The P(3HB) degradation model was built and simulated in MATLAB Simbiology in the similar fashion as that seen in the modelling section of Module 1. This model encompasses gene expression of PhaZ1 (P(3HB) depolymerase) controlled by a xylose inducible promoter[http://parts.igem.org/Part:BBa_I741018]and the kinetics of PhaZ1 degrading the polymer P(3HB) into shorter oligomers or 3HB monomers.

1.1 Ordinary differential equations

Genetic expression and regulation of PhaZ1

Values, sources and assumptions

Derivations

1.Derivation of the maximal expression rate,β

• Average molecular weight (Mw) of a base pair = 660g/mol[http://www.geneinfinity.org/sp/sp_dnaprop.html][http://www.lifetechnologies.com/uk/en/home/references/ambion-tech-support/rna-tools-and-calculators/dna-and-rna-molecular-weights-and-conversions.html]
• Average mass of a base pair = 660g/mol x 1.66x10^-24 = 1.1x10^-21g
• Volume of an E.coli cell = 1µm³[http://kirschner.med.harvard.edu/files/bionumbers/fundamentalBioNumbersHandout.pdf] = 1x10^-15L
  • ∴Mass concentration =
  • ∴Molar concentration of 1 base pair in the volume of E.coli = = 1.66x10^-6 mM
• BioBrick assembly plasmid pSB1C3 is a high copy number plasmid (100-300 copies per cell)[http://parts.igem.org/Part:pSB1C3?title=Part:pSB1C3]
  • assume 200 copies per cell
• ∴ concentration of the gene per cell = N x 200 x 1.66x10^-6mM, where N = number of base pairs
  • ∴ concentration of the gene phaZ1 (N = 1245)[http://bacteria.ensembl.org/cupriavidus_metallidurans_ch34/Gene/Summary?g=Rmet_1017;r=Chromosome:1106373-1107617;t=ABF07903] in the volume of an E.coli cell is = 0.41mM
• Transcription rate in E.coli= 80bp/s[http://kirschner.med.harvard.edu/files/bionumbers/fundamentalBioNumbersHandout.pdf] = 80 x 1.66x10^-6mM/s = 80 x 1.66x10^-6 x 60mM/min = 7.97x10^-3mM/min
• ∴ Rate of mRNA_phaZ1 production under the control of pBAD = 7.97x10^-3 ÷ 0.41 = 0.019/min

2.Protein production rate of phaZ1, k₂

• Average molecular weight(Mw) of an amino acid(aa)= 110g/mol[http://www.genscript.com/conversion.html][http://www.promega.com/~/media/Files/Resources/Technical%20References/Amino%20Acid%20Abbreviations%20and%20Molecular%20Weights.pdf]
• Average mass of an amino acid = 110g/mol x 1.66x10^-24=1.83x10^-22g/L
  • ∴Mass concentration of one aa in the volume of an E.coli = = 1.83x10^-6g/L
  • ∴Molar concentration of one aa = = 1.66x10^-5mM
• Translation rate = 20aa/s = (20 x 1.66x10^-5 x 60)mM/min = 0.020mM/min
• PhaZ1 comprises of 414aa[http://bacteria.ensembl.org/cupriavidus_metallidurans_ch34/Gene/Summary?g=Rmet_1017;r=Chromosome:1106373-1107617;t=ABF07903]
  • ∴concentration of PhaZ1's aa in the volume of an E.coli= 1.66x10^-5mM x 414 = 6.87x10^-3mM
• ∴ Rate of protein production = 0.020 ÷ 6.87x10^-3 = 2.9/min

1.2 Enzyme kinetics

PhaZ1 reaction with P(3HB)

Values, sources and assumptions

1.3 Simulation results

picture here

Metabolic modelling

Introduction of the metabolic model

The metabolic model predicts the interaction of our pathway with endogenous pathways. In synthetic biology, an ideal system is fully orthogonal. However, if the synthetic pathway uses some metabolites from the metabolism pathways, the metabolic fluxes (the rate of conversion between metabolites) will be affected. If the cell is overloaded by losing too much metabolites, it would either reject the synthetic pathway or burn out. As for the optimization of PHB production in our MAPLE system, metabolic analysis need to be carried out to estimate the effects on the cell metabolism from increases in the PHB production.

