Modeling the impact of the indigenous microbial population on the maximum population density of Salmonella on alfalfa

Within a microbial risk assessment framework, modeling the maximum population density (MPD) of a pathogenic microorganism is important but often not considered. This paper describes a model predicting the MPD of Salmonella on alfalfa as a function of the initial contamination level, the total count of the indigenous microbial population, the maximum pathogen growth rate and the maximum population density of the indigenous microbial population. The model is parameterized by experimental data describing growth of Salmonella on sprouting alfalfa seeds at inoculum size, native microbial load and Pseudomonas fluorescens 2–79. The obtained model fits well to the experimental data, with standard errors less than ten percent of the fitted average values. The results show that the MPD of Salmonella is not only dictated by performance characteristics of Salmonella but depends on the characteristics of the indigenous microbial population like total number of cells and its growth rate. The model can improve the predictions of microbiological growth in quantitative microbial risk assessments. Using this model, the effects of preventive measures to reduce pathogenic load and a concurrent effect on the background population can be better evaluated. If competing microorganisms are more sensitive to a particular decontamination method, a pathogenic microorganism may grow faster and reach a higher level. More knowledge regarding the effect of the indigenous microbial population (size, diversity, composition) of food products on pathogen dynamics is needed in order to make adequate predictions of pathogen dynamics on various food products.     

Predictive modeling of mixed microbial populations in food products: evaluation of two-species models

Predictive microbiology is an emerging research domain in which biological and mathematical knowledge is combined to develop models for the prediction of microbial proliferation in foods. To provide accurate predictions, models must incorporate essential factors controlling microbial growth. Current models often take into account environmental conditions such as temperature, pH and water activity. One factor which has not been included in many models is the influence of a background microflora, which brings along microbial interactions. The present research explores the potential of autonomous continuous-time/two-species models to describe mixed population growth in foods. A set of four basic requirements, which a model should satisfy to be of use for this particular application, is specified. Further, a number of models originating from research fields outside predictive microbiology, but all dealing with interacting species, are evaluated with respect to the formulated model requirements by means of both graphical and analytical techniques. The analysis reveals that of the investigated models, the classical Lotka-Volterra model for two species in competition and several extensions of this model fulfill three of the four requirements. However, none of the models is in agreement with all requirements. Moreover, from the analytical approach, it is clear that the development of a model satisfying all requirements, within a framework of two autonomous differential equations, is not straightforward. Therefore, a novel prototype model structure, extending the Lotka-Volterra model with two differential equations describing two additional state variables, is proposed to describe mixed microbial populations in foods.     

A thermodynamic theory of microbial growth

Our ability to model the growth of microbes only relies on empirical laws, fundamentally restricting our understanding and predictive capacity in many environmental systems. In particular, the link between energy balances and growth dynamics is still not understood. Here we demonstrate a microbial growth equation relying on an explicit theoretical ground sustained by Boltzmann statistics, thus establishing a relationship between microbial growth rate and available energy. The validity of our equation was then questioned by analyzing the microbial isotopic fractionation phenomenon, which can be viewed as a kinetic consequence of the differences in energy contents of isotopic isomers used for growth. We illustrate how the associated theoretical predictions are actually consistent with recent experimental evidences. Our work links microbial population dynamics to the thermodynamic driving forces of the ecosystem, which opens the door to many biotechnological and ecological developments.     

