Metabolic function optimization -
cerevisiae see Strains and media section above. The set of all flux vectors v satisfying the above constraints defines the feasible solution space , representing the capability of the metabolic network as a system.
For a given objective function, we numerically determine an optimal flux distribution for this problem using an implementation of the simplex method [43].
In the particular case of growth maximization, the objective vector c is taken to be parallel to the biomass flux, which is modeled as an effective reaction that converts metabolites into biomass. To find a set of reactions from which none can be removed without forcing zero growth, we start with the set of all reactions and recursively reduce it until no further reduction is possible.
At each recursive step, we first compute how much the maximum growth rate would be reduced if each reaction were removed from the set individually. Then, we choose a reaction that causes the least change in the maximum growth rate, and remove it from the set.
We repeat this step until the maximum growth rate becomes zero. The set of reactions we have just before we remove the last reaction is a desired minimal reaction set. Note that, since the algorithm is not exhaustive, the number of reactions in this set is an upper bound and approximation for the minimum number of reactions required to sustain positive growth.
The authors thank Linda J. Broadbelt for valuable discussions and for providing feedback on the manuscript. The authors also thank Jennifer L. Reed and Adam M. Feist for providing information on their in silico models. Conceived and designed the experiments: AEM. Performed the experiments: NG.
Analyzed the data: TN NG AEM. Wrote the paper: TN AEM. Article Authors Metrics Comments Media Coverage Reader Comments Figures. Abstract Metabolic reactions of single-cell organisms are routinely observed to become dispensable or even incapable of carrying activity under certain circumstances.
Author Summary Cellular growth and other integrated metabolic functions are manifestations of the coordinated interconversion of a large number of chemical compounds. Sauro, University of Washington, United States of America Received: June 30, ; Accepted: October 20, ; Published: December 5, Copyright: © Nishikawa et al.
Introduction A fundamental problem in systems biology is to understand how living cells adjust the usage pattern of their components to respond and adapt to specific genetic, epigenetic, and environmental conditions.
Download: PPT. Figure 1. Optimal A and non-optimal B reaction activity in the reconstructed metabolic network of E. coli in glucose minimal medium Materials and Methods. Table 1. Reversibility of metabolic reactions in the reconstructed networks. Results Typical Nonoptimal States We model cellular metabolism as a network of metabolites connected through reaction and transport fluxes.
Mass balance. Environmental conditions. Figure 2. Number of active and inactive reactions in the metabolic networks of H. Table 2. Metabolic reactions in typical non-optimal states of the simulated metabolisms. Growth-Maximizing States We now turn to the maximization of growth rate, which is often hypothesized in flux balance-based approaches and found to be consistent with observation in adaptive evolution experiments [31] — [34].
Figure 3. Portions of E. coli metabolic network under maximum growth condition. Conditional inactivity. Typical Linear Objective Functions Although we have focused so far on maximizing the biomass production rate, the true nature of the fitness function driving evolution is far from clear [44] — [47].
Figure 4. Probability distribution of the number of active reactions in nonzero-growth states that optimize typical objective functions.
Table 3. Metabolic reactions in maximum growth states of the simulated metabolisms. Experimental Evidence Our results help explain previous experimental observations.
Table 4. Experimentally determined fluxes of intracellular reactions involved in the glycolysis, pentose phosphate pathway, TCA cycle, and amino acid biosynthesis of E. coli K12 MG under aerobic and anaerobic conditions [50].
Table 5. Experimentally determined fluxes of intracellular reactions involved in the glycolysis, metabolic steps around pyruvate, TCA cycle, glyoxylate cycle, gluconeogenesis, and pentose phosphate pathway of S.
cerevisiae strain CEN. PKD grown under glucose, maltose, ethanol, and acetate limitation [51]. Table 6. Fraction of inactive reactions in the simulated metabolism of E.
cerevisiae under maximum growth condition. Table 7. Experimentally determined fluxes of reversible and irreversible reactions of wild-type E. coli JM versus its pyruvate kinase-deficient mutant PB25 [53]. Figure 5.
Distribution of the number of active reactions in the E. coli metabolic network after a single-reaction knockout. Discussion Combining computational and analytical means, we have uncovered the microscopic mechanisms giving rise to the phenomenon of spontaneous reaction silencing in single-cell organisms, in which optimization of a single metabolic objective, whether growth or any other, significantly reduces the number of active reactions to a number that appears to be quite insensitive to the size of the entire network.
This reaction is regarded in the biochemical literature as irreversible under physiological conditions in the cell, and is constrained as such in the modeling literature [14] , [32] , [75] , [76]. Similar effective irreversibility is at work for any transport or internal reaction that is a unique producer of one or more chemical compounds in the cell.
Feasible Solution Space Under steady-state conditions, a cellular metabolic state is represented by a solution of a homogeneous linear equation describing the mass balance condition, 6 where S is the m × N stoichiometric matrix and is the vector of metabolic fluxes.
Finding Minimum Reaction Set for Nonzero Growth To find a set of reactions from which none can be removed without forcing zero growth, we start with the set of all reactions and recursively reduce it until no further reduction is possible. Supporting Information.
Text S1. s 0. Acknowledgments The authors thank Linda J. Author Contributions Conceived and designed the experiments: AEM. References 1. Giaever G, Chu AM, Ni L, Connelly C, Riles L, et al. Nature — View Article Google Scholar 2.
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Start Today. Call Today! New Year's Resolutions: Setting Realistic Weight Loss Goals January 4, Losing weight is already a challenging process, but even more so if you set unrealistic goals that are too difficult or even impossible to achieve For linear chains of different length with maximum productivity index values, the distribution of control coefficients with regard to the three parameters has a characteristic profile independent of the length of the chain.
Finally, this control profile changes when other variables are optimized, and we compare the theoretical results with the control profile of the first steps of glycolysis in rat liver. Abstract It is widely accepted that some performance function has been optimized during the evolution of metabolic pathways.
Publication types Research Support, Non-U.
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