Introduction

• General Introduction
Cells need energy to perform different types of jobs (chemical, osmotic, mechanical, thermal, light and/or electric works) and matter for their construction, renewal, growth and multiplication. To meet this challenge, microorganisms have several solutions called 'trophic types' depending on the sources of energy, electrons (redox power) and matter (Figure 1). Their trophic type depends on the enzymatic baggage of each organism. By adding or removing certain activities, the trophic type can therefore change.

Figure 1: Overview of trophic types and energy transfers during metabolism. Acronyms: ATP (adenosine triphosphate), FAD (flavin adenine dinucleotide); FADH2 (reduced form of FAD), NAD⁺ (nicotinamide adenine dinucleotide), NADH, H⁺ (reduced form of NAD⁺).

Metabolism (metabolê, “change” in Greek) is a set of complex and incessant processes of transformation of matter and energy by the cell during edification (anabolism, generally endergonic reactions i.e. energy capture, associated to reductions) and degradation (catabolism, generally exergonic reactions i.e. energy release, associated to oxidations) phenomena. The source of energy can be either the light (phototrophy) and the redox potential contained in reduced molecules (chemotrophy). In both cases, a donor of electrons is required. The three energy vectors with the cell are: i) molecules with high hydrolysis potential such as ATP, ii) the redox power which governs the balance between oxidations and reductions, and iii) the transmembrane electrochemical potential. These three vectors are interchangeable (e.g. the consumption of the protomotrice force allows the production of ATP).

The CO2CURE project aims at implementing a CO₂ fixation module in Streptomyces which are chemoorganoheterotroph bacteria. What a challenge!

At least six cycles or pathways of CO₂ fixation exist in nature. The most widespread is the Calvin-Benson-Bassham (CBB) cycle, or simply the Calvin cycle. This cycle is a series of biochemical reactions that allows photosynthetic or chemosynthetic organisms to convert inorganic CO₂ into glucose. Three enzymes characterize this CO₂ fixation pathway: the ribulose-1,5-diphosphate carboxylase/oxygenase (RuBisCO) (Figure 2), the phosphoribulokinase (PRK) (Figure 2) and the sedoheptulose-1,7-bisphosphatase (SBPase).

Introducing this cycle inside heterotrophic organisms could potentially allow them use atmospheric CO₂ to create useful compounds, essentially creating ‘hemiautotrophic’ organisms (or ‘chemoorganoautotrophs’, since an organic source of electrons will still be required). However, we must keep in mind that the metabolism of any organism is a machine that has been carefully calibrated over hundreds of millions of years of evolution. As such, it seems a tad over-optimistic that introducing something as major as the Calvin cycle wouldn't send that machine into complete disarray and for our heterotrophic organism to correctly integrate the Calvin cycle into its metabolism. We propose to study ways to model the metabolism of Streptomyces, to better understand what is the best way to introduce the Calvin cycle.

The abbreviations we will use:

• G3P: Glyceraldehyde triphosphate
• DHAP: Dihydroxyacetone phosphate
• GPM: Phosphoglycerate mutase
• PRK: Phosphoribulokinase
• RuBisCO: Ribulose-1,5-bisphosphate carboxylase-oxygenase

• Introduction to the Model
Luckily, we were not the first researchers trying to introduce the Calvin cycle inside an heterotrophic organism. In 2016, an article entitled “Sugar Synthesis from CO₂ in Escherichia coli” (Antonovsky et al., Cell, 2016) [1] successfully introduced a variant of the Calvin cycle in E. coli. They managed, for the first time in history, to achieve a completely functional carbon fixation cycle inside a heterotrophic organism. In this model, only 2 enzymes are required to complete a variant of the CBB cycle: the RuBisCO and PRK. In the presence of these two enzymes, the pentose-phosphate pathway (PPP) and glycolysis enzymes can implement a variant of the Calvin cycle (devoid of SBPase) (Figure 2).

