Overview
In our project, we aim to develop a sustainable and efficient method for biodegrading α-pinene, a natural organic compound with various industrial applications but also high toxicity and resistance to degradation. Α-pinene poses a potential threat to human health and the environment, and we engineered bacteria to convert it into environmentally friendly products, isonovalal. To investigate and optimize the performance of our engineered bacteria, we used two modelling approaches: α-pinene degradation model and growth competition model.
1.α-pinene degradation Model - utilized to simulate the complete biochemical processes occurring in the reaction system, offering theoretical feasibility predictions to our project.
2.Growth competition system - Utilized for simulating the dynamic fluctuations in population size when two bacterial strains involved in degradation reactions coexist, aiming to furnish predictive insights into the survival status of bacteria within the context of our project.
α-pinene degradation Model
We employed SimBiology to construct a model of the α-pinene degradation pathway, which comprising two steps: the conversion of α-pinene to α-pinene oxide by the P450m enzyme and the subsequent conversion of pinene oxide to isonovalal by the Pra-Pol enzyme. Then we introduced plasmids harboring these two enzymes into E. coli strains I and II, respectively. By simulating the model at different time points, we can observe the changes in substrate consumption, intermediate accumulation, and product formation. We can also optimize the reaction conditions and parameter settings to improve the degradation efficiency and product selectivity. Additionally, We utilize SimBiology's plotting functions to visualize the changes of substrate and product concentrations over time, facilitating the observation of variations under different conditions. This provides us with a valuable reference for experimental design and optimization decisions.
Figure 1. Model established by Simbiology
α-Pinene Oxidation
To better degrade α-Pinene, the first step is often to convert it to α-pinene oxide due to the introduction of an epoxide group, which makes the molecule more reactive and amenable to further chemical transformations. The epoxide group in α-pinene oxide can be attacked by nucleophiles or can be opened up by acids or bases, facilitating further degradation into less toxic compounds. This conversion is an essential step in a structured approach to detoxifying α-pinene, making it a more manageable and less hazardous compound to handle in subsequent degradation processes. In order to achieve the above oxidation step, we have the following process in engineering bacteria E. coli.
The core compound of interest, α-Pinene, undergoes oxidation in the presence of the enzyme P450BM-3 QM. This enzymatic action results in the formation of α-Pinene oxide. It also produces by-products trans-verbenol and myrtenol. The production ratio of the three of them is about 5:2:1. But in comparison, this enzyme has the highest conversion of α-Pinene oxide.
$$ alpha-Pinene + NADPH \mathrel{\mathop{\xrightarrow{\text{P450BM-3 QM}}}} alpha-Pinene \ oxide $$ $$+ Myrtenol + trans-Verbenol + NADP^{+} $$
Here NADPH is used as a reducing agent. It is a crucial cofactor used in various biological reactions and primarily serves as an electron donor. To increase the availability of NADPH within the bacteria, glucose is transported into the engineering bacteria through the GLF transporter protein. GLF is the glucose facilitator protein, which plays a role in aiding the uptake of unphosphorylated glucose, which is a part of the recombinant intracellular NADPH regeneration system. Through the co-expression of GLF and NADP-dependent GlcDH (Glucose Dehydrogenase) from Bacillus megaterium, yields in the biocatalytic process, as well as the reaction efficiency, are finally increased.
$$ NADP^{+} + Glucose \overset{GlcDH}{\longrightarrow} Gluconate + NADPH + H^{+} $$
After that, α-Pinene oxide is then diffused into the extracellular environment and further degraded.
In order to expedite the optimization process for the above biotechnological applications, such as testing oxidation efficiency, validating reaction outcomes and comparing with experimental data, especially when dealing with multifaceted enzymatic reactions, computational modelling emerges as an essential tool.
Here, we first used Fick's first law to model the transcellular transportation of glucose and α-Pinene oxide:
$$ J_{Glucose} = -D\frac{dC_{Glucose}}{dx} $$
$$ J_{α-Pinene \ oxide } = -D\frac{dC_{α-Pinene \ oxide }}{dx} $$
J is the diffusion flux
D is the diffusion coefficient or diffusivity
dC/dx is the concentration gradient
Figure 2. The change of concentration of extracellular and engineering bacteria Ⅰ glucose over time during trans-membrane transportation. x- time in seconds, y- concentration in micromoles.
Figure 3. The change of concentration of extracellular, engineering bacteriaⅠand engineering bacteria Ⅱ α-Pinene oxide over time during trans-membrane transportation. x- time in seconds, y- concentration in micromoles.
