The changes in the energy metabolism of human muscle induced by training.

The biochemical effects of training programmes have been studied with a kinetic model of central metabolism, using enzyme activities and metabolite concentrations measured at rest and after 30 s maximum-intensity exercise, collected before and after long and short periods of training, which differed only by the duration of the rest intervals. After short periods of training the glycolytic flux at rest was three times higher than it had been before training, whereas during exercise the flux and energy consumption remained the same as before training. Long periods of training had less effect on the glycolytic flux at rest, but increased it in response to exercise, increasing the contribution of oxidative phosphorylation.

Transcriptional noise and cellular heterogeneity in mammalian macrophages.

Transcriptional noise is known to play a crucial role in heterogeneity in bacteria and yeast. Mammalian macrophages are known to exhibit cell-to-cell variation in their responses to pathogens, but the source of this heterogeneity is not known. We have developed a detailed stochastic model of gene expression that takes into account scaling effects due to cell size and genome complexity. We report the results of applying this model to simulating gene expression variability in mammalian macrophages, demonstrating a possible molecular basis for heterogeneity in macrophage signalling responses. We note that the nature of predicted transcriptional noise in macrophages is different from that in yeast and bacteria. Some molecular interactions in yeast and bacteria are thought to have evolved to minimize the effects of the high-frequency noise observed in these species. Transcriptional noise in macrophages results in slow changes to gene expression levels and would not require the type of spike-filtering circuits observed in yeast and bacteria.

Evolution of 'design' principles in biochemical networks.

Computer modelling and simulation are commonly used to analyse engineered systems. Biological systems differ in that they often cannot be accurately characterised, so simulations are far from exact. Nonetheless, we argue in this paper that evolution results in recurring, dynamic organisational principles in biological systems, and that simulation can help to identify them and analyse their dynamic properties. As a specific example, we present a dynamic model of the galactose utilisation pathway in yeast, and highlight several features of the model that embody such 'design principles'.

Occurrence of paradoxical or sustained control by an enzyme when overexpressed: necessary conditions and experimental evidence with regard to hepatic glucokinase.

It is widely assumed that the control coefficient of an enzyme on pathway flux decreases as the concentration of enzyme increases. However, it has been shown [Kholodenko and Brown (1996) Biochem. J. 314, 753-760] that enzymes with sigmoidal kinetics can maintain or even gain control with an increase in enzyme activity or concentration. This has been described as 'paradoxical control'. Here we formulate the general requirements for allosteric enzyme kinetics to display this behaviour. We show that a necessary condition is that the Hill coefficient of the enzyme should increase with an increase in substrate concentration or decrease with an increase in product concentration. We also describe the necessary and sufficient requirements for the occurrence of paradoxical control in terms of the flux control coefficients and the derivatives of the elasticities. The derived expression shows that the higher the control coefficient of an allosteric enzyme, the more likely it is that the pathway will display this behaviour. Control of pathway flux is generally shared between a large number of enzymes and therefore the likelihood of observing sustained or increased control is low, even if the kinetic parameters are in the most favourable range to generate the phenomenon. We show that hepatic glucokinase, which has a very high flux control coefficient and displays sigmoidal behaviour within the hepatocyte in situ as a result of interaction with a regulatory protein, displays sustained or increased control over an extended range of enzyme concentrations when the regulatory protein is overexpressed.

Analysis and prediction of the effect of uncertain boundary values in modeling a metabolic pathway.

The integration of large quantities of biological information into mathematical models of cell metabolism provides a way for quantitatively evaluating the effect of parameter changes on simultaneous, coupled, and, often, counteracting processes. From a practical point of view, the validity of the model's predictions would critically depend on its quality. Among others, one of the critical steps that may compromise this quality is to decide which are the boundaries of the model. That is, we must decide which metabolites are assumed to be constants, and which fluxes are considered to be the inputs and outputs of the system. In this article, we analyze the effect of the experimental uncertainty on these variables on the system's characterization. Using a previously defined model of glucose fermentation in Saccharomyces cerevisiae, we characterize the effect of the uncertainty on some key variables commonly considered to be constants in many models of glucose metabolism, i.e., the intracellular pH and the pool of nucleotides. Without considering if this variability corresponds to a possible true physiological phenomenon, the goal of this article is to illustrate how this uncertainty may result in an important variability in the systemic responses predicted by the model. To characterize this variability, we analyze the utility and limitations of computing the sensitivities of logarithmic-gains (control coefficients) to the boundary parameters. With the exception of some special cases, our analysis shows that these sensitivities are good indicators of the dependence of the model systemic behavior on the parameters of interest.

Advantages and disadvantages of aggregating fluxes into synthetic and degradative fluxes when modelling metabolic pathways.

It is now widely accepted that mathematical models are needed to predict the behaviour of complex metabolic networks in the cell, in order to have a rational basis for planning metabolic engineering with biotechnological or therapeutical purposes. The great complexity of metabolic networks makes it crucial to simplify them for analysis, but without violating key principles of stoichiometry or thermodynamics. We show here, however, that models for branched complex systems are sometimes obtained that violate the stoichiometry of fluxes at branch points and as a result give unrealistic metabolite concentrations at the steady state. This problem is especially important when models are constructed with the S-system form of biochemical systems theory. However, the same violation of stoichiometry can occur in metabolic control analysis if control coefficients are assumed to be constant when trying to predict the effects of large changes. We derive the appropriate matrix equations to analyse this type of problem systematically and to assess its extent in any given model.

Effects of feedback inhibition on transit time in a linear pathway of Michaelis-Menten-type reactions.

An analysis of the effects of external and internal metabolites on the steady-state behavior of linear pathways comprising a sequence of three Michaelis-Menten-type reactions with and without a simple feedback inhibition (i.e. an interaction of an internal metabolite with the pathway) is performed with respect to the transit time tau by its formulation as rectangular-hyperbolic functions of the flux J, instead of direct expressions in terms of the external metabolite concentrations. For a given concentration of the external metabolite M1 (substrate of the pathway) or M4 (product of the pathway), the flux J has a lower value in the pathway with feedback inhibition than in the pathway without feedback inhibition. With variation in the M1 concentration the transit time tau shows a concave relationship with the flux J which is virtually identical for both pathways, yielding a minimum at a certain value of J. With variation in the M4 concentration the transit time tau monotonously decreases with higher value of J, and for a given value of J the feedback inhibition allows a lower transit time. This effect is enhanced with stronger feedback inhibition, and is in turn greatly reduced with higher values of total concentration and rate constants for the first enzyme in the pathway.