Model

Our efforts to model our organsisms' metabolic networks

Genome-scale modelling of cyanobacterial electron transfer via flux balance analysis

Background

For our goal of developing a solar panel powered by living organisms, improving cell's conductivity is the key step of our project. Our solution is the heterologous expression of the Mtr pathway from Shewanella oneidensis MR-1 in cyanobacteria. The Mtr pathway, particularly the MtrCAB complex including MtrA, MtrB and MtrC proteins, has been shown to facilitate efficient extracellular electron transfer (EET) in Shewanella (Bretschger et al., 2007). In addition to the MtrCAB complex, another crucial component of the Mtr pathway is the CymA protein. CymA is a tetraheme c-type cytochrome located in the inner membrane, functioning as an electron transporter, and transferring electrons from the quinone pool in the inner membrane to the Mtr pathway components, thereby greatly facilitating the electron flow towards the extracellular environment (Marritt et al., 2012). Figure 1 provides a visual representation of the electron transport mechanism in Shewanella.

Figure 1. An illustration of the electron transport system in Shewanella, which exports electrons from cytoplasm to extracellular space. Taken and adapted from Jensen et al., 2010.

Considering the inherent challenges associated with bioengineering experiments, we intend to computationally model the cyanobacteria's electron transport system to better guide the wet lab experiment design for enhanced electron transport capabilities.

Genome-scale model and flux balance analysis

Genome-scale models (GSMs) have emerged as a comprehensive tool to encapsulate the metabolic and regulatory intricacies of microorganisms. It provides a detailed map of its metabolic pathways, along with its electron transport chain (ETC), biomass production and nutrients exchange with external environment. The biomass production is a pseudo reaction represented by all the essentials for cell’s growth (Feist and Palsson, 2010). Figure 2 shows an example of a genome-scale reconstruction of cyanobacteria.

Figure 2. An example metabolic map of cyanobacteria, including ETC reactions (bottom left), biomass production and nutrients' exchange reactions (top left). Taken from Knoop et al., 2013.

To analyse the metabolic capabilities of organisms represented by GSMs or validate the correctness of GSMs, Flux Balance Analysis (FBA) is a widely used computational method. It is a constraint-based optimization approach that predicts the steady-state flux distribution of metabolic reactions in a given network (Orth et al., 2010). The numbers next to the arrows in Figure 2. indicates the fluxes of the corresponding reactions in the unit of millimole per gram dry weight per hour (mmol/gDW/h), obtained by FBA when optimizing a pre-defined objective reaction. Mathematically, FBA involves the formulation of a linear programming problem where the objective is to maximize (or minimize) a particular metabolic flux, such as biomass production, subject to stoichiometric and capacity constraints. The constraints ensure that the predicted fluxes adhere to the laws of mass conservation and are within biologically feasible limits. The mathematical representation of FBA is shown below.

Mathematical representation of Flux Balance Analysis (FBA). The objective function is denoted as Z = cT * v. Here, cT is the transpose of the coefficient vector, which has a length equal to the total number of reactions. As it typically represents biomass or a single desired metabolic product, this coefficient vector is sparse, with a value of 1 at the position corresponding to the target reaction and 0 elsewhere. v is the vector of reaction fluxes. The equation S * v = 0 ensures steady-state mass balance, where S is the stoichiometric matrix encompassing the entire metabolic network. The inequalities l ≤ v ≤ u impose lower (l) and upper (u) bounds on the fluxes, accounting for constraints such as enzyme capacities or nutrient availability.

We aimed to adapt the most advanced GSM of cyanobacteria for Mtr bio-engineered strains and simulate electron generation in both wild-type and Mtr bio-engineered strains. By comparing the electron generation under different restrictions of certain exchange reactions, we could identify the optimal and most important chemical requirements to maximize electron export to the extracellular space for Mtr engineered strains using FBA.

Methodology

Materials

We used the most recent and advanced Synechocystis model iSynCJ816, containing 932 metabolites and 1047 reactions. For model processing, FBA, and subsequent analyses, the COBRA Toobox v3.0 for Matlab and COBRApy for the Python programming language are employed. The model’s parameters are upper and lower bounds of all the contained reactions, which are kept in default in following analyses if not specified.