Next, we employed a double substrate Michaelis-Menten model to understand and predict the behaviour of enzymes. Drawing inspiration from a prior study on melanin production in Saccharomyces cerevisiae, which utilized a double substrate model for efficient screening , we aimed to adopt a similar strategy. Our kinetic parameters Km and Vmax used for modeling are referenced from Basner and Antranikian (5) and Schewe, Kaup and Schrade (2).
$$ V_{NADPH} = \frac{V_{max}C_{NADP^{+}}C_{Glucose}}{(C_{NADP^{+}}+K_{m}^{NADP^{+}})(C_{Glucose} + K_{m}^{Glucose})} $$
$$ V_{α-Pinene \ oxide} = \frac{V_{max}C_{α-Pinene}C_{NADPH}}{(C_{α-Pinene}+K_{m}^{α-Pinene})(C_{NADPH} + K_{m}^{NADPH})} $$
Figure 4. The change of NADPH concentration over time in engineering bacteria Ⅰ. x- time in seconds, y- concentration in micromoles.
Figure 5. The change of α-Pinene oxide, myrtenol, and trans-Verbenol concentration over time in engineering bacteria Ⅰ. x- time in seconds, y- concentration in micromoles.
In summary, through the implementation of our designed model, we succeeded in visualizing the change in substance concentration over time using plots such as glucose, NADPH and α-Pinene oxide. These tools have also achieved accurate simulations and predictions of the oxidation process under study, and validated our understanding of the reactions.
Conversion of Α-Pinene Oxide to Isonovalal
After oxidizing α-pinene, the next step is trying to convert the α-pinene oxide into harmless products. Here, a second system is designed in bacteria to convert the α-pinene oxide into isonovalal, which is a volatile aldehyde that has a pleasant fruity odor and can be used as a flavoring agent or a precursor for other compounds. The lyase enzyme that catalyzes this reaction is called α-pinene oxide lyase (Prα-POL) and has been purified and characterized from Pseudomonas rhodesiae. To fulfill the conversion, there are two different biocatalysts for us to choose from:
1.Pseudomonas rhodesiae PF1, a natural strain that can perform this reaction.
2.Recombinant escherichia coli (Rec E. coli), a recombinant strain that expresses the α-pinene oxide lyase (Prα-POL) enzyme from Pseudomonas rhodesiae.
To understand and optimize the biotransformation process we choose to use, we developed a mathematical model based on the Michaelis-Menten kinetics. The model describes the reaction rate of α-pinene oxide conversion to isonovalal as a function of substrate concentration, enzyme concentration, and kinetic parameters.
Our hypothesis is that the model can help predict the experimental data obtained from our wet lab experiments and help us compare the performance and choose between these the two biocatalysts. We also expect that the model can reveal some insights into the factors that affect the reaction efficiency and selectivity.
To be converted to isonovalal, extracellular α-pinene oxide should enter the bacteria first. Α-pinene oxide is a kind of small molecule that passes through the cell membrane by free diffusion.
According to Fick ’s law, the rate of diffusion depends on the concentration gradient of a-pinene oxide across the membrane, as well as its solubility and permeability in the membrane. The equation is expressed as:
$$ J_{α-Pinene \ oxide } = -D\frac{dC_{α-Pinene \ oxide }}{dx} $$
where J is the flux of a-pinene oxide, D is the diffusion coefficient, (dc/dx) is the concentration gradient.
Then inside the bacteria, α-pinene oxide encounters Prα-POL enzyme that catalyzes its conversion to isonovalal. This conversion of a-pinene oxide by Prα-POL does not involve any intermediate products or cofactors. It is a single-step reaction that does not require any additional molecules.
Figure 6. Reaction of conversion of a-pinene oxide into isonovalal.
According to the Michaelis-Menten equation, the following equations are used to model the reaction rate:
$$v = \frac{V_{max}[ α-pinene oxide]}{K_m + [α-pinene oxide]}$$
$$Vm = kcat*[ Prα-POL]$$
where v is the reaction rate, Vmax is the maximum reaction rate, [S] is the substrate concentration, Km is the Michaelis constant, and [E] is the enzyme concentration.
We used SimBiology library in MATLAB to generate the model. The model parameters were estimated from literature data. The kinetic parameters for P. rhodesiae PF1 were obtained (1) , while those for recombinant E. coli expressing Prα-POL (2). The enzyme concentration was calculated from the biomass concentration and the specific enzyme activity.
Then we used this model to run simulations to compare the reaction rate and select the best strain for the bioconversion of a-pinene oxide to isonovalal.
