A mathematical model of competition between fiber and mucin degraders in the gut provides a possible explanation for mucus thinning.

The human gut microbiota relies on complex carbohydrates (glycans) for energy and growth, primarily dietary fiber and host-derived mucins. We introduce a mathematical model of a glycan generalist and a mucin specialist in a two-compartment chemostat model of the human colon. Our objective is to characterize the influence of dietary fiber and mucin supply on the abundance of mucin-degrading species within the gut ecosystem. Current mathematical gut reactor models that include the enzymatic degradation of glycans do not differentiate between glycan types and their degraders. The model we present distinguishes between a generalist that can degrade both dietary fiber and mucin, and a specialist species that can only degrade mucin. The integrity of the colonic mucus barrier is essential for overall human health and well-being, with the mucin specialist Akkermanisa muciniphila being associated with a healthy mucus layer. Competition, particularly between the specialist and generalists like Bacteroides thetaiotaomicron, may lead to mucus layer erosion, especially during periods of dietary fiber deprivation. Our model treats the colon as a gut reactor system, dividing it into two compartments that represent the lumen and the mucus of the gut, resulting in a complex system of ordinary differential equations with a large and uncertain parameter space. To understand the influence of model parameters on long-term behavior, we employ a random forest classifier, a supervised machine learning method. Additionally, a variance-based sensitivity analysis is utilized to determine the sensitivity of steady-state values to changes in model parameter inputs. By constructing this model, we can investigate the underlying mechanisms that control gut microbiota composition and function, free from confounding factors.

Multiscale Modeling of Uranium Bioreduction in Porous Media by One-Dimensional Biofilms.

We formulate a multiscale mathematical model that describes the bioreduction of uranium in porous media. On the mesoscale we describe the bioreduction of uranium [VI] to uranium [IV] using a multispecies one-dimensional biofilm model with suspended bacteria and thermodynamic growth inhibition. We upscale the mesoscopic (colony scale) model to the macroscale (reactor scale) and investigate the behavior of substrate utilization and production, attachment and detachment processes, and thermodynamic effects not usually considered in biofilm growth models. Simulation results of the reactor model indicate that thermodynamic inhibition quantitatively alters the dynamics of the model and neglecting thermodynamic effects may over- or underestimate chemical concentrations in the system. Furthermore, we numerically investigate uncertainties related to the specific choice of attachment and detachment rate coefficients and find that while increasing the attachment rate coefficient or decreasing the detachment rate coefficient leads to thicker biofilms, performance of the reactor remains largely unaffected.

Thermodynamic Inhibition in a Biofilm Reactor with Suspended Bacteria.

We formulate a biofilm reactor model with suspended bacteria that accounts for thermodynamic growth inhibition. The reactor model is a chemostat style model consisting of a single replenished growth promoting substrate, a single reaction product, suspended bacteria, and wall attached bacteria in the form of a bacterial biofilm. We present stability conditions for the washout equilibrium using standard techniques, demonstrating that analytical results are attainable even with the added complexity from thermodynamic inhibition. Furthermore, we numerically investigate the longterm behaviour. In the computational study, we investigate model behaviour for select parameters and two commonly used detachment functions. We investigate the effects of thermodynamic inhibition on the model and find that thermodynamic inhibition limits substrate utilization/production both inside the biofilm and inside the aqueous phase, resulting in less suspended bacteria and a thinner biofilm.

Hemodynamic assessment of diastolic function for experimental models.

Traditionally, the evaluation of cardiac function has focused on systolic function; however, there is a growing appreciation for the contribution of diastolic function to overall cardiac health. Given the emerging interest in evaluating diastolic function in all models of heart failure, there is a need for sensitivity, accuracy, and precision in the hemodynamic assessment of diastolic function. Hemodynamics measure cardiac pressures in vivo, offering a direct assessment of diastolic function. In this review, we summarize the underlying principles of diastolic function, dividing diastole into two phases: 1) relaxation and 2) filling. We identify parameters used to comprehensively evaluate diastolic function by hemodynamics, clarify how each parameter is obtained, and consider the advantages and limitations associated with each measure. We provide a summary of the sensitivity of each diastolic parameter to loading conditions. Furthermore, we discuss differences that can occur in the accuracy of diastolic and systolic indices when generated by automated software compared with custom software analysis and the magnitude each parameter is influenced during inspiration with healthy breathing and a mild breathing load, commonly expected in heart failure. Finally, we identify key variables to control (e.g., body temperature, anesthetic, sampling rate) when collecting hemodynamic data. This review provides fundamental knowledge for users to succeed in troubleshooting and guidelines for evaluating diastolic function by hemodynamics in experimental models of heart failure.

