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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    ABSTRACT: A model for metabolism of the last bacterial common ancestor based on biomimetic analysis of the metabolic systems of phylogenetically ancient bacteria is developed. The mechanism of natural selection and evolution of the autocatalytic chemical systems under the effect of natural homeostatic parameters, such as chemical potentials, temperature, and pressure of environment is proposed. Competition between particular parts of the autocatalytic network with positive-plus-negative feedback resulted in the formation of particular systems of primary autotrophic, mixotrophic, and heterotrophic metabolism. The model of the last common ancestor as a combination of coupled metabolic cycles among population of protocells is discussed. Physicochemical features of these metabolic cycles determined the major principles of natural selection towards ancestral bacterial taxa.
    Paleontological Journal 12/2013; 47(9). DOI:10.1134/S003103011309013X · 0.51 Impact Factor
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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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    ABSTRACT: Structural kinetic modeling (SKM) enables the analysis of dynamical properties of metabolic networks solely based on topological information and experimental data. Current SKM-based experiments are hampered by the time-intensive process of assigning model parameters and choosing appropriate sampling intervals for Monte-Carlo experiments. We introduce a toolbox for the automatic and efficient construction and evaluation of structural kinetic models (SK models). Quantitative and qualitative analyses of network stability properties are performed in an automated manner. We illustrate the model building and analysis process in detailed example scripts that provide toolbox implementations of previously published literature models. The source code is freely available for download at
    Bioinformatics 07/2012; 28(19):2546-7. DOI:10.1093/bioinformatics/bts473 · 4.98 Impact Factor
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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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    ABSTRACT: The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many dynamical systems in mathematical biology exhibit steady-state behaviour one also wants to understand nonlocal dynamics beyond equilibrium points. In this paper we analyze predator-prey dynamical systems and extend the method of generalized models to periodic solutions. First, we adapt the equilibrium generalized modeling approach and compute the unique Floquet multiplier of the periodic solution which depends upon so-called generalized elasticity and scale functions. We prove that these functions also have to satisfy a flow on parameter (or moduli) space. Then we use Fourier analysis to provide computable conditions for stability and the moduli space flow. The final stability analysis reduces to two discrete convolutions which can be interpreted to understand when the predator-prey system is stable and what factors enhance or prohibit stable oscillatory behaviour. Finally, we provide a sampling algorithm for parameter space based on nonlinear optimization and the Fast Fourier Transform which enables us to gain a statistical understanding of the stability properties of periodic predator-prey dynamics.
    Discrete and Continuous Dynamical Systems - Series B 05/2011; 18(3). DOI:10.3934/dcdsb.2013.18.693 · 0.77 Impact Factor
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