Representation of exported electrons in wildtype

Electrons exported out of the cell are typically accepted by external electron acceptors. This electron transfer can be represented using iron (Fe) as a proxy for the electron, given its involvement in redox reactions. While various metals can act as electron carriers, for the simplification of this model, we assume iron to be the primary electron carrier due to its prevalent role in electron export processes. In the wildtype Synechocystis, the electron transfer can be depicted as the conversion of ferrous iron (Fe2+) to ferric iron (Fe3+) in the extracellular space. Therefore, the following reaction is added to the original GSM: fe2_e --> fe3_e, where the “_e” denotes extracellular metabolites. The flux of this reaction is then used to represent the amount of exported electron in wildtype.


Representation of exported electrons in Mtr-engineered strains

With the expression of CymA and MtrCAB in cyanobacteria, electrons undergo a series of processes before being exported to the extracellular space. The electron transfer begins with plastoquinone (PQ), subsequently passing through CymA and MtrA proteins, and finally being transferred to MtrC and the external electron acceptor. To capture this process, the following redox reactions were incorporated into the original GSM:

  1. Plastoquinone to CymA (cytosolic membrane): pqh2_y + cyma --> pq_y + cymah2 (CymA acts as quinol dehydrogenase)
  2. CymA reducing MtrA (periplasmic space): cymah2 + mtra --> cyma + mtrah2
  3. MtrA to MtrC (transition from periplasm to outer membrane): mtrah2 + mtrc --> mtra + mtrch2
  4. MtrC to external electron acceptors (extracellular space): mtrch2 --> mtrc

Apart from pqh2_y (plastoquinol) and pq_y (plastoquinone), where “_y” denotes the cytosolic membrane, all the other metabolites were newly added to the model. These can be viewed as pseudo metabolites, representing the redox states of CymA, MtrA and MtrC proteins. All these reactions are added as irreversible, as the Mtr pathway functions to move electrons out of the cell and the process is essentially unidirectional under physiological conditions (Coursolle and Gralnick, 2010). The electron transfer to the external electron acceptor is quantified by the flux of the final reaction, which signifies the oxidation of the MtrC protein.


Simulating exported electrons with FBA

The initial step for FBA in simulating electron export is to maximize biomass production, as the primary objective of cells is growth. We would focus on mixotrophic biomass production which aligns with our experimental conditions where cells can utilize both light and organic carbon sources for growth.

After maximizing biomass growth using FBA, this growth rate is fixed by setting both the upper and lower bounds of the biomass reaction to the FBA solution, while keeping other reactions’ bounds unchanged. Next, the objective function is set to maximize the electron transfer to the extracellular space, as defined above. Since cyanobacteria are photosynthetic organisms, this process was performed under both dark and light conditions separately.


Selection of exchange reactions and Flux Variability Analysis

To identify the most influential chemical requirements affecting electron transfer in Mtr-engineered cyanobacteria, it is beneficial to focus on specific exchange reactions. These reactions represent the interface between the cell and its environment, indicating the uptake and secretion of corresponding chemical compounds. The selection of these exchange reactions is based on their relevance and potential impact on cellular metabolism and electron transfer processes. Therefore, we first chose the following exchange reactions:

  • Photon exchanges: Represents the light uptake, which is fundamental for photosynthetic organisms like cyanobacteria
  • H2O, Oxygen (O2), exchanges: Basic and essential elements for the growth of cyanobacteria
  • Carbon dioxide (CO2), Acetate and Glucose exchanges: Carbon sources
  • Ammonia (NH4) and Nitrate (NO3) exchanges: Nitrogen sources
  • Phosphate exchange: Phosphate is essential for ATP synthesis, a crucial energy molecule that can influence electron transfer processes

Flux Variability Analysis (FVA) is a computational method used to determine the range (both maximum and minimum) of fluxes through metabolic reactions while still satisfying the organism's physiological constraints (O’Brien et al., 2015). It is performed by consecutively setting each reaction as objective and performing FBA to maximize and minimize its flux. For these selected exchange reactions, FVA was performed to ascertain their truly possible upper and lower bounds. This facilitates easier control on those reactions and sets the stage for more detailed studies on their impact on electron transfer.