Transport-limited reactions in microbial systems

Predicting microbial metabolic rates and emergent biogeochemical fluxes remains challenging due to the many unknown population dynamical, physiological and reaction-kinetic parameters and uncertainties in species composition. Here, we show that the need for these parameters can be eliminated when population dynamics and reaction kinetics operate at much shorter time scales than physical mixing processes. Such scenarios are widespread in poorly mixed water columns and sediments. In this ‘fast-reaction-transport’ (FRT) limit, all that is required for predictions are chemical boundary conditions, the physical mixing processes and reaction stoichiometries, while no knowledge of species composition, physiology or population/reaction kinetic parameters is needed. Using time-series data spanning years 2001–2014 and depths 180–900 m across the permanently anoxic Cariaco Basin, we demonstrate that the FRT approach can accurately predict the dynamics of major electron donors and acceptors (Pearson r ≥ 0.9 in all cases). Hence, many microbial processes in this system are largely transport limited and thus predictable regardless of species composition, population dynamics and kinetics. Our approach enables predictions for many systems in which microbial community dynamics and kinetics are unknown. Our findings also reveal a mechanism for the frequently observed decoupling between function and taxonomy in microbial systems.     

Division synchrony and the dynamics of microbial populations: A size-specific model

A discrete, environmentally coupled, size-specific model of microbial population dynamics in continuous culture is presented. It is mathematically simpler than other models based on similar assumptions and lends itself to numerical and analytic solutions. It displays several phenomena which have been reported in the experimental literature but which are not well understood; specifically, a loose relationship between biomass and numbers (i.e., a time lag between mass growth and cell division) and a critical damping of biomass while numbers continue to oscillate. In addition, the model provides several new predictions: The stable biomass distribution is independent of the environmental factors considered in the model and uniformly distributes the biomass among the size classes. The rate of approach to stability and the frequency of waves through the size distributions are a function of the flow rate and the variance in rate of growth and size at division. The model should provide a useful basis for studying the effects of size specificity on the dynamics of microbial populations cultured in chemostats.     

Transport equations for a microbial predator-prey community

A transport equation is used which describes the temporal behavior of interacting populations in changing environments. The formulation takes into account the internal state variables of the individuals. The general theory is applied to the transient analysis of a microbial predator-prey system using an approximate model for the specific cell growth rate and multigroup formulism to approximate the mass distribution within the population. Experimental results in aTetrahymena pyriformis— Aerobacter aerogenes system have been used to evaluate the group parameters and test the validity of the theoretical predictions.     

Microbial abundance in the rhizosphere: A computer model

Summary A mathematical model is described which can predict the abundance of microorganisms in the rhizosphere (as g microbial dry weight/cm³ soil) in relation to distance from the root surface and time since the root started exuding substrate. The growth rate of the microorganisms at each point in the soil is assumed to be controlled by the concentration of soluble organic substrate. The concentration of substrate changes due to (1) its production by the root and diffusion through the soil, (2) its production in the soil by breakdown of insoluble organic matter, and (3) its use by the microorganisms. Values for all of the required input parameters have been obtained from the literature.The model predicts that a high population density will develop near the root surface, but the density will fall off steeply with increasing distance from the root. At the root surface microbial growth continues for many days, provided exudation by the root continues at a steady rate, but further away the population reaches a peak and then declines. This is because the amount of substrate reaching the outer soil is no longer adequate to support the maintenance requirement of the population. Starting with a microbial concentration of 2 g/cm³, and using what are considered to be average values for other input parameters, the microbial concentrations predicted after 10 days are 1509 g/cm³ at the root surface, and 2.2 g/cm³ at 1.8 mm from the root. The model also predicts the substrate concentrations in the soil: these reach a maximum within the first day and then decline, reaching by 10 days values not very different from those in root-free soil.The model is used to predict the effect on microbial and substrate concentrations of changes in soil water content, root density, root exudation rate, initial microbial concentration and microbial response to substrate concentration. Where the predictions of the model can be tested against observed data there is good agreement. re]19760308     

Wall growth in laboratory fermenters

The influence of microorganisms growing on the walls of laboratory fermenters was investigated and a model to describe of microbial lysis and the formation of growth inhibitory products in a continuous fermentation process was developed. The predictions were compared with results from an earlier model for growth of microorganisms on surfaces.     

