Mathematics and biology

CITATION: Hofmeyr, J. H. S. 2017. Mathematics and biology. South African Journal of Science, 113(3/4), Art. #a0203, doi:10.17159/sajs.2017/a0203.The original publication is available at http://sajs.co.zaNo abstract availablehttps://www.sajs.co.za/article/view/3628Publisher's versio

Tracing regulatory routes in metabolism using generalised supply-demand analysis

CITATION: Christensen, C. D., Hofmeyr, J. H. S. & Rohwer, J. M. 2015. Tracing regulatory routes in metabolism using generalised supply-demand analysis. BMC Systems Biology, 9(1): 89, doi: 10.1186/s12918-015-0236-1.Publication of this article was funded by the Stellenbosch University Open Access Fund.The original publication is available at http://bmcmusculoskeletdisord.biomedcentral.comBackground: Generalised supply-demand analysis is a conceptual framework that views metabolism as a molecular economy. Metabolic pathways are partitioned into so-called supply and demand blocks that produce and consume a particular intermediate metabolite. By studying the response of these reaction blocks to perturbations in the concentration of the linking metabolite, different regulatory routes of interaction between the metabolite and its supply and demand blocks can be identified and their contribution quantified. These responses are mediated not only through direct substrate/product interactions, but also through allosteric effects. Here we subject previously published kinetic models of pyruvate metabolism in Lactococcus lactis and aspartate-derived amino acid synthesis in Arabidopsis thaliana to generalised supply-demand analysis. Results: Multiple routes of regulation are brought about by different mechanisms in each model, leading to behavioural and regulatory patterns that are generally difficult to predict from simple inspection of the reaction networks depicting the models. In the pyruvate model the moiety-conserved cycles of ATP/ADP and NADH/NAD+ allow otherwise independent metabolic branches to communicate. This causes the flux of one ATP-producing reaction block to increase in response to an increasing ATP/ADP ratio, while an NADH-consuming block flux decreases in response to an increasing NADH/NAD+ ratio for certain ratio value ranges. In the aspartate model, aspartate semialdehyde can inhibit its supply block directly or by increasing the concentration of two amino acids (Lys and Thr) that occur as intermediates in demand blocks and act as allosteric inhibitors of isoenzymes in the supply block. These different routes of interaction from aspartate semialdehyde are each seen to contribute differently to the regulation of the aspartate semialdehyde supply block. Conclusions: Indirect routes of regulation between a metabolic intermediate and a reaction block that either produces or consumes this intermediate can play a much larger regulatory role than routes mediated through direct interactions. These indirect routes of regulation can also result in counter-intuitive metabolic behaviour. Performing generalised supply-demand analysis on two previously published models demonstrated the utility of this method as an entry point in the analysis of metabolic behaviour and the potential for obtaining novel results from previously analysed models by using new approaches.http://bmcsystbiol.biomedcentral.com/articles/10.1186/s12918-015-0236-1Publisher's versio

The logic of kinetic regulation in the thioredoxin system

<p>Abstract</p> <p>Background</p> <p>The thioredoxin system consisting of NADP(H), thioredoxin reductase and thioredoxin provides reducing equivalents to a large and diverse array of cellular processes. Despite a great deal of information on the kinetics of individual thioredoxin-dependent reactions, the kinetic regulation of this system as an integrated whole is not known. We address this by using kinetic modeling to identify and describe kinetic behavioral motifs found within the system.</p> <p>Results</p> <p>Analysis of a realistic computational model of the <it>Escherichia coli </it>thioredoxin system revealed several modes of kinetic regulation in the system. In keeping with published findings, the model showed that thioredoxin-dependent reactions were adaptable (i.e. changes to the thioredoxin system affected the kinetic profiles of these reactions). Further and in contrast to other systems-level descriptions, analysis of the model showed that apparently unrelated thioredoxin oxidation reactions can affect each other via their combined effects on the thioredoxin redox cycle. However, the scale of these effects depended on the kinetics of the individual thioredoxin oxidation reactions with some reactions more sensitive to changes in the thioredoxin cycle and others, such as the Tpx-dependent reduction of hydrogen peroxide, less sensitive to these changes. The coupling of the thioredoxin and Tpx redox cycles also allowed for ultrasensitive changes in the thioredoxin concentration in response to changes in the thioredoxin reductase concentration. We were able to describe the kinetic mechanisms underlying these behaviors precisely with analytical solutions and core models.</p> <p>Conclusions</p> <p>Using kinetic modeling we have revealed the logic that underlies the functional organization and kinetic behavior of the thioredoxin system. The thioredoxin redox cycle and associated reactions allows for a system that is adaptable, interconnected and able to display differential sensitivities to changes in this redox cycle. This work provides a theoretical, systems-biological basis for an experimental analysis of the thioredoxin system and its associated reactions.</p

Mathematics and biology

CITATION: Hofmeyr, J. H. S. 2017. Mathematics and biology. South African Journal of Science, 113(3/4), Art. #a0203, doi:10.17159/sajs.2017/a0203.The original publication is available at http://sajs.co.zaNo abstract availablehttps://www.sajs.co.za/article/view/3628Publisher's versio

The regulatory design of an allosteric feedback loop: the effect of saturation by pathway substrate.

Aspects of metabolic regulation can be fruitfully studied with a combination of generic modelling, control analysis and graphical analysis using rate characteristics. This paper analyses a prototypical supply-demand system consisting of a biosynthetic subsystem subject to allosteric inhibition by its product and a demand process that consumes this product. The effect of changes in affinity of the committing supply enzyme for the pathway substrate on the regulatory properties of the supply subsystem is compared for the Monod-Wyman-Changeux and the reversible Hill allosteric enzyme models. We found that the Hill model has a distinct advantage in that the steady-state concentration at which it maintains the product is set by the half-saturating product concentration and is independent of changes in the degree of saturation for substrate. In contrast, with the Monod-Wyman-Changeux model this set point varies with affinity for substrate. Explicitly incorporating reversibility in all rate equations made it possible to distinguish between kinetic and thermodynamic aspects of regulation. Combining the supply and demand rate characteristics allows us to explore both the control distribution at steady state and the regulatory performance of the system over a wide range of demand activities

Pages 377–385

incorporate cooperative enzymes into metabolic model

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An abstract cell model that describes the self-organization of cell function in living system