demonstrated minimal objective filler permanence beyond six months, with peak volume enhancement between one and three months. Adoption of objective 3D mathematical metrics into the assessment of soft tissue filler outcomes is critical to obtaining more accurate product-to-product comparisons.

The performance of a microbial fuel cell depends strongly on anode geometry: a multidimensional modeling study.

A multidimensional biofilm model is developed to simulate biofilm growth on the anode of a Microbial Fuel Cell (MFC). The biofilm is treated as a conductive material, and electrons produced during microbial growth are assumed to be transferred to the anode through a conductive biofilm matrix. Growth of Geobacter sulfurreducens is simulated using the Nernst-Monod kinetic model that was previously developed and later validated in experiments. By implementing a conduction-based biofilm model in two dimensions, we are able to explore the impact of anode density and arrangement on current production in a MFC.

A geometric analysis of mastectomy incisions: Optimizing intraoperative breast volume.

INTRODUCTION: The advent of acellular dermis-based tissue expander breast reconstruction has placed an increased emphasis on optimizing intraoperative volume. Because skin preservation is a critical determinant of intraoperative volume expansion, a mathematical model was developed to capture the influence of incision dimension on subsequent tissue expander volumes. METHODS: A mathematical equation was developed to calculate breast volume via integration of a geometrically modelled breast cross-section. The equation calculates volume changes associated with excised skin during the mastectomy incision by reducing the arc length of the cross-section. The degree of volume loss is subsequently calculated based on excision dimensions ranging from 35 mm to 60 mm. RESULTS: A quadratic relationship between breast volume and the vertical dimension of the mastectomy incision exists, such that incrementally larger incisions lead to a disproportionally greater amount of volume loss. The vertical dimension of the mastectomy incision - more so than the horizontal dimension - is of critical importance to maintain breast volume. Moreover, the predicted volume loss is more profound in smaller breasts and primarily occurs in areas that affect breast projection on ptosis. CONCLUSIONS: The present study is the first to model the relationship between the vertical dimensions of the mastectomy incision and subsequent volume loss. These geometric principles will aid in optimizing intra-operative volume expansion during expander-based breast reconstruction.

The influence of fluid flow on modeling quorum sensing in bacterial biofilms.

In this paper, we study quorum sensing in Pseudomonas aeruginosa biofilms. Quorum sensing is a process where bacteria monitor their population density through the release of extra-cellular signalling molecules. The presence of these molecules affects gene modulation leading to changes in behaviour such as the release of virulence factors. Here, we use numerical methods to approximate a 2-D model of quorum sensing. It is observed that the shape of the biofilm can have a profound effect on the onset of quorum sensing. This has serious repercussions for experimental observations since biofilms of the same biomass but different shapes can produce quite different results.

Modeling how soluble microbial products (SMP) support heterotrophic bacteria in autotroph-based biofilms.

Multi-species biofilm modeling has been used for many years to understand the interactions between species in different biofilm systems, but the complex symbiotic relationship between species is sometimes overlooked, because models do not always include all relevant species and components. In this paper, we develop and use a mathematical model to describe a model biofilm system that includes autotrophic and heterotrophic bacteria and the key products produced by the bacteria. The model combines the methods of earlier multi-species models with a multi-component biofilm model in order to explore the interaction between species via exchange of soluble microbial products (SMP). We show that multiple parameter sets are able to describe the findings of experimental studies, and that heterotrophs growing on autotrophically produced SMP may pursue either r- or K-strategies to sustain themselves when SMP is their only substrate. We also show that heterotrophs can colonize some distance from the autotrophs and still be sustained by autotrophically produced SMP. This work defines the feasible range of parameters for utilization of SMP by heterotrophs and the nature of the interactions between autotrophs and heterotrophs in multi-species, multi-component biofilms.

A two-dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment.

We present a two-dimensional biofilm growth model in a continuum framework using an Eulerian description. A computational technique based on the eXtended Finite Element Method (XFEM) and the level set method is used to simulate the growth of the biofilm. The model considers fluid flow around the biofilm surface, the advection-diffusion and reaction of substrate, variable biomass volume fraction and erosion due to the interfacial shear stress at the biofilm-fluid interface. The key assumptions of the model and the governing equations of transport, biofilm kinetics and biofilm mechanics are presented. Our 2D biofilm growth results are in good agreement with those obtained by Picioreanu et al. (Biotechnol Bioeng 69(5):504-515, 2000). Detachment due to erosion is modeled using two continuous speed functions based on: (a) interfacial shear stress and (b) biofilm height. A relation between the two detachment models in the case of a 1D biofilm is established and simulated biofilm results with detachment in 2D are presented. The stress in the biofilm due to fluid flow is evaluated and higher stresses are observed close to the substratum where the biofilm is attached.

Compartmental neural simulations with spatial adaptivity.

Since their inception, computational models have become increasingly complex and useful counterparts to laboratory experiments within the field of neuroscience. Today several software programs exist to solve the underlying mathematical system of equations, but such programs typically solve these equations in all parts of a cell (or network of cells) simultaneously, regardless of whether or not all of the cell is active. This approach can be inefficient if only part of the cell is active and many simulations must be performed. We have previously developed a numerical method that provides a framework for spatial adaptivity by making the computations local to individual branches rather than entire cells (Rempe and Chopp, SIAM Journal on Scientific Computing, 28: 2139-2161, 2006). Once the computation is reduced to the level of branches instead of cells, spatial adaptivity is straightforward: the active regions of the cell are detected and computational effort is focused there, while saving computations in other regions of the cell that are at or near rest. Here we apply the adaptive method to four realistic neuronal simulation scenarios and demonstrate its improved efficiency over non-adaptive methods. We find that the computational cost of the method scales with the amount of activity present in the simulation, rather than the physical size of the system being simulated. For certain problems spatial adaptivity reduces the computation time by up to 80%.

Influence of the hydrodynamic environment on quorum sensing in Pseudomonas aeruginosa biofilms.

We provide experimental and modeling evidence that the hydrodynamic environment can impact quorum sensing (QS) in a Pseudomonas aeruginosa biofilm. The amount of biofilm biomass required for full QS induction of the population increased as the flow rate increased.

The impact of quorum sensing and swarming motility on Pseudomonas aeruginosa biofilm formation is nutritionally conditional.

The role of quorum sensing in Pseudomonas aeruginosa biofilm formation is unclear. Some researchers have shown that quorum sensing is important for biofilm development, while others have indicated it has little or no role. In this study, the contribution of quorum sensing to biofilm development was found to depend upon the nutritional environment. Depending upon the carbon source, quorum-sensing mutant strains (lasIrhlI and lasRrhlR) either exhibited a pronounced defect early in biofilm formation or formed biofilms identical to the wild-type strain. Quorum sensing was then shown to exert its nutritionally conditional control of biofilm development through regulation of swarming motility. Examination of pilA and fliM mutant strains further supported the role of swarming motility in biofilm formation. These data led to a model proposing that the prevailing nutritional conditions dictate the contributions of quorum sensing and swarming motility at a key juncture early in biofilm development.