Analysis

There are three main questions we have answer in result analysis

1. How many CO₂ (air) uptake by engineering E. coli?
2. How many CO₂ can be fixed in biomass?
3. If the pyruvate trend match biomass trend?

Amount of CO₂ uptake

At first, we set up a closed system to model CO₂ uptake by E. coli. After a period of time, concentration of CO₂ uptake reached a balance. The result can tell that more than 50% air CO₂ diffuse into E. coli in a closed system.

However, we cannot set a CO₂ utilization system in a closed system. No matter our application is continuous culture or fed-batch culture, air CO₂ concentration will be constant, which means a boundary condition. Therefore, we model again under open system. Under constant air CO₂ condition, CO₂ diffusion speed changed with time and we categorized them into three phases, which are steady climb phase, transition phase, and saturated phase. The time segments of these three phases depend on CA activity. We assume A, B, C as time intervals of three phases. The cover area in the result shows that different time interval refers to different amount of CO₂ uptake by E. coli. Its CO₂ uptake rate change with time as well. As a result, we collect the CO₂ uptake rate and then calculate with the xylose consumed rate and pyruvate produced rate. What’s more, the main reaction of CO₂ in engineered E. coli happened between rubp to 3PGA, which is another part we are going to discuss.

1. Engineered E. coli with CA


Time A was about 10 min (or 700 s) with [CO₂ uptake] reach 1 mM, causing 25% CO₂ uptake in total.

Time B was about 1 hour (or 3500 s) with [CO₂ uptake] equals to [air CO₂], causing 75% CO₂ uptake in an hour.

Time C was about 1.5 hour (or 8000 s) for [CO₂ uptake] reach balance with the highest CO₂ uptake percentage, 90%.

Time interval	Xylose supplied	Concentration CO2 uptake (mM)	Xylose (mM/s)	Pyruvate (mM/s)	Total CO2 uptake percentage
A	0.2%	1	0.008	0.016	25%
B	0.2%	2.045	0.00264	0.00528	75%
C	0.2%	2.15	0.001131	0.002263	90%

Table 1

xylose consumed rate and pyruvate produced rate under different CO₂ uptake time interval with CA

2. Engineered E. coli without CA


Time A was about 10 min (or 700 s) with [CO₂ uptake] reach 1 mM, causing 25% CO₂ uptake in total.

Time B was about 1 hour (or 3500 s) with [CO₂ uptake] equals to [air CO₂], causing 75% CO₂ uptake in an hour.

Time C was about 1.5 hour (or 8000 s) for [CO₂ uptake] reach balance with the highest CO₂ uptake percentage, 90%.

Time interval	Xylose supplied	Concentration CO2 uptake (mM)	Xylose (mM/s)	Pyruvate (mM/s)	Total CO2 uptake percentage
A	0.2%	1	0.0036345	0.007504	28%
B	0.2%	2.045	0.0017486	0.003888	72%
C	0.2%	2.15	0.001631	0.00388	88%

Table 2

xylose consumed rate and pyruvate produced rate under different CO₂ uptake time interval without CA



A



B



C

Fig. 3 result of xylose and pyruvate under A, B, C, time interval

Actually, xylose consumed rate is slightly related to has little relationship with the CO₂ uptake rate, since that xylose metabolism wasn’t just a single pathway. What we can analysis is that the pyruvate produced rate being correlation with CO₂ uptake rate, which help us to define the question that how much CO₂ uptake by engineered E. coli. It can also fit with experiment data easily. Next, we discuss about the true CO₂ reaction in E. coli CO₂ utilization bypass pathway. Every single mole of CO₂ uptake will react with one mole of rubp and then produce 2 mole of 3PGA.



Fig. 4 result of rubp and 3PGA during CO₂ uptake

Since that rubp and 3PGA are just intermediate products in metabolism, their concentration is quite low. Besides, results of three CO₂ uptake time interval showed similar. We still can see that 3PGA produced is 2 times larger then rubp produced. We then calculate their produced rate in three CO₂ uptake time interval.

Time interval	Rubp produced rate (mM/s)	3PGA produced rate (mM/s)
A	4.25E-09	6.35E-10
B	3.89E-09	8.42E-09
C	1.76E-09	3.71E-09

Carbon metabolism flux

The main Xylose metabolism in E. coli was PP pathway and glycolysis. As for recombinant E. coli, it has multiple xylose metabolic pathways, and we can simplify them into original pathway and CO₂ Bypass pathway. Therefore, we need to define the percentage of xylose, which is consumed by engineered E. coli, entering CO₂ bypass pathway and utilize CO₂.

It costs a lot of time to get absolute metabolic flux of CO₂ in engineered E. coli and require feed of ¹³CO₂ during cultivation. Since the metabolic flux of the original metabolic pathway is quite stable, the relative metabolic flux of CO₂-utilization over that of the original metabolic pathway could show a quantitative understanding on the CO₂ utilization efficiency. This relative value was MFI_CO2^[1], a term as metabolic flux index of CO₂-utilization pathway in heterotrophic engineered E. coli. This is the percentage of xylose that we mentioned above.

To define the MFI_CO2, we use CO₂ fixed by the CO₂ bypass pathway, noted as b, divided by the 3PGA generated from the central pathway, noted as a. We also assume c is mol of 3PGA¬0 and d is mol of 3PGA’ that channels into downsteam metabolism. After metabolism, (a+b) mol of 3PGA₀ and b mol of 3PGA’ are generated.

Besides, X and Y represent the actual 3PGA detected from the original pathway and CO₂ bypass pathway, which show in 3PGA₀ and 3PGA’ in the fig. 1, respectively. In the experiment, we use 13C-labeled CO₂ and unlabeled sugar to get the amount of 3PGA₀ and 3PGA’. However, it was reported that 3.45% of unlabeled 3PGA, which is noted as 3PGA’, will convert to its isotopic during the culturing E. coli strains in medium. Eventually, we concluded these situation into two equations.

$${y = b + 3.45\% \times (a+b) - d ......(1)}$$

$${x = (1-3.45\%) \times (a+b) - c ....(2)}$$

Since d/c = y/x under a metabolic steady-state, we derive equation (1) and (2) into a final relationship between a, b, x, and y.

$${MFI(Metabolic flux index) = {b \over a} = {{0.97y-0.03x} \over {1.03x-0.97y}}}$$

As a result, we only need the amount of 3PGA₀ and 3PGA’ to calculate MFI_CO2. Through modelling, we supply 0.4% xylose and 5% CO₂ to get the data of 3PGA₀ and 3PGA’, which helps us to adjust the rate between xylose and CO₂ sources.

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