Flux analysis for providing more urea

1. Abstract

This section is about a metabolic engineering study we did about the urea cycle. On the first part we show how we used “elementary flux modes” (Schuster et al., 2000) to analyze the function of the compounds involved in the urea cycle. Mainly we deduced which compounds act as sources of carbon and sources of nitrogen for the production of urea. On the second part of this study we show how we determined elementary flux modes of the urea cycle to find ways to increase the yield of urea. We focused on a strategy which involves increasing the concentration of four components of the cycle and which we concluded would yield more urea. To confirm our results future experiments will be done.

Fig. 5 The reactions related with the urea cycle

2. Introduction

2.1 What is Elementary Flux Modes?

In Metabolic Engineering, mathematical modeling is an effective way to increase the products of a reaction. In particular, Flux Analysis, which is based on the hypothesis that the system is in a steady state, is effective to find how to increase these products. 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. As a method of metabolic flux analysis, it is based on the hypothesis that the concentration of the reactants and products involved in the cycle does not change.

2.2 Analyzing the function of the compounds involved in the Urea Cycle by determining the elementary flux modes

By determining the elementary flux modes of a cycle we can have a more clear view of the function of each of the compounds involved in the cycle being analyzed. Based on the elementary flux modes of the urea cycle, in this study we could deduce that HCO₃^- acts as the source of carbon for urea production and that both L-glutamine and NH₃ act as nitrogen sources for the formation of urea.

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2.3 Finding Modes to Increase the Urea production by E. coli

In this study we determined elementary flux modes to maximize urea production by E. coli. We found that there are two main strategies to increase urea production: one is to increase the amount of carbamoyl phosphate (which formation is known to be the rate-limiting step of the urea cycle). The other one is to increase the concentration of four components of the urea cycle: L-ornithine, L-citrulline, N-(L-arginino)succinate and L-arginine. We deduced the latter strategy by determining the elementary modes of the urea cycle, and therefore in this study we will focus on the description of this strategy.

Fig. 8 Two ways to increase urea production

3. Results

In our study, we considered the enzymatic reactions shown in Table 3 to determine the elementary flux modes related to urea production by E. coli. The scheme the overall reaction system is shown in Fig. 5 below.

By determining the elementary flux modes to produce urea inside E. coli, we found two important results:

1. We confirmed both L-glutamine and NH₃ act as nitrogen providers in the urea cycle, as well as deducing that HCO₃^- acts as the source of carbon for urea production. These modes did not make use of organic intermediates. Even though L-glutamine is consumed in order to to transfer the side-chain ammonium group needed for the production of carbamoyl phosphate (which in turn transfers the ammonium group to the urea cycle), free ammonium ion can restore L-glutamine from L-glutamate (which is a byproduct of the reaction that yields carbamoyl phosphate as a product).

2. We concluded that increasing the concentration of L-ornithine will increase the concentration of three related compounds (L-citrulline, N-(L-arginino)succinate, and L-arginine) and this will ultimately lead to an increase in the production of urea. We also noted that since the L-aspartate amino acid, which is needed in the urea cycle we considered(Fig. 5), is normally consumed in protein biosynthesis, so it should be supplied in the culture medium or synthetized by ,E. coli in order to be able to increase the amount of urea and to maintain the cycles that produce it.

Below is a detailed description of these three results.

3.1 Analyzing the function of the compounds involved in the Urea Cycle by determining the elementary flux modes

The first step was to determine the flux modes which need of L-glutamine as an input (Mendel et al., 1996). We did this by calculations based on a matrix as the tableau shown below.

We found eight modes that can produce urea without using organic intermediates. These are shown in Fig. 6. Each reaction formula is shown in Table 4. In particular, we focused on one the mode displayed in Fig. 7.

