1. Objective of co-culture model
1.1 Introduction
Our research project focuses on the cooperative production of citronellol and linalool by S. cerevisiae and E. coli. First, yeast synthesizes geraniol; after geraniol accumulates inside the yeast cells, it is secreted outside the cells and then diffuses into E. coli. Finally, E. coli cells utilize geraniol to synthesize citronellol and linalool (Fig. 1).
Fig.1 Co-culture system of S. cerevisiae and E. coli.
We use a co-culture system of yeast and E. coli for the production of citronellol and linalool. Since the two microorganisms share the same carbon source (glucose), under general conditions of identical inoculation, E. coli grows faster than yeast cells, which inhibits the growth of yeast cells. To address this issue, we adopt a sequential inoculation approach: first, we allow the yeast cells to grow to a certain concentration (and they may have already started synthesizing geraniol), and then inoculate E. coli into the yeast culture system. Taking advantage of the characteristic that E. coli grows faster than yeast cells, when E. coli grows to a certain concentration, the yeast cells will just have secreted geraniol outside the cells - this geraniol can then be utilized by E. coli to synthesize citronellol and linalool.
Both extracellular geraniol and the citronellol and linalool synthesized by E. coli exhibit inhibitory effects on the growth of E. coli. This inhibitory effect can be utilized to achieve the balance of the co-culture system and ultimately reach a stable state.
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1.2 Exploration outline and aim
Now we construct a mathematical model to describe the co-culture system of yeast and E. coli for the production of citronellol and linalool. The basic framework of the system is as follows:
• Yeast utilizes glucose for growth and synthesizes geraniol, which is then secreted outside the cells.
• E. coli utilizes glucose for growth, takes up extracellular geraniol, and converts it into citronellol and linalool.
• The two microorganisms share the same carbon source (glucose).
• We adopt sequential inoculation: yeast is inoculated first; after it grows to a certain concentration (and may have started synthesizing geraniol), E. coli is then inoculated.
• Extracellular geraniol, citronellol, and linalool exert inhibitory effects on the growth of E. coli. We aim to utilize this inhibitory effect to achieve the balance of the co-culture system and ultimately reach a stable state.
It is expected that the model will address the following key issues:
• Optimal inoculation time: At which hour after yeast cultivation should E. coli be added?
• Optimal inoculation ratio: What should be the initial concentrations of yeast and E. coli?
• System stability: Can the system achieve the expected dynamic balance? How long can the balanced state be maintained?
• Yield prediction: Under given conditions, what is the final yield of citronellol and linalool that can be obtained?
• Bottleneck analysis: Is the primary factor limiting the yield the supply rate of geraniol, the transformation capacity of E. coli, or product inhibition?
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2. Co-culture model
2.1 General assumptions and parameters
For easy to read, substances are represented by theire captital initials. The following tables list the variables and parameters we need to consider, as well as their abbreviations (Table 1-4).
Here, we assume that geraniol is consumed for the production of these two products, and the yields of the two products are the same. However, in the kinetic equation, we calculate them separately. In this context, Y_E_Ger can be understood as the total yield. Since we calculate the two products separately in the equation, the total yield actually needs to be allocated. For simplicity, we assume that the yield of geraniol converted to citronellol and the yield of geraniol converted to linalool are both 0.4 g/g, resulting in a total yield of 0.8 g/g. Alternatively, we could use two independent yields, but here we use one total yield and then distribute it equally between the two products.
The inoculation time of E. coli (t_inoculate_E) is 12 h (Table 5), and the initial concentration of E. coli (E₀) is 0.01 g/L (added at t = 12 h).
In the differential equation, the concentration of E. coli is zero before the inoculation time. We can control the addition of E. coli in the ODE (Ordinary Differential Equation) function by judging the time.
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2.2 Core kinetic equations
2.2.1 Microbial growth equation (Logistic growth + inhibition)：
It is assumed that yeast follows logistic growth, while being limited by glucose and potentially inhibited by products (if geraniol inhibits yeast).
