PHB Modelling

Understanding the rate of production and secretion of PHB


In order for Cellucoat to be a suitable produce packaging material that can stand against traditional material like plastic and its alternatives, it needs to be of comparable strength. However, bacterial cellulose (BC) on its own lacks the strength required to be just that material. Therefore, the incorporation of polyhydroxybutyrate (PHB) can allow it to attain additional mechanical properties that make it a more comparable alternative to traditional plastic packaging.

Our production of PHB is leveraged on iGEM Calgary 2017’s part (BBa_K934001) which created a PHB production and secretion system. It included a process whereby Hly-A tagged phasin is produced in E. coli, allowing for the secretion of PHB via the type I secretion pathway (1). Phasin has a role in allowing for PHB granule size regulation and the ability of the cell to secrete PHB granules. So, our work involved proposing new part designs that leveraged upon changing the strength of the ribosomal binding site (RBS) of the phasin coding sequence. This is to have an effect on phasin expression levels, which would allow for more phasin production and increase the secretion of PHB into the BC. Ultimately, this would imply a change in the mechanical properties of the material making it a more suitable alternative in the packaging industry.

To have an understanding of PHB production and the phasin secretion system, although conducting lab experiments we wanted to use modelling to validate this system. Hence, we set out to build a deterministic model capable of helping us look into the rate of PHB and Phasin production, and how phasin production controls the secretion rate of PHB granules. Ultimately determining if this was a sustainable amount capable of strengthening our BC.

Model Design

When it came to describing the production and of PHB, phasin, and the phasin secretion system we had to be as thorough as possible by ensuring we account for all possible pathways that influence it. Our search led us to a predictive mathematical model created by Dixon designed to describe and ultimately optimize the metabolic pathways involved in the production of PHB in E. coli (2). The model is implemented in MATLAB 2010 using the SimBiology model builder module. This model goes through most of the metabolic pathways used in PHB production which are glycolysis, acetyl coenzyme A (acetyl-CoA) synthesis, tricarboxylic acid (TCA) cycle, glyoxylate bypass, and PHB synthesis (2). To describe the kinetics mechanism of each reaction in the pathway, enzymes in charge of reaction were identified. Kinetic equations were then identified and used to model each reaction’s dynamics.

These reactions are dependent on the amount of enzyme which is solely a result of the rate at which the enzymes are transcribed and translated and degraded. Thus, the model also incorporated several equations to express the production of enzymes to the promoters and transcription factors in charge of each enzyme identified. To improve the accuracy of the model, it was fitted to other published models and experimental data (2).

Figure 1. Schematic Overview of the Model Diagram as represented in MATLAB 2010

Figure 2. Legend of the icons used in the Model as described by Dixon (2)

Modifying the existing model

Although a robust model, it did not capture all the details we needed to adequately describe our PHB production and phasin secretion system. So, we added on to it and changed some of the parameters to be more reflective of our design.

One of such changes we made was adding in a component that accounted for phasin production in the cell. The original model accounts for enzyme production as a function of promoters and transcription factors. PHB is produced as a result of three enzymes which are β-ketothiolase, Acetoacetyl-CoA reductase and Poly-β-hydroxybutyrate polymerase (PHB synthase) that convert AcetylCoA to PHB. The genes that encode for these enzymes are transcribed using the lac promoter and the model states that the transcription factors Crp, H-NS, and LacI are used in regulating the lac operon. Furthermore, this translates to the rate and amount of PHB synthesis.

Since phasin is inserted on the same plasmid as these enzymes in charge of PHB production, we assumed that the same transcription factors would also be used in regulating its transcription. Thus, we based phasin production on these transcription factors as is the manner of the model.

Equation 1. Equation 1 describes the concentration of protein as a function of multiple transscription factors (2). This was used to describe the production of phasin and the other enzymes involved in PHB synthesis.

Figure 3. Schematic representation of the relationship between transcription factors LacI, CRP and H-NS and the production of enzymes PhaA, PhaB, PhaC, and Phasin

After incorporating phasin production into the model it was necessary that we translate its production to how it interacts with PHB in order to regulate its size and allow for its secretion from E. coli. We assumed that PHB and Phasin formed a complex which its production could then be related to a kinetic mechanism. Using mass action law we then created an equation that we used to describe the reaction of PHB and phasin to form the PHB-Phasin complex.