As shown in Fig. 7, we deduced that the carbon atom of urea is provided from HCO₃^- , which is a byproduct of respiration and therefore is already an abundant compound in the bacterial cytoplasm. On the other hand, we also confirmed that carbamoyl phosphate is a nitrogen source for urea production.We also found that the function of L-glutamine in the urea cycle is to provide nitrogen for urea production via carbamoyl phosphate, because ammonium ion can restore L-glutamine from L-glutamate (which is a byproduct of the reaction that yields carbamoyl phosphate as a product). This conclusion was confirmed experimentally by Mendel et al. (1996). Also, since only providing a nitrogen source is enough to increase urea production by E. coli, we can also conclude that the aritificial urea cycle in E. coli is stoichiometrically well designed. By comparing Fig. 5 and Fig. 7 we can also observe that, in Fig. 7, the reaction which converts L-glutamate to L-ornithine is not needed for urea production.

3.2 Finding Modes to Increase the Urea production by E. coli

There are two ways to obtain more products from a cycle of reactions: increasing the speed the reactions and increasing the concentration of the reactants. This becomes obvious if we think of the cycle as a track which is travelled by cars (the reactants), and the products as the total sum of the number of laps made by every car. If we double the speed of the cars the number of laps will also double (Fig. 8, lower left). Similarly, if we double the number of cars, the number of laps will double as well (Fig. 8, lower right). We applied this analogy to the urea cycle, where the metabolites in the cycle are represented by the cars and the total number of laps represents the total urea yield (as shown in the figure below).
Increasing the velocity of the cars corresponds to increasing the amount of carbamoyl phosphate in the urea cycle, because the reaction which converts L-glutamine to carbamoyl phosphate is the rate-limiting reaction of the cycle. On the other hand, increasing the number of the cars correspond to increasing the concentration of the compounds of the urea cycle. We focused on increasing the concentration the compounds of the urea cycle to find ways to increase the urea yield.

Fig. 8 Two ways to increase urea production

L-ornithine, L-citrulline, N-(L-arginino)succinate and L-arginine are four important compounds of the urea cycle. As can be seen in Fig. 7, these compounds form a sub-cycle that directly yields urea. Therefore, by increasing the yield of this cycle we can increase the production of urea in E. coli.

We determined the elementary modes which produce these four important compounds. All elementary flux modes which produce these compounds from L-glutamine or from compounds in TCA cycle produce L-ornithine as intermediate or final product (these modes are shown in Fig. 9 and each reaction formula is shown in Table 5), it can be concluded that increasing the concentration of L-ornithine will increase the production of urea. One of the L-ornithine producing modes is shown in Fig. 10.

The reactions we determined increase the above mentioned four compounds of the urea cycle are shown in Fig. 9. All modes include the reaction that yields L-ornithine by converting L-glutamate to L-ornithine.
We also confirmed that E. coli has no feasible routes for production of these four components other than those indicated in Fig. 5. Therefore, we can conclude that the reaction which converts L-glutamate to L-ornithine is a key reaction to increase the reaction rates in the urea cycle and thereby to increase urea production. It should be noted that one of the reactions of the cycle shown in Fig. 5 (the one in the lowest part of the image) requires ATP, NADPH, Acetyl-CoA, and L-glutamate. With the exception of L-glutamate, all of these compounds are already abundant in the cell. Therefore, in future wet experiments, we will focus on studying the effects of supplying L-glutamate to E. coli. We will confirm that by supplying L-glutamate the concentration of intermediates like L-ornithine can be increased and therefore urea production can be increased.

Furthermore, to supply L-glutamine, L-glutamate and L-arginine is effective way to increase the amount of ornithine.(Fig. 11)

Fig. 11 Ornithine is made from L-glutamine, L-glutamate and L-arginine

We also noted that since L-aspartate is consumed in protein biosynthesis, this amino acid should be supplied from in the medium or produced by E. coli itself not only for increasing the amount of urea production, but also for maintaining the cycle.

In conclusion, increasing the concentration of L-glutamine, L-glutamate, L-arginine and L-aspartate is an effective way to increase the amount of urea produced.

4. Future Work

As a future work, we will experimentally confirm our results to show that activating the reactions which supply these amino acids is an effective way to increase the production of urea by E. coli.

Reference