On the stability of metabolic cycles. J Theor Biol

Bioinformatics Program, 24 Cummington St, Boston, MA, United States. addresses:
Journal of Theoretical Biology (Impact Factor: 2.12). 10/2010; 266(4):536-49. DOI: 10.1016/j.jtbi.2010.07.023
Source: PubMed


We investigate the stability properties of two different classes of metabolic cycles using a combination of analytical and computational methods. Using principles from structural kinetic modeling (SKM), we show that the stability of metabolic networks with certain structural regularities can be studied using a combination of analytical and computational techniques. We then apply these techniques to a class of single input, single output metabolic cycles, and find that the cycles are stable under all conditions tested. Next, we extend our analysis to a small autocatalytic cycle, and determine parameter regimes within which the cycle is very likely to be stable. We demonstrate that analytical methods can be used to understand the relationship between kinetic parameters and stability, and that results from these analytical methods can be confirmed with computational experiments. In addition, our results suggest that elevated metabolite concentrations and certain crucial saturation parameters can strongly affect the stability of the entire metabolic cycle. We discuss our results in light of the possibility that evolutionary forces may select for metabolic network topologies with a high intrinsic probability of being stable. Furthermore, our conclusions support the hypothesis that certain types of metabolic cycles may have played a role in the development of primitive metabolism despite the absence of regulatory mechanisms.

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    • "In different variants of metabolic topologies of autocatalytic cycles with positive feedback, resistance to external disturbances is observed (Reznik and Segrè, 2010), whereas the combination of cycles in general produces a branching network of catalytic pathways, the competition between which generates an additional degree of distributed robustness of the system as a whole (Goldstein, 2006). In addition, the combination of cycles results in the appearance of negative feedback (Tsokolov, 2010; Marakushev and Belonogova, 2011), providing the entire system with one more new quality, i.e., capability of adaptation to environments by natural selection. "
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    • "The SKM-experiments presented so far used customized algorithms in which the SK-models had been constructed manually 'from scratch' for each pathway (Steuer et al., 2006; Grimbs et al., 2007; Steuer et al., 2007; Reznik and Segrè, 2010). While this might be sufficient for small systems like in the mentioned examples, the construction of SK-models for larger systems, or even systems of genomic scale is not feasible manually. "
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    • "Despite the large class of models that one treats simultaneously it is often easy to interpret scale parameters and elasticities in applications [20]. Thereby a generalized model enables us to draw conclusions about a whole class of differential equations, for further examples see [22] [48] [46] [42] [12]. "
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