If we were to experiment with other parameters, we would also observe similar feats to the aforementioned. For instance, we may choose to use our model to predict the effects of enzyme engineering of phaA or bktB. This be in the form of modification of the turnover number or the enzyme’s catalytic capacity (k_cat) or of its specificity to each of its substrates. For example, it may be possible to engineer the binding pocket of the enzyme to be less conducive for acetyl-CoA thus accentuating the preference for propionyl-CoA substrate.

Unfortunately, with the current model testing the various Michaelis constants (K_m) is not possible. This is due to how the reactions producing PHB and PHV are parallel to each other (as commented on above). Thus, we decided to test a wide range of turnover rates for phaA and bktB. One of the main observations that resonates with previous simulations. The maximal predicted molar composition of PHV is shown to also be approximately 30%; the composition remains the same while the total PHBV produced increases as long as the reagents are not limiting.

Testing the dynamic model reveals its severe limitations when it does encompass the various relevant pathways for PHA biosynthesis. To optimize it would require a significant array of data. One of the main caveats in using this type of model to understand cell factory design is that it is does not account for cell growth. We represent the mixture of enzymes as a single-compartment, homogeneous system and thus cannot use it to predict growth phenotypes. For this latter purpose, it was decided to use a constraint-based modeling approach.

References 

• Moreno-Sánchez, R., Saavedra, E., Rodríguez-Enríquez, S. and Olín-Sandoval, V. 2008. Metabolic Control Analysis: A Tool for Designing Strategies to Manipulate Metabolic Pathways. Journal of Biomedicine and Biotechnology, 2008, pp.1-30.
• Srirangan, K., Liu, X., Tran, T., Charles, T., Moo-Young, M. and Chou, C. 2016. Engineering of Escherichia coli for direct and modulated biosynthesis of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) copolymer using unrelated carbon sources. Scientific Reports, 6(1).
• Gonzalez-Garcia, R., McCubbin, T., Wille, A., Plan, M., Nielsen, L. and Marcellin, E. 2017. Awakening sleeping beauty: production of propionic acid in Escherichia coli through the sbm operon requires the activity of a methylmalonyl-CoA epimerase. Microbial Cell Factories, 16(1).
• Horng, Y., Chien, C., Huang, C., Wei, Y., Chen, S., Lan, J. and Soo, P. (2013). Biosynthesis of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) with co-expressed propionate permease (prpP), beta-ketothiolase B (bktB), and propionate-CoA synthase (prpE) in Escherichia coli. Biochemical Engineering Journal, 78, pp.73-79.
• Hiroe, A., Tsuge, K., Nomura, C.T., Itaya, M. and Tsuge, T., 2012. Rearrangement of gene order in the phaCAB operon leads to effective production of ultra-high-molecular-weight poly [(R)-3-hydroxybutyrate] in genetically engineered Escherichia coli. Applied and environmental microbiology, pp.AEM-07715.
• Imperial, S. and Centelles, J. 2014. Enzyme Kinetic Equations of Irreversible and Reversible Reactions in Metabolism. Journal of Biosciences and Medicines, 02(04), pp.24-29.
• Cornish-Bowden, A. 1993. Enzyme specificity in reactions of more than one co-substrate. Biochemical Journal, 291(1), pp.323.2-324.
• Anjum, A., Zuber, M., Zia, K., Noreen, A., Anjum, M. and Tabasum, S. 2016. Microbial production of polyhydroxyalkanoates (PHAs) and its copolymers: A review of recent advancements. International Journal of Biological Macromolecules, 89, pp.161-174.

Constraint-based modeling of E. coli  metabolic network with added PHA pathway

Overview 

Methods based on constraint-based reconstruction and analysis (COBRA) stem from a set of fundamental concepts: the designation of physicochemical constraints on reaction networks, a mathematically-derived representation of cell objectives (e.g. growth and maintenance) and a genome-wide scope of metabolism (Lewis, Nagarajan and Palsson, 2012). Constraints in biochemical networks serve to generate accurate representation of the system. The main constraining factors are: substrate and enzyme availability, mass and charge balances and thermodynamics. Two critical assumptions of this type of model is that mass and energy are conserved and that the system is in steady-state (i.e. there is no internal accumulation of metabolites).

The constraints of a network are represented mathematically by a matrix delineated by coefficients representing the stoichiometries of metabolites in each reaction. For example, a coefficient of -1 indicates one molecule of the reactant is consumed in the corresponding reaction, a coefficient of 1 conversely signifies the production of one molecule and a coefficient of 0 indicates a metabolite that does not participate in the reaction. This along with constraints regarding the maximal and minimal fluxes of reactions demarcate a solution space of feasible distributions that satisfy the designated constraints, representing possible states of the microbial network.

