Our digital twin model was implemented using the MATLAB COBRA toolbox for genome-scale metabolic modeling. The toolbox was accessed using the COBRA package for python (Ebrahim et al., 2013).
The initial metabolic reaction list ‘ICW1057’ for P. fluorescens SBW25 was obtained from the only genome-scale metabolic model for P. fluorescens (Haung and Lin, 2019). ICW1057 reaction list was used as the foundation for helper and main strain, however, this model showed poor results as key reactions like glucose uptake were missing. By stimulating growth on minimal media with known P. fluorescens, further missing reactions and metabolites were identified (https://bacdive.dsmz.de/strain/12851). 57 reactions and 30 metabolites were added to the ICW1057 model to obtain the growth behavior for the ReMixHD strain P. fluorescens DSM50090 (see Table 2.1 and 2.2). The improved reaction list for the P. fluorescens DSM50090 model is available here.
ID | Name | Compartments | Strain | |
0 | cpd10001_c0 | Terephtalic_Acid_c0 | c0 | Main |
1 | cpd10002_c0 | Poly_Ethylene_c0 | c0 | Helper |
2 | cpd10003_c0 | Ethylene_Glycol_c0 | c0 | Helper |
3 | cpd10004_c0 | DCD_c0 | c0 | Main |
4 | cpd10005_c0 | Octanol_c0 | c0 | Main, Helper |
5 | cpd10006_c0 | Hexanol_c0 | c0 | Main, Helper |
6 | cpd10007_c0 | Decanol_c0 | c0 | Main, Helper |
7 | cpd10008_c0 | Heptanol_c0 | c0 | Main, Helper |
8 | cpd10009_c0 | Pentanol_c0 | c0 | Main, Helper |
9 | cpd10010_c0 | Nonanol_c0 | c0 | Main, Helper |
10 | cpd10011_c0 | Undecanol_c0 | c0 | Main, Helper |
11 | cpd10012_c0 | Dodecanol_c0 | c0 | Main, Helper |
12 | cpd10013_c0 | Dodecanoyl_CoA_c0 | c0 | Main, Helper |
13 | cpd10014_c0 | Undecanoyl_CoA_c0 | c0 | Main, Helper |
14 | cpd10015_c0 | Decanoyl_CoA_c0 | c0 | Main, Helper |
15 | cpd10016_c0 | Nonanoyl_CoA_c0 | c0 | Main, Helper |
16 | cpd10017_c0 | Octanoyl_CoA_c0 | c0 | Main, Helper |
17 | cpd10018_c0 | Heptanoyl_CoA_c0 | c0 | Main, Helper |
18 | cpd10019_c0 | Hexanoyl_CoA_c0 | c0 | Main, Helper |
19 | cpd10020_c0 | Pentanoyl_CoA_c0 | c0 | Main, Helper |
20 | cpd10021_c0 | Butanoyl_CoA_c0 | c0 | Main, Helper |
21 | cpd00029_e0 | Acetate_e0 | e0 | Main, Helper |
22 | cpd10003_e0 | Ethylene_Glycol_e0 | e0 | Main, Helper |
23 | cpd10002_e0 | Poly_Ethylene_e0 | e0 | Helper |
24 | cpd00224_e0 | L_Arabinose_e0 | e0 | Main, Helper |
25 | cpd00036_e0 | Succinate_e0 | e0 | Main, Helper |
26 | cpd00161_e0 | Threonine_e0 | e0 | Main, Helper |
27 | cpd00363_e0 | Ethanol_e0 | e0 | Main, Helper |
28 | cpd10001_e0 | Terephtalic_Acid_e0 | e0 | Main |
29 | cpd10022_e0 | PET_e0 | e0 | Main |
ID | Name | Compartments | Strain | |
0 | EX_cpd00013_1_e0 | EX_NH3_1_e0 | -> e0 | Main, Helper |
1 | IM_cpd00027 | IM_Glucose | c0 -> e0 | Main, Helper |
2 | IM_cpd00033 | IM_Glycine | c0 -> e0 | Main, Helper |
3 | IM_cpd00078 | IM_Tryptophane | c0 -> e0 | Main, Helper |
