# In Silico Identification of Microbial Partners to Form Consortia with Anaerobic Fungi

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Strains and Culture Conditions

#### 2.2. Growth and Metabolite Measurements

#### 2.3. Evaluation and Selection of Model Organisms

#### 2.4. Dynamic Flux Balance Analysis Formulation

- The flux bounds, Equation (2), are updated. Typically, Michaelis–Menten kinetics are assumed [39]. Since detailed expression for glucose and xylose uptake rates are not known for all the organisms, we assumed, for comparative fairness,$$\begin{array}{cc}\hfill {v}_{\mathrm{min},\phantom{\rule{4.pt}{0ex}}\mathrm{glucose}}& =max\left({v}_{\mathrm{Glc}}^{max},-\frac{G+\Delta t{f}_{G}^{\mathrm{produced}}}{\Delta tX{m}_{\mathrm{glucose}}}\right),\phantom{\rule{4.pt}{0ex}}\hfill \\ \hfill {v}_{\mathrm{max},\phantom{\rule{4.pt}{0ex}}\mathrm{glucose}}& =0,\phantom{\rule{4.pt}{0ex}}\hfill \\ \hfill {v}_{\mathrm{min},\phantom{\rule{4.pt}{0ex}}\mathrm{xylose}}& =max\left({v}_{\mathrm{Xyl}}^{max},-\frac{Z+\Delta t{f}_{Z}^{\mathrm{produced}}}{\Delta tX{m}_{\mathrm{xylose}}}\frac{1}{1+\frac{G}{0.005}}\right),\phantom{\rule{4.pt}{0ex}}\hfill \\ \hfill {v}_{\mathrm{max},\phantom{\rule{4.pt}{0ex}}\mathrm{xylose}}& =0,\phantom{\rule{4.pt}{0ex}}\hfill \end{array}$$
- A linear program feasibility problem,$$\begin{array}{cc}\underset{{\mathbf{s}}_{\mathbf{1}},{\mathbf{s}}_{\mathbf{2}}}{\mathrm{min}}\hfill & \sum _{i=1}^{N}{s}_{1,i}+{s}_{2,i}\phantom{\rule{3.33333pt}{0ex}}(\mathrm{where}\phantom{\rule{4.pt}{0ex}}N\phantom{\rule{4.pt}{0ex}}\mathrm{is}\phantom{\rule{4.pt}{0ex}}\mathrm{the}\phantom{\rule{4.pt}{0ex}}\mathrm{number}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{fluxes}),\phantom{\rule{4.pt}{0ex}}\hfill \\ \mathrm{s}.\mathrm{t}.\hfill & \mathbf{S}\mathbf{v}+{\mathbf{s}}_{\mathbf{1}}-{\mathbf{s}}_{\mathbf{2}}=\mathbf{b}\phantom{\rule{3.33333pt}{0ex}}\left(\mathrm{where}\phantom{\rule{4.pt}{0ex}}\mathbf{b}\phantom{\rule{4.pt}{0ex}}\mathrm{is}\phantom{\rule{4.pt}{0ex}}\mathrm{typically}\phantom{\rule{4.pt}{0ex}}\mathrm{the}\phantom{\rule{4.pt}{0ex}}\mathrm{zero}\phantom{\rule{4.pt}{0ex}}\mathrm{vector}\phantom{\rule{4.pt}{0ex}}\mathrm{in}\phantom{\rule{4.pt}{0ex}}\mathrm{this}\phantom{\rule{4.pt}{0ex}}\mathrm{context}\right),\phantom{\rule{4.pt}{0ex}}\hfill \\ & {\mathbf{v}}_{\mathrm{min}}\le \mathbf{v}\le {\mathbf{v}}_{\mathrm{max}},\phantom{\rule{4.pt}{0ex}}\hfill \\ & 0\le {s}_{1,i},{s}_{2,i}\phantom{\rule{3.33333pt}{0ex}}\forall i\in \left[1,\dots ,N\right],\phantom{\rule{4.pt}{0ex}}\hfill \end{array}$$
- A standard FBA linear program (LP) is solved to determine the optimal growth rate of the organism given the constraints of step 1. This problem,$$\begin{array}{cc}\underset{\mathbf{v}}{\mathrm{max}}\hfill & \mu \left(\mathbf{v}\right),\phantom{\rule{4.pt}{0ex}}\hfill \\ \mathrm{s}.\mathrm{t}.\hfill & \mathbf{S}\mathbf{v}+{\mathbf{s}}_{\mathbf{1}}-{\mathbf{s}}_{\mathbf{2}}=\mathbf{b},\phantom{\rule{4.pt}{0ex}}\hfill \\ & {\mathbf{v}}_{\mathrm{min}}\le \mathbf{v}\le {\mathbf{v}}_{\mathrm{max}},\phantom{\rule{4.pt}{0ex}}\hfill \end{array}$$
- A secondary LP,$$\begin{array}{cc}\underset{\mathbf{v}}{\mathrm{min}}\hfill & \sum _{i}{\gamma}_{i}\phantom{\rule{3.33333pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}i\in \mathcal{M},\phantom{\rule{4.pt}{0ex}}\hfill \\ \mathrm{s}.\mathrm{t}.\hfill & \mathbf{S}\mathbf{v}+{\mathbf{s}}_{\mathbf{1}}-{\mathbf{s}}_{\mathbf{2}}=\mathbf{b},\phantom{\rule{4.pt}{0ex}}\hfill \\ & {\mathbf{v}}_{\mathrm{min}}\le \mathbf{v}\le {\mathbf{v}}_{\mathrm{max}},\phantom{\rule{4.pt}{0ex}}\hfill \\ & \mu \left(\mathbf{v}\right)={\mu}^{*},\phantom{\rule{4.pt}{0ex}}\hfill \\ & -{\gamma}_{i}\le 1-\frac{{v}_{t-1,i}}{{v}_{t-1,i}-{v}_{t-2,i}}-\frac{{v}_{t,i}}{{v}_{t-1,i}-{v}_{t-2,i}}\le {\gamma}_{i}\phantom{\rule{3.33333pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}i\in \mathcal{M},\phantom{\rule{4.pt}{0ex}}\hfill \end{array}$$
- Using an integration scheme of choice, e.g., backward Euler, the full dynamic profile of the system may be iteratively simulated. If products are being generated at each time step, Equation (1) needs to include those fluxes as well.