• Yeast growth rate: μ_Y = μ_Ymax * (G/(K_YG + G)) * (1 - Y/Y_max) * I_Y(Ger) [I_Y(Ger) is the inhibition factor of geraniol on yeast; set to 1 if there is no inhibition.]
• Geraniol production by yeast: It is assumed that geraniol production is growth-associated (Leudeking-Piret model): dGer/dt = α_Y * dY/dt + β_Y * YE. coli Growth
• E. coli growth rate: μ_E = μ_Emax * (G/(K_EG + G)) * (1 - E/E_max) * I_E(Ger, Cit, Lin) [I_E is the inhibition factor of geraniol, citronellol, and linalool on E. coli.]
2.2.2 Specific growth rate (Monod kinetics):
2.2.3 Product inhibition term (Zeng & Deckwer Model):
For example:
Pc, X is the critical inhibition concentration of product P on microbial cells X.
Inhibition Factors：
• For yeast: If geraniol causes inhibition, then I_Y(Ger) = 1 / (1 + Ger/K_IY_Ger)
• For E. coli: I_E(Ger, Cit, Lin) = 1 / (1 + Ger/K_IE_Ger + Cit/K_IE_Cit + Lin/K_IE_Lin)
2.2.4 Metabolite kinetics equations:
Glucose Consumption: Glucose is consumed for the growth and maintenance metabolism of the two strains.
Geraniol (Production by Yeast + Consumption by E. coli): Geraniol is produced by yeast, consumed by E. coli (converted into citronellol and linalool as a substrate), and may undergo a certain degree of degradation.
Citronellol/Linalool (Production by E. coli): It is assumed that E. coli converts geraniol into citronellol and linalool, with possibly different conversion rates. Here, we can simplify the assumption by either setting a fixed ratio for the conversion of geraniol to citronellol and linalool, or using two independent equations.
Notes on Symbols：
• μ: Specific growth rate; μ_max: Maximum specific growth rate
• G: Glucose concentration; Y: Yeast biomass concentration; E: E. coli biomass concentration
• Ger: Geraniol concentration; Cit: Citronellol concentration; Lin: Linalool concentration
• K: Half-saturation constant (e.g., K_YG: Half-saturation constant of yeast for glucose)
• Y_XX: Yield coefficient (e.g., Y_YG: Yeast yield coefficient on glucose)
• α, β: Leudeking-Piret model parameters (α: Growth-associated coefficient; β: Non-growth-associated coefficient)
• m: Maintenance coefficient; k_deg: Degradation rate constant
• K_I: Inhibition constant (e.g., K_IY_Ger: Inhibition constant of geraniol on yeast)
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3. Model analysis
We used MATLAB to write and run these codes (co_culture_main.m and odesystem_ultimate.m) for simulating this process, and we expect to observe:
• Microbial Growth Curve: Yeast grows first, and E. coli grows rapidly 12 h after inoculation.
• Product Kinetics: Geraniol accumulates initially, and is then converted into citronellol and linalool.
• Inhibitory Effect: As products accumulate, the inhibitory effect gradually intensifies and eventually reaches equilibrium.
• System Stability: The system may reach a quasi-steady state.
Fig.2 Co-culture system of Yeast and E. coli.
From the figure 2, we can see that after E. coli is inoculated 12 h after the growth of yeast cells, the system can eventually reach a steady state (at approximately 30 h). The biomass after reaching the steady state is respectively as follows: final yeast: 23.089 g/L (Max: 23.089); final E. coli: 6.911 g/L (Max: 6.911); Biomass Ratio: 3.34:1 If we aim to increase the proportion of E. coli in the system, we can advance the inoculation time.
Fig.3 Geraniol to Products Conversion.
The target we set is for geraniol to accumulate to 2 g/L; in actual system operation, however, the peak concentration of geraniol is only 0.502 g/L. This is a positive outcome, as it indicates that geraniol is rapidly converted into end products as soon as it is produced (Fig. 3).
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Fig.4 Inhibition Management. |
Fig.5 Production Pipeline. |
Glucose is almost completely consumed (99.8%). The production efficiency is 9.27% and the carbon utilization rate is 73.1%, both of which are good indicators (Fig. 4).