Dealing with Uncertainty in Spatially Explicit Population Models

It has been argued that spatially explicit population models (SEPMs) cannot provide reliable guidance for conservation biology because of the difficulty of obtaining direct estimates for their demographic and dispersal parameters and because of error propagation. We argue that appropriate model calibration procedures can access additional sources of information, compensating the lack of direct parameter estimates. Our objective is to show how model calibration using population-level data can facilitate the construction of SEPMs that produce reliable predictions for conservation even when direct parameter estimates are inadequate. We constructed a spatially explicit and individual-based population model for the dynamics of brown bears (Ursus arctos) after a reintroduction program in Austria. To calibrate the model we developed a procedure that compared the simulated population dynamics with distinct features of the known population dynamics (=patterns). This procedure detected model parameterizations that did not reproduce the known dynamics. Global sensitivity analysis of the uncalibrated model revealed high uncertainty in most model predictions due to large parameter uncertainties (coefficients of variation CV 0.8). However, the calibrated model yielded predictions with considerably reduced uncertainty (CV 0.2). A pattern or a combination of various patterns that embed information on the entire model dynamics can reduce the uncertainty in model predictions, and the application of different patterns with high information content yields the same model predictions. In contrast, a pattern that does not embed information on the entire population dynamics (e.g., bear observations taken from sub-areas of the study area) does not reduce uncertainty in model predictions. Because population-level data for defining (multiple) patterns are often available, our approach could be applied widely.     

Modeling shifts in microbial populations associated with health or disease

Stable microbial communities associated with health can be disrupted by altered environmental conditions. Periodontal diseases are associated with changes in the resident oral microflora. For example, as gingivitis develops, a key change in the microbial composition of dental plaque is the ascendancy of Actinomyces spp. and gram-negative rods at the expense of Streptococcus spp. We describe the use of an in vitro model to replicate this population shift, first with a dual-species model (Actinomyces naeslundii and Streptococcus sobrinus) and then using a microcosm model of dental plaque. The population shift was induced by environmental changes associated with gingivitis, first by the addition of artificial gingival crevicular fluid and then by a switch to a microaerophilic atmosphere. In addition to the observed population shifts, confocal laser scanning microscopy also revealed structural changes and differences in the distribution of viable and nonviable bacteria associated with the change in environmental conditions. This model provides an appropriate system for the further understanding of microbial population shifts associated with gingivitis and for the testing of, for example, antimicrobial agents.     

The probability of evolutionary rescue: towards a quantitative comparison between theory and evolution experiments

Evolutionary rescue occurs when a population genetically adapts to a new stressful environment that would otherwise cause its extinction. Forecasting the probability of persistence under stress, including emergence of drug resistance as a special case of interest, requires experimentally validated quantitative predictions. Here, we propose general analytical predictions, based on diffusion approximations, for the probability of evolutionary rescue. We assume a narrow genetic basis for adaptation to stress, as is often the case for drug resistance. First, we extend the rescue model of Orr & Unckless (Am. Nat. 2008 172, 160–169) to a broader demographic and genetic context, allowing the model to apply to empirical systems with variation among mutation effects on demography, overlapping generations and bottlenecks, all common features of microbial populations. Second, we confront our predictions of rescue probability with two datasets from experiments with Saccharomyces cerevisiae (yeast) and Pseudomonas fluorescens (bacterium). The tests show the qualitative agreement between the model and observed patterns, and illustrate how biologically relevant quantities, such as the per capita rate of rescue, can be estimated from fits of empirical data. Finally, we use the results of the model to suggest further, more quantitative, tests of evolutionary rescue theory.     