We further define the reconstructed model with a statement of the cell or microorganism's objectives: in most cases, that would be the urge to grow as much as possible! There have been other disputed goals that the cell may wish to achieve such as the minimization of energy use (i.e. ATP storage). These objective functions are added onto the GEM to refine the possible states that are attained by the cell in the context of the goal (García Sánchez and Torres Sáez, 2014). For example, a biomass function (Feist and Palsson, 2010), a pseudo-reaction constructed to describe the rate and proportion at which precursors for biosynthesis of crucial components (e.g. amino acids) are made, can be used to predict the specific growth rate of the cell. These functions can then be maximized or minimized using optimization (e.g. linear programming).

Linear programming is a mathematical optimization method used to find the maximum or minimum of a mathematical model wherein the requirements are defined by linear relationships. The main algorithm that employs this technique - and is a staple in GEM analysis - is the flux balance analysis (FBA). In FBA, the objective function and environmental constraints (e.g. different carbon sources, available oxygen levels, etc.) are defined and the system is solved using linear programming (Orth, Thiele and Palsson, 2010). With FBA being the most basic form of analysis, there may be more than one optimal solution; these are often accounted for through more sophisticated techniques that employ mixed-integer linear programming (e.g. flux variability analysis, FVA) or even quadratic programming (e.g. minimization of metabolic adjustment, MOMA).

Aims 

Using the constraint-based model, we can delve into questions concerning the holistic behavior of the microbial cell factory, especially facets such as growth and overall productivity. We may look into how the addition of new and more sustainable substrate sources, may impact the cell growth and PHA yield. We maybe able to identify a maximal yield without compromising growth. Additionally, using the COBRA Toolbox, we can also simulate the metabolic network in cases of overexpression or knockout of certain pathway enzymes such succinyl-CoA synthase (sucCD) and investigate it would have predicted effects on product yield in our strain of E. coli.

The Model 

For the constraint-based modeling of growth and PHA biosynthesis in our recombinant strain of E. coli , we derived our GEM from iJO1366, the most comprehensive GEM of E. coli   K-12 to date (Orth et al., 2011), and added onto it the heterologous pathway for PHA biosynthesis encoded by the pha operon.

To carry out these operations computationally, we used the COBRA Toolbox (Schellenberger et al., 2011) created by the lab of Bernhard Ørn Palsson at University of San Diego. Built for the MATLAB suite, the toolbox can be used to implement FBA as well as a plethora of other powerful (and awesome) functions. Using the toolbox, we added in the biochemical pathway for PHBV biosynthesis to develop the basis for projections into how we may optimize PHBV production in the E. coli  chassis.

Using the COBRA Toolbox to reconstruct and analyze a genome-scale model



To learn more about the COBRA Toolbox developed by the Palsson Group, please click here!

Results and Discussion 

To first investigate how to best optimize the growth of E. coli as a biological host for PHA production, uptake of different carbon sources into the iJO1366 GEM were compared in silico using the COBRA toolbox. In order to best characterize the growth phenotype (denoted by setting the biomass function as the objective in FBA) associated with uptake of the carbon source, separate simulations were operated per single source. This was carried out by setting the uptake of the carbon source of interest to -20 mmol/gDW-h (note the negative coefficient represents an influx of material into the system) while holding associated uptake rates of all other carbon sources at zero. The predicted specific growth rates were highest when grown on glucose or fructose. Based on the model, the PHB biosynthesis rates were proportional to the specific growth rates; thus, only the former is shown below.

The main proposed sustainable source of carbon is pot ale, by-products obtained locally from distilleries. The three main components that pot ale comprises are, from highest to lowest in abundance, acetic acid, lactic acid and propionic acid (Graham et al., 2012). Each component was tested independently (as their conjugate bases) at the aforementioned -20 mmol/gDW-h uptake rate; the results from the FBA showed that at equimolar amounts, propionate yielded the relative highest growth rate followed subsequently by lactate and acetate.

The results of pot ale utilization were initially dubious, which showed that the overall growth rate would be higher than with glucose. We deduced that the apparent outlier was due to the fact that pot ale was represented in the simulation by setting the uptake rates of each individual component (lactate, acetate and propionate) to -20 mmol/gDW-h. We then sought to normalize and weight the relative abundance of each compound in the pot ale. Using data on the relative composition of the by-product, the relative abundance of acetic acid, lactic acid and propionic acid were used as “weights” to compute the relative uptakes of the individual components, normalizing for the amount of material taken into the system per unit of pot ale.

In silico predictions of PHB production rate with various substrates



To affirm our predictions, we compiled experimental data on the growth of our strain in two conditions: a 3% glucose + M9 media vs. a 1% glucose + M9 media + pot ale. The pot ale was provided kindly by the local Glenkinchie distillery in Edinburgh, UK.

Unfortunately, the time points along the growth curve due to the fact that the experiments were done several weeks apart and that our schedule did not permit as consistent collection of data. Thus, we may not be able to observe the various phases of microbial growth from the data. However, we may be able to note the maximal growth of the culture in the various media.