Methods

We altered the metabolic model by Angela Dixon in her paper “Predictive Mathematical Model for Polyhydroxybutyrate Synthesis in Escherichia coli”. [http://digitalcommons.usu.edu/engineering_datasets/1/] The metabolic model is built in Simbiology, which is an extension in MATLAB especially for biological system. The model consists two metabolic pathways: Glycolysis and TCA cycle. The reactions in the metabolic pathways are defined by ordinary differential equations and kinetic parameters. The model also contains a synthetic pathway that produce P(3HB) from acetyl-coA. The pathway consists three enzymes which are PhaA, PhaB and PhaC. The reasons we chose this model:

1. The model is based on ODEs instead of FBA (flux balance analysis) method, which is a common methods of metabolic analysis. However, FBA cannot determine the real time concentration of the metabolites whereas it can be done by models of ODEs.

2. Only single gene deletion or addition can be performed in FBA. More than that, the metabolic model here can perform modification on any single or multiple genes and reactions through Simbiology.

3. The FBA model is static, it cannot analyze the dynamic interactions between our synthetic pathways with the metabolic pathways. As both our P(3HB) synthesis model and the metabolic model are in the same platform. It was really easy to integrate our pathway into the metabolic model.

In our project, we have a different pathway:

1. We use 3HB as one of the input.

2. Existence of ato system in the E.coli MG1655 strain.

3. We removed phaA in our case because we use 3HB as the major source to produce P(3HB) to avoid too much acetyl-coA be taken from the metabolic pathways.

Therefore, we substitute the original pathway with our synthetic pathway. Moreover, we added our gene expression models for the enzymes into the metabolic model as well. In terms of the consistency of the model, we changed the units of our synthetic pathway into micro molar and seconds.

Here is the combination of our model with the metabolic model

Keys:

We also carried out a parameter estimations of the initial concentrations of several substrates in our synthetic pathway. The reason is we have single-cell scaled magnitude for them originally (fM level), but there are much higher magnitudes in any of the species in the metabolic pathways (mM level). Therefore, we scaled up the pathway in order to maintain the consistency of the model. As for the metabolites which are involved in our pathway, we cloned the blocks of them from the metabolic pathway in Simbiology and deliberately put them into our pathway. That means our pathway dynamically interact with the metabolic pathways.

Here is the table for the updated initial concentrations for the species in our synthetic pathway: All the kinetic data and initial concentrations of the metabolites in the metabolic pathways are referenced in the paper[http://digitalcommons.usu.edu/engineering_datasets/1/]:

ATP analysis:

In our optimization of P(3HB) production module, we discovered that increasing in the PhaB expression can efficiently increase the yield of P(3HB). It’s important to see whether increase in the PhaB expression would dramatically change the fluxes in the metabolic pathways or not. As ATP is the essential energy carriers in the cell, we carried a parameter scan for the variation in ATP concentrations levels under different concentration of PhaB.

There is an approximately 5.3% drop in the concentration of ATP when increasing the phaB concentration from 50uM to 200uM. It suggests that increasing the efficiency in our pathway will reduce the efficiency of energy transports in the cell. However, it’s still unsure about the effect of 5.3% drop in ATP concentration on the cell growth.

Large scale PHB production and implementation in MAPLE

In our MAPLE system, the bioplastic Polyhydroxybutyrate P(3HB) is produced from both 3HB monomers and glucose. 3HB is the degradation product from the wasted P(3HB）plastic and glucose is the product from the degradation of mixed waste in Module 1. Therefore, the overall PHB production rates need to be defined by considering different situations:

1. In module 1, we have glucose as the only source to produce PHB.

2. In module 2, we have both glucose and 3HB as resources.

Introduction

The efficiency of Polylactic acid is important for the performance of MAPLE. Therefore, we chose a strong enzyme Proteinase K which is suggested by many literature as an efficient PLA degrading enzyme. We performed several assays in order to determine the kinetic properties of Proteinase K. The PLA degradation model was then built based on the experimental results.

Objective and Design

1. With the defined kinetic properties of Proteinase K. The model can predict the time needed to degrade a certain amount of PLA. The information is important as it estimates the efficiency of the MAPLE system when degrading the large amount of plastic.Therefore, further improvements can be made if the system is not efficient.

