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. Author manuscript; available in PMC: 2012 Nov 1.

Published in final edited form as: Metab Eng. 2011 Sep 1;13(6):666–673. doi: 10.1016/j.ymben.2011.08.003

Metabolic evolution of AS411 during anaerobic growth on glucose. (A) Change in specific growth rate over evolution time during serial dilution. Filled symbols represent cultures that have been evaluated in controlled bioreactor experiments. (B) Performance of the evolved cells after an evolution time of 329 hrs (AS411E0); 487 hrs (AS411E1); 600 hrs (AS411E2); 642 hrs (AS411E3). Evolved cells have higher specific growth rates and ethanol production rates in comparison to their parent, AS411. (C) Total reaction entropy for AS411 ( ) and the evolved cell cultures ( AS411E1; AS411E3) as a function of probabilities of elementary modes. The plot shows the shift in metabolic state of cells towards the predicted state of a fully evolved system where the entropy is maximized and the usage probabilities are according to the Boltzmann distribution law. The symbol represents the fully evolved system estimated from the asymptotic value of the fitting functions of probabilities shown in Fig. 3 at infinite evolution time. (D) Change in rate of entropy generation, computed from the product of the total reaction entropy and the uptake rate of glucose, as a function of evolution time. Circles represent the experimentally determined rate of entropy production while the line represents the rate of entropy production calculated from the fitting functions of probabilities given in Fig. 3. The plot suggests that the cell system has a natural tendency to evolve with time towards an asymptotic state with maximum rate of entropy production.

Inline graphic — Metabolic evolution of AS411 during anaerobic growth on glucose. (A) Change in specific growth rate over evolution time during serial dilution. Filled symbols represent cultures that have been evaluated in controlled bioreactor experiments. (B) Performance of the evolved cells after an evolution time of 329 hrs (AS411E0); 487 hrs (AS411E1); 600 hrs (AS411E2); 642 hrs (AS411E3). Evolved cells have higher specific growth rates and ethanol production rates in comparison to their parent, AS411. (C) Total reaction entropy for AS411 ( ) and the evolved cell cultures ( AS411E1; AS411E3) as a function of probabilities of elementary modes. The plot shows the shift in metabolic state of cells towards the predicted state of a fully evolved system where the entropy is maximized and the usage probabilities are according to the Boltzmann distribution law. The symbol represents the fully evolved system estimated from the asymptotic value of the fitting functions of probabilities shown in Fig. 3 at infinite evolution time. (D) Change in rate of entropy generation, computed from the product of the total reaction entropy and the uptake rate of glucose, as a function of evolution time. Circles represent the experimentally determined rate of entropy production while the line represents the rate of entropy production calculated from the fitting functions of probabilities given in Fig. 3. The plot suggests that the cell system has a natural tendency to evolve with time towards an asymptotic state with maximum rate of entropy production.