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

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## Abstract

**:**

## 1. Introduction

## 2. Theory and Methods

^{®}ode23tb solver, a trapezoidal rule and the backward differentiation solver [28].

_{2}are set to non-equilibrium values of 2 mM and 0.1 mM, respectively. Likewise, the cofactors CoA, ATP, ADP, orthophosphate, NAD, NADH, NADP and NADPH are also fixed boundary species; these concentrations were taken from a mass spectrometry analysis of absolute metabolite concentrations from Bennett et al. [25] The redox pair employed to shuttle electrons into the mitochondrial respiratory chain were taken to have equal chemical potentials, as done in previous modeling of the TCA cycle [17].

## 3. Results

_{2}, and with those for the cofactors CoA, ATP, ADP, orthophosphate, NAD, NADH, NADP and NADPH prevent the intermediates of glycolysis and the TCA cycle from reaching equilibrium.

## 4. Discussion

_{i}) may be used in many reactions, the impact on flux can be multiplicative.

## Supplementary Materials

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**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 4.**Energetics of glycolysis reactions. Columns from left to right indicate: (G) $-\Delta {G}_{rxn}$, (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.**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.

**Table 1.**Product of the reaction product concentrations for the optimization predictions and expected values, and resulting value of the loss function L (Equation (8)). Full common names are provided as supplementary Table S2.

Product of Concentrations | |||
---|---|---|---|

Reaction | Predicted | Expected | L |

CSm | 4.85 × 10^{−6} | 1.00 × 10^{−6} | 1.58 |

SUCOASm | 6.62 × 10^{−9} | 1.00 × 10^{−9} | 1.89 |

ENO | 6.65 × 10^{−1} | 1.00 × 10^{−3} | 6.50 |

PGM | 1.33 | 1.00 × 10^{−3} | 7.19 |

HEX1 | 4.26 × 10^{−2} | 1.00 × 10^{−6} | 10.66 |

PGI | 4.58 × 10^{1} | 1.00 × 10^{−3} | 10.73 |

GAPD | 4.82 × 10^{−2} | 1.00 × 10^{−6} | 10.78 |

PYRt2m | 8.43 × 10^{2} | 1.00 × 10^{−3} | 13.64 |

PGK | 1.09 | 1.00 × 10^{−6} | 13.90 |

PYK | 5.84 | 1.00 × 10^{−6} | 15.58 |

PFK | 9.21 × 10^{2} | 1.00 × 10^{−6} | 20.64 |

PDHm | 8.66 | 1.00 × 10^{−9} | 22.88 |

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**MDPI and ACS Style**

Cannon, W.R.; Zucker, J.D.; Baxter, D.J.; Kumar, N.; Baker, S.E.; Hurley, J.M.; Dunlap, J.C.
Prediction of Metabolite Concentrations, Rate Constants and Post-Translational Regulation Using Maximum Entropy-Based Simulations with Application to Central Metabolism of *Neurospora crassa*. *Processes* **2018**, *6*, 63.
https://doi.org/10.3390/pr6060063

**AMA Style**

Cannon WR, Zucker JD, Baxter DJ, Kumar N, Baker SE, Hurley JM, Dunlap JC.
Prediction of Metabolite Concentrations, Rate Constants and Post-Translational Regulation Using Maximum Entropy-Based Simulations with Application to Central Metabolism of *Neurospora crassa*. *Processes*. 2018; 6(6):63.
https://doi.org/10.3390/pr6060063

**Chicago/Turabian Style**

Cannon, William R., Jeremy D. Zucker, Douglas J. Baxter, Neeraj Kumar, Scott E. Baker, Jennifer M. Hurley, and Jay C. Dunlap.
2018. "Prediction of Metabolite Concentrations, Rate Constants and Post-Translational Regulation Using Maximum Entropy-Based Simulations with Application to Central Metabolism of *Neurospora crassa*" *Processes* 6, no. 6: 63.
https://doi.org/10.3390/pr6060063