# ECMpy, a Simplified Workflow for Constructing Enzymatic Constrained Metabolic Network Model

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Workflow of ECMpy

_{cat}values. The stoichiometric constraints (Equation (1)) and reversibility constraints (Equation (2)) used were the same as in flux balance analysis [24]. A new enzymatic constraint (Equation (3)) was introduced into the model, where ptot and f represent the total protein fraction in E. coli and the mass fraction of enzymes, respectively. The enzyme mass fraction f was calculated based on Equation (4) where A

_{i}and A

_{j}represented the abundances (mole ratio) of the i-th protein (p_num represented proteins expressed in the model) and j-th protein (g_num represented proteins expressed in the whole proteome). MW

_{i}and k

_{cat}

_{,i}were molecular weight and turnover number of an enzyme catalyzing reaction i. For reactions catalyzed by multiple isoenzymes, a reaction can be split into multiple reactions. For reactions catalyzed by enzyme complex, using the minimum value of protein in complex ($\frac{{k}_{cat,i}}{M{W}_{i}}=min\left(\frac{{k}_{cat,ij}}{M{W}_{ij}},j\in m\right)$, m is the number of proteins in complex). ${\sigma}_{i}$ was the saturation coefficient of i-th enzyme.

#### 2.2. Calibration of the Original k_{cat} Values

_{cat}values to some extent to improve the agreement of model predictions with experimental data), similar to the way in GECKO and AutoPACMEN [17]. We proposed two principles (enzyme usage and

^{13}C flux consistency) to adjust the original k

_{cat}values, as follows: First, a reaction with an enzyme usage exceeding 1% of the total enzyme content requires parameter correction; Second, a reaction with the k

_{cat}multiplied by 10% of the total enzyme amount (${v}_{i}=\frac{10\%\times {E}_{total}\times {\sigma}_{i}\times {k}_{cat,i}}{M{W}_{i}}$) is less than the flux determined by

^{13}C experiment needs to be corrected. All the k

_{cat}data used for correction comes from BRaunschweig ENzyme DAta base (BRENDA) and System for the Analysis of Biochemical Pathways - Reaction Kinetics databases (SABIO-RK) (using the maximum k

_{cat}value).

#### 2.3. Simulation

^{−1}to 0.65 h

^{−1}) and glucose is supplied infinitely. Besides, we calculated the reaction enzyme cost (Equation (7)), energy synthesis enzyme cost (Equation (8)) and oxidative phosphorylation ratio (Equation (9)) to explore the adjustment strategy of E. coli’s overflow metabolic pathway.

## 3. Results

#### 3.1. Construction of the Enzyme-Constrained Model of iML1515 by ECMpy

_{cat}which was obtained in labour-intensive, low-throughput in vitro assays and resulted in only a small fraction of cellular enzymes having a measured k

_{cat}even in model organisms [30]. That is why we used the k

_{cat}values derived from machine learning methods performed by Heckmann et al. [23]. In the model, k

_{cat}values were assigned to 2432 enzymatic reactions, and the coverage exceeds 60% (including isozyme split reactions and reversible split reactions, exclude exchange reactions), which is larger than the GECKO and sMOMENT (the number of reactions that matched EC number and substrate at the same time was only about 387). The protein fraction ptot was set at 0.56 g gDW

^{−1}based on the experimentally measured macromolecular composition of E. coli cells [31,32]. The E. coli protein abundance values were obtained from the Protein abundance database (PAXdb) (https://pax-db.org/, accessed on 25 December 2021) [33] and the ‘whole organism (integrated)’ dataset with the highest coverage and credibility was selected. According to Equation (4), f was calculated to be 0.406 g enzyme/g protein.

^{−1}, but the conversion of phosphoenolpyruvate to the TCA pathway was still abnormal (Figure S2). Subsequently, we compared with the

^{13}C experimental data [34] and found that the k

_{cat}value of two reactions (PDH: pyruvate to acetyl-CoA and AKGDH: 2-oxoglutarate to succinyl-CoA) is low, which is mainly caused by the subunit composition of these two reactions is complicated and the protein molecular weight is very large. After calibration using

^{13}C data (changed two reactions, Table S2), the growth rate increased to 0.6802 h

^{−1}, and the consistency with the pathway obtained by

^{13}C data reached 92.1% (Figure S3). Different from other methods for constructing enzyme-constrained models, our method considers the composition of protein subunits and realizes enzyme constraint by simply adding the total enzyme amount equation (Table 1). Therefore, the enzyme-constrained model we constructed does not change the stoichiometric matrix format (because the isoenzyme reaction and reversible reaction were split, the number of reactions increased), and the solution and subsequent operations of the entire model are consistent with the classical constraint-based model. We used AutoPACMEN to build the GECKO and sMOMENT model of iML1515, and compared them with ECMpy. We found that when considering the subunit composition of protein, the growth rate predicted by GECKO and sMOMENT model is lower, and the flux distribution of the pathway is abnormal from the

^{13}C data, especially the EMP pathway (Figure 2, purple boxes).

#### 3.2. Overflow Metabolism of E. coli

^{−1}). As shown in Figure 3a,b, the eciML1515 model (the kinetic parameters for each reaction see Table S3) could precisely simulate the switch point where acetate production started. The simulation results indicated that at high growth rates, the acetate producing fermentation pathway was activated due to its low enzyme cost in comparison with the energetically-efficient oxidative respiratory pathway (0.62 g vs. 2.38 g enzyme for 1 mol ATP/h, Table S4).