#### 2.5. Simulation Parameters

## 3. Results and Discussion

#### 3.1. Anaerobic Fungi Release an Assortment of Products to Enable Consortia Formation

#### 3.2. Dynamic Simulations Predict Consortia Partner Feasibility

#### 3.2.1. Heterotroph Partnership with Anaerobic Fungi

#### 3.2.2. Autotroph Partnership with Anaerobic Fungi

## 4. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Anaerobic gut fungi release excess sugars for microbial partnership during growth on corn stover. The solid black line denotes the profile of the accumulated pressure. Other colors represent distinct fermentable sugars generated during growth, as indicated. The vertical bars are standard deviations of errors for each triplicate measurement. (

**a**) N. californiae; (

**b**) Neocallimastix sp. S1; (

**c**) A. robustus.

**Figure 2.**Dynamic simulation of C. ljungdahlii shows that it consumes all the excess sugars released by A. robustus. The vertical red line indicates the point where both sugars were depleted. Even though the fungal enzymes continuously release sugars, the rate at which they release them is exactly equal to the consumption rate beyond the vertical red line. Simulation artifacts cause the growth to continue linearly beyond this point. All the simulations assume an inoculation time at 72 h into the experiment. This allows the slower-growing gut fungi to establish themselves and produce fermentable products prior to the start of the co-culture.

**Figure 3.**Computationally predicted growth profile of M. barkeri biomass accumulation over time shows a strong dependence on the fungal metabolic by-products. Hydrogen and carbon dioxide, produced by the fungi, are consumed by the methanogen. Simultaneous inoculation is assumed because the microbes do not compete for their preferred carbon source. All gas concentrations are in mmol/L.