Figure 2: Overview of the interplay between the CO₂-fixation and energy modules after introducing the RuBisCO and PRK in a heterotrophic bacteria. Several intermediates of these cycles are key elements for cell construction. The reduced forms of redox power (NADH,H⁺, FADH₂) can be oxidized to produce energy. This is for example the case in Streptomyces. Within these bacteria, these molecules are oxidized in an aerobic chain using oxygen as the terminal electron acceptor. This process allows to produce a proton gradient used in particular to produce ATP molecules by the ATP synthase. Please note that, for clarity, the number of molecules obtained in each reaction is not indicated.

However, simply introducing these enzymes was not enough to allow carbon fixation inside E. coli. The researchers found that they needed to prevent carbon flow between the carbon fixation module and the energy module by inactivating a specific gene, gpm encoding the 2,3-bisphosphoglycerate-dependent phosphoglycerate mutase (short name: phosphoglyceromutase, GPM). They also found through directed evolution that the ribose-phosphate diphosphokinase (PRS), an enzyme that converts ribose 5-phosphate into phosphoribosyl pyrophosphate (further used notably for nucleotide and certain aminoacids synthesis), needed its activity to be carefully calibrated in order to E. coli to be able to grow in elevated CO₂ conditions. An organic electron donor (pyruvate) was still required for growth. This is why this trophic type has been called ‘hemiautotrophy’.

To continue further, we need a quick reminder about pyruvate. As the starting molecule of the citric acid cycle, produced by the glycolysis, it is a key point of the energetic metabolism. The citric acid cycle is the process that synthetizes molecules of ATP, the source of electrons (and thus energy) transfer for most of the cell’s reactions, through oxidations. In order to obtain energetic molecules at the end, we need electron-giving molecules at the beginning: this is where pyruvate enters. It serves as a link between the digestion of nutritive compounds like sugars and ATP (and heat, through reactions) production. The complete processes through which the pyruvate is produced differs in function of organisms: glycolysis is always present, but the first modules in the electron-giving compounds production chain change in function of their trophic type. An autotrophic organism can primarily receive energetic electrons from an abiotic source of energy through photosynthesis or chemosynthesis, uses it to reduce CO₂ and then synthetizes intermediary molecules like sugars to store and move energy. It thus only needs inorganic compounds, such as CO₂ or minerals from its environment. On the opposite, heterotrophic organisms need an organic source of energy in order to live. They often digest sugars produced by autotrophic organisms, and start their energy metabolism at this point, using O₂ or fermentation as an oxidant. Finally, mixotrophic organisms take from both worlds: they have the metabolic ability to fix and reduce CO₂, but they also digest complex organic molecules from their environment and use them as a source of energy. Hemiautotrophy is thus really close to this trophic type, with the particularity that it needs energetic electrons from the heterotrophic part of its metabolism to fix CO₂.

We were especially interested in modeling the metabolism of Streptomyces involved in energy production and studying the impact of the introduction of the Calvin cycle with RuBisCo and PRK, along with the respective impact of GPM and PRS.

We needed to study the relations between the cycles, and to make hypotheses in this direction. This also allows us to make some simplifications. For example, we did not need absolute data about reactivity, but only information about the proportional relations within the molecules of the cycles.

Building our model

So, we want to model the metabolism of Streptomyces but what does that consist of exactly? First, let's take a look at how a metabolic network is organized.

A metabolic network can be summarized as a vast array of enzymatic reactions with each reaction having a single or possibly multiple reactants and products. Here are some examples of fundamental enzymatic reactions shared across many organisms (Figures 3 and 4).

Figure 3: Conversion of the glucose into glucose-6-phosphate (G6P), the first step of glycolysis. Please note that this reaction consumes ATP (not represented).

Figure 4: Conversion of the glucose-6-phosphate (G6P) into fructose-6-phosphate (F6P), the second step of glycolysis.

These reactions can be summarized as the transformation of one metabolite into another. Where it gets complicated and where the network part of "metabolic network" really starts to appear is when you consider that a metabolite is usually involved in multiple reactions. Indeed, a metabolite is often the product and reactant of separate reactions. If you consider ATP for example, just listing all of the reactions it is involved in would probably double the size of our wiki.

This is why we did not focus on the individual reactions themselves but rather on the "flow" of each metabolite expressed over time. As such, the flow over time of a metabolite "A" can be summarized as:

The inflow_A will represent the reactions where A is a product and the outflow_A will represent the reactions where A is a reactant. As such we can write:

Where reaction_P1 to reaction_Pi are all the rates the reactions where A is a product and reaction_R1 to reaction_Rj are the rates of the reactions where A is a reactant.