Importance of exchanges based on random forest regression

Machine learning, particularly regression-based models, can help in understanding the complicate relationships between various metabolic reactions and their impact on cellular objectives. Random forest, a popular ensemble learning method, stands out in this context. It constructs multiple decision trees during training and outputs the classes for classification or mean prediction for regression. One of the advantages of random forest is its ability to rank features based on their importance, which in our case, can help in identifying the most influential exchange reactions on electron transfer.

With the selected exchange reactions, FBA process above was executed multiple times, each time with random variations in the fluxes of these reactions, but always within the bounds established by FVA. This iterative process generated a dataset where the features were the fluxes of the exchange reactions, and the label was the optimized electron flux as defined for Mtr-engineered strains. The dataset was then trained by random forest regression in Scikit-learn package, and the feature importance of interested exchange reactions was obtained.


Sensitivity analysis

Sensitivity analysis is a technique employed to determine how variations in an independent variable influence a specific dependent variable. In the context of metabolic modelling and FBA, sensitivity analysis can help elucidate how changes in the availability of certain nutrients or substrates (represented by the flux of exchange reactions) can influence and optimise cellular objectives, such as growth rate and electron transfer efficiency.

The most influential exchange reactions on electron transfer identified by random forest regression will be taken for a deeper investigation. For each selected exchange reaction, its flux value was systematically varied within its permissible range determined by FVA; At each flux value, FBA process was performed to optimise for the electron flux for Mtr-engineered strains, and then the resulting electron flux and biomass growth were recorded.

Results

Assumptions
  1. Steady-state assumption: The standard FBA operates under steady state, meaning that the concentrations of intracellular metabolites remain constant over time.
  2. Optimal growth conditions: It is assumed that the cyanobacteria are grown under ideal environmental conditions. This includes optimal medium composition, temperature, pH, humidity, etc.
  3. Continuous nutrient supply: It is assumed that the supply of essential nutrients is uninterrupted, ensuring that the cells do not experience nutrient stress or limitation for their normal activity. This is also the pre-requisite for the constant nutrients exchange (uptake) rates and a steady state.
  4. Growth priority: Assuming that cells prioritize growth over other metabolic activities under whatever conditions.
  5. Electron acceptors: While various metals may act as electron acceptors, it is assumed that electrons are primarily transferred to iron (Fe), simplifying the electron transfer process.
  6. Mtr pathway dominance: Upon the incorporation of the Mtr pathway, it is assumed that electrons are no longer exported outside the cell using iron as the primary carrier. This is based on the enhanced efficiency of the Mtr pathway in facilitating electron transfer.
  7. Solubility of metabolites: The model and simulation do not differentiate between soluble and insoluble states of metabolites, assuming that this distinction does not significantly impact the overall metabolic activity and fluxes.
  8. Plasmid overexpression: It is assumed that the genes of interest (those for the Mtr pathway) are overexpressed from plasmids, and that this overexpression is sufficient for the desired metabolic effects (efficient electron transfer). Furthermore, the overexpression does not detrimentally affect other parts of the metabolic network or the overall cellular health.

Simulated electron flux with FBA

FBA was performed after including the representation for electron transport to extracellular space in both wildtype and Mtr-engineered strains GSM. The primary objective was to maximize cellular growth. Once the optimal growth rate was determined, it was fixed as a constraint, and the electron transfer was then maximized under both dark and light conditions. The results of these simulations are summarised in Table 1.

Table 1. Optimal electron flux under dark and light conditions, in wildtype and Mtr-engineered strains, while maximizing the growth. (Unit: mmol/gDW/h)

The FBA results indicate a consistent optimal biomass growth rate for both strains: 0.0645 under dark conditions and 0.1256 under light conditions. It suggests that the integration of the Mtr pathway does not adversely affect the cyanobacteria's inherent growth capabilities. Instead, the light condition is seen as a more dominant factor influencing growth.

While the growth rate essentially doubles with light exposure, the electron transfer in the wildtype strain also precisely doubles under light conditions compared to dark. In contrast , the Mtr-engineered strain exhibits a wide range of electron transfer rates under light, ranging from 0.15 to 87k, largely dependent on the photon uptake rate. Notably, the electron flux in the Mtr-engineered strains is several orders of magnitude higher than in the wildtype, regardless of the lighting conditions. This reflects the efficiency of the Mtr pathway in facilitating electron transfer processes.


