Usefulness of the total and differential somatic cell count based udder health group concept for evaluating herd management practices and udder health in dairy herds.

Subclinical mastitis and associated economic losses are a steady challenge in the dairy industry. The combination of the well-established somatic cell count (SCC) parameter and the new differential SCC (DSCC) opens up the possibility to categorise cows into four different udder health groups (UHG) based on results from a single milk recording/dairy herd improvement (DHI) test: UHG A: healthy/normal, ≤ 200,000 cells/mL and DSCC ≤ 65 %; B: suspicious, ≤ 200,000 cells/mL and DSCC > 65 %; C: (subclinical) mastitis, > 200,000 cells/mL and DSCC > 65 %; D: chronic/persistent mastitis, > 200,000 cells/mL and DSCC ≤ 65 %. The objectives of this study were to investigate 1) herd management practises among herds in different UHG categories and 2) herd performance parameters depending on the proportion of cows in UHG A. A total number of 41 herds in Styria, Austria, and Thuringia, Germany, were visited and interviewed for the first part of the study. The herds were categorised into 3 UHG categories depending on the proportion of cows in UHG A: I = >65 %; II = 55-65 %; and III = <55 %. Those with good udder health and best herd performance (+9 % milk yields, +11 % longevity, -35 % antibiotic treatments) applied distinct preventive measures, in particular excellent cubicle management and early antibiotic treatment (P < 0.05 each). However, preventive measures were applied to a lower extent in other herds. Herds were categorised differently using the UHG concept compared to SCC alone as the UHG-based categorisation allowed to clearer distinguish herds with medium-good from those with good udder health. A total number of 129,812 regular milk recording/DHI test day results of 890 Austrian and 183 German herds was used for the second part of the study. Results revealed a trend of increasing daily production as proportions of cows in UHG A increase. In conclusion, the UHG concept allowed clearer distinction of herds with good, medium-good, and poor udder health and could be used to promote practises leading to better animal health, less antibiotic treatments, and higher milk quality.

Quantitative evaluation of respiration induced metabolic oscillations in erythrocytes.

The changes in the partial pressures of oxygen and carbon dioxide (P(O(2)) and P(CO(2))) during blood circulation alter erythrocyte metabolism, hereby causing flux changes between oxygenated and deoxygenated blood. In the study we have modeled this effect by extending the comprehensive kinetic model by Mulquiney and Kuchel [P.J. Mulquiney, and P.W. Kuchel. Model of 2,3-bisphosphoglycerate metabolism in the human erythrocyte based on detailed enzyme kinetic equations: equations and parameter refinement, Biochem. J. 1999, 342, 581-596.] with a kinetic model of hemoglobin oxy-/deoxygenation transition based on an oxygen dissociation model developed by Dash and Bassingthwaighte [R. Dash, and J. Bassingthwaighte. Blood HbO(2) and HbCO(2) dissociation curves at varied O(2), CO(2), pH, 2,3-DPG and temperature levels, Ann. Biomed. Eng., 2004, 32(12), 1676-1693.]. The system has been studied during transitions from the arterial to the venous phases by simply forcing P(O(2)) and P(CO(2)) to follow the physiological values of venous and arterial blood. The investigations show that the system passively follows a limit cycle driven by the forced oscillations of P(O(2)) and is thus inadequately described solely by steady state consideration. The metabolic system exhibits a broad distribution of time scales. Relaxations of modes with hemoglobin and Mg(2+) binding reactions are very fast, while modes involving glycolytic, membrane transport and 2,3-BPG shunt reactions are much slower. Incomplete slow mode relaxations during the 60 s period of the forced transitions cause significant overshoots of important fluxes and metabolite concentrations - notably ATP, 2,3-BPG, and Mg(2+). The overshoot phenomenon arises in consequence of a periodical forcing and is likely to be widespread in nature - warranting a special consideration for relevant systems.

Complexity reduction of biochemical rate expressions.

MOTIVATION: The current trend in dynamical modelling of biochemical systems is to construct more and more mechanistically detailed and thus complex models. The complexity is reflected in the number of dynamic state variables and parameters, as well as in the complexity of the kinetic rate expressions. However, a greater level of complexity, or level of detail, does not necessarily imply better models, or a better understanding of the underlying processes. Data often does not contain enough information to discriminate between different model hypotheses, and such overparameterization makes it hard to establish the validity of the various parts of the model. Consequently, there is an increasing demand for model reduction methods. RESULTS: We present a new reduction method that reduces complex rational rate expressions, such as those often used to describe enzymatic reactions. The method is a novel term-based identifiability analysis, which is easy to use and allows for user-specified reductions of individual rate expressions in complete models. The method is one of the first methods to meet the classical engineering objective of improved parameter identifiability without losing the systems biology demand of preserved biochemical interpretation. AVAILABILITY: The method has been implemented in the Systems Biology Toolbox 2 for MATLAB, which is freely available from http://www.sbtoolbox2.org. The Supplementary Material contains scripts that show how to use it by applying the method to the example models, discussed in this article.