Reaction 1. Reaction 1 describes the binding of intracellular PHB and Phasin to form a "PHB-Phasin complex" that can be secreted using type 1 secretion system in E. coli

Figure 4. Schematic representation of the PHB production pathway and binding with Phasin (Pin) inside the cell

As expanded upon earlier, the incorporation of phasin allows for PHB granules to be secreted out of the cell and we wanted to capture this in the model. The original model assumes PHB stays inside the E. coli cell and is not secreted. So we made a new component and added to the model a reaction relating to secretion of the PHB-phasin complex and the breaking down of the complex into PHB granules and Phasin.

Reaction 2. Reaction 2 describes "PHB-Phasin complex" being seperated into extracellular PHB and Phasin(Pout)

Figure 5. Schematic representation of the "PHB-Phasin" complex being produced and secreted outside the cell

Lastly, an additional change we made to the model was to account for degradation of both PHB and phasin as the model had not done so earlier although it had captured that of the enzymes. This was to ensure that when simulations were run , only the net amount was revealed, hence making the model a more accurate depiction of the actual system.

Figure 6. Schematic representation of the degradation of phasin(Pin) and PHB

Simulation Results

After implementing all of our changes and changing parameters for some of the other reactions, we ran the resulting model as a simulation. The resulting plots are as follows:

Figure 7. Production of β-ketothiolase (PhaA), Acetoacetyl-CoA (PhaB) reductase and Poly-β-hydroxybutyrate polymerase (PHB synthase - (PhaC)) that convert AcetylCoA to PHB

Figure 8. Change in PHB concentration

Figure 9. Change in intracellular Phasin (Pin) concentration

Figure 10. Change in "PHB-Phasin" complex

Figure 11. Change in extracellular PHB (PHBout) concentration

Analysing the simulation run gave us an understanding that the Phasin secretion system is a sufficient system that can lead to the secretion of PHB. One notable key thing is that at the 150,000 seconds mark of the model it is evident that the intracellular concentration of PHB is reduced to zero. This resulted in the decrease in the production “PHB-Phasin” complex. This can lead to a reduction in the amount of PHB secreted and can decrease the desired mechanical properties of BC. Hence, there has to be a mitigation strategy implemented to ensure that the production of PHB is not halted. This can be such as ensuring increased amounts of substrate being given to the chassis during fermentation. In the wet lab the implementation of an intermittent feeding strategy achieves just this. This is because K. xylinus can grow for long periods and to sustain a consistent production of PHB, there has to be sufficient amounts of substrate.

The modified MATLAB model can be found here

Future Considerations

Modelling difference in RBS

In designing our PHB producing parts an important component that we wanted to add was testing out several strengths of the ribosome binding strengths in order to increase phasin production rate. Although these would be conducted in lab experiments, in silico tests can enable us to have an understanding of how these varying ribosome binding strength can affect phasin production and PHB secretion. However, in the current iteration of the model, the ribosome binding strength is not taken into account as enzyme and protein production is a function of the several promoters and transcription factors that affect their production. Therefore, as a future outlook we would modify the model to take into account how varying ribosome binding strength can affect phasin production. By validating this both in silico and in vivo we can then validate maximal possible PHB secretion is attained. Thus, ensure our BC has the necessary mechanical properties needed to function as an adequate produce package.

Experimental Validation

In order to make the model more precise and accurate, data collected from wet lab experiments can be used to fit the model. This would allow for refining of parameters and hence allow for a more predictive model. Not only can lab experiments be used to fit the model but the experiments can also be used to validate that the model is accurate enough. This is important because the model can then be used to predict other iterations of the production such as industrial scale productions.

Software Utilization

The current model is implemented in SimBiology from MATLAB 2010 software. This was a challenge to use as it’s an outdated software replaced by more current versions. Although still workable, it proved difficult to implement and modify the model. So future implementations of the model should involve replicating the current model in the latest version of SimBiology. This would allow for an easier framework and better functionality of the model.


  1. Part:BBa K2260002:Experience - [Internet]. [cited 2022 Sep 11]. Available from:
  2. Dixon A. Designing predictive mathematical models for the metabolic pathways associated with polyhydroxybutyrate synthesis in escherichia coli. 2011 [cited 2022 Oct 10]; Available from: