Economics of periodic enzyme activities

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Linear pathway models (model files and simulation movies)

The following models demonstrate adaptive and spontaneous enzyme rhythms in simple metabolic pathways. I consider a pathway of four reactions in four variants: (i) fully reversible; (ii) almost irreversible (small reverse rate constants); (iii) competing, non-enzymatic consumption of intermediates; (iv) loop-shaped pathway with an entry point for substrate and an exit point for product. In the first two models, a varying substrate level promotes adaptive enzyme rhythms along the chain. In the last two models, such rhythms are even beneficial without an external rhythm. Finally, I studied a pathway of two reactions in which fluctuations of the intermediate would be costly. A cycle of storage and recovery reactions helps avoid such fluctuations and becomes activated when the external substrate oscillates.

Each pathway model has been studied under two alternative assumptions. First, assuming that cells realise their enzyme rhythms both by (slow) gene expression and (fast) covalent modification of enzymes ("expression rhythm"); here, expression changes slowly, while modifications change fast in comparison to the metabolic dynamics). Second, in a hypthetical scenario ("fast rhythm") in which enzyme levels can change very fast by expression changes only. SBML files are provided. In the movies, the two different versions are shown at different frequencies.

Model structures in SBML and SBtab format, as well as simulation reports and visual animations, are provided below.

Linear chain (fully reversible) [SBML] [SBtab]
Movies Expression rhythm | Fast rhythm

Linear chain (partly reversible) [SBML] [SBtab]
Movies Expression rhythm | Fast rhythm

Linear chain (with dilution) [SBML] [SBtab]
Movies Expression rhythm | Fast rhythm

Loop pathway [SBML] [SBtab]
Movies Expression rhythm | Fast rhythm

Storage of intermediate [SBML] [SBtab]
Expression rhythm / Fast rhythm