#### 3.3. Maximum Growth Rate of E. coli on Different Carbon Sources

_{cat}values of enzymes in the uptake pathways of these two substrates may be underestimated. Besides, we found that ECMpy is better than GECKO and sMOMENT for the simulation of growth rate on 24 different carbon sources (all consider protein subunits, but ECMpy corrected for enzyme kinetic parameters), and the simulation results of all enzyme-constrained models are also better than non-enzyme-constrained models (Figure 4a–d). This may also mean more precise measurement of the enzyme kinetic parameters could improve model prediction.

#### 3.4. Simulation of the Trade-Off between Enzyme Usage Efficiency and Biomass Yield

## 4. Discussion

_{cat}values to some extent to improve the agreement of model predictions with experimental data [17]. A system kinetic parameter correction method has been presented in the sMOMENT workflow [17], which helps identify such unreliable parameters and improve model prediction accuracy. However, this calibration workflow is time-consuming, going through protein pool calibration, manual k

_{cat}adjustment and automated k

_{cat}calibration, and there are some unreasonable places, such as the manual correction is simply expanded by 10 times or reduced by 10 times. In recently, GECKO 2.0 (https://doi.org/10.1101/2021.03.05.433259, accessed on 25 December 2021) provided an automatic procedure, in which the top enzymatic limitation on growth rate is identified and its correspondent k

_{cat}is then iteratively replaced by the highest one available in BRENDA for the given enzyme class until the growth rate fit is normal [42]. Currently, we propose a simpler calibration process that requires only two steps (enzyme usage and

^{13}C flux consistency, see method) to update the k

_{cat}for a small number of reactions to achieve a better growth rate fit. This new calibration process will facilitate the construction of high-quality enzyme constraint models.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Flux Comparison of iML1515, ECMpy, GECKO and sMOMENT. From left to right:

^{13}C experimental data (black), prediction results of iML1515 model (red), prediction results of eciML1515 constructed by ECMpy (green), prediction results of eciML1515 constructed by GECKO (blue), and prediction results of eciML1515 constructed by sMOMENT (yelllow).

**Figure 3.**Comparison of Simulation Results of the Enzyme-constrained Model eciML1515 and the Stoichiometric Model iML1515. Simulation of overflow metabolism at different growth rates using eciML1515 (

**a**) and iML1515 (

**b**). (

**c**) Simulated different overflow metabolism of E. coli and S. cerevisiae. (

**d**) The different overflow metabolic pathways of E. coli and S. cerevisiae.

**Figure 4.**Predicted E. coli Growth Rates on Different Carbon Sources Using ECMpy (

**a**), iML1515 (

**b**), GECKO and sMOMENT (

**c**). (

**d**) Distribution of prediction errors of internal fluxes from different models (GECKO and sMOMENT with consideration of protein subunits).

**Figure 5.**The metabolic behaviours of E. coli at different glucose uptake rates. (

**a**) Simulated growth rates at different glucose uptake rates. (

**b**) The trade-off between biomass yield and enzyme efficiency.

Items | MOMENT | GECKO | AutoPACMEN | ECMpy |
---|---|---|---|---|

Subunit number | (not consider) × | (consider) √ | × (provide interface) | √ |

Proteomics | × | √ | √ | √ |

Saturation | 1 | 0.46 | 1 | 1 |

Mass fraction of enzymes | 0.56 | 0.448 | 0.095 | 0.227 |

Adding methods of enzyme constraints | add enzyme concentrations for each reaction and add the enzymes solvent capacity constraint | change stoichiometric matrix, and introduce a large number of pseudo-reaction and pseudo-metabolite | change stoichiometric matrix, and introduce one pseudo-reaction and pseudo-metabolite | only add a total enzyme constraint |

Reaction reversibility | not split | split | part split | split |

Isozyme | a reaction can be catalyzed by multiple enzymes | a reaction can be catalyzed by multiple enzymes | always assumes that the enzyme with the minimal cost is used | a reaction can be catalyzed by multiple enzymes |

Filling method of missing k_{cat} | the median turnover number across all reactions | match the kcat value to other substrates, organisms, or even introduce wild cards in the EC number. | Similar to GECKO | enzyme cost=0 |

Model calibration | × | √ | √ | √ |

Model type | Not provided | XML | XML | JSON |

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**MDPI and ACS Style**

Mao, Z.; Zhao, X.; Yang, X.; Zhang, P.; Du, J.; Yuan, Q.; Ma, H. ECMpy, a Simplified Workflow for Constructing Enzymatic Constrained Metabolic Network Model. *Biomolecules* **2022**, *12*, 65.
https://doi.org/10.3390/biom12010065

**AMA Style**

Mao Z, Zhao X, Yang X, Zhang P, Du J, Yuan Q, Ma H. ECMpy, a Simplified Workflow for Constructing Enzymatic Constrained Metabolic Network Model. *Biomolecules*. 2022; 12(1):65.
https://doi.org/10.3390/biom12010065

**Chicago/Turabian Style**

Mao, Zhitao, Xin Zhao, Xue Yang, Peiji Zhang, Jiawei Du, Qianqian Yuan, and Hongwu Ma. 2022. "ECMpy, a Simplified Workflow for Constructing Enzymatic Constrained Metabolic Network Model" *Biomolecules* 12, no. 1: 65.
https://doi.org/10.3390/biom12010065