Figure 7. Comparison of reaction rate and degradation rate of Pseudomonas rhodesiae and rec E. coli for a-pinene oxide to isonovalal conversion. x- time in seconds, y- concentration in micromoles.
The result shows that rec E. coli has a higher reaction rate than Pseudomonas rhodesiae, indicating a higher expression level or activity of Prα-POL in rec E. coli. Since the enzyme activity of Prα-POL is similar in both strains, the expression level may be the main factor contributing to this 40-fold difference of reaction rate.
The simulation suggested that rec E. coli is more efficient than Pseudomonas rhodesiae in converting a-pinene oxide to isonovalal with a relative huge increase in expression level.
Therefore, recombinant escherichia coli is chosen to build the conversion system, which proves to show higher efficiency and stability.
Integral simulation and analysis
In our project, we constructed an α-Pinene degradation pathway using two engineered bacteria. SimBiology was utilized to integrate the above two steps and simulate the entire reaction system. Our model encompasses the degradation reaction of pinene and incorporates a series of reaction equations to elucidate the chemical conversion occurring at various steps. These equations encompass solid transformation, intermediate formation, and final product release. By incorporating reaction rate parameters, substrate concentrations, and other experimental measurements into our model, we successfully simulated several crucial outcomes.
Figure 8. Simulation of reactions in bacteria I. x- time in seconds, y- concentration in micromoles.
Figure 8 shows the products change of reaction A ([α-Pinene] + [NADPH] + [P450BM-3 QM] -> [α-Pinene oxide] + [trans-Verbenol] + Myrtenol + [NADP+] + [P450BM-3 QM]) in engineering bacteriaⅠ. According to the previous finding, the ratio of three products α-Pinene oxide, trans-verbenol and myrtenol is 5:2:1 (2). The ratio of trans-Verbenol and myrtenol can be easily found. However, while α-Pinene oxide is out-diffused and ingested by engineering bacteria II, its concentration in bacteria I increase and subsequently decreases to 0. Interestingly, the concentration of α-Pinene remains around 0. One potential explanation is the high Km in reaction A, which leads to the rapid consumption of α-Pinene.
Figure 9. NADP+ and NADPH changes in bacteria I. x- time in seconds, y- concentration in micromoles.
In Figure 9 the changes in NADP+ and NADPH levels are demonstrated. With the quick response of reaction A, [NADPH] decreases and [NADP+] increases rapidly at the beginning. As the degradation of α-Pinene comes to an end, glycolysis in E. coli can provide enough energy, thus restoring [NADPH] and [NADP+] to their normal level. However, while NADPH and NADP+ are involved in numerous reactions, this simulation may be incomplete.
Figure 10. The oxidation of the pinene to pinene-oxide and its transmission. x- time in seconds, y- concentration in micromoles.
Figure 10. shows the integrated result of engineering bacteria I, α-Pinene in the environment can be degraded efficiently. Meanwhile, the concentration of the immediate product α-Pinene oxide in E. coli I, II and the environment present similar changes that increase at first and then drop to 0. As α-Pinene and its oxide are both toxic substances, the result indicates the effective degradation of all hazardous substances.
Figure 11. The conversion of pinene oxide to isonovalal. x- time in seconds, y- concentration in micromoles.
Figure 11. reflects the reaction in engineering E. coli II. The toxic immediate product α-Pinene oxide is converted to the toxic-free substance isonovalal and free diffuses to the extracellular environment. Taking one with another, engineering bacteria I and II converted α-Pinene to α-Pinene oxide and then isonovalal, realizing the removal of harmful substance α-Pinene. This process coincides with our purpose to ‘develop a sustainable and efficient method for converting pinene into environmentally friendly products.
In summary, Simbiology's modeling and simulation capabilities played a pivotal role in our iGEM project. Through simulating the pinene degradation pathway, we can gain deeper insights into the dynamic behavior of the pathway, assess the efficacy of the model, and predict various operational strategies' outcomes. This establishes a robust theoretical foundation for our project and serves as a guiding framework for further research.
Growth Competition Model
In this section, we are attempting to build a model for two strains of Escherichia coli coexisting in the same reaction vessel. Since the two-step degradation of α-pinene is a consecutive reaction, bacteria occupying the same ecological niche share the same environment. This leads to mutual competition for resources between them, and there is a possibility that one strain of bacteria may be eliminated, resulting in the failure of our product functionality.
Lotka-Volterra competition system is a mathematical model that describes the population dynamics of two species that share the same resource space and compete for limited resources. We used this model to simulate the co-culture of 2 strains of bacteria in the same container, where they constitute a typical competitive system.
