Evaluation of culture-based and molecular detection methods for Campylobacter in New Zealand raw cows' milk.

AIMS: This study evaluated the performance of a commercial molecular detection method (mericon Campylobacter triple kit real-time/quantitative (q)PCR) and a selective plating medium (R&F Campylobacter jejuni/Campylobacter coli Chromogenic Plating Medium (CCPM)) against a culture-based reference method (ISO 10272-1:2017 detection procedure B) for the detection of Campylobacter from raw milk enrichment broths. METHODS AND RESULTS: New Zealand raw cows' milk and Ultra-High Temperature-processed milk samples were inoculated with 50, 125 and 500 colony forming units of C. jejuni and C. coli cocktail per analytical unit. Samples were tested for Campylobacter after 0, 24- and 48 h refrigeration. ISO 10272-1:2017 proved to be a sensitive detection method (77/80 positive samples); detection only failed for some milk samples tested 48 h postinoculation. CCPM was as effective as Cefoperazone Charcoal Deoxycholate Agar for selective plating of Campylobacter raw milk enrichments (78/80 positive samples). However, the qPCR detected Campylobacter in only 42/80 samples and qPCR reaction inhibition was observed. CONCLUSIONS: The ISO 10272-1:2017 method was a more sensitive method for Campylobacter detection from raw milk than the mericon Campylobacter triple kit qPCR, and CCPM was a useful complementary medium to mCCDA where one of these media is required by the standard. SIGNIFICANCE AND IMPACT OF THE STUDY: In regions where testing is required or recommended, optimized methods for Campylobacter detection from raw milk will reduce risk to the raw milk consumer. Although molecular methods are generally touted as a rapid alternative to culture, issues with inhibition due to matrix components mean that culture-based methods might provide the most sensitive option for Campylobacter detection in raw milk. Findings also emphasize the importance of minimizing the time between milk collection and testing for Campylobacter.

Quantifying the uncertainty of transfer of Cronobacter spp. between fomites and floors and touch points in dairy processing plants.

Cronobacter spp. are opportunistic pathogens that must be controlled in infant powder manufacturing plants. This study evaluated the spread of Cronobacter cells via contact surfaces within a dairy manufacturing environment. Transfer rates of Cronobacter spp. were determined from vectors for transmission including moveable fomites (e.g. trolley wheels and boots) and gloved hands to various types of recipient surfaces (stainless steel, linoleum and resin-coated concrete) typical for dairy manufacturing environments. Overall, with a starting inoculum of 106 CFU/mL, approximately 104 CFU/mL Cronobacter cells were transferred from each fomite onto each recipient surface during the initial transfer event. Gloved hands transferred the highest number of Cronobacter cells, followed by polyvinylchloride boots and then polyurethane trolley wheels. We demonstrate, using a combination of experimental data and uncertainty analysis, that if a movable fomite (boots or trolley wheels), or gloves became contaminated, Cronobacter could be spread over a wide area within a manufacturing plant. To the authors' knowledge, this is the first quantitative estimation of the spread of Cronobacter within a dairy manufacturing plant, that can also be practically applied as a tool for providing information in making risk management decisions. In particular, the estimation of spread suggests areas for cleaning and sanitation within a dairy manufacturing environment during a contamination event.

Estimating Bacterial Pathogen Levels in New Zealand Bulk Tank Milk.

Zoonotic bacteria such as Campylobacter, Listeria, and Shiga toxin-producing Escherichia coli have been found in bulk tank milk in many countries, and the consumption of raw milk has been implicated in outbreaks of disease in New Zealand. Fecal contamination at milking is probably the most common source of pathogenic bacteria in bulk tank milk. Raw milk was collected from 80 New Zealand dairy farms during 2011 and 2012 and tested periodically for Campylobacter, E. coli O157, Listeria monocytogenes, and Salmonella. Milk quality data such as coliform counts, total bacterial counts, and somatic cell counts also were collected. By treating the total bacterial count as a proxy for fecal contamination of milk and utilizing farm and animal level prevalence and shedding rates of each pathogen, a predictive model for the level of pathogenic bacteria in bulk tank raw milk was developed. The model utilizes a mixture distribution to combine the low level of contamination inherent in the milking process with isolated contamination events associated with significantly higher pathogen levels. By simulating the sampling and testing process, the predictive model was validated against the observed prevalence of each pathogen in the survey. The predicted prevalence was similar to the observed prevalence for E. coli O157 and Salmonella, although the predicted prevalence was higher than that observed in samples tested for Campylobacter.