Importance of nutrients uptake in Mtr-engineered strains

1000 data points were generated by iteratively assigning random values to each of the selected exchange reactions and subsequently performing FBA to obtain the optimal electron transfer flux. The data set was then trained by random forest regression. This process was executed for both dark and light conditions, and the resulting feature importance is shown in Figure 3.

Figure 3. Feature importance of selected exchange reactions as derived from random forest regression, under dark (A) and light (B) conditions.

Under dark conditions, the exchanges of H2O and oxygen are notably dominant. The other five exchanges also play a role but with relatively less contributions. In contrast, under light conditions, water uptake emerges as the most influential factor, having an impact on extracellular electron transfer nearly three times greater than all the other exchanges.


Sensitivity analysis

Figure 3 shows the prominence of water and oxygen exchanges, and to deeply investigate their influences on electron transfer in the Mtr-engineered strains, a sensitivity analysis was conducted. This involved systematically varying the fluxes of these two exchanges within their feasible bounds from FVA and observing the corresponding changes in the optimal electron transfer rate obtained by FBA. The variations of electron flux and growth in response to varying H2O and oxygen exchange fluxes are shown in Figure 4.

Figure 4. Variations in electron flux and biomass growth as a function of H2O and oxygen exchange rates under dark (A, C) and light conditions (B, D). (Unit: mmol/gDW/h)

For both H2O and O2, the biomass growth exhibits a similar trend: as the exchange rates increase (indicating reduced uptake or even secretion), the growth initially rises to a peak before subsequently declining. In contrast, the extracellular electron transfer displays an inverse relationship. As water exchange rates increase, the electron transfer consistently diminishes until it reaches nearly zero. For oxygen, the electron transfer starts at zero and experiences a sharp increase when the oxygen exchange rate becomes relatively high, even transitioning to oxygen release under light conditions. Additionally, the presence of light postpones the shift points observed in both growth and electron transfer.

The sensitivity analysis provides reliable evidence that water and oxygen play crucial roles in influencing both growth and electron transfer in Mtr-engineered Synechocystis. The opposite trends of electron transfer fluxes for water and oxygen exchanges suggest that optimizing the balance between water and oxygen uptake, under both light and dark conditions, could be a key strategy in enhancing the electron transport efficiency of Mtr-engineered strains.

Conclusion

Through GSM and FBA analysis, it becomes evident that wild-type cyanobacteria have limited capability to export electrons, while Mtr pathway plays the essential role in enhancing this process. The system's electron transfer is particularly sensitive to certain variation of nutrients, with water and oxygen being outstanding in our study. Achieving a balanced control of water and oxygen exchanges can be a direction in optimizing electron export in Mtr-engineered strains.

References

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Coursolle, D. and Gralnick, J.A., 2010. Modularity of the Mtr respiratory pathway of Shewanella oneidensis strain MR‐1. Molecular microbiology, 77(4), pp.995-1008.

Feist, A.M. and Palsson, B.O., 2010. The biomass objective function. Current opinion in microbiology, 13(3), pp.344-349.

Jensen, H.M., Albers, A.E., Malley, K.R., Londer, Y.Y., Cohen, B.E., Helms, B.A., Weigele, P., Groves, J.T. and Ajo-Franklin, C.M., 2010. Engineering of a synthetic electron conduit in living cells. Proceedings of the National Academy of Sciences, 107(45), pp.19213-19218.

Knoop, H., Gründel, M., Zilliges, Y., Lehmann, R., Hoffmann, S., Lockau, W. and Steuer, R., 2013. Flux balance analysis of cyanobacterial metabolism: the metabolic network of Synechocystis sp. PCC 6803. PLoS computational biology, 9(6), p.e1003081.

Marritt, S.J., McMillan, D.G., Shi, L., Fredrickson, J.K., Zachara, J.M., Richardson, D.J., Jeuken, L.J. and Butt, J.N., 2012. The roles of CymA in support of the respiratory flexibility of Shewanella oneidensis MR-1.

O’Brien, E.J., Monk, J.M. and Palsson, B.O., 2015. Using genome-scale models to predict biological capabilities. Cell, 161(5), pp.971-987.

Orth, J.D., Thiele, I. and Palsson, B.Ø., 2010. What is flux balance analysis?. Nature biotechnology, 28(3), pp.245-248.