From what is shown, it is evident that glucose is the more significant contributor to biomass and growth as was predicted by the model. The conditions wherein M9 was supplemented with 1% glucose and pot ale showed that pot ale was not entirely conducive to growth. This should be verified with a control where the culture was grown only on pot ale. This experiment was initially carried out but terminated due to difficulties.

Growth curve on pot ale vs. glucose in M9 media



Taking a step further, we sought to predict the production rates of the co-polymer PHBV from various substrates. As was reflected in the above data, PHBV production rates among the lowest when the culture was grown on acetate/propionate and pot ale media. However, supplementation of the pot ale with glucose showed a significant increase in the rate of PHBV production, which matches what the data we collected demonstrated.

A study by Bhatia et al. looked into the effect of supplementation by succinate and glycerol. In their conclusion, they purported that glycerol was a strong contributing factor to expanded capacity for biomass growth, while propionate in the presence of succinate influenced the PHV content of the copolymer. However, these observations applied to a strain wherein the gene sucCD encoding succinyl-CoA synthase was overexpressed. We would like to test whether this may be expected in a strain without the over expression profile.

In silico predicted rates of PHBV production with various substrate combinations



We observed an increased production rate of PHBV when acetate and propionate was supplemented with glycerol instead of glucose; however, the projected rate did not increase when pot ale was the main substrate. Furthermore, when succinate was the main substrate with supplementation by glucose, the projected rate of synthesis was the highest. We speculate that this may be because glycerol and succinate may have roles in restoring the redox potential in the metabolism of the organism.

First, glycerol is known as a better carbon source for making reducing chemicals as its catabolism can restore the reducing equivalents in the cell. Also, succinate’s conversion to fumarate by succinate dehydrogenase is also a main contributor to restoring available NADH. From this, we surmise that redox may become a main bottleneck in PHA biosynthesis as phaB reductase enzyme will heavily depend on these conditions.

Additionally, overexpression of enzymes such as succinyl-CoA synthase may not favor PHA biosynthesis. Because PHA production does not favor the survival of the cell, it may prioritize other pathways to ensure maximal growth. Thus, the overexpression of the enzyme may in fact have the reverse effect as the reaction is reversible. Originally, increase in the enzyme activity was attempted using the COBRA Toolbox but showed no apparent differences from a native WT scenario. Thus, we decided to observe what changes would occur were the enzyme to be grossly deleted (representing a gene knockout).

In silico flux distribution of E. coli metabolism under sucCD deletion



Mapping out the redistributed flux showed that in order to promote growth, the cell would attempt to channel material through the glyoxylate cycle instead of the now incomplete TCA cycle. Of course, this would not be favorable as it would compromise on the production of GTP for energy. We were quite surprised to note that the reduction in the growth rate was less than 1%.

However, this turned out not to be the case when we grew various strains overexpressing sucAB (SC2) and sucCD (SC3). In fact, the growth of the strains were compromised when the TCA enzymes were overexpressed (seen in the plot). With the presented data, we cannot yet discern between whether or not this impeded growth is due to the increased activity of the enzymes or the metabolic burden introduced by the plasmid. To investigate further, we should also test the capacity of the various strains to utilize propionate or the ability to synthesize higher titers of PHBV.

Growth of E. coli with various overexpression profiles (sucABCD)



References

• Lewis, N., Nagarajan, H. and Palsson, B. 2012. Constraining the metabolic genotype–phenotype relationship using a phylogeny of in silico methods. Nature Reviews Microbiology, 10(4), pp.291-305.
• García Sánchez, C. and Torres Sáez, R. 2014. Comparison and analysis of objective functions in flux balance analysis. Biotechnology Progress, 30(5), pp.985-991.
• Feist, A. and Palsson, B. 2010. The biomass objective function. Current Opinion in Microbiology, 13(3), pp.344-349.
• Orth, J., Thiele, I. and Palsson, B. 2010. What is flux balance analysis?. Nature Biotechnology, 28(3), pp.245-248.
• Orth, J., Conrad, T., Na, J., Lerman, J., Nam, H., Feist, A. and Palsson, B. 2011. A comprehensive genome-scale reconstruction of Escherichia coli metabolism--2011. Molecular Systems Biology, 7(1), pp.535-535.
• Schellenberger, J., Que, R., Fleming, R., Thiele, I., Orth, J., Feist, A., Zielinski, D., Bordbar, A., Lewis, N., Rahmanian, S., Kang, J., Hyduke, D. and Palsson, B. 2011. Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2.0. Nature Protocols, 6(9), pp.1290-1307.
• Bhatia, S., Yi, D., Kim, H., Jeon, J., Kim, Y., Sathiyanarayanan, G., Seo, H., Lee, J., Kim, J., Park, K., Brigham, C. and Yang, Y. 2015. Overexpression of succinyl-CoA synthase for poly (3-hydroxybutyrate-co-3-hydroxyvalerate) production in engineered Escherichia coli BL21(DE3). Journal of Applied Microbiology, 119(3), pp.724-735.