What is the rate of a reaction? Simply the speed at which the reactants are transformed into the products. We'll now use the letter "k" to refer to rates of reactions.

Once we have multiple metabolites, we can create a system:

For each metabolite, the sum of all positive "k"s is the inflow and the sum of all negative ones, the outflow.

Now, we can see the baseline for our model. We can go one step further by introducing our first hypothesis H₁. We'll consider that all metabolites intrinsic to our system must have a net flow equal to zero. This hypothesis is inspired by the flux balance analysis method [2][3]. It can be justified by the fact that in order for a metabolic system to be sustainable, most metabolites will be synthesized according to how much they are needed. For an organism, having a surplus of intermediary metabolites is often a waste of energy. We can now write the previous system as:

Purely for fun, we can quickly solve this system and find that this implies:

Meaning the rate of reaction 1 is double that of reactions 2, 3, 4, 5 and that reactions 2, 3, 4, 5 all share the same rate. The amount of information we gathered from this simple system goes to show just how powerful H₁ is.

Gathering the data

In order to model the metabolism of any organism. It's vital to first collect data on all the metabolic reactions it is able to catabolize. For this purpose we used KEGG, the Kyoto Encyclopedia of Genes and Genomes.

"KEGG is a database resource for understanding high-level functions and utilities of the biological system, such as the cell, the organism and the ecosystem, from molecular-level information, especially large-scale molecular datasets generated by genome sequencing and other high-throughput experimental technologies." Quote by KEGG.

After deciding we wanted to model Streptomyces ambofaciens, the strain we were the most familiar with at the time, we used this database to gather a list of every single enzymatic reaction that S. ambofaciens is able to catalyze.

Though we only focused on S. ambofaciens, taking a look at the metabolism of other strains on KEGG revealed that most metabolic pathways in Streptomyces were very similar strain to strain, especially in regards to the ones we were interested in the pentose-phosphate pathway, glycolysis and Krebs cycle.

Our second hypothesis, H₂ was formulated at this point: since the metabolism of the different heterotrophic strains were so similar we decided the metabolic network of S. ambofaciens could be used to draw conclusions on the entire genus. Of course, we are discounting strains who are autotrophic and/or are able to naturally complete the CBB cycle.

Figure 5: Global view of our system of reactions, before simplifying it (i.e. removing some compounds and reactions) in order to model it. Note that during TCA, one molecule of GTP is produced. This molecule can be easily converted to ATP by the cell. For simplicity and for further modeling, we have indicated ATP in our model (and in this figure).

Though, it is already stripped down, conforming to some of our primordial hypotheses: we do not study the reversibility of the reactions and model them by using their main direction, we assume that it is an isolated, uncompartimented system, and we only consider the most important coreactants: ATP/ADP, NADP/NADPH, NAD/NADH and CO2. The fixated molecule of CO2 of the Calvin cycle is framed in red, and our 3 enzymes of interest (PRK, RuBisCo and GPM) are in red.

Stripping our data down to the essentials

Now of course, we didn't actually need every single enzymatic reaction S. ambofaciens is able to catalyze to build our model. We were only interested in a few specific pathways involved in energy and biomass production:

• The Calvin cycle: not natively found in S. ambofaciens. We simply used the model carbon fixation pathway for natural autotrophic organisms.
• The Krebs cycle or the Citric Acid Cycle or tricarboxylic acid cycle (TCA): this cycle is responsible for turning glucose into the energy needed for carbon fixation (Figure 2).
• The Pentose Phosphate Pathway (PPP): to put it simply, the PPP is the link between glucose and biomass production. This cycle is at the origin of the production of key elements for cell construction, in particular of ribose-5-phosphate (important for DNA/RNA building and histidine synthesis for instance) and the reduced form of nicotinamide adenine dinucleotide phosphate (NADPH, H⁺), which is important for anabolism (Figure 2). It also leads to the release of a CO₂ molecule.