4 | IM_cpd00100 | IM_Glycerol | c0 -> e0 | Main, Helper |
5 | EX_cpd00029_e0 | EX_Acetate_e0 | -> e0 | Main, Helper |
6 | IM_cpd00029 | IM_Acetate | c0 -> e0 | Main, Helper |
7 | EX_cpd10003_e0 | EX_Ethylene_Glycol_e0 | -> e0 | Main, Helper |
8 | IM_cpd10003 | IM_Ethylene_Glycol | c0 -> e0 | Main, Helper |
9 | EX_cpd10002_e0 | EX_Poly_Ethylene_e0 | -> e0 | Helper |
10 | IM_cpd10002 | IM_Poly_Ethylene | c0 -> e0 | Helper |
11 | EX_cpd00224_e0 | EX_L_Arabinose_e0 | -> e0 | Main, Helper |
12 | IM_cpd00224 | IM_L_Arabinose | c0 -> e0 | Main, Helper |
13 | EX_cpd00036_e0 | EX_Succinate_e0 | -> e0 | Main, Helper |
14 | IM_cpd00036 | IM_Succinate | c0 -> e0 | Main, Helper |
15 | EX_cpd00161_e0 | EX_Threonine_e0 | -> e0 | Main, Helper |
16 | IM_cpd00161 | IM_Threonine | c0 -> e0 | Main, Helper |
17 | EX_cpd00363_e0 | EX_Ethanol_e0 | -> e0 | Main, Helper |
18 | IM_cpd00363 | IM_Ethanol | c0 -> e0 | Main, Helper |
19 | EX_cpd10001_e0 | EX_Terephtalic_Acid_e0 | -> e0 | Main |
20 | IM_cpd10001 | IM_Terephtalic_Acid | c0 -> e0 | Main |
21 | EX_PET_e0 | -> PET_e0 | -> e0 | Main |
22 | rxn20047_c0 | PET_e0 -> Terephtalic acid + Ethylene_glycol | -> e0 | Main |
23 | rxn20001_c0 | Terephtalic_Acid_c0 -> DCD_c0 | -> c0 | Main |
24 | rxn20002_c0 | DCD_c0 -> Protocatechuate_c0 | -> c0 | Main, Helper |
25 | rxn20003_c0 | 4_Carboxymuconolactone_c0 -> 3_oxoadipate_enol_lactone_c0 | -> c0 | Main, Helper |
26 | rxn20004_c0 | Ethylene_Glycol_c0 -> Glycolaldehyde_c0 | -> c0 | Main, Helper |
27 | rxn20005_c0 | Glycolaldehyde_c0 -> Glycolate_c0 | -> c0 | Main, Helper |
28 | rxn20006_c0 | Poly_Ethylene -> relative splitting | -> c0 | Main, Helper |
29 | rxn20007_c0 | Hexanol_c0 -> Hexanoate_c0 | -> c0 | Main, Helper |
30 | rxn20008_c0 | Octanol_c0 -> octanoate_c0 | -> c0 | Main, Helper |
31 | rxn20009_c0 | Decanol_c0 -> Decanoate_c0 | -> c0 | Main, Helper |
32 | rxn20010_c0 | Hexanoate_c0 -> Hexanoyl_CoA_c0 | -> c0 | Main, Helper |
33 | rxn20011_c0 | octanoate_c0 -> Octanoyl_CoA_c0 | -> c0 | Main, Helper |
34 | rxn20012_c0 | Decanoate_c0 -> Decanoyl_CoA_c0 | -> c0 | Main, Helper |
35 | rxn20013_c0 | Pentanol_c0 -> Pentanoyl_CoA_c0 | -> c0 | Main, Helper |
36 | rxn20014_c0 | Heptanol_c0 -> Heptanoyl_CoA_c0 | -> c0 | Main, Helper |
37 | rxn20015_c0 | Nonanol_c0 -> Nonanoyl_CoA_c0 | -> c0 | Main, Helper |
38 | rxn20016_c0 | Undecanol_c0 -> Undecanoyl_CoA_c0 | -> c0 | Main, Helper |
39 | rxn20017_c0 | Undecanol_c0 -> Undecanoyl_CoA_c0 | -> c0 | Main, Helper |
40 | rxn20018_c0 | Dodecanoyl_CoA_c0 -> Decanoyl_CoA_c0 | -> c0 | Main, Helper |
41 | rxn20019_c0 | Decanoyl_CoA_c0 -> Octanoyl_CoA_c0 | -> c0 | Main, Helper |
42 | rxn20020_c0 | Octanoyl_CoA_c0 -> Hexanoyl_CoA_c0 | -> c0 | Main, Helper |
43 | rxn20021_c0 | Hexanoyl_CoA_c0 -> Butanoyl_CoA_c0 | -> c0 | Main, Helper |
44 | rxn20022_c0 | Butanoyl_CoA_c0 -> Acetyl_CoA_c0 | -> c0 | Main, Helper |