Modeling of Pathogen Indicator Organisms in a Small-Scale Agricultural Catchment Using SWAT

Degradation of water quality from microbial contaminants associated with agricultural activities has significant implications for source protection of potable water. Novel environmental approaches must be adopted to assess risks from waterborne pathogenic microbes. The objective of this study was to evaluate applicability of the Soil and Water Assessment Tool (SWAT) to predict daily concentrations of E. coli in a small-scale agricultural catchment in Ireland. The study area is based on the Kilshanvey catchment located in the west of Ireland. E. coli data (n = 25) from June 2006 to June 2007 were utilized for comparison with the model's predictions. Statistical analysis indicates an unsatisfactory to fair level of correlation for the model's predictions (R² = 0.03–0.35, NSE = –0.42–0.29). A sensitivity analysis identified direct stream deposition and die-off rates for E. coli as having a significant impact on the model's predictions. Our results suggest that the model is adequate to assess the magnitude of various microbial sources within catchments but capability to replicate daily observations is uncertain. However, model outputs could provide adequate data to develop a human exposure assessment to pathogen indicator organisms in surface water and assist policy-makers in developing appropriate risk management strategies.     

Phenomenological Model for Predicting the Catabolic Potential of an Arbitrary Nutrient

The ability of microbial species to consume compounds found in the environment to generate commercially-valuable products has long been exploited by humanity. The untapped, staggering diversity of microbial organisms offers a wealth of potential resources for tackling medical, environmental, and energy challenges. Understanding microbial metabolism will be crucial to many of these potential applications. Thermodynamically-feasible metabolic reconstructions can be used, under some conditions, to predict the growth rate of certain microbes using constraint-based methods. While these reconstructions are powerful, they are still cumbersome to build and, because of the complexity of metabolic networks, it is hard for researchers to gain from these reconstructions an understanding of why a certain nutrient yields a given growth rate for a given microbe. Here, we present a simple model of biomass production that accurately reproduces the predictions of thermodynamically-feasible metabolic reconstructions. Our model makes use of only: i) a nutrient''s structure and function, ii) the presence of a small number of enzymes in the organism, and iii) the carbon flow in pathways that catabolize nutrients. When applied to test organisms, our model allows us to predict whether a nutrient can be a carbon source with an accuracy of about 90% with respect to in silico experiments. In addition, our model provides excellent predictions of whether a medium will produce more or less growth than another () and good predictions of the actual value of the in silico biomass production.     

Constraints on microbial metabolism drive evolutionary diversification in homogeneous environments

Understanding the evolution of microbial diversity is an important and current problem in evolutionary ecology. In this paper, we investigated the role of two established biochemical trade-offs in microbial diversification using a model that connects ecological and evolutionary processes with fundamental aspects of biochemistry. The trade-offs that we investigated are as follows:(1) a trade-off between the rate and affinity of substrate transport; and (2) a trade-off between the rate and yield of ATP production. Our model shows that these biochemical trade-offs can drive evolutionary diversification under the simplest possible ecological conditions: a homogeneous environment containing a single limiting resource. We argue that the results of a number of microbial selection experiments are consistent with the predictions of our model.     

Synthesizing traditional biogeography with microbial ecology: the importance of dormancy

The discovery of biogeographical patterns among microbial communities has led to a focus on the empirical evaluation of the importance of dispersal limitation in microbial biota. As a result, the spatial distribution of microbial diversity has been increasingly studied while the synthesis of biogeographical theory with microbial ecology remains undeveloped. To make biogeographical theory relevant to microbial ecology, microbial traits that potentially affect the distribution of microbial diversity need to be considered. Given that many microorganisms in natural environments are in a state of dormancy and that dormancy is an important microbial fitness trait, I provide a first attempt to account for the effects of dormancy on microbial biogeography by treating dormancy as a fundamental biogeographical response. I discuss the effects of dormancy on the equilibrium theory of island biogeography and on the unified neutral theory of biodiversity and biogeography, and suggest how the equilibrium theory of island biogeography can produce predictions approaching those of the Baas‐Becking hypothesis (i.e. everything is everywhere, but the environment selects). In addition, I present a conceptual model of the unified neutral theory of biodiversity and biogeography, generalized to account for dormancy, from which a full model can be constructed for species with or without dormant life history stages.     