Monoculture parameters successfully predict coculture growth kinetics of Bacteroides thetaiotaomicron and two Bifidobacterium strains.

Microorganisms rarely live in isolation but are most often found in a consortium. This provides the potential for cross-feeding and nutrient competition among the microbial species, which make it challenging to predict the growth kinetics in coculture. In this paper we developed a mathematical model to describe substrate consumption and subsequent microbial growth and metabolite production for bacteria grown in monoculture. The model characterized substrate utilization kinetics of 18 Bifidobacterium strains. Some bifidobacterial strains demonstrated preferential degradation of oligofructose in that sugars with low degree of polymerization (DP) (DP≤3 or 4) were metabolized before sugars of higher DP, or vice versa. Thus, we expanded the model to describe the preferential degradation of oligofructose. In addition, we adapted the model to describe the competition between human colonic bacteria Bacteroides thetaiotaomicron LMG 11262 and Bifidobacterium longum LMG 11047 or Bifidobacterium breve Yakult for inulin as well as cross-feeding of breakdown products from the extracellular hydrolysis of inulin by B. thetaiotaomicron LMG 11262. We found that the coculture growth kinetics could be predicted based on the respective monoculture growth kinetics. Using growth kinetics from monoculture experiments to predict coculture dynamics will reduce the number of in vitro experiments required to parameterize multi-culture models.

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.

Modelling female reproductive function in farmed animals.

Impaired reproduction in farmed animals is a major cost to agriculture, and this is exacerbated by the implementation of intensive production systems. Addressing this has been the focus of a significant body of research. While considerable advances have been made in biological experiments and understanding, a systems insight into the mechanisms that underlie reproductive function in mammals is needed. Mathematical modelling offers a means to develop a systems approach to reproduction by coalescing information and predicting outcomes of interventions. There has been steady progress in the development of mathematical models addressing various issues of reproduction over the last decade, from cell-signalling pathways through to herd management. We review these developments and their insights as well as their limitations. In addition, we identify other areas that need development, and how modelling might usefully contribute to these areas of reproduction science.

A mathematical model of pregnancy recognition in mammals.

In this paper we develop a mathematical model of the luteal phase of the reproductive cycle in mammals with the aim to generate a systems understanding of pregnancy recognition. Pregnancy recognition is initiated by the production of interferon tau (IFNtau) by the growing conceptus. This ensures that the maternal corpus luteum (CL) remains viable to secrete progesterone, which is critical for providing a uterine microenvironment suitable for embryonic growth. Our mathematical model describes the interactions among the CL, the reproductive hormones and the hormone receptors in the uterus. It also characterises the complex interactions amongst the uterine oestrogen, progesterone and oxytocin receptors that control the sensitivity of the uterus to oestrogen, progesterone and oxytocin, respectively. The model is represented by a dynamical system and exhibits qualitative features consistent with the known experimental results in sheep. A key factor identified was a time-dependent threshold for the IFNtau signal below which the presence of the embryo might not be recognised and thus pregnancy would likely fail. Furthermore, the model indicated that if the IFNtau signal is later than around day 13 of the cycle, then pregnancy will not be recognised irrespective of the IFNtau concentration. The thresholds in the concentration and time of the IFNtau signal is a screening mechanism whereby only embryos of sufficient quality are able to prevent luteolysis (i.e. regression of the CL). The effect of progesterone secretion rate from the CL on pregnancy recognition was investigated. The model suggests that if the secretion rate is low then the initiation of the IFNtau signal is delayed, which in turn compromises the likelihood of a pregnancy being recognised by the CL. Furthermore, pregnancy recognition does not occur below a critical threshold in the progesterone secretion rate. In summary, the model can be used to identify the most favourable conditions for pregnancy recognition.

