# Team:Dundee/Project/ProductionExport

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- | In conclusion, the model predicted that by over-expressing the Tat machinery in a realistic manner, periplasmic PP1 levels could potentially be increased almost 20-fold. Moreover, further simulations revealed that almost all of this fold increase was controlled by TatB-C over-exression. | + | In conclusion, the model predicted that by over-expressing the Tat machinery in a realistic manner, periplasmic PP1 levels could potentially be increased almost 20-fold. Moreover, further simulations revealed that almost all of this fold increase was controlled by TatB-C over-exression. Increasing TatA assemblies alone provided only a marginal fold increase in PP1 export. In contrast, the model predicted that over-expression of the TatB-C complex was responsible for almost all of the 20-fold increase produced. Therefore, and taking into account stress-induced problems likely to be related to multiple enhancements, we suggested to the Wet Team that the most efficient and effective option for mop improvement would be to over-express TatB-C. </p> |

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## Revision as of 10:27, 28 October 2013

**Production & Export**

The ToxiMop is an engineered *E. coli* bacterium that expresses PP1 and can be used as a molecular mop to remove microcystin from contaminated water. Central to successfully engineering this machine was to better understand PP1 production and export with in the cell. Considering the export of PP1 was crucial as we hypothesised that microcystin binding would predominantly take place in the periplasm.

We explored both the Twin Arginine Translocase (Tat) and General Secretory (Sec) pathways as potential export routes for PP1. However, initial Western blot results indicated that PP1 was exported into the periplasm much more successfully via the Tat pathway than via Sec. Therefore, production and export based on Tat transport, was selected as a modelling focus to allow us to optimise the construction of our prototype ToxiMop.

## Building a Model for Tat Transport

The Tat machinery is a biological pathway that transports folded proteins from the cytoplasm into the periplasm. It consists of three small membrane proteins; TatA, TatB and TatC.

TatB and TatC together form a TatB-C complex. The protein destined for transport has a signal sequence at its N-terminus which is recognised by and binds to the TatB-C complex. This positions the protein ready for export. TatA proteins then polymerise and form a ring structure surrounding the protein allowing it to penetrate the membrane and pass into the periplasm. The signal peptide is cleaved off and this frees up the TatB-C complex and TatA proteins for further transport.

**Figure 1:** Processes involved in Tat transport.

## Tat-dependent Transport of PP1

PP1 has a molecular mass of 37kDa. Reasonably assuming that PP1 is spherical, it would require 20 TatA proteins to form a ring large enough to accommodate it and enable it to penetrate the membrane [1]. We define this structure as a TatA assembly.

For transport, PP1 in the cytoplasm (PP1_{cyto}) binds to TatB-C, forming a PP1 TatB-C complex (PP1B-C). The TatA assembly then surrounds the PP1 TatB-C complex. We define this product as PP1_{export}. PP1_{export} is then exported into the periplasm (PP1_{peri}), releasing the TatA assembly and TatB-C back into the membrane to assist in further rounds of transport.

We make the following further assumptions:

- TatA assemblies are pre-formed from TatA proteins
- PP1 exported to the periplasm remains in the periplasm
- All other processes are reversible

**Figure 2:** Ring structures formed by polymerisation of TatA proteins. Taken from Rodriguez *et al.* [2]

Hence we have the following framework for Tat transport of PP1:

## Production

Before transport, PP1 first needed to be produced. This involved inserting the PP1-encoding gene into a plasmid vector and transforming the plasmid into host cells. These cells then expressed the gene.

We now consider the transcription and translation required for this gene expression. This simple production scheme is derived by assuming that both mRNA and protein can degrade. Due to the heterologous nature of PP1, its degradation constant is particular significant.

Using the law of mass action and appropriate rate constants, we created a mathematical system that represents each reaction. Rate reaction values and equations are shown below:

Reaction name | Constant | Value |
---|---|---|

Transcription | K_{Tc} |
0.03833nM.s^{-1} |

mRNA degradation | K_{mdeg} |
0.0077 s^{-1} |

Translation | K_{Tl} |
0.75 s-^{1} |

PP1 degradation | K_{pdeg} |
0.0192 s^{-1} |

**Table 1:** PP1 production rate constants [3].

Our team developed a series of MATLAB programs to solve the models discussed here. The code for these programs along with further analysis is available at the repository [4]. The program v1_odes_solver_PP1Production solves this system numerically.

Our model predicts that, in steady state, the cytoplasm of each *E. coli* chassis would contain approximately 1200 PP1 molecules. This gives a crude indication of how many cells would be required to mop up given quantities of microcystin. We used this information to examine the practicality of our ToxiMop. For example, if we assume that all the PP1 is exported to the periplasm and exploit the one-to-one binding of microcystin with PP1, then the model predicts that 0.6g of cells are required to clean up one litre of contaminated water that is classified as unsafe by World Health Organisation (WHO) regulations. We note that the production of this mass of cells was easily achievable by our Wet Team.