Even after this first simplification step, the amount of data we had to process through still was unwieldy. We needed to simplify further…

Fortunately we found a way, let's take a look at the following system:

Let's also consider that B is not involved in any other reaction other than reaction 1 and 2.
We'll have:

From this we can derive that:

Which implies that we can rewrite the system as,

Completely nullifying B. Using similar methods, we can also simplify the system:

Into:

Through strategic and careful use of these methods we managed to simplify our data into a simpler model (Figure 6).

Figure 6: Combination of specific pathways involved in energy and biomass production in an organism. The CO₂ fixation module is also known as Calvin cycle. The Energy Module is also known as Citric acid cycle (TCA).

Acronyms: 3PG (3-phosphoglyceric acid); FAD (flavin adenine dinucleotide); FADH₂ (reduced form of FAD), RuBP (ribulose 1,5-bisphosphate).

Results

Now that our model was finally completed, we tested out different scenarios.

Simulating the primary metabolism of Streptomyces ambofaciens

To do this, we really only needed the bottom part of our model including the Energy module. We tried out feeding some pyruvate into the model and evaluating the production of ATP, FADH₂, and NADPH,H⁺ (Figure 7). We can write:

Figure 7: Modeling the energy module using several k parameters.

Quickly, we noticed that if we consider the system to be perfectly efficient, implied by H₁, then the rates of reactions 1, 2 and 3 must all be equal to the inflow of pyruvate (k_input). Indeed, we can derive from the system:

Since we didn't know the exact values for the k constants of each reaction. We could instead represent all of the system's solutions as a vector space.

Moreover, we noticed that the solutions to our system were equivalent to the vector space:

This is useful when taking a more computational approach.

Before we moved on to the full model, we simulated the quantities of molecules over time with a constant rate of pyruvate input (Figure 8).

Figure 8: Simulation of the base metabolism of Streptomyces ambofaciens, ≈1200 points, base quantities of all metabolites: 1 mol, using custom software solutions.

We first ran a simulation with an initial amount of 1 mole per metabolite.

As expected, the amount of intermediary metabolites : Acetyl-CoA, Citric Acid, Oxaloacetic Acid stayed the same during the entire simulation. Moreover we observed the production energy for S. ambofaciens in the form of ATP, FADH₂ and NADPH, H⁺.

Note: the quantities in mole and the time in seconds should not be taken at face value, we don't have experimental results to compare our model to. We are only looking at general trends.

As we are dealing with small quantities, our system has particular kinetics, and we introduced a simple law of mass action parameter in our simulation to see if that would modify our results. We introduced a constant for each reaction where the rate of a reaction would be accelerated if there were more available reactants. This turned our initial system into:

Note: when the quantity of a reactant of any reaction reaches 0, we disable that reaction.

This had no effect on the simulations where the initial amount of metabolites was 1 mole (Figure 9).

Figure 9: Simulation of the base metabolism of Streptomyces ambofaciens, ≈1200 points, base quantities of all metabolites: 1 mol, using custom software solutions, adjusted for mass action law.

We also took a look at random initial amounts of metabolites to gain a better understanding of the stability of our system (Figure 10).

Figure 10: Three different simulations of the base metabolism of Streptomyces ambofaciens, ≈1200 points, base quantities of all metabolites uniformly sampled on [0, 1], using custom software solutions.

We first looked at only the base system (not adjusted for the mass action law). We found that, no matter the initial amount of metabolites, the system would always be able to produce energy and that the amount of all the intermediary metabolites always stayed at its initial value.

Figure 11: Simulations of the base metabolism of Streptomyces ambofaciens, ≈1200 points, base quantities of all metabolites uniformly sampled on [0, 1], using custom software solutions, adjusted for mass action law.

Then we looked at our adjusted system (Figure 11). The system seemed mostly stable. Most scenarios ended with stable amounts of intermediary metabolites and increasing amounts of energy metabolites. In some rare occurrences, when there was too much initial imbalance between intermediary metabolites, the system could run out of specific metabolites, making the cycle no longer possible (last).

In conclusion to these preliminary simulations, our model for the base metabolism of S. ambofaciens is successful. From it we can model the production of energy metabolites which will be necessary for the fixation of inorganic CO₂ through a variant of the Calvin cycle.