Insulin transport within skeletal muscle transverse tubule networks.

It has recently been observed in situ in mice that insulin takes approximately 10 min to be transported 20 microm into the t-tubule networks of skeletal muscle fibers. The mechanisms for this slow transport are unknown. It has been suggested that the biochemical composition of the t-tubular space that may include large molecules acting as gels and increased viscosity in the narrow tubules may explain this slow diffusion. In this article, we construct a mathematical model of insulin transport within the t-tubule network to determine potential mechanisms responsible for this slow insulin transport process. Our model includes insulin diffusion, insulin binding to insulin receptors, t-tubule network tortuosity, interstitial fluid viscosity, hydrodynamic wall effects, and insulin receptor internalization and recycling. The model predicted that depending on fiber type there is a 2-15 min delay in the arrival time of insulin between the sarcolemma and inner t-tubules (located 20 microm from the sarcolemma) after insulin injection. This is consistent with the experimental data. Increased viscosity in the narrow t-tubules and large molecules acting as gels are not the primary mechanisms responsible for the slow insulin diffusion. The primary mechanisms responsible for the slow insulin transport are insulin binding to insulin receptors and network tortuosity.

A risk assessment approach applied to the growth of Erwinia carotovora in vegetable juice for variable temperature conditions.

Risk assessment for food spoilage relies on probabilistic models of microbial growth to predict the likelihood that microbial populations will exceed predefined spoilage levels. To assist in the design and management of industrial food quality systems, predictive microbiological models have to incorporate major risk factors such as the variability in the microbial strain, environment and initial contamination levels. In addition, the application of results measured under laboratory conditions to the less controlled environment of an industrial process usually also involves uncertainty. Extra information regarding this uncertainty must be factored into industrial microbial risk assessment. In this paper, based on our previous analysis of the growth of Erwinia carotovora we show how different factors contribute to the risk of microbial spoilage of vegetable juice and we demonstrate an effective way of including these factors into risk assessment models. The association of risk components with different unavoidable and manageable factors is also valuable for the development of optimal strategies for reducing microbial risk.

Estimation of microbial growth using population measurements subject to a detection limit.

In this paper we develop a maximum likelihood estimation procedure for determining the mean and variance in microbial population size from microbial population measurements subject to a detection limit. Existing estimation methods generally set non-detectable measurements equal to the detection limit and are highly biased. Because changes in the mean and variance in the microbial population size are typical in industrial processes we also outline statistical tests for detecting such changes when measurements are subject to a detection limit, which is critical for process control. In an industrial process there may also potentially be variability in the microbial growth rate due to variation in the microbial strain, environment, and food characteristics. Accordingly, we also present a maximum likelihood procedure for estimating microbial growth model parameters and their variance components from microbial population measurements subject to a detection limit. Such information can be used to generate the mean and variance through time of the microbial population size, which is vital for the application of predictive microbiological models to risk assessment and food product shelf-life estimation.

Mathematically modeling the effects of electrically stimulating skeletal muscle.

A framework for modeling the activation of skeletal muscle is presented for studying functional electrical stimulation. A mathematical model of the cellular responses of skeletal muscle, created at AgResearch (Ruakura, New Zealand www.agresearch.co.nz), has been integrated with an anatomical, finite element model of the semitendinosus muscle, which was constructed from CT scans of the hind limb of a sheep. The tibial nerve was also constructed from digitized CT scans, and has been modeled using the Hodgkin Huxley neural model. The relevant cellular equations have been solved over these geometries. The results obtained, i.e speed of action potential propagation through the nerve and muscle, and the duration of twitch force, agree with published values.