**Table 1.**Genome-scale models of potential consortia partners for the un-modeled anaerobic gut fungi used in this work.

Organism | Notes | Reference |
---|---|---|

Clostridium ljungdahlii str. 13528 | Bacterium, obligate anaerobe, acetogen | [21] |

Escherichia coli str. K-12 substr. MG1655 | Bacterium, facultative anaerobe | [22] |

Escherichia coli str. ZSC113 | Bacterium, facultative anaerobe, glucose deficient | [23] |

Lactococcus lactis subsp. cremoris MG1363 | Bacterium, facultative anaerobe | [24] |

Methanosarcina barkeri str. Fusaro | Methanogen, obligate anaerobe | [25] |

Saccharomyces cerevisiae S288C | Fungus, facultative anaerobe | [26] |

Organism | ${\mathit{v}}_{\mathbf{Glc}}\phantom{\rule{3.33333pt}{0ex}}\left[\frac{\mathbf{mmol}}{{\mathbf{g}}_{\mathbf{DW}}\mathbf{h}}\right]$ | ${\mathit{v}}_{\mathbf{Xyl}}\phantom{\rule{3.33333pt}{0ex}}\left[\frac{\mathbf{mmol}}{{\mathbf{g}}_{\mathbf{DW}}\mathbf{h}}\right]$ |
---|---|---|

Clostridium ljungdahlii str. 13528 | 5 | 5 |

Escherichia coli str. K-12 substr. MG1655 | 10.5 | 6 |

Escherichia coli str. ZSC113 | 0 | 6 |

Lactococcus lactis subsp. cremoris MG1363 | 14.5 | 0 |

Methanosarcina barkeri str. Fusaro | 0 | 0 |

Saccharomyces cerevisiae S288C | 6.44 | 0 |

Product | ${\mathit{k}}_{1}$ (g/L/h or psi/h) | ${\mathit{k}}_{2}$ (1/h) | ${\mathit{k}}_{3}$ (h) |
---|---|---|---|

Glucose | 1.39 | 0.05 | 148.17 |

Xylose | 0.53 | 0.05 | 150.41 |

Pressure | 75.04 | 0.06 | 76.51 |

Organism | Growth Rate in M2 (1/h) | Growth rate in MC [15] (1/h) |
---|---|---|

N. californiae | 0.029 | 0.046 |

A. robustus | 0.033 | 0.065 |

Neocallimastix sp. S1 | 0.027 | No data |

**Table 5.**Growth rate and end point metabolic by-product concentrations produced by each partner microbe assuming inoculation after 72 h of fungal growth. The end point concentrations are taken when the fermentable substrates were depleted for each organism.

Organism | Growth Rate (1/h) | Ethanol (g/L) | Acetate (g/L) | Formate (g/L) |
---|---|---|---|---|

C. ljungdahlii | 0.08 | 0 | 0.35 | 0 |

E. coli MG1655 | 0.17 | 0.02 | 0.02 | 0.03 |

E. coli ZSC113 | 0.04 | 0.01 | 0.02 | 0.03 |

L. lactis | 0.04 | 0.13 | 0.32 | 0.51 |

S. cerevisiae | 0.12 | 0.02 | 0 | 0 |

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**MDPI and ACS Style**

Wilken, S.E.; Saxena, M.; Petzold, L.R.; O’Malley, M.A. In Silico Identification of Microbial Partners to Form Consortia with Anaerobic Fungi. *Processes* **2018**, *6*, 7.
https://doi.org/10.3390/pr6010007

**AMA Style**

Wilken SE, Saxena M, Petzold LR, O’Malley MA. In Silico Identification of Microbial Partners to Form Consortia with Anaerobic Fungi. *Processes*. 2018; 6(1):7.
https://doi.org/10.3390/pr6010007

**Chicago/Turabian Style**

Wilken, St. Elmo, Mohan Saxena, Linda R. Petzold, and Michelle A. O’Malley. 2018. "In Silico Identification of Microbial Partners to Form Consortia with Anaerobic Fungi" *Processes* 6, no. 1: 7.
https://doi.org/10.3390/pr6010007