Simulating the introduction of the Calvin cycle in S. ambofaciens

Figure 12 : Overview of the complete model including all parameters.

Acronyms: 3PG (3-phosphoglyceric acid); FAD (flavin adenine dinucleotide); FADH₂ (reduced form of FAD), RuBP (ribulose 1,5-bisphosphate).

Above is a complete overview of our model (Figure 12). The model gave us the following system:

Like previously, we found the possible solutions of this system.

Which gave us the vector space with the following basis:

We obtained a three dimensional array, this means our system has infinitely many solutions. To perform some simulations like before, we wanted to hone in on a specific solution. To do this we filtered the vector space using the following criterias:

• All k constants must be superior to zero. It doesn't make sense for our system to have negative k constants as that would mean for those specific reactions to be reversed.
• The biomass, ATP, FADH₂ and NADPH,H⁺ rates must all be superior or equal to zero. For S. ambofaciens to correctly function, it needs to produce energy metabolites as well as biomass, this is why we can assume all these rates to be positive. This translates to:

• Lastly, for easier analysis, let's try to get rates similar to our first simulation.

Using these criteria as guides, as it was impossible to satisfy them all, we settled on the following solution.

This meant that we had almost the same system as before, except we halved the input of pyruvate. We also quickly noticed that we would have a deficit of ATP making the system unstable (Figure 13). Nevertheless we went ahead and performed some simulations.

Figure 13: Simulation of the base metabolism and Calvin cycle of Streptomyces ambofaciens, ≈1200 points, base quantities of all metabolites: 1 mol, using custom software solutions.

In this simulation, the amount of intermediary metabolites biomass doesn't change, such as the first simulation without CO₂ fixation. Here we are in a stability situation for these molecules.

But, the main issue is the fall in ATP concentration. This decline is problematic because ATP production is one of the most important factors for a sustainable metabolism. Indeed, ATP is essential for an organism/ a cell, without it the cell can’t live.

Nevertheless, in a mitochondria , 1 NADH, H⁺ can produce 2.5 ATP and 1 FADH₂ can produce 1.5 ATP. So, if we make an average of 1 NADH, H⁺ and 1 FADH₂ ( = 2 NADH, H⁺/FADH₂), they can produce 4 ATP together. Even if our result is not based on real experimental values the ratio of NADH, H⁺/FADH₂ and ATP is still true.

So, in order to see if the excess of NADH, H⁺, FADH₂ could counterbalance the lack of ATP, let's check if the deficit of ATP is less than twice the amount of NADH, H⁺, FADH₂ in absolute value. Because of the linearity of curves we can check one point only to understand the trends.

At the end, we can observe a concentration of +0.3 for NADH, H⁺/FADH₂, so it can give us a concentration of 2 x 0.3 ATP. But, the ATP loss is -1 and 1 > 0.6. So, even if we have more NADH, H⁺ and FADH₂, it can’t fill the ATP gap. Thus, the insertion of RuBisCO and PRK only doesn't allow a viable metabolism.

We also tried doing a simulation where we let excess NADH, H⁺ and FADH₂ get converted into ATP. We found that such a system resulted in negative or no biomass growth.

So, we need to find a solution so that the biomass isn’t converted into “useless” energy.

Figure 14: Simulation of the base metabolism with Calvin cycle of Streptomyces ambofaciens, ≈1200 points, base quantities of all metabolites: 1 mol, using custom software solutions, adjusted for mass action law.

We then tested these conditions with our model which takes into account the mass action law(Figure 14). The simulations show the same trends. Therefore, our result seems to be independent of the modeling system and so it may reflect the inability to generate ‘hemiautotrophy’ with only the insertion of RuBisCO and PRK.

Simulating the introduction of the Calvin cycle in Streptomyces ambofaciens and inactivation of GPM enzyme

Figure 15: Overview of the complete model with inactivation of GPM and all parameters.

Acronyms: 3PG (3-phosphoglyceric acid); FAD (flavin adenine dinucleotide); FADH₂ (reduced form of FAD), RuBP (ribulose 1,5-bisphosphate).

