Difference between revisions of "Team:Virginia/Model"

Flux Balance Analysis

Recent advances in computational biology led to emergence of databases with whole-genome metabolic networks, which for simplicity we will call models. They describe the flow of metabolites within a particular organism. Applying constraint-based methods (see this figure) to a particular model allows one to make quantitative predictions about cell phenotype while eliminating many complex parameters. Of particular interest to our project is flux balance analysis (FBA)^[1], which allows us to predict optimal steady-state biomass yield, which is tightly correlated with cell growth rate and is the most likely observed phenotype^[1,2]. One major advantage of FBA is that it does not require knowledge of enzymatic parameters. This figure^[3] elucidates the mathematics of FBA.

One of the primary questions for the project is the following. Will the synthetic P. denitrificans strain containing the device grow better than a wild type strain in the presence of ammonia? It is important to know the answer to this question because the To answer this question, we performed comparative analysis of the two Paracoccus strains using FBA on the corresponding whole-genome metabolic model. The analysis pipeline involved a slew of open-source computational tools, which we will describe below.

First, we reconstructed a metabolic model of Paracoccus denitrificans strain DSM 413 on a complete medium using ModelSEED^[4]. A complete medium is such that any nutrient, including ammonia, is available for uptake. Thus, the set of reactions included in the model is the largest of all possible sets. Although the largest, this set is incomplete because certain essential reactions that result in cell growth may be missing. In the next step, the model is gapfilled with the reactions necessary for measurable cell growth.

To quantify the difference between wild-type and synthetic strains, we must include several new reactions, metabolites and genes (e.g. oxygenation of ammonia by the AMO enzyme complex) into the model generated by ModelSEED. Such functionality is not available in ModelSEED. To implement this, we turned to COBRApy: Constraint-Based Reconstruction and Analysis^[5] package written in Python. However, COBRApy does not natively work with ModelSEED models. To overcome this compatibility issue, we used Mackinac package^[6] to convert the ModelSEED model into COBRApy-compatible format. Using COBRApy, we then added the new reactions into the model and performed FBA to compare the biomass yields, and hence the growth rates, of the two Paracoccus strains. The script is available here.

First, the FBA was run on the gapfilled unmodified (wild-type) model, which initially contained 1550 reactions and 1556 metabolites. The optimal biomass yield was found to be \( 224.3248 (\text{g dry weight}\cdot\text{h})^{-1} \). Next, we added the nitrification reactions, whose list is given below. \(\ce{Q}\) and \(\ce{QH_2}\) represent ubiquinone and ubiquinol, respectively. \( \text{UqO} \) is the ubiquinone oxidoreductase enzyme which catalyzes the last reaction, and is already present in the proteome of P. denitrificans. \[ \ce{NH_3 + QH_2 + O_2 ->[\text{AMO}] H_2O + Q + NH_2OH} \] \[ \ce{NH_3 + NAD + H_2O ->[\text{AMO}] 2H^+ + NADH + NH_2OH} \] \[ \ce{NH_2OH + O_2 ->[\text{HAO}] NO_2^- + H^+ + H_2O} \] \[ \ce{NH_2OH + 2Q + H_2O ->[\text{HAO}] NO_2^- + 2QH_2} \] \[ \ce{QH_2 ->[\text{UqO}] 2H^+ + Q} \] With the new model containing 1555 reactions and 1559 metabolites (with metabolites hydroxylamine, Q and QH2 added), the optimal biomass yield of the modified model was found to be \( \boxed{228.6980~(\text{g dry weight}\cdot\text{h})^{-1}} \).

Exchange Fluxes and Flux Variability Analysis

To gain a deeper understanding of how inclusion of new genes affects the metabolism of the cell, it is important to consider the difference in exchange fluxes between the wild type and synthetic strain. Exchange fluxes determine the intake and expulsion of certain extracellular metabolites, such as glucose, H⁺, or certain dipeptides. The set of exchange reactions also determines the composition of the growth medium. The set of fluxes that gives rise to the optimal biomass, however, is not unique. This includes exchange fluxes. The system of stoichiometric equations for FBA is usually underdetermined, which means that there are actually infinitely many solutions to the problem, all of which are optimal up to certain degree of significance. In other words, to investigate the significance of all exchange fluxes with respect to the optimum, we need to move away from analyzing specific numbers determined by FBA and instead consider ranges, or variations of fluxes that allow for the optimal solution.

To obtain the allowed range of fluxes, we employ a technique called Flux Variability Analysis (FVA). The main parameter of FVA is the so called fraction of optimum, which specifies the allowed deviation from the optimal biomass. In essence, during FVA we perturb each specified exchange flux in both directions under the constraint that the solution must within the fraction of optimum, thereby obtaining the allowed lower and upper bounds on the flux. If the fraction equals 1 (i.e. no deviation from the optimal biomass yield is allowed, in contrast to 0.95, which corresponds to 95% of the optimum), then any fluxes within the obtained range will reproduce the optimal solution. COBRApy package contains a module of functions which performs FVA on an existing model (see script for details).

From the data obtained during FVA, one can see that the addition of nitrification circuit does, in fact, enhance the metabolism of the entire cell. However, the data are insufficient to determine how exactly the additional reactions and metabolites allow for such improvement.

Nitrite Exchange Knock-out and New Project Directions

To visualize metabolic pathways in our model, we used escher. Bla

Results, Summary and Discussion

Analysis of the data obtained from FBA revealed that the biomass yield of the P. denitrificans strain containing our device is greater than the wild-type yield by nearly 2%, which means that our bacterium will use the inserted nitrification pathway in order to enhance its metabolism. As such, our device potentially confers fitness advantage. We predict that our synthetic strain will out-compete the native wild-type strain if both strains are growing in the same environment, including sewage sludge. If our device is used in wastewater treatment facilities, we predict that there will be no need to artificially sustain the new culture.

As was stated earlier, the expected cell phenotype is the one with the largest biomass yield. This is only true under the assumption that the cell lives in an ideal or near-ideal environment with no over-population. Several studies have shown that under different growth environments or culture densities, cells can exhibit non-optimal yield metabolism^[7,8], which means that pathways different from those obtained through FBA will be employed by the cell. We do not know whether wastewater causes a similar shift in metabolism of Paracoccus denitrificans. However, seeing as it is able to thrive in such environment gives enough reason to believe that the growth rate will not lose correlation with the biomass. Furthermore, it should be noted that this model is oblivious to protein structure and kinetics, and as such is unable to capture the full scale of effects caused by inserting the above genes into the model.

In this section, we describe a simplistic kinetic model of bioreactors which are able to perform both nitrification and denitrification. In particular, sequential batch reactors and bioreactors containing our synthetic strain of P. denitrificans are described by the model. Literature search led to discovery of a denitrification model called Activated Sludge Model with Indirect Coupling of Electrons (ASM-ICE), proposed by Pan et al. in 2013. Mathematica notebook is available here.

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