Dynamic modeling of cooperative protein secretion in microorganism populations

Interactions between microorganisms can have a crucial effect on their population dynamics. Typically, interactions are mediated through the environment by molecules and proteins that are products of cell metabolism and physiology; they therefore reflect the internal dynamics of the single cell. In this work we aim to integrate single-cell properties of gene expression that affect indirect interactions between microorganisms under challenging conditions, into a quantitative model of population dynamics. Specifically we address the problem of a microbial population secreting a protein that can actively extract a growth-limiting resource, such as a simple sugar or iron, from the environment. The genes coding for the protein can undergo random epigenetic transitions between active and silenced states, and can be repressed by the product of their reaction. We model cooperative and competitive interactions between protein producing and non-producing phenotypes by nonlinear dynamical systems and analyze them both in terms of asymptotic states and of transient dynamics. Our model shows that phenotypic transitions allow a stable coexistence of the two phenotypes, and enables us to make predictions regarding the conditions required for such coexistence and the typical timescales of transient dynamics. It also shows how repression by the reaction product induces a feedback at the population-environment level that can result in limit cycle dynamics. The relation of these results to experiments are discussed.     

Measurement and mathematical modelling of competition between fast- and slow-growing ordinary heterotrophic organisms in low and high substrate-loaded systems

Ordinary heterotrophic organisms (OHO) of an activated sludge wastewater treatment system showed an atypical growth behaviour when they are inoculated to batch aerobic growth tests with a high substrate-loaded condition. For example, the OHO maximum specific growth rates on readily biodegradable substrates (μ _H) increased with a high ratio of substrate concentration to OHO active biomass concentration (So/Xo), although they were assumed to be constant in a conventional microbial growth kinetic model with a single OHO population group. We, therefore, set a hypothesis in that the change of OHO maximum specific growth rates in the batch test condition is caused by turnover of fast-growing OHO population against slow-growing OHO population. And, a competitive microbial growth kinetic model of the fast- and slow-growing OHO population groups was developed and validated with model-data fitting analysis for the batch test results. The competitive microbial growth kinetic model of process selection, rather than that of kinetic selection, was capable of simulating microbial growth kinetics in high substrate-loaded dynamic systems (i.e., batch tests) and low substrate-loaded steady-state systems (i.e., continuously operated wastewater treatment systems), better than the conventional non-competitive growth kinetic model.     

Integrating mixed microbial population dynamics into modeling energy transport during the initial stages of the aerobic composting of a switchgrass mixture

A mathematical model which integrates empirically derived microbial growth kinetics with heat and mass transfer phenomena and substrate degradation kinetics has been developed to capture the dynamics of the aerobic composting of a switchgrass and dog food mixture over a period of 64 h. The model incorporated three microbial populations of yeasts, bacteria and fungi that metabolized composting material consisting of sugars and starches, cellulose and hemicelluloses to produce heat and utilize oxygen in a static, cylindrical reactor employing forced aeration. Model predictions captured well the dynamics obtained experimentally between physical and microbial variables and the model has the potential to become a predictive tool for substrate degradation during aerobic composting processes.     

On the accuracy of a diffusion approximation to a discrete state–space Markovian model of a population

The traditional Kolmogorov equations treat the size of a population as a discrete random variable. A model is introduced that extends these equations to incorporate environmental variability. Difficulties with this discrete model motivate approximating the population size as a continuous random variable through the use of diffusion processes. The set of cumulants for both the population size and the environmental factors affecting the population size characterize the population–environmental system. The evolution of this set, as predicted by the diffusion approximation, closely matches the corresponding predictions for the discrete model. It is also noted that the simulation estimates of the cumulants against which the predictions of the diffusion model are checked can vary considerably between simulations — despite averaging over a large number of simulation runs. The precision of the simulation estimates–both over time and with differing cumulant order–is discussed.