As described just before, insertion of the CO₂ fixation module makes the metabolism unstable. We were convinced that a change in reaction rates could solve this instability. Moreover, this phenomenon was also described in the article based on E. coli ( “Antonovsky et al., Cell, 2016) [1] . In order to solve this problem, they cut the link between the CO₂ fixation module and the energy module, by deleting the gpm gene. So, we decided to do the same. By doing this, we obtained a new system of equations in which the GPM activity no longer appears (Figure 15).

Like previously, we solved the kernel of reaction rates of intermediate metabolites matrix, with the aim of solving our system. We then obtained a two dimensional array, different to the previous one.

This array represents the solutions space of our homogeneous system. In order to discriminate our solutions we have based ourselves on the same hypothesis as the case with gpm.

The inhibition of GPM allows the decoupling of the Calvin cycle and the Energy cycle. This situation facilitates the obtaining of solutions respecting our conditions. In this case we have chosen the following solution (see the Part webpage, describing a sgRNA targeting the gpm gene in Streptomyces).

It is interesting to note that with this solution, the carbon fixation cycle is working at "one tenth" the speed of the base energy metabolism.

To ensure the validity of this new solution, we went ahead and performed some simulations.

Figure 16: Simulation of the base metabolism including the Calvin cycle and gpm inactivation in Streptomyces ambofaciens, ≈1200 points, base quantities of all metabolites: 1 mol, using custom software solutions.

First of all, as expected, we found the trends of the natural metabolism simulation. Indeed, the levels of biomass, ATP, FADH₂ and NADH, H⁺ increase with time (Figure 16). This result is very interesting because it shows a sustainable metabolism induced by RuBisCO and PRK insertion and gpm inhibition. Nevertheless, according to our simulation, the metabolism seems to be less viable than the natural one. In fact, the amount of ATP increases less quickly. Though it would be reasonable to think that the excess of FADH₂ and NADH, H⁺ could counterbalance the lack of ATP in this situation, as both of these molecules can be converted to ATP (does not happen in this simulation).

Figure 17: Simulation of the base metabolism including Calvin cycle and gpm inactivation in Streptomyces ambofaciens, ≈1200 points, base quantities of all metabolites: 1 mol, using custom software solutions, adjusted for mass action law.

When looking at simulations adjusted for mass action law, results were less encouraging (Figure 17). The system proved to be unstable in the long run though we must note that it functioned longer than the system with active gpm. It still seems like GPM inhibition greatly increases the stability.

Next, we also looked at uniformly sampled initial concentration, just like our initial base metabolism simulations. With unadjusted (for mass action law) conditions we found only stable systems.

Figure 18: Simulation of the base metabolism including the Calvin cycle, the inactivation of gpm gene and the conversion of excess FADH₂ and NADH, H⁺ into ATP in Streptomyces ambofaciens, ≈1200 points, base quantities of all metabolites uniformly sampled on [0, 1], using custom software solutions, adjusted for mass action law.

Our last simulation (Figure 18) involves the conversion of excess of NADH, H⁺ and FADH₂ into ATP. With this new condition a stable system is found at the beginning, just like the last simulation (Figure 17). However, in contrast to the previous one, the system stays stable, which seems to support our assumption.

Conclusion

Using the deterministic FBA (flux balance analysis) model, we examined the metabolism of S. ambofaciens to investigate the possibility of creating a hemiautotrophic organism after introducing PRK and RuBisCO.

Indeed, by introducing these two enzymes in the metabolism of Streptomyces, we endowed it with every reaction needed for carbon fixation from CO₂. The next step was to verify if this modification did not stir up trouble in the entire system, making it less efficient or even nonfunctional.

Our model showed that, first, the introduction of PRK and RuBisCO alone are not enough to obtain a sustainable metabolism: the new system is less stable than the initial one, as an important part of biomass is shunted towards the TCA cycle.

Secondly, we have shown that gpm has a key role in this biomass repartition, and that an inactivation of its activity pushes the system towards stability, by stopping the shunt of biomass to the energy module.

We finally achieved a durable stable state of the system (with inhibited gpm), with applied law of mass-action, by allowing conversion of excess energy metabolites into ATP.

Thanks to our simulation we found that in order to achieve our project we must introduce PRK, RuBisCO, and will also need to explore gpm inhibition.