Assumptions
In our reaction system, we chose to construct two genetically engineered bacteria. By using a two-step separation reaction, we degraded α-pinene into α-pinene oxide, and subsequently degraded it into isonovalval. The enzymes responsible for these two steps are P450m and Pra-Pol, respectively. We transferred the plasmids containing these two enzymes into E. coli and designated them as strains I and II.
To ensure that the biodegradation reactions occur in the same container, strains I and II will be co-cultured. In this coexistence system, these two bacteria constitute a typical Lotka-Volterra competitive system (3).
The Lotka-Volterra competition system is derived from Logistic equations. The Logistic equation is described as the following:
$$\frac{dN}{dt} = rN\frac{K-N}{K}$$
It represents two populations sharing the same resource space, leading to competition due to limited resource utilization. Strains I and II satisfy this condition. We define the maximum population density (i.e., carrying capacity) that strains I and II can reach in our biphasic system as K1 and K2, respectively. The instantaneous growth rates of each individual in these two populations are represented by r1 and r2.
Method
Therefore, the growth dynamics of these two populations can be expressed using the following differential equations:
$$\frac{dN_{1}}{dt} = rN_{1}(1-\frac{N_{1}+\alpha N_{2}}{K_{1}})$$
$$\frac{dN_{2}}{dt} = rN_{2}(1-\frac{N_{2}+\beta N_{1}}{K_{2}})$$
Where α represents the competition coefficient of strain I against strain II, indicating how much inhibitory effect one strain II bacteria has on its own population compared to one strain I. β represents the competition coefficient of strain I against strain II. The term (1 - N1/K1) can be understood as the available space for one type of bacteria, considering the carrying capacity (K1). However, in a competitive system, it's necessary to account for the space already occupied by the other bacterium. Therefore, an additional term αN2/K1 is included, representing the space occupied by the other bacterium, scaled by the competition coefficient α. This reflects the competition for resources in the shared environment (4).
In our engineered bacteria construction, strain II, in addition to Pra-Pol, was also introduced with two enzymes, Glf and gldch. These enzymes accelerate the glucose uptake efficiency of strain II, promote NADPH production, enhance nutrient uptake, and improve survival resistance. However, strain II faces higher intra-population competition pressure than strain I, and the uptake of α-pinene oxide by strain II, which is produced by strain I, may result in cytotoxicity.
Simulation and data analysis
In our actual experiments, strain II in the co-culture system was not able to express Glf. The α and β value will only be slightly different. Here we assume that α=0.1 and β=0.15.
To determine the values of K (carrying capacity) and r (instantaneous growth rate), we separately cultured each bacterial strain in the same environment and measured their bacterial density over time using absorbance values (4).
According to the conversion relationship between E. coli bacterial concentration and OD600 values from the literature, the relationship between bacterial density and time is as follows:
Figure 12. Standard Curve for the relationship between the OD600 value and Colony forming units of E. coli Upper figure Taken from https://www.zhihu.com/people/a-fu-94-96. The figure below illustrates the OD600 absorbance obtained in our experiment.
To fit and compute the parameters K and r of the model, we utilized the curve_fit function from the scipy.optimize library in Python, which employs a non-linear least-squares optimization method：
Figure 13. The growth curve of separately cultured bacteria constrains I and II and estimated logistic growth
According to single-culture experiments showing above,
| K1 = 6.74*10^7 CFU/ml | K2 = 9.19*10^7 CFU/ml |
| r1 = 1.07*10^7 CFU/(ml*hour) | r2 = 0.88*10^7 CFU/(ml*hour) |
Now, incorporating this into the competition model, we observe that the two bacteria can reach a stable equilibrium.
Figure 14. The curve represents the simulation of population-size growth dynamics of constrain I and II when co-cultured.
However, the assumption of this differential equation is that the influence of a single species can rapidly diffuse into the population. The growth of population shows many discrete characteristics. Further models can be improved using logistic mapping and applying RNN into population size expectation.
Supplementary Material
Figure S1：Parameters in Simbiology Model Builder
References
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2. Schewe H, Kaup BA, Schrader J. Improvement of P450BM-3 whole-cell biocatalysis by integrating heterologous cofactor regeneration combining glucose facilitator and dehydrogenase in E. coli. Appl Microbiol Biotechnol. 2008 Feb;78(1):55–65.
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4. Wang ZA, Xu J. On the Lotka-Volterra competition system with dynamical resources and density-dependent diffusion. J Math Biol. 2021 Jan;82(1–2):7.
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