Thermodynamic Inhibition in Chemostat Models : With an Application to Bioreduction of Uranium.

We formulate a mathematical model of bacterial populations in a chemostat setting that also accounts for thermodynamic growth inhibition as a consequence of chemical reactions. Using only elementary mathematical and chemical arguments, we carry this out for two systems: a simple toy model with a single species, a single substrate, and a single reaction product, and a more involved model that describes bioreduction of uranium[VI] into uranium[IV]. We find that in contrast to most traditional chemostat models, as a consequence of thermodynamic inhibition the equilibria concentrations of nutrient substrates might depend on their inflow concentration and not only on reaction parameters and the reactor's dilution rate. Simulation results of the uranium degradation model indicate that thermodynamic growth inhibition quantitatively alters the solution of the model. This suggests that neglecting thermodynamic inhibition effects in systems where they play a role might lead to wrong model predictions and under- or over-estimate the efficacy of the process under investigation.

Simulation-Based Exploration of Quorum Sensing Triggered Resistance of Biofilms to Antibiotics.

We present a mathematical model of biofilm response to antibiotics, controlled by a quorum sensing system that confers increased resistance. The model is a highly nonlinear system of partial differential equations that we investigate in computer simulations. Our results suggest that an adaptive, quorum sensing-controlled, mechanism to switch between modes of fast growth with little protection and protective modes of slow growth may confer benefits to biofilm populations. It enhances the formation of micro-niches in the inner regions of the biofilm in which bacteria are not easily reached by antibiotics. Whereas quorum sensing inhibitors can delay the onset of increased resistance, their advantage is lost after up-regulation. This emphasizes the importance of timing for treatment of biofilms with antibiotics.

A Mathematical Model of Forager Loss in Honeybee Colonies Infested with Varroa destructor and the Acute Bee Paralysis Virus.

We incorporate a mathematical model of Varroa destructor and the Acute Bee Paralysis Virus with an existing model for a honeybee colony, in which the bee population is divided into hive bees and forager bees based on tasks performed in the colony. The model is a system of five ordinary differential equations with dependent variables: uninfected hive bees, uninfected forager bees, infected hive bees, virus-free mites and virus-carrying mites. The interplay between forager loss and disease infestation is studied. We study the stability of the disease-free equilibrium of the bee-mite-virus model and observe that the disease cannot be fought off in the absence of varroacide treatment. However, the disease-free equilibrium can be stable if the treatment is strong enough and also if the virus-carrying mites become virus-free at a rate faster than the mite birth rate. The critical forager loss due to homing failure, above which the colony fails, is calculated using simulation experiments for disease-free, treated and untreated mite-infested, and treated virus-infested colonies. A virus-infested colony without varroacide treatment fails regardless of the forager mortality rate.

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.

A Mathematical Model of the Honeybee-Varroa destructor-Acute Bee Paralysis Virus System with Seasonal Effects.

A mathematical model for the honeybee-varroa mite-ABPV system is proposed in terms of four differential equations for the: infected and uninfected bees in the colony, number of mites overall, and of mites carrying the virus. To account for seasonal variability, all parameters are time periodic. We obtain linearized stability conditions for the disease-free periodic solutions. Numerically, we illustrate that, for appropriate parameters, mites can establish themselves in colonies that are not treated with varroacides, leading to colonies with slightly reduced number of bees. If some of these mites carry the virus, however, the colony might fail suddenly after several years without a noticeable sign of stress leading up to the failure. The immediate cause of failure is that at the end of fall, colonies are not strong enough to survive the winter in viable numbers. We investigate the effect of the initial disease infestation on collapse time, and how varroacide treatment affects long-term behavior. We find that to control the virus epidemic, the mites as disease vector should be controlled.