2. The model also involves the gene expression model of the Proteinase K with an inducible promoter. Therefore, gene expression can be regulated by adjusting the inducer concentration. The overall plastic degradation can be regulated by the gene expression.

3. The secretion model is also contained in the model which assumes the efficiency of enzyme secretion to the culture.

Specifications of the model

Polylactic acid (PLA) degradation involves proteinase K:

The overall PLA degradation model is shown as below:

There are two compartments which represents cells and the culture from left to right. The "cell" compartment contains the gene expression module whereas the "culture" compartment contains the degradation module. The "secretion" block that connects two compartments is the secretion module.

Parameters and assumptions

Gene expression module of Proteinase K

1.Derivation of the maximal expression rate,β

• Average molecular weight (Mw) of a base pair = 660g/mol[http://www.geneinfinity.org/sp/sp_dnaprop.html][http://www.lifetechnologies.com/uk/en/home/references/ambion-tech-support/rna-tools-and-calculators/dna-and-rna-molecular-weights-and-conversions.html]
• Average mass of a base pair = 660g/mol x 1.66x10^-24 = 1.1x10^-21g
• Volume of an E.coli cell = 1µm³[http://kirschner.med.harvard.edu/files/bionumbers/fundamentalBioNumbersHandout.pdf] = 1x10^-15L
  • ∴Mass concentration =
  • ∴Molar concentration of 1 base pair in the volume of E.coli = = 1.66x10^-6 mM
• BioBrick assembly plasmid pSB1C3 is a high copy number plasmid (100-300 copies per cell)[http://parts.igem.org/Part:pSB1C3?title=Part:pSB1C3]
  • assume 200 copies per cell
• ∴ concentration of the gene per cell = N x 200 x 1.66x10^-6mM, where N = number of base pairs
  • ∴ concentration of the gene proteinase K (N = 1194) in the volume of an E.coli cell is = 0.40mM
• Transcription rate in E.coli = 80bp/s[http://kirschner.med.harvard.edu/files/bionumbers/fundamentalBioNumbersHandout.pdf] = 80 x 1.66x10^-6mM/s = 80 x 1.66x10^-6 x 60mM/min = 7.97x10^-3mM/min
• ∴ Rate of mRNA_Proteinase K production under the control of pBAD = 7.97x10^-3 ÷ 0.40 = 0.020/min

• Average molecular weight(Mw) of an amino acid(aa)= 110g/mol[http://www.genscript.com/conversion.html][http://www.promega.com/~/media/Files/Resources/Technical%20References/Amino%20Acid%20Abbreviations%20and%20Molecular%20Weights.pdf]
• Average mass of an amino acid = 110g/mol x 1.66x10^-24=1.83x10^-22g/L
  • ∴Mass concentration of one aa in the volume of an E.coli = = 1.83x10^-6g/L
  • ∴Molar concentration of one aa = = 1.66x10^-5mM
• Translation rate = 20aa/s = (20 x 1.66x10^-5 x 60)mM/min = 0.020mM/min
• Proteinase K comprises of 398aa[http://www.ncbi.nlm.nih.gov/nuccore/X14689.1]
  • ∴concentration of Proteinase K's aa in the volume of an E.coli = 1.66x10^-5mM x 398 = 6.61x10^-3mM
• ∴ Rate of protein production = 0.020 ÷ 4.25x10^-3 = 3.0/min

Degradation

The reaction equation of the PLA degradation is:

[Polylactic acid]+[Proteinase K]= 660 [lactic acid] + [Proteinase K]

Assumptions:

We assumed 1 mole of polylactic acid can produce 660 moles of lactic acid.

The molecular weight of a single polylactic acid monomer is 90 g/mol [http://www.chemspider.com/Chemical-Structure.592.html]whereas the molecular weight of the solid polylactic acid is around 59500 g/mol.[http://www.sciencedirect.com/science/article/pii/S0014305711003582]Therefore, the short-chain polylactic acid consists approximately 660 monomers. 660 molecules of lactic acid will be produced by degrading one chain of polymer.

We also assumed a simple Michaelis-Menten mechanism for proteinase K

"[Proteinase K]" here is the concentration of the enzyme Proteinase K in mM, whereas "[Polylactic acid]" represents the concentration of polylactic acid in mM as well.