**Figure 3:** Concentration of cytoplasmic PP1 as a function of time and give by solutions of equation (3).

**Figure 4:** Numbers of PP1 molecules in the cytoplasm as a function of time given by solutions of equation (3). Note that 1200sec is approximately equivalent to one cell generation time.

## Production & Export

Combining our separate schemes for protein production (2) and Tat transport (1), we built a model that describes PP1 Production & Export. Parameter values and the model equations are shown below.Reaction name | Constant | Value |
---|---|---|

Transcription | K_{Tc} |
0.03833 nM.s^{-1} |

mRNA degradation | K_{mdeg} |
0.0077 s^{-1} |

Translation | K_{Tl} |
0.75 s^{-1} |

PP1 degradation | K_{pdeg} |
0.0192 s^{-1} |

Recognition binding | K_{1} |
8E3 M^{-1}s^{-1} |

Recognition unbinding | K_{r1} |
8E3 M^{-1}.s^{-1} |

Assembly association | K_{2} |
200E4 M^{-1}s^{-1} |

Assembly disassociation | K_{r2} |
0.00167 s^{-1} |

Export | K_{3} |
10 s^{-1} |

**Table 2:** PP1 production & export rate constants [3].

## Deterministic Model

To solve the system of ODEs (5), we applied the appropriate initial conditions. The only non-zero initial conditions are the number of TatB-C complexes and TatA proteins. It is known that there are approximately 15 TatB-C complexes and 600 TatA proteins in a normal*E. coli*cell [5]. Hence, in our model we use 15 TatB-C complexes and 30 TatA assemblies.

The program v1_odes_solver_PP1_TatProduction_export solves this system. The deterministic model predicted that after approximately one cell generation time only around 200 PP1 molecules had been exported to the periplasm. This was much less than we anticipated, given the high levels of cytoplasmic PP1 computed above. Indeed, based on these figures, up to 3.3g of cells would be required to clean up one litre of contaminated water as defined by WHO regulations.

**Figure 5:** PP1 concentrations in the cytoplasm and in the periplasm.

**Figure 6:** Number of PP1 molecules in the cytoplasm and in the periplasm (after one cell generation time 1164 and 202, respectively).

## Stochastic Model

In order to check whether these deterministic results were reasonable, we next considered a stochastic modelling approach. Some of the components in the ODE model above are in low abundance. To examine whether low copy number had a significant effect on either PP1 production or export numbers, we formulated and analysed a stochastic model.The stochastic model, although better representing the random nature associated with such biochemical processes, did not produce significantly different results. Instead the model showed that because high and low fluctuations cancel each other out, the deterministic solutions were a good approximation of the stochastic means for PP1cyto and PP1peri.

**Figure 7:** Stochastic realisations (grey) of PP1_{cyto} and stochastic mean (orange) using the code in [7].

**Figure 8:** Stochastic realisations (grey) of PP1_{peri} and stochastic mean (blue) using the code in [7].

**Figure 9:** PP1_{cyto} Stochastic realisations (grey) & Deterministic Solution (orange) using code in [8].

**Figure 10:** PP1_{peri} Stochastic realisations (grey) & Deterministic Solution (blue) using code in [8].

## Model predicts failure of basic mop

As discussed above, the model predicts that 3.3g of the basic mop cells would be required to clean up one litre of contaminated water as defined by WHO regulations. This equates to an impractically large quantity. However, the Wet Team started testing the ToxiMop with these basic cells, to test for proof of principle. Their initial experiment involved taking 20 µl from a 100 µg/ml microcystin solution and mixing it into a beaker with 200ml of TBS. 1g of ToxiMop cells was then added to the solution in a dialysis bag. Early results indicated that the ToxiMop was ineffective in mopping up the microcystin. Using the mathematical models introduced above, the dry team tried to get better understanding of why the mop was proving ineffective.

## Increasing Tat Machinery

We next used our model to investigate how PP1 export could be enhanced. Our first thought was that this could be achieved by increasing the amount of Tat machinery per cell as the existing model predicted that in steady state, a significant proportion of the PP1 molecules were retained within the cytoplasm and thus could not assist in the binding of microsystin. By increasing the Tat machinery, we hypothesised that augmented transport from this bank of proteins to periplasm would have the desired effect. Experimentally, this increase could be achieved by inserting selected genes into a plasmid with a copy number of 20. This would allow us to obtain 20 extra copies of the selected Tat machinery proteins. Therefore our cells could theoretically produce 20 times the quantity of targeted proteins. The modelling options we considered were; increasing all of the Tat components, increasing TatA assemblies and increasing TatB-C complexes.The simulations below show the effect of increasing the machinery above the default level (30 TatA assemblies & 15 TatB-C complexes) to 20 times these values.