A modeling and simulation study of the role of suspended microbial populations in nitrification in a biofilm reactor.

Many biological wastewater treatment processes are based on bacterial biofilms, i.e. layered aggregates of microbial populations deposited on surfaces. Detachment and (re-)attachment leads to an exchange of biomass between the biofilm and the surrounding aqueous phase. Traditionally, mathematical models of biofilm processes do not take the contribution of the suspended, non-attached bacteria into account, implicitly assuming that these are negligible due to the relatively small amount of suspended biomass compared to biofilm biomass. In this paper, we present a model for a nitrifying biofilm reactor that explicitly includes both types of biomass. The model is derived by coupling a reactor mass balance for suspended populations and substrates with a full one-dimensional Wanner-Gujer type biofilm model. The complexity of this model, both with respect to mathematical structure and number of parameters, prevents a rigorous analysis of its dynamics, wherefore we study the model numerically.Our investigations show that suspended biomass needs to be considered explicitly in the model if the interests of the study are the details of the nitrification process and its intermediate steps and compounds. However, suspended biomass may be neglected if the primary interests are the overall reactor performance criteria, such as removal rates. Furthermore, it can be expected that changes in the biofilm area, attachment, detachment, and dilution rates are more likely to affect the variables primarily associated with the second step of nitrification, while the variables associated with the first step tend to be more robust.

Flow currents and ventilation in Langstroth beehives due to brood thermoregulation efforts of honeybees.

Beekeepers universally agree that ensuring sufficient ventilation is vital for sustaining a thriving, healthy honeybee colony. Despite this fact, surprisingly little is known about the ventilation and flow patterns in bee hives. We take a first step towards developing a model-based approach that uses computational fluid dynamics to simulate natural ventilation flow inside a standard Langstroth beehive. A 3-D model of a Langstroth beehive with one brood chamber and one honey super was constructed and inside it the honeybee colony was distributed among different clusters each occupying the different bee-spaces between frames in the brood chamber. For the purpose of modeling, each honeybee cluster was treated as an air-saturated porous medium with constant porosity. Heat and mass transfer interactions of the honeybees with the air, the outcome of metabolism, were captured in the porous medium model as source and sink terms appearing in the governing equations of fluid dynamics. The temperature of the brood that results from the thermoregulation efforts of the colony is applied as a boundary condition for the governing equations. The governing equations for heat, mass transport and fluid flow were solved using Fluent(©), a commercially available CFD program. The results from the simulations indicate that (a) both heat and mass transfer resulting from honeybee metabolism play a vital role in determining the structure of the flow inside the beehive and mass transfer cannot be neglected, (b) at low ambient temperatures, the nonuniform temperature profile on comb surfaces that results from brood incubation enhances flow through the honeybee cluster which removes much of the carbon-dioxide produced by the cluster resulting in lower carbon-dioxide concentration next to the brood, (c) increasing ambient (outside) air temperature causes ventilation flow rate to drop resulting in weaker flow inside the beehive. Flow visualization indicates that at low ambient air temperatures the flow inside the beehive has an interesting 3-D structure with the presence of large recirculating vortices occupying the space between honey super frames above the honeybee clusters in the brood chamber and the structure and strength of the flow inside and around the honeybee clusters changes as we increase the ambient air temperature outside the beehive.

Persistence in a single species CSTR model with suspended flocs and wall attached biofilms.

We consider a mathematical model for a bacterial population in a continuously stirred tank reactor (CSTR) with wall attachment. This is a modification of the Freter model, in which we model the sessile bacteria as a microbial biofilm. Our analysis indicates that the results of the algebraically simpler original Freter model largely carry over. In a computational simulation study, we find that the vast majority of bacteria in the reactor will eventually be sessile. However, we also find that suspended biomass is relatively more efficient in removing substrate from the reactor than biofilm bacteria.

A mathematical model of discrete attachment to a cellulolytic biofilm using random DEs.

We propose a new mathematical framework for the addition of stochastic attachment to biofilm models, via the use of random ordinary differential equations. We focus our approach on a spatially explicit model of cellulolytic biofilm growth and formation that comprises a PDE-ODE coupled system to describe the biomass and carbon respectively. The model equations are discretized in space using a standard finite volume method. We introduce discrete attachment events into the discretized model via an impulse function with a standard stochastic process as input. We solve our model with an implicit ODE solver. We provide basic simulations to investigate the qualitative features of our model. We then perform a grid refinement study to investigate the spatial convergence of our model. We investigate model behaviour while varying key attachment parameters. Lastly, we use our attachment model to provide evidence for a stable travelling wave solution to the original PDE-ODE coupled system.

Impact of Microbial Uptake on the Nutrient Plume around Marine Organic Particles: High-Resolution Numerical Analysis.

The interactions between marine bacteria and particulate matter play a pivotal role in the biogeochemical cycles of carbon and associated inorganic elements in the oceans. Eutrophic plumes typically form around nutrient-releasing particles and host intense bacterial activities. However, the potential of bacteria to reshape the nutrient plumes remains largely unexplored. We present a high-resolution numerical analysis for the impacts of nutrient uptake by free-living bacteria on the pattern of dissolution around slow-moving particles. At the single-particle level, the nutrient field is parameterized by the Péclet and Damköhler numbers (0 < Pe < 1000, 0 < Da < 10) that quantify the relative contribution of advection, diffusion and uptake to nutrient transport. In spite of reducing the extent of the nutrient plume in the wake of the particle, bacterial uptake enhances the rates of particle dissolution and nutrient depletion. These effects are amplified when the uptake timescale is shorter than the plume lifetime (Pe/Da < 100, Da > 0.0001), while otherwise they are suppressed by advection or diffusion. Our analysis suggests that the quenching of eutrophic plumes is significant for individual phytoplankton cells, as well as marine aggregates with sizes ranging from 0.1 mm to 10 mm and sinking velocities up to 40 m per day. This microscale process has a large potential impact on microbial growth dynamics and nutrient cycling in marine ecosystems.

Antagonistic control of microbial pathogens under iron limitations by siderophore producing bacteria in a chemostat setup.

Certain bacteria develop iron chelation mechanisms that allow them to scavenge dissolved iron from the environment and to make it unavailable to competitors. This is achieved by producing siderophores that bind the iron which is later liberated internally in the cell. Under conditions of iron limitation, siderophore producing bacteria have therefore an antagonistic growth advantage over other species. This has been observed in particular in agricultural and aquacultural systems, as well as in food microbiology. We investigate here the possibility of a probiotic biocontrol strategy to eradicate a well established, often pathogenic, non-chelating population by supplementing the system with generally regarded as safe siderophore producing bacteria. Set in a chemostat setup, our modeling and simulation studies suggest that this is indeed possible in a finite time treatment.

A mathematical model of quorum sensing regulated EPS production in biofilm communities.

BACKGROUND: Biofilms are microbial communities encased in a layer of extracellular polymeric substances (EPS). The EPS matrix provides several functional purposes for the biofilm, such as protecting bacteria from environmental stresses, and providing mechanical stability. Quorum sensing is a cell-cell communication mechanism used by several bacterial taxa to coordinate gene expression and behaviour in groups, based on population densities. MODEL: We mathematically model quorum sensing and EPS production in a growing biofilm under various environmental conditions, to study how a developing biofilm impacts quorum sensing, and conversely, how a biofilm is affected by quorum sensing-regulated EPS production. We investigate circumstances when using quorum-sensing regulated EPS production is a beneficial strategy for biofilm cells. RESULTS: We find that biofilms that use quorum sensing to induce increased EPS production do not obtain the high cell populations of low-EPS producers, but can rapidly increase their volume to parallel high-EPS producers. Quorum sensing-induced EPS production allows a biofilm to switch behaviours, from a colonization mode (with an optimized growth rate), to a protection mode. CONCLUSIONS: A biofilm will benefit from using quorum sensing-induced EPS production if bacteria cells have the objective of acquiring a thick, protective layer of EPS, or if they wish to clog their environment with biomass as a means of securing nutrient supply and outcompeting other colonies in the channel, of their own or a different species.

A competition model between Pseudomonas fluorescens and pathogens via iron chelation.

In this study we present a competition model between a non-chelator (e.g. pathogen) microorganism and an iron chelator microorganism (e.g. Pseudomonas fluorescens). This latter is a beneficial bacteria that can inhibit the growth of the non-chelator through its iron chelating capability. This phenomena of iron chelation is shown to prevent the pathogen from proliferating to numbers capable of causing disease. A mathematical model is formulated and used to study this competition. The model proposes a new and simple conceptual explanation of interactions. It is a nonlinear system of ordinary differential equations. A qualitative analysis of the model for the batch case (no inflow or outflow from the system) is carried out and the global behavior of the model variables is studied. For the chemostat case, the equilibrium points were derived and their stability was performed through extensive numerical simulations. It is found that iron chelation is able to control the non-chelator microorganism growth under a wide range of conditions.

Mathematical modelling of population and food storage dynamics in a honey bee colony infected with Nosema ceranae.

Unusually high wintering losses of Apis mellifera in recent years has raised concerns regarding the well-being and productivity of honey bees across the globe. While these losses are likely multi-factorial, a proposed contributor are diseases, including those caused by parasites. We formulate and present a mathematical model for a colony of Apis mellifera honey bees infected with the microsporidian parasite Nosema ceranae. The model is numerically analyzed to determine the effects of N. ceranae infection on population and food storage dynamics and their subsequent implications towards colony survival and annual honey yield. Depending on the strength of disease, it is possible for either parasite fadeout, co-existence between bees and N. ceranae, or colony failure to occur. In all cases, the yield of honey collected by the beekeeper is reduced. We further extend the model to include various treatment schemes with the, now discontinued, antimicrobial fumagillin. Treatment with fumagillin can reduce the risk of colony failure and will increase honey yield compared to when no treatment is applied.

Discrete attachment to a cellulolytic biofilm modeled by an Itô stochastic differential equation.

We propose a mathematical framework for introducing random attachment of bacterial cells in a deterministic continuum model of cellulosic biofilms. The underlying growth model is a highly nonlinear coupled PDE-ODE system. It is regularised and discretised in space. Attachment is described then via an auxiliary stochastic process that induces impulses in the biomass equation. The resulting system is an Itô stochastic differential equation. Unlike the more direct approach of modeling attachment by additive noise, the proposed model preserves non-negativity of solutions. Our numerical simulations are able to reproduce characteristic features of cellulolytic biofilms with cell attachment from the aqueous phase. Grid refinement studies show convergence for the expected values of spatially integrated biomass density and carbon concentration. We also examine the sensitivity of the model with respect to the parameters that control random attachment.

A modeling and simulation study of siderophore mediated antagonism in dual-species biofilms.

BACKGROUND: Several bacterial species possess chelation mechanisms that allow them to scavenge iron from the environment under conditions of limitation. To this end they produce siderophores that bind the iron and make it available to the cells later on, while rendering it unavailable to other organisms. The phenomenon of siderophore mediated antagonism has been studied to some extent for suspended populations where it was found that the chelation ability provides a growth advantage over species that do not have this possibility. However, most bacteria live in biofilm communities. In particular Pseudomonas fluorescens and Pseudomonas putida, the species that have been used in most experimental studies of the phenomenon, are known to be prolific biofilm formers, but only very few experimental studies of iron chelation have been published to date for the biofilm setting. We address this question in the present study. METHODS: Based on a previously introduced model of iron chelation and an existing model of biofilm growth we formulate a model for iron chelation and competition in dual species biofilms. This leads to a highly nonlinear system of partial differential equations which is studied in computer simulation experiments. CONCLUSIONS: (i) Siderophore production can give a growth advantage also in the biofilm setting, (ii) diffusion facilitates and emphasizes this growth advantage, (iii) the magnitude of the growth advantage can also depend on the initial inoculation of the substratum, (iv) a new mass transfer boundary condition was derived that allows to a priori control the expect the expected average thickness of the biofilm in terms of the model parameters.