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. 2018 Jun;6(6):63.
doi: 10.3390/pr6060063. Epub 2018 May 28.

Prediction of Metabolite Concentrations, Rate Constants and Post-Translational Regulation Using Maximum Entropy-Based Simulations with Application to Central Metabolism of Neurospora crassa

William R Cannon  1 , Jeremy D Zucker  1 , Douglas J Baxter  2 , Neeraj Kumar  1 , Scott E Baker  3 , Jennifer M Hurley  4 , Jay C Dunlap  5
Affiliations

Prediction of Metabolite Concentrations, Rate Constants and Post-Translational Regulation Using Maximum Entropy-Based Simulations with Application to Central Metabolism of Neurospora crassa

William R Cannon et al. Processes (Basel). 2018 Jun.

Abstract

We report the application of a recently proposed approach for modeling biological systems using a maximum entropy production rate principle in lieu of having in vivo rate constants. The method is applied in four steps: (1) a new ordinary differential equation (ODE) based optimization approach based on Marcelin's 1910 mass action equation is used to obtain the maximum entropy distribution; (2) the predicted metabolite concentrations are compared to those generally expected from experiments using a loss function from which post-translational regulation of enzymes is inferred; (3) the system is re-optimized with the inferred regulation from which rate constants are determined from the metabolite concentrations and reaction fluxes; and finally (4) a full ODE-based, mass action simulation with rate parameters and allosteric regulation is obtained. From the last step, the power characteristics and resistance of each reaction can be determined. The method is applied to the central metabolism of Neurospora crassa and the flow of material through the three competing pathways of upper glycolysis, the non-oxidative pentose phosphate pathway, and the oxidative pentose phosphate pathway are evaluated as a function of the NADP/NADPH ratio. It is predicted that regulation of phosphofructokinase (PFK) and flow through the pentose phosphate pathway are essential for preventing an extreme level of fructose 1,6-bisphophate accumulation. Such an extreme level of fructose 1,6-bisphophate would otherwise result in a glassy cytoplasm with limited diffusion, dramatically decreasing the entropy and energy production rate and, consequently, biological competitiveness.

Keywords: mass action kinetics; maximum entropy production; metabolism; statistical thermodynamics.

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Conflict of interest statement

Conflicts of Interest: The authors declare no conflict of interest.

Figures

Figure 1.
Figure 1.
Map of net odds (Equation (7)) for reactions of glycolysis and the tricarboxylic acid (TCA) cycle. Values next to each reaction name indicate the net flux through the reaction, and two flux values are provided for each reaction. The first value (left) is the flux after maximum entropy optimization. The second value (right) is the flux after the same optimization but including regulation at PFK (by ATP) and PDHm (by acetyl-CoA). Reaction and metabolite abbreviations are derived from the BiGG database [34]; full common names are provided as supplementary Tables S1 and S2. The metabolic pathway visualizations here and in Figure 5 were created with Escher [35].
Figure 2.
Figure 2.
Concentrations as a function of time in maximum entropy optimization without regulation.
Figure 3.
Figure 3.
Concentrations as a function of time in maximum entropy optimization with regulation.
Figure 4.
Figure 4.
Energetics of glycolysis reactions. Columns from left to right indicate: (G) −ΔGrxn, (P) power, (R) resistance, and (F) flux. Red indicates high values and blue indicates low values. Values are in arbitrary, relative units but the specific values are provided in supplementary Notebook_S3. The phosphofructokinase reaction has dramatically different characteristics than the other reactions because feedback regulation of ATP turns it into a potentiometer. The metabolic pathway visualization was created with Pathway Tools [44].
Figure 5.
Figure 5.
Reaction flux through upper glycolysis and the pentose phosphate pathway as a function of the NADP/NADPH ratio. (Left) Low values of the ratio combined with high values of ATP result in approximately equal flow of material through upper glycolysis and the non-oxidative branch of the pentose phosphate pathway, minimizing the production of fructose 1,6-bisphosphate; (Middle) a NADP/NADPH ratio of 1 results in flow through each of upper glycolysis, non-oxidative and oxidative pentose phosphate pathways, with the oxidative pentose phosphate pathway containing approximately 65% of the flow of material; (Right) a high value of the ratio results in the cycling of flow iteratively through the oxidative pentose phosphate pathway while flow through upper glycolysis is minimal.
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