The parameters for the kinetic equations are:

Derivation:Turnover number (Kcat) = Vmax*Mw/[proteinase K] = 2348.4

The efficiency of Secretion is assumed to be 90% secretion over 2 hours.[http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1251600/] The rate of secretion in the model is therefore:

rate of secretion = 0.9[concentration of Proteinase K]/120 (mM/mins)

Simulations and Results

The initial concentration of Polylactic acid is 40mM, which can be converted to 2380g/L. The derivation is: 40*59500/1000 = 2380g/L. There is approximately 2kg of polylactic acid in the 1 litre bioreactor. It's a really large amount of plastic, the simulation result is:

The simulation result shows a fast degradation of that large amount of polylactic acid by proteinase K. 40mM of the plastic can be completely degraded in 6 minutes. The reason for fast degradation is that we have relative large kinetic parameters for the enzyme. Polylactic acid was not used as the substrate in our kinetic assays. Therefore, we made an assumption that polylactic acid in the model has similar length of chain as that of the substrate in the assays.

Summary

Our chassis can grow and survive in reasonable concentrations of P(3HB) and 3HB. To increase tolerance to 3HB we have re-designed our system to include expression of Bdh2 (BBa_K1149050, 3HB dehydrogenase), which breaks down 3HB to acetoacetate. Acetoacetate toxicity was examined and these data are being utilised along with our metabolic models to determine the effects of differing levels of 3HB and acetoacetate on bioplastic (P3HB) production.

MG1655 transformed with either native phaCAB or empty vector (control) plasmid were grown for 6h in LB containing 3-HB or P-3HB to assess any potential toxicities associated with these bioplasrics.

3-hydroxybutyrate (3HB)

Toxicity of 3-hydroxybutyrate in LB with phaCAB and EV expression. 3HB was tested at 5 concentrations for toxicity - 1 μM, 100 μM, 1 mM, 10 mM and 237 mM. Between 10 mM and 237 mM, there is a clear toxicity effect observed. Data points show final time point after 6h growth for each concentration. Growth was at 37°C with shaking over 6h. Error bars are SEM, n=4. Figure made by Imperial College London 2013 iGEM.

Poly(3-hydroxybutyrate) P(3HB)

Toxicity of Poly(3-hydroxybutyrate) in LB with phaCAB and EV expression. P3HB toxicity was only tested at one concentration in LB - 31 μg/L, it was also tested at 31 mg/L however the resulting OD was over 1, so this data was not considered accurate. Growth was at 37°C with shaking over 6h. Error bars are SEM, n=4. Figure made by Imperial College London 2013 iGEM.

Conclusion:3HB is toxic above 10mM and P(3HB) had no effect on growth at 31 μg/L. These data can be utilised to determine the maximum level of 3HB which should be present in our final bioreactor design. We have shared these data with our modelling team in order to determine maximum P(3HB) production at or below 10mM (3HB). In light of these data we have modified our design to include the expression of bdh2 (BBa_K1149050)</b>, which is a 3HB dehydrogenase that can convert 3HB into acetoacetate, a common metabolite in E.coli. Expression of bdh2 should overcome the toxicity limit of 3HB, since E. coli can metabolise acetoacetate</b>To this end we tested whether an increase in acetoacetate would present any toxicities.

Acetoacetate

Toxicity of acetoacetate in LB with phaCAB and EV expression. Acetoacetate was also tested for toxicity at 4 concentrations - 1 μM, 100 μM, 1mM and 287 mM. In phaCAB and EV this manifested itself between 1 mM and 287 mM. Data points show final time point after 6h growth for each concentration. Growth was at 37°C with shaking over 6h. Error bars are SEM, n=4. Figure made by Imperial College London 2013 iGEM.

Conclusion:Acetoacetate toxicity lies somewhere between 1mM and 287 mM.

