Mads Madsen

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.

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.

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.

Positive effects on bone mineralisation and muscular fitness after 10 months of intense school-based physical training for children aged 8–10 years: the FIT FIRST randomised controlled trial

Objectives We investigated whether musculoskeletal fitness of school children aged 8–10 years was affected by frequent intense PE sessions. Design and participants 295 Danish school children aged 8–10 years were cluster randomised to a small-sided ball game group (SSG) (n=96, four schools, five classes), a circuit strength training group (CST) (n=83, four schools, four classes) or a control group (CON, n=116, two schools, five classes). Intervention SSG or CST was performed 3×40 min/week over 10 months. Whole-body dual-energy X-ray absorptiometry (DXA) scans were used to determine areal bone mineral density (aBMD), bone mineral content (BMC) and lean body mass (LBM). Flamingo balance, standing long jump and 20-m sprint tests were used to determine muscular fitness. Results Analysis of baseline-to-10 months change scores showed between-group differences in favour of the interventions in whole-body aBMD (SSG vs CON: 8 mg/cm2, 95% CI 3 to 13; CST vs CON: 7 mg/cm2, 95% CI 2 to 13, p<0.05) and leg BMC (SSG vs CON: 11 g, 95% CI 4 to 18; CST vs CON: 11 g, 95% CI 3 to 18, p<0.05). SSG had higher change scores in leg aBMD compared with CON and CST (SSG vs CON: 19 mg/cm2, 95% CI 11 to 39, p<0.05; SSG vs CST: 12 mg/cm2, 95% CI 3 to 21, p<0.05), and CST had higher change scores in whole-body BMC compared with CON (CST vs CON: 25 g, 95% CI 10 to 39, p<0.05). Both training types resulted in higher change scores in postural balance (SSG vs CON: 2.4 fewer falls/min, 95% CI 0.3 to 4.5, CST vs CON: 3.6 fewer falls/min, 95% CI 1.3 to 5.9, p<0.05) and jump length (SSG vs CON: 10%, 95% CI 5 to 16%; CST vs CON: 9%, 95% CI 3 to 15%, p<0.05). No between-group differences were observed for sprint performance or LBM (p>0.05). Conclusions In conclusion, 3×40 min/week with SSG or CST over a full school year improves bone mineralisation and several aspects of muscular fitness of children aged 8–10 years, suggesting that well-organised intense physical education classes can contribute positively to develop musculoskeletal health in young children. Trial registration number NCT02000492, post results.

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.

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.

Alpha adrenergic receptor blockade increases capillarization and fractional O2 extraction and lowers blood flow in contracting human skeletal muscle

To assess the effect of elevated basal shear stress on angiogenesis in humans and the role of enhanced skeletal muscle capillarization on blood flow and O2 extraction.