45 | rxn20023_c0 | Undecanoyl_CoA_c0 -> Nonanoyl_CoA_c0 | -> c0 | Main, Helper |
46 | rxn20024_c0 | Nonanoyl_CoA_c0 -> Heptanoyl_CoA_c0 | -> c0 | Main, Helper |
47 | rxn20025_c0 | Heptanoyl_CoA_c0 -> Pentanoyl_CoA_c0 | -> c0 | Main, Helper |
48 | rxn20026_c0 | Pentanoyl_CoA_c0 -> Propionyl_CoA_c0 | -> c0 | Main, Helper |
49 | rxn20028_c0 | Ribulose -> Glyceraldehyd_3_phosphat | -> c0 | Main, Helper |
50 | rxn20029_c0 | PQQH2 -> PQQ | -> c0 | Main, Helper |
51 | rxn20031_c0 | Maltose -> 2Glucose | -> c0 | Main, Helper |
52 | rxn20032_c0 | kynurenine -> anthranilat | -> c0 | Main, Helper |
53 | rxn20033_c0 | Anthralinat _> Catechol | -> c0 | Main, Helper |
54 | EX_Glucose_e0 | -> EX_Glucose_e0 | -> e0 | Main, Helper |
55 | rxn20039_c0 | Butanoyl_CoA -> Succinat | -> c0 | Main, Helper |
56 | rxn20045_c0 | Poly_ethylene -> Butanoyl_CoA | -> c0 | Main, Helper |
By adding the terephthalic metabolism, as introduced in the wetlab, to the preexisting model and linking it to the wild-type beta-ketoadipate pathway, a new model was created simulating our main strain. Following this pathway, terephthalic acid is introduced to the TCA cycle. The helper strain was established using the same base model and the PET and PE depolymerization pathways were added, as well as the AlkB mediated oxidation into n-alkanols. The introduced alkanols are naturally linked to the fatty acid metabolism of the helper strain.
The completed helper and main strain models were optimized for maximum biomass flux and cleaned of infeasible fluxes by implementing loopless FBA. The non-growth associated ATP-maintenance reaction was set to a minimal reaction rate of 46.3 mmol/gDW/h to maintain the physiologically necessary ATP usage to keep the cell alive (Chen et al., 2011). It was assumed that the flux observed in E. coli during aerobic growth is the same for P. fluorescens due to lacking data.
The comparison of measured and predicted growth rates on minimal media with one carbon was chosen as a reliable and easy method to assess models performance. The carbon sources tested are metabolites from the citric acid cycle and central carbon metabolism.
The maximum growth rate of P. fluorescens was determined in 3 biological replicates as a baseline. 18 different carbon sources with a concentration of 1% (w/v) were tested on M9 minimal media to cover a broad spectrum of pathways and to eliminate potential diauxic growth effects.
Once the pre-cultures in LB medium reached an OD600 of 0.1, the cells were washed with M9 minimal salts without carbon sources removing excess LB medium. The washed preculture was inoculated 1:10 in 200µl and plated on 96-well plates with M9 minimal medium. OD600 was measured every 10 min for 24 h using a TECAN Spark spectrometer and the maximum growth rate was determined using the Growthcurver package in R 4.1.3 (Sprouffske & Wagner, 2016).