Mathematical modelling of prolactin-receptor interaction and the corollary for prolactin receptor gene expression in skin.

A mathematical model of prolactin regulating its own receptors was developed, and compared with experimental data on a qualitative level. The model incorporates the kinetics of prolactin-receptor interactions and subsequent signalling by prolactin-receptor dimers to regulate the production of receptor mRNA and hence the receptor population. The model relates changes in plasma prolactin concentration to prolactin receptor (PRLR) gene expression, and can be used for predictive purposes. The cell signalling that leads to the activation of target genes, and the mechanisms for regulation of transcription, were treated empirically in the model. The model's parameters were adjusted so that model simulations agreed with experimentally observed responses to administration of prolactin in sheep. In particular, the model correctly predicts insensitivity of receptor mRNA regulation to a series of subcutaneous injections of prolactin, versus sensitivity to prolonged infusion of prolactin. In the latter case, response was an acute down-regulation followed by a prolonged up-regulation of mRNA, with the magnitude of the up-regulation increasing with the duration of infusion period. The model demonstrates the feasibility of predicting the in vivo response of prolactin target genes to external manipulation of plasma prolactin, and could provide a useful tool for identifying optimal prolactin treatments for desirable outcomes.

A dynamic model for ovulation rate reveals an effect of the estrogen receptor genotype on ovarian follicular development in the pig.

A mathematical model that describes the recruitment and growth of ovarian follicles was fitted to data on ovulation rate and the measurements of plasma estradiol collected at times during the estrous cycle for individual gilts. The method of least squares was used to obtain estimates of the parameters of the mathematical model. The estimated model parameters were the maximum estradiol production for a follicle, development of each follicle after commitment, and a function describing the initial estradiol production of committed follicles. The estimated parameters for each pig were classified by estrogen receptor (ER) genotype (AA or BB) and analyzed using a multivariate analysis of variance. There were differences between genotypes (P < 0.05) for the parameter that described the initial distribution of individual follicles at recruitment. Gilts with ER genotype BB recruited follicles that varied more in size but had fewer very small follicles, indicating that the ER gene affects the relative estradiol secretion of the follicles at commitment. This analysis is an example of a general approach to genetic studies that uses a mathematical model of the physiology as a statistical basis for estimating gene action.

Partitioning of the variance in the growth parameters of Erwinia carotovora on vegetable products.

The objective of this paper was to estimate and partition the variability in the microbial growth model parameters describing the growth of Erwinia carotovora on pasteurised and non-pasteurised vegetable juice from laboratory experiments performed under different temperature-varying conditions. We partitioned the model parameter variance and covariance components into effects due to temperature profile and replicate using a maximum likelihood technique. Temperature profile and replicate were treated as random effects and the food substrate was treated as a fixed effect. The replicate variance component was small indicating a high level of control in this experiment. Our analysis of the combined E. carotovora growth data sets used the Baranyi primary microbial growth model along with the Ratkowsky secondary growth model. The variability in the microbial growth parameters estimated from these microbial growth experiments is essential for predicting the mean and variance through time of the E. carotovora population size in a product supply chain and is the basis for microbiological risk assessment and food product shelf-life estimation. The variance partitioning made here also assists in the management of optimal product distribution networks by identifying elements of the supply chain contributing most to product variability.

Modeling the interaction of milking frequency and nutrition on mammary gland growth and lactation.

