Our Model
In the math modeling subteam, we performed flux balance analysis to explore the interaction between core processes of bacterial metabolism and the degradation of PCBs that represent the central focus of our team’s work this year.
Flux Balance Analysis
Flux balance analysis (FBA) is a mathematical method for simulating metabolism in genome-scale reconstructions of metabolic networks. Simulations performed using FBA are computationally inexpensive and can calculate steady-state metabolic fluxes for large models (over 2000 reactions) in a few seconds on modern personal computers. FBA finds applications in bioprocess engineering to systematically identify modifications to the metabolic networks of microbes used in fermentation processes that improve product yields of industrially important chemicals such as ethanol and succinic acid. In our case, we aimed to apply flux balance analysis to understand the interplay between the core metabolic processes required to enable bacterial growth, as in a bioreactor, and the cellular processes involved in the degradation of polychlorinated biphenyls (PCBs), a toxin which is commonly found in water systems. Our long-term vision is to design a bioreactor containing bacteria which have been engineered to break down PCBs. In our math modeling subteam, we focused on applying flux balance analysis to understand the properties of the bacterial metabolic system which must be optimized in order to efficiently engineer bacteria to perform this task.
| pcb7_dechlorination | pcb6_dechlorination | pcb5_dechlorination | SK_pcb4_c | |
|---|---|---|---|---|
| pcb_7c | -1.0 | 0.0 | 0.0 | 0.0 |
| pcb_6c | 1.0 | -1.0 | 0.0 | 0.0 |
| pcb_5c> | 0.0 | 1.0 | -1.0 | 0.0 |
| pcb_4c> | 0.0 | 0.0 | 1.0 | -1.0 |
| atp_c> | 0.0 | 0.0 | 0.0 | 0.0 |
| adp_c> | 0.0 | 0.0 | 0.0 | 0.0 |
| Lower bound: | 0.0 | 0.0 | 0.0 | 0.0 |
| Upper bound: | 1000.0 | 1000.0 | 1000.0 | 2.0 |
Reaction Pathways
To perform flux balance analysis, we first decided to work with E. coli, a bacteria whose metabolic reconstruction has been thoroughly studied, making it a strong candidate for performing flux balance analysis. We used the core metabolic model of E. coli included in the CobraPy software [1], which contains a total of 95 reactions defined over 72 metabolites, catalyzed by enzymes encoded by a total of 137 different genes. Flux balance analysis enables us to simultaneously look across this expansive metabolic network to ensure that the flow of metabolites through our bioreactor is able to support these core metabolic processes even in our engineered bacterial system.
The novel focus of our team’s iGEM project was the focus on degrading PCBs, which relies on a family of PCB dechlorinases encoded by the genes pcbA1, pcbA4, and pcbA5.
Our FBA modeled the enzymatic activity of pcbA1, pcbA4, and pcbA5 in terms of metabolite flow through a series of reactions, focusing on the preservation of mass balance rather than attempting to model the specific enzyme kinetics of the system. This approach enables us to optimize our model as much as possible and still keep it simple, and not relying on an extensive set of parameter estimates which may be challenging to measure.
Implementation Details
In order to perform flux balance analysis, we used the software CobraPy. In order to appropriately model prokaryotic metabolism we focused on the bacterium E. coli, whose metabolic reconstruction has been thoroughly studied. In addition to the 95 reactions encompassed in the core metabolic model, we sought to summarize the equations above in the following three equations. We simplify our problem by choosing not to specify the position of the chloride group, instead focusing on the total number of chlorides in the molecule. Even though chlorine removal from different positions is performed by different enzymes, flux balance analysis enables flexible incorporation of gene requirements using Boolean expressions, so this simplification was made possible simply by joining the enzymes used in the distinct reactions with an “OR”. We decided to optimize both flux through these PCB dechlorination reactions as well as flux through a ‘growth’ reaction designed to simulate the metabolic reactions which support bacterial growth. We assumed constant inflow of PCBs to the system (as would be feasible in an open bioreactor system), with a cap on the uptake of (chlorinated) PCBs into our bacteria of 2 mmol per gDW (gram dry weight) per hour. This estimate was based on previous work describing glucose uptake in E. coli. In addition to the optimization of these two objectives (bacterial growth and PCB degradation) separately, we explored joint optimization in a third model.
Results
An example of flux balance analysis output generated by our model is shown below. We found that since the genes and metabolites that we used for these reactions do not intersect with those involved in the core metabolic model of E. coli, optimization of our two objectives was performed independently, implying that bacterial growth will not be impeded by our incorporation of the dechlorinase enzymes in our bacterial system. Instead, in the presence of constant PCB inflow, PCB degradation is limited by the rate of uptake in the system. And bacterial growth, optimized in the first model, is optimized the same whether these dechlorinase enzymes are included in the system or not.
Future Considerations
There are several potential improvements that could be made to this analysis. Most importantly, our finding that optimization of growth rate and optimization of PCB breakdown are entirely independent is a direct consequence of the fact that the core metabolic model useddoes not contain overlapping metabolites with reactions used to model PCB degradataion. However, we believe that further research on the influence of the byproducts of PCB breakdown, such as hydrochloric acid, on E. coli metabolism would be likely to suggest an interdependence between these two pathways. Specifically, that production of hydrochloric acid would slow E. coli growth substantially. Additionally, further work could be done to explore the validity of our assumption of constant inflow and our estimate that the rate of PCB uptake would have an upper limit of 2 mmol per gDW per hour.
References
[1] Documentation for COBRApy. Documentation for COBRApy - cobra 0.25.0 documentation. (n.d.). Retrieved October 13, 2022, from https://cobrapy.readthedocs.io/en/latest/index.html
[2] Bedard, D. L. (2014). PCB dechlorinases revealed at last. Proceedings of the National Academy of Sciences, 111(33), 11919–11920. https://doi.org/10.1073/pnas.1412286111