Dynamical quorum sensing: Population density encoded in cellular dynamics.

Mutual synchronization by exchange of chemicals is a mechanism for the emergence of collective dynamics in cellular populations. General theories exist on the transition to coherence, but no quantitative, experimental demonstration has been given. Here, we present a modeling and experimental analysis of cell-density-dependent glycolytic oscillations in yeast. We study the disappearance of oscillations at low cell density and show that this phenomenon occurs synchronously in all cells and not by desynchronization, as previously expected. This study identifies a general scenario for the emergence of collective cellular oscillations and suggests a quorum-sensing mechanism by which the cell density information is encoded in the intracellular dynamical state.

Quantitative characterization of cell synchronization in yeast.

Metabolic oscillations in baker's yeast serve as a model system for synchronization of biochemical oscillations. Despite widespread interest, the complexity of the phenomenon has been an obstacle for a quantitative understanding of the cell synchronization process. In particular, when two yeast cell populations oscillating 180 degrees out of phase are mixed, it appears as if the synchronization dynamics is too fast to be explained. We have probed the synchronization dynamics by forcing experiments in an open-flow reactor, and we find that acetaldehyde has a very strong synchronization effect that can account quantitatively for the classical mixing experiment. The fast synchronization dynamics is explained by a general synchronization mechanism, which is dominated by a fast amplitude response as opposed to the expected slow phase change. We also show that glucose can mediate this kind of synchronization, provided that the glucose transporter is not saturated. This makes the phenomenon potentially relevant for a broad range of cell types.

Reduction of a biochemical model with preservation of its basic dynamic properties.

The complexity of full-scale metabolic models is a major obstacle for their effective use in computational systems biology. The aim of model reduction is to circumvent this problem by eliminating parts of a model that are unimportant for the properties of interest. The choice of reduction method is influenced both by the type of model complexity and by the objective of the reduction; therefore, no single method is superior in all cases. In this study we present a comparative study of two different methods applied to a 20D model of yeast glycolytic oscillations. Our objective is to obtain biochemically meaningful reduced models, which reproduce the dynamic properties of the 20D model. The first method uses lumping and subsequent constrained parameter optimization. The second method is a novel approach that eliminates variables not essential for the dynamics. The applications of the two methods result in models of eight (lumping), six (elimination) and three (lumping followed by elimination) dimensions. All models have similar dynamic properties and pin-point the same interactions as being crucial for generation of the oscillations. The advantage of the novel method is that it is algorithmic, and does not require input in the form of biochemical knowledge. The lumping approach, however, is better at preserving biochemical properties, as we show through extensive analyses of the models.

On the mechanisms of glycolytic oscillations in yeast.

This work concerns the cause of glycolytic oscillations in yeast. We analyse experimental data as well as models in two distinct cases: the relaxation-like oscillations seen in yeast extracts, and the sinusoidal Hopf oscillations seen in intact yeast cells. In the case of yeast extracts, we use flux-change plots and model analyses to establish that the oscillations are driven by on/off switching of phosphofructokinase. In the case of intact yeast cells, we find that the instability leading to the appearance of oscillations is caused by the stoichiometry of the ATP-ADP-AMP system and the allosteric regulation of phosphofructokinase, whereas frequency control is distributed over the reaction network. Notably, the NAD+/NADH ratio modulates the frequency of the oscillations without affecting the instability. This is important for understanding the mutual synchronization of oscillations in the individual yeast cells, as synchronization is believed to occur via acetaldehyde, which in turn affects the frequency of oscillations by changing this ratio.

Chemical interpretation of oscillatory modes at a Hopf point.

We present two complementary methods for studying the oscillatory mechanisms in a chemical reaction network in the neighbourhood of a supercritical Hopf bifurcation. The first method is a modification of metabolic control analysis (a form of sensitivity analysis), and focuses on the reactions rather than the chemical species. By rephrasing metabolic control analysis in terms of the amplitude equation of the Hopf bifurcation, we show that control of amplitude and frequency of the oscillations should be considered separately, and that the amplitude control is directly related to the control of the stability of the stationary state. Generally, the frequency of the oscillations is controlled by more reactions than the amplitude is, and those reactions controlling amplitude will generally also exert control of the frequency. The second method focuses on the role of the chemical species. By considering their relative phases and amplitudes, the method reveals to what extent a simple activator-inhibitor interpretation of the amplitude equation associated with the Hopf bifurcation corresponds to an equally simple chemical interpretation. If applicable, the method identifies the activating and inhibiting modes chemically. Prior knowledge of the underlying reaction network is not needed, only phase and amplitude measurements are used in the analysis. Hence, this method is a top-down approach well suited for systems biology. Both methods are exemplified by calculations on the Oregonator model for the Belousov-Zhabotinsky reaction.