Cell survival signaling in the bovine mammary gland during the transition from lactation to involution.

In dairy cows, mammary gland involution, and thus a decline in milk production, occurs following peak lactation. To examine the cell signaling pathways regulating involution of the mammary gland, signal transducer and activator of transcription factors (STAT5 and 3), suppressors of cytokine signaling (SOCS1-3 and CIS), insulin-like growth factors (IGF1 and 2), and protein kinase B (Akt) were examined. Mammary involution was induced by termination of milking, and alveolar tissue was collected from 52 nonpregnant, primiparous, mid-lactation Holstein-Friesian cows killed at 0, 6, 12, 18, 24, 36, 72, and 192h postmilking. Qualitative immunohistochemistry showed that activated (phosphorylated) STAT5-P was localized in nuclei of mammary epithelial cells at the early time points, with detection levels decreasing by 24h postmilking. In contrast, STAT3-P was barely detectable at the early time points, with detection levels increasing following longer postmilking periods. This was supported by Western analysis, which showed a decline in STAT5 and STAT5-P protein levels by 24h postmilking, no change in STAT3 levels, and an increase in STAT3-P protein (barely detectable at the early time points) by 72h postmilking. Quantitative real-time reverse transcription PCR analysis showed SOCS1 and SOCS3 mRNA increased by 72h postmilking compared with 6h postmilking. The SOCS2 mRNA remained unchanged across the time series, whereas CIS decreased by 18h postmilking and remained lower compared with that at 6h postmilking until 72h postmilking. The IGF1 mRNA increased by 192h postmilking, whereas IGF2 mRNA decreased by 18h postmilking compared with 6h postmilking. The IGFBP5 mRNA and protein levels of Akt and Akt-P remained unchanged over the time series. These results show that reciprocal activation of STAT5 and STAT3 occurs at the onset of mammary gland involution in the bovine, albeit at a slower rate than in rodents. Mathematical modeling of the pathways indicated that activated STAT3 could block the STAT5 pathway by upregulating SOCS3. The regulation of IGF1-Akt signaling suggests that by 192h postmilking in dairy cows, the involution process is still in the reversible phase, with quiescent mammary epithelial cells not yet in the senescent phase.

A modified version of the Molly rumen model to quantify methane emissions from sheep.

We modified the rumen submodel of the Molly dairy cow model to simulate the rumen of a sheep and predict its methane emissions. We introduced a rumen hydrogen (H2) pool as a dynamic variable, which (together with the microbial pool in Molly) was used to predict methane production, to facilitate future consideration of thermodynamic control of methanogenesis. The new model corrected a misspecification of the equation of microbial H2 utilization in Molly95, which could potentially give rise to unrealistic predictions under conditions of low intake rates. The new model included a function to correct biases in the estimation of net H2 production based on the default stoichiometric relationships in Molly95, with this function specified in terms of level of intake. Model parameters for H2 and methane production were fitted to experimental data that included fresh temperate forages offered to sheep at a wide range of intake levels and then tested against independent data. The new model provided reasonable estimates relative to the calibration data set, but a different parameterization was needed to improve its predicted ability relative to the validation data set. Our results indicate that, although feedback inhibition on H2 production and methanogen activity increased with feeding level, other feedback effects that vary with diet composition need to be considered in future work on modeling rumen digestion in Molly.

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.

Modelling muscle energy-metabolism in anaerobic muscle.

A mathematical model of anaerobic muscle energy-metabolism was developed to predict pH and the concentrations of nine muscle metabolites over time. Phosphorous-31 Nuclear Magnetic Resonance was used to measure time-course data for some phosphate metabolites and pH in anoxic M. semitendinosus taken from three slaughtered sheep. Muscles were held at 35 degrees C during the experiment. Measurement commenced 25 min post mortem and concluded before rigor mortis. The model was fitted to these data within experimental error, by simultaneously varying model parameter values and initial substrate concentrations. The model was used to simulate the period from death until metabolic activity ceased, in order to predict the different stages of metabolic response to anoxia. The model suggested that alkalinisation would occur in all three muscles in the first few minutes after the onset of anoxia, followed by a steady decline in pH. For two of the muscles this decline continued until rigor, with final pH values of 5.60 and 6.07. For the other muscle, pH reached a low of 5.60 near rigor but then increased to a final value of 5.73. A rise in pH after rigor has been observed but not previously explained in the literature. The modelling results suggest it was caused by the alkalising effect of adenosine monophosphate deamination being greater at low pH than the acidifying effect of inosine monophosphate dephosphorylation.

A statistical approach to identifying the batch of origin of mixed-meat products using DNA profiles.

Comparison of DNA samples at different points of a supply chain offers a powerful means of verifying tracing systems for primal cuts of meat. However, this approach is problematic for products made from ground (or mixed) meat because such products are typically made from an unknown (and random) number of unidentified animals. We present a statistical method that uses DNA profiles to verify or refute the contention that a particular mixed-meat product came from a particular manufacturing batch. This method involves randomly isolating a number of individual DNA samples (comprising an unknown number of individual genotypes) from the end product and comparing them with a set of DNA samples (also comprising an unknown number of individuals) that had been collected randomly before preparation of a manufacturing batch. Confidence levels are given for refuting spurious claims, and the development of optimum sampling strategies is discussed. The results are discussed in relation to batch verification of mixed-meat products in the food industry, with an emphasis on traceability issues.

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.

Modeling the effect of energy status on mammary gland growth and lactation.

The impact of nutrition on lactation can be separated into acute effects, affecting day-to-day yield, and chronic effects, which govern the persistency of lactation and rate of decline of the lactation curve. A mathematical model of the mammary gland was constructed to investigate both acute and chronic effects. Mammary growth is expressed in terms of the dynamics of populations of active (secreting) and quiescent (engorged) alveoli. The secretion rate of active alveoli is expressed in terms of the energy status of the dam. The model was fitted to data from a 2 x 2 factorial trial in which lactation curves were measured for heifers of two different genotypes (North American and New Zealand Holstein-Friesians) fed two different diets [grass and total mixed rations (TMR)]. Total formation of alveoli during pregnancy and lactation was statistically the same across all groups despite differences between diets, in the rate of formation of alveoli at parturition. The senescence rate of alveoli was significantly higher for heifers fed grass compared with heifers fed TMR, which corresponds to better persistency for heifers fed TMR. Heifers fed TMR had a higher rate of reactivation of quiescent alveoli than heifers fed grass, which also contributes to increased persistence for heifers fed TMR. There was a genotype x diet interaction in the rate of quiescence of active alveoli: the North American-Grass group had a higher rate of quiescence than the other three groups, perhaps reflecting differences in selection pressures between the New Zealand and North American genotypes.

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.