Enzyme activity of PHB depolymerase (phaz1)

It can be seen from the Western Blot results that phaz1 [http://parts.igem.org/Part:BBa_K1149010 BBa_K1149010] was being expressed. To show that this enzyme has esterase activity, colourimetric assays were performed using the substrate analog para-Nitrophenyl butyrate. When the ester bond in this substrate is cleaved, 4-Nitrophenol is released. This is accompanied by an increase in absorbance at the wavelength 405 nm and a colour change from colourless to yellow. The concentration of 4-Nitrophenol produced could then be calculated with the Beer-Lambert Law, as the extinction coefficient of 4-NP at 405 nm is 18,000 M-1 cm-1. This experiment was performed with both the crude cell lysate and purified PHB depolymerase. Our data shows that this enzyme is definitely active.

para-Nitrophenyl butyrate is cleaved by PHB depolymerase to release 4-Nitrophenol. This is accompanied by an increase in absorbance at 405 nm. Figure adapted from TU Darmstadt 2012 iGEM

When the substrate para-Nitrophenyl butyrate is added to the reaction mixture of purified PHB depolymerase (phaz1) in phosphate buffer, there is a colour change from colourless to yellow. Figure by Imperial College London iGEM 2013.

Cell lysate assay

After 48 hours of growing and inducing the phaz1 culture, the cells were lysed by probe-sonication, spun down and resuspended in 50mM Tris-HCl buffer. A reaction mixture containing 5 µL of crude phaz1 lysate, 4 µL of para-Nitrophenyl butyrate solution and 1 mL of 50 mM Tris-HCl pH 7.4 buffer was incubated in the [http://www.eppendorf.com/int/index.php?sitemap=2.1&action=products&contentid=1&catalognode=87236 Eppendorf BioSpectrometer] for 570 seconds, whilst the absorbance at 405 nm was automatically recorded every 30 seconds.

The increase in absorbance that accompanies the cleavage of para-Nitrophenyl butyrate by PHB depolymerase (phaz1). Figure by Imperial College London 2013 iGEM

The concentration of 4-Nitrophenol released by PHB depolymerase (phaz1) activity. Empty Vector and Substrate alone were used as negative controls. Figure by Imperial College London 2013 iGEM

The above graph shows that greater esterase activity occurs when the phaz1 cell lysate is in the reaction mixture. The graph shows that there is also esterase activity occuring in the Empty Vector and Substrate alone reaction mixtures, but this is due to the imidazole present in the Tris-HCl buffer, which acts as a general base catalysis. [http://pubs.acs.org/doi/pdf/10.1021/ja00874a035 (6)]

Purified enzyme assay

Since the phaz1 [http://parts.igem.org/Part:BBa_K1149010 BBa_K1149010] construct contains a His tag, the protein could be purified by metal affinity chromatography. The colourimetric assay was carried out, as with the cell lysate. 100 mM potassium phosphate (pH 7.4) buffer was used instead of the Tris-HCl buffer, to eliminate the esterase activity caused by imidazole in the buffer used previously. Every 30 seconds for 30 minutes the absorbance at 405 nm of the reaction mixture was recorded. The reaction mixture contained 1 ml of phosphate buffer, 2.5 µL of purified PHB depolyermase (stock concentration 0.230 mg/ml) and para-Nitrophenyl butyrate to make final concentrations of 50 µM, 100 µM, 150 µM, 200 µM and 250 µM of substrate.

The purified PHB depolyermase (phaz1) is definitely active. The graph shows that more 4-Nitrophenol is produced with greater concentrations of para-Nitrophenyl butyrate. Figure by Imperial College London 2013 iGEM

The above graph shows how the concentration of 4-Nitrophenol produced is greater when the para-Nitrophenyl butyrate substrate concentration is greater. This data shows that we have successfully purified active PHB depolyermase.

SDS PAGE gel shows that PHB depolymerase was purified from the crude cell extract. Figure by Imperial College London 2013 iGEM

Clearing Zone Assay

Clearing zone experiment was conducted to semi-quantitatively test the ability of PhaZ1 to break down P3HB. PhaZ1 cell lysate was tested on a P3HB LB agar plate. The protocol can be found here.

PhaZ1 showing P3HB degradation ability by generating a clear zone on a P3HB LB agar plate. A. No difference between empty vector cell lysate and PhaZ1 cell lysate right after they were pipetted into the wells. B. PhaZ1 in the cell lysate started to clear P3HB around the well after 1 day. C. PhaZ1 created a clear zone around the well after 3 days, whereas it was still cloudy around the empty vector cell lysate well.