Flux analysis for providing more urea

*The orange letters are the abbreviated names of the enzymes involved. The red letters are the enzyme expressed by introducing rocF gene. For complete names of the enzymes see Table 3.

1. Introduction

In metabolic engineering, mathematical modeling is the effective way to increase the products. Flux analysis, based on the hypothesis that the system is in steady state, is the effective way to find expect how to increase the products. In this work, we firstly focused on the concept of 'elementary flux modes' (Schuster et al, 2000), which provides metabolic routes both stoichiometrically and thermodynamically feasible.
One elementary mode shows that the carbon atom of urea derives from HCO₃^- which abounds in bacterial cytoplasm. Furthermore, in spite of L-glutamine consumption to transfer the side-chain ammonium group for production of carbamoyl phosphate which transfers the ammonium group to the urea cycle, ammonium ion can restore L-glutamine from L-glutamate which is a byproduct of the carbamoyl phosphate production. These findings suggest that there was little difference in the condition of containing NH₃ or L-glutamine in the culture to obtain more urea. This finding is proven in previous report's experiment. (Mendel et al, 1996) We also confirmed that the urea cycle in E.coli is well designed in a stoichiometrically point of view.
To provide more urea, there are two strategies. First one is to increase the amount of carbamoyl phosphate which is the reactant of the rate-limiting step of the urea cycle. The second one is to increase the amount of four components of the urea cycle: L-ornithine, L-citrulline, N-(L-arginino)succinate, L-arginine. We thus identified the elementary flux modes which produce these compounds from L-glutamate or compounds in TCA cycle: 2-oxoglutarate, oxaloacetate, L-malate, fumarate. In all modes, ornithine was intermediate or final product to produce the four components of the urea cycle. Furthermore, all modes include the reaction which converts L-glutamate to L-ornithine to produce L-ornithine. We also confirmed that E. coli have no feasible route for production of the four compounds other than those indicated in Fig.5. Therefore, ornithine production needs the reaction which requires ATP, NADPH, Acetyl-CoA, and L-glutamine, is the necessary step in this strategy. We will confirm the effect of L-glutamate supplement in future wet experiments for not only urea production but also the intermediates like L-ornithine. Positions of L-arginine and L-glutamate in the reaction network show that supplement of these compounds has similer effect on urea production.
From another point of view that L-aspartate is consumed in protein biosynthesis, this compounds should be supplied from medium or produced by E. coli itself not only for increasing the amount of urea but for maintenance of the cycle.

What is elementary flux mode

"The concept of elementary flux mode provides a mathematical tool to define and comprehensively describe all metabolic routes that are both stoichiometrically and thermodynamically feasible for a group of enzymes". (Schuster et al, 2000) We can determine the modes which are able to work at steady state by this analysis.
As application of elementary flux modes, we can expect what substrates are needed to produce to the substances of interest. Furthermore, we can find expect which enzymes to overexpress or knockout so as to maximize the products we want.

2. Results

Overall reactions related with the urea cycle We considered the enzymatic reactions shown in Table 3 to determine the elementary flux modes. The scheme of the reaction is shown in Fig.5.

*The orange letters are the abbreviated names of the enzymes involved. The red letters are the enzyme expressed by introducing rocF gene. For complete names of the enzymes see Table 3.

One of the urea producing cycles without supplying the intermediates

At first, we attempted to get the elementary flux modes in the condition whose input is L-glutamine like previous reports. (Mendel et al, 1996) We determined the elementary flux modes by calculating matrix like. The initial tableau is shown below.

We calculated and got the final tableau.
The way to calculate is here..

We got eight modes shown in Fig.6. Each reaction formula is shown in Table 4. We focused on one of the urea producing modes in these eight modes as shown in Fig.7.

If we compared Fig.5 and Fig.7, we can see that in the mode displayed in Fig.7 the reaction which converts L-glutamate to L-ornithine is not needed for urea production.
As shown in Fig.7, the carbon atom of urea derives from HCO₃^- which abounds in bacterial cytoplasm.

Considering about nitrogen sources of urea, one of the nitrogen is derived from carbamoyl phosphate. Carbamoyl phosphate transfers the ammonium group to the urea cycle from L-glutamine. Therefore, it seems that L-glutamine is the effective nitrogen source. However, free ammonium ion can restore L-glutamine from L-glutamate which is a byproduct of the carbamoyl phosphate production. It means that L-glutamine and NH₃ have the same role to be the nitrogen source for urea. These finding suggest that there was little difference in the condition of containing NH₃ or L-glutamine in the culture to obtain more urea. This finding is proven in previous report's experiment. (Mendel et al, 1996) We also confirmed that the urea cycle in E. coli is well designed in a stoichiometrically point of view.

Increasing the four components of the urea cycle to provide more urea
To obtain more urea, we introduced the easy allegory. There are 3 cars in the cycle. We count the number of the cars driving in front of us during some period of time. There are two ways to increase in the number we count. One way is increasing the velocity of the cars. The other way is increasing the number of the cars driving in the cycle. The cars in this allegory are compounds of the urea cycle. The number we count are the product, urea. Increasing the velocity of the cars means to increase the amount of carbamoyl phosphate because the reaction which converts L-glutamine to carbamoyl phosphate is the rate-limiting. On the other hand, increasing the number of the cars means to increase the amount of compounds of the urea cycle. We chose the second way to determine how to increase the urea.
All elementary flux modes which produce these compounds from L-glutamine or compounds in TCA cycle produce L-ornithine as intermediate or final product. These modes are shown in Fig.8. Each reaction formula is shown in Table 5. One of the L-ornithine producing modes is shown in Fig.9.

As shown in Fig.9, we can provide L-ornithine by using a reaction which converts L-glutamate to L-ornithine. Furthermore, all modes include the reaction which converts L-glutamate to L-ornithine to produce L-ornithine. We also confirmed that E. coli have no feasible route for production of the four compounds other than those indicated in Fig.8. Therefore, the reaction which convert L-glutamate to L-ornithine is a key reaction to increase the reaction rates in the urea cycle. This reaction requires ATP, NADPH, Acetyl-CoA, and L-glutamate. We will confirm the effect of L-glutamate supplement in future wet experiments for not only urea production but also the intermediates like L-ornithine.

The effect of protein biosynthesis to urea production
From another point of view that L-aspartate is consumed in protein biosynthesis, this compounds should be supplied from medium or produced by E. coli itself not only for increasing the amount of urea but for maintenance of the cycle.

In conclusion, we confirmed that the urea cycle in E.coli is well designed in a stoichiometrically point of view.
Furthermore, to supply L-glutamine, L-glutamate, L-arginine and L-aspartate is effective way to increase the amount of urea.

3. Future work

According our results, we found that increasing

Reference
[1] Stefan Schuster, et al. A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic network, Nat Biotechnol(2000) 18:326-32
[2] Mendel Tuchman, et al. Enhanced production of arginine and urea by genetically engineered Escherichia coli K-12 strains, Apple Environ Microbiol(1997) 63: 38-8