## Increasing TatA & TatB-C Complexes

**Figure 11:**PP1_{cyto} Stochastic means for the corresponding TatB-C Complex-TatA Assembly combinations [11]

**Figure 12:** PP1_{peri} Stochastic means for the corresponding TatB-C Complex-TatA Assembly combinations [11]

## Increasing TatA Assemblies Only

**Figure 13:** PP1_{cyto} Stochastic means for the corresponding number of TatA Assemblies [9]

**Figure 14:** PP1_{peri} Stochastic means for the corresponding number of TatA Assemblies [9]

**Figure 15:** Change in number of PP1_{peri} with increasing number of TatA Assemblies [9]

**Figure 16:** Mass of Cells required for ToxiMop experiment based on the number of TatA Assemblies [9]

Increasing the number of TatA assemblies, marginally increases the number of PP1 being exported over that for the wild type. With such a small increase, the mass of cells required for our ToxiMop experiment remains fairly high. Therefore, we could not recommend this action.

## Increasing TatB-C Complexes Only

**Figure 17:** PP1_{cyto} Stochastic means for the corresponding number of TatB-C Complexes [10]

**Figure 18:** PP1_{peri} Stochastic means for the corresponding number of TatB-C Complexes [10]

**Figure 19: ** Change in number of PP1peri with increasing TatB-C Complexes [10]

**Figure 20:** Mass of cells required for ToxiMop experiment based on the number of TatB-C Complexes [10]

As shown in the figures above, increasing the number of TatB-C complexes, predicts an 18-fold increase in the number of PP1 molecules exported into the periplasm. This change is sufficient to significantly improve the efficiency of our ToxiMop cells - with such an increase, the mass of cells required for clean-up is reduced by a factor of eighteen.

## Conclusion

In conclusion, the model predicted that by over-expressing the Tat machinery in a realistic manner, periplasmic PP1 levels could potentially be increased almost 20-fold. Moreover, further simulations revealed that almost all of this fold increase was controlled by TatB-C over-exression. Increasing TatA assemblies alone provided only a marginal fold increase in PP1 export. In contrast, the model predicted that over-expression of the TatB-C complex was responsible for almost all of the 20-fold increase produced. Therefore, and taking into account stress-induced problems likely to be related to multiple enhancements, we suggested to the Wet Team that the most efficient and effective option for mop improvement would be to over-express TatB-C.

## References

- 1. Leake, Mark C., et al. "Variable stoichiometry of the TatA component of the twin-arginine protein transport system observed by in vivo single-molecule imaging." Proceedings of the National Academy of Sciences 105.40 (2008): 15376-15381.
- 2. Rodriguez,Fernanda, et al. “Structural model for the protein-translocating element of the twin-arginine transport system.” Proceedings of the National Academy of Sciences 110( 2013). 1092-101.

- 3. Stamatakis, Michail, and Nikos V. Mantzaris. "Comparison of Deterministic and Stochastic Models of the
*lac*Operon Genetic Network." Biophysical journal 96.3 (2009): 887-906. - 4. MATLAB program repository: https://github.com/cdjohnston/CraigiGEM-MATLAB
- 5. Palmer, Tracy, and Ben C. Berks. "The twin-arginine translocation (Tat) protein export pathway." Nature Reviews Microbiology 10.7 (2012): 483-496.
- 6. Higham, Desmond J. "Modeling and simulating chemical reactions." SIAM review 50.2 (2008): 347-368.
- 7. https://github.com/cdjohnston/CraigiGEM-MATLAB/blob/master/Production%20%26%20Export/Stochastic%20Models/v1_ssa_PP1_TATproduction_export.m
- 8. https://github.com/cdjohnston/CraigiGEM-MATLAB/blob/master/Production%20%26%20Export/Stochastic%20Models/v2_ssa_PP1_TATproduction_export.m
- 9. https://github.com/cdjohnston/CraigiGEM-MATLAB/blob/master/Production%20%26%20Export/Stochastic%20Models/v6_ssa_PP1_TATproduction_export.m
- 10. https://github.com/cdjohnston/CraigiGEM-MATLAB/blob/master/Production%20%26%20Export/Stochastic%20Models/v7_ssa_PP1_TATproduction_export.m
- 11. https://github.com/cdjohnston/CraigiGEM-MATLAB/blob/master/Production%20%26%20Export/Stochastic%20Models/v8_ssa_PP1_TATproduction_export.m