The in silico growth rates were produced by setting all fluxes of exchange reactions with metabolites not contained in the medium to zero and optimized for biomass. A direct comparison of the predicted growth rates rpredicted and the measured rates rmeasured was not possible, as the two values are proportional but not identical. By implementing a proportionality constant termed scaling factor k to account for this difference, the two datasets can be compared:
The equation was rearranged and k was adjusted so the rescaled mean sum of squares converged to zero. This step was repeated twice with the upper and lower values of the 1 sigma interval of the measured growth rates to estimate the 1σ interval of the scaling factor.
The carbon sources were also chosen to avoid the overfitting of particular degradation pathways.
All following simulations were obtained by following this workflow: First, all exchange fluxes of components not present in the simulated medium were set to zero. Flux constraining and biomass optimization was performed. Using the scaling factor k, the whole model was scaled down to yield physiologically correct results. The scaled predicted fluxes were used for yield and degradation prediction.
The co-culture was simulated using the two metabolic models for the helper and the main strain. A shared medium was created including the limited amounts of nutrients to be observed. By subtracting the consumed nutrient values of both strains from the initial medium values, biomass growth was linked to depletion of nutrients. The growth of the biomass is terminated when all energy sources in the medium are consumed. Predictions with cFBA followed the same workflow described for FBA, however, the objective function was altered to optimize for the sum of the biomass fluxes of helper and main strain.
For dFBA simulations, an initial medium composition of 200 mmol carbon source (20 mmol for polymer degradation) was set. Other necessary non-carbon metabolites (e.g oxygen, carbondioxide, water, etc.) were set to 10 mol to ensure that the growth simulation is not limited by them. The fluxes are calculated and multiplied by a small, constant time interval to give the approximate change in media composition over the time frame. A time step of 0.1 h was found to give good resolution with moderate calculation time. Subtracting this change from the initial medium composition gives a new initial medium composition. The process is repeated until the substrate concentration in the medium reaches negative values. At each timestep, a vector of media concentration is stored for plotting and analysis.
dFBA of the coculture model was performed similarly to the dFBA of a singular model. However, the optimization step at each time point included two optimizations on the same medium composition. One optimization calculates the biomass and the substrate effects for the main strain, the other for the helper strain. The media compositions were updated accordingly and stored for later analysis.
To identify the metabolic rations with the highest impact on the helper strains growth, its biomass flux was simulated on PET/PE minimal medium and in an unlimited medium containing all possible extracellular metabolites. Then each reaction was knocked-out individually and the effect on the PET/PE and full medium growth recorded. Knockouts that resulted in less than 1% of initial growth rate on both media were deemed essential and present good candidates for controlling the helper strain’s growth.
To assess the future potential applications of the ReMixHD system, we developed a function to compute up-scaling processes. This method is capable of simulating a chemostat (also known as a continuous bioreactor), which maintains constant media composition and cell density, allowing for consistent cell growth at maximum growth rate.
Our up-scaling model utilizes the bioreactor's volume, elapsed time, and substrate properties to predict the degradation of various substrates, the production of biomass, emitted CO2, and polyhydroxyalkanoates (PHA). This extrapolation function is based on the following assumptions: A cell of P. fluorescens has a comparable dry weight to E. coli, estimated at 3 x 10-13 grams (Neidhardt et al., 1996). In the bioreactor, a dominant cell density of OD = 1.2 is observed. Assuming that 0.1 OD units correspond to 7 x 105 cells/ml, this results in a cell count of 8.4 x 109 cells/l.
Next, the total weight of dry biomass in the bioreactor can be calculated. From there, the determination of the biomass produced during a degradation process depends on the growth rate and duration. The generated PHA mass is derived from the potential storage capacity of PHA in P. fluorescens, which is reported to be 15% of the cell dry weight according to (Vladu et al., 2019).
Subsequently, the quantity of the degraded substrate was calculated. This was achieved by multiplying the substrate's uptake rate with CDWbioreactor, t, and the molecular weight of our substrate.
To compute the emitted CO2, the model uses the molecular weight of CO2 as a multiplier for its flux. This value is multiplied by CDWbioreactor and t.
This model serves as an extrapolation for industrial-scale predictions of degradation rates, product yields, and CO2 emissions. It is extensible to include the status of co-cultures, such as the proportion of helper and main strain.
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