Production Timeline: Geraniol Peak: 0.502 g/L at 30.0 h; Citronellol Peak: 3.122 g/L at 120.0 h; Linalool Peak: 2.429 g/L at 120.0 h (Fig. 5).
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Fig.6 Production Kinetics. |
Fig.7 Product Yield Evolution. |
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Fig.8 Cumulative Product Formation. |
Fig.9 Final Product Spectrum. |
Figures 6 to figure 9 above summarize the production status of the products: Final Geraniol: 0.500 g/L，Final Citronellol: 3.122 g/L，Final Linalool: 2.429 g/L，Total Products: 5.551 g/L.
Fig.10 System Economics (Theroetical).
Final Glucose: 0.100 g/L (Consumed: 99.8%); EFFICIENCY: Production: 9.27% (g-product/g-glucose); Carbon Utilization: 73.1% (Fig. 10).
In-depth analysis of results:
Although the target for geraniol (2 g/L) was not achieved, this is actually a positive phenomenon: the geraniol utilization rate reaches 99.5%, indicating that E. coli efficiently converts the intermediate into valuable end products (with a total output of 5.551 g/L). This is more economically valuable than simply accumulating geraniol, and represents an ideal industrial production model.
In practical applications, this model - characterized by low intermediate accumulation and high end-product output - is exactly what we pursue, for the following reasons:
• Reduced toxic accumulation: The low concentration of geraniol results in minimal inhibition of microorganisms;
• Enhanced economic value: The value of end products is far higher than that of the intermediate;
• System stability: It enables balanced microbial growth and metabolism.
A vector that allows two promoters to be induced by two different inducers on the same plasmid is generally referred to as a "dual-expression vector" or "orthogonal expression system". The core of this design lies in the use of two orthogonal promoter-inducer systems. The term "orthogonal" means there is no cross-reactivity between the two systems: inducer A only activates promoter A without affecting promoter B, and vice versa. However, there is currently no "ready-to-use" commercial single plasmid that directly integrates two such promoters, so we have to construct an orthogonal combinatorial plasmid ourselves.
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4. Results and conlusion for this model
Initial Glucose: 60.0 g/L
E.coli inoculation: 12.0 h (STRATEGIC DELAY)
Target: Geraniol >2g/L, Total Products >5g/L
BIOMASS:
Final Yeast: 23.089 g/L (Max: 23.089)
Final E.coli: 6.911 g/L (Max: 6.911), Biomass Ratio: 3.34:1
METABOLITES:
Final Glucose: 0.100 g/L (Consumed: 99.8%)
Final Geraniol: 0.500 g/L
Final Citronellol: 3.122 g/L
Final Linalool: 2.429 g/L
TOTAL PRODUCTS: 5.551 g/L
EFFICIENCY:
Production: 9.27% (g-product/g-glucose)
Carbon Utilization: 73.1%
PRODUCTION TIMELINE:
Geraniol Peak: 0.502 g/L at 30.0 h
Citronellol Peak: 3.122 g/L at 120.0 h
Linalool Peak: 2.429 g/L at 120.0 h
E.coli Inoculation: 12.0 h
PERFORMANCE ASSESSMENT: This model is successful.
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5. Experimental verification and optimization
The construction of this model is successful. Next, we conducted a preliminary verification in the laboratory using the experimental parameters from the model, and the results are consistent with the model's predictions. To further increase the yield, there are still some parameters that need to be continuously optimized in future work, mainly including the optimization of the inoculation time and concentration of E. coli, as well as the optimization of fermentation conditions. This will facilitate the scale-up from the laboratory scale to the production scale in the future.
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References
[1] Minty JJ, Singer ME, Scholz SA, et al. Design and characterization of synthetic fungal-bacterial consortia for direct production of isobutanol from cellulosic biomass. Proc Natl Acad Sci U S A. 2013;110(36):14592-14597. doi:10.1073/pnas.1218447110
[2] Zhou K, Qiao K, Edgar S, Stephanopoulos G. Distributing a metabolic pathway among a microbial consortium enhances production of natural products. Nat Biotechnol. 2015;33(4):377-383. doi:10.1038/nbt.3095.