A mathematical model of biological mechanisms regulating lactation is constructed. In particular, the model allows prediction of the effect of milking frequency on milk yield and mammary regression, and the interaction of nutrition and milking frequency in determining yield. Possible interactions of nutrition with milking frequency on alveolar dynamics are highlighted. The model is based upon the association of prolonged engorgement (as a consequence of milk accumulation) of active secretory alveoli with changes in gene expression that result in impairment and, ultimately, cessation of milk secretion. The emptying of alveoli at milking, following alveolar contraction induced by oxytocin, prevents this process and also allows quiescent alveoli to reactivate. Prolonged engorgement results in apoptosis of the secretory cells and, hence, regression of the mammary gland. Milk yield is linked to alveolar populations, with secretion rates being modulated by nutrition and udder fill effects. The model was used to investigate different management scenarios, and is in agreement with experimental results. The model shows that while milking frequency drives alveolar population, and therefore potential milk production, actual production varies considerably with nutrition. A significant portion of the loss associated with once-daily milking was due to udder fill rather than loss of secretory tissue. The model showed qualitative agreement with experimental data, on the acute and chronic effects of temporary once-daily milking.

Influence of milking frequency on mammary gland dynamics.

The effects of milking frequency on milk production is a key question for the dairy industry. Milk production is related to the number of active alveoli in the mammary gland and movement between active and quiescent alveolar pools is influenced by the milking frequency. In this paper, we analyse a mechanistic model based on known biological inputs that describes the effect of milking frequency on the alveolar composition of the mammary gland. It is shown that the model can qualitatively reproduce the correct alveolar dynamics. We also investigate the model robustness and parameter sensitivity. Additionally, by making the plausible assumption that the senescence rate of alveoli is proportional to the number of quiescent alveoli present, we obtain an analytical solution requiring periodic resetting.

Stochastic modelling of the growth of a microbial population under changing temperature regimes.

The application of models of microbial growth to the design of food safety systems requires consideration of the effect of arbitrary changes in external variables on growth of bacteria. In particular, the effect of changes in external variables, such as temperature, on the probability that the microbial population size will not exceed acceptable levels at a given time needs to be predicted. This paper presents a method of calculating the time-dependent probability distribution of the microbial population size under arbitrary changes of temperature through time. To illustrate this method, the effect of a sudden temporary increase in temperature on the evolution of the probability distribution of Lactobacillus plantarum population size is presented. The effect of this change in temperature on the time taken for the population to reach a critical size, with a given probability, is also calculated and the application of this calculation to the design of HACCP protocols is discussed.

Predictive microbiology and food safety.

The evaluation of risk in food safety requires knowledge of the probability that microbial population sizes will not exceed defined levels. This probability is evaluated assuming that the growth of the microbial population can be described by the Gompertz equation with the variance of growth depending on the population size. It is shown that the probability density associated with this phenomenon is skewed, so that the risk of a high microbial population is greater than that which would be estimated using a symmetrical probability distribution such as the Gaussian. Maximum likelihood estimates of the parameters of the Gompertz equation based on the derived probability density are calculated using data published by Zwietering et al. [23] for the growth of Lactobacillus plantarum under different temperatures. The probability that a microbial population of a given size will exceed an unacceptable level within a given time is calculated for growth at two temperatures, 10 and 25 degrees C. The implication of these theoretical results for the management of risk in food safety and in the design of hazard analysis critical control point procedures is discussed.

A model of follicular development and ovulation in sheep and cattle.

A dynamic model to describe ovarian follicular development following commitment has been developed. It identifies follicular growth with oestradiol production and assumes that this growth is the result of intra-ovarian stimulation, gonadotrophin stimulation, and inhibitory interactions among the follicles, where larger follicles suppress the growth of the smaller follicles. The variables of the model are the levels of oestradiol in each follicle at commitment, the rate of change of oestradiol production by individual follicles during follicular development, and the level of oestradiol that will induce luteinizing hormone (LH) surge. Changes in the variables of the model could be associated with both genetic and environmental effects. The behaviour of the model is consistent with experimental observations. The model can be expanded to include exogenous follicle-stimulating hormone (FSH) administration assuming that FSH is associated with advancing the maturation of gonadotrophin-dependent follicles without affecting the number of committed follicles. The use of the model to explore FSH administration strategies is demonstrated. The model confirms that the response to FSH administration depends on both the amount of FSH and the time of administration. The largest number of double ovulations occurred when FSH was given at the time of the deviation of the dominant and subordinate follicles.