Team:Dundee/Project/ProductionExport

Introduction

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 PP1 production and export. This was crucial as the microcystin binding interaction predominantly takes place with PP1 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. 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.

Making the following 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]

We arrive at this framework to describe Tat transport of PP1.

Production

Before we can transport any PP1, we first need to produce the protein. 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 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 create a mathematical system that represents each reaction. These values and equations are shown below:

Reaction name	Constant	Value
Transcription	KTc	0.03833 nM.s-1
mRNA degradation	Kmdeg	0.0077 s-1
Translation	KTl	0.75 s-1
PP1 degradation	Kpdeg	0.0192 s-1

Figure 3: Table 1 - PP1 production rate constants [2].

Our team developed a series of MATLAB programs to solve the models which we considered. The code for these programs along with further analysis is available at this repository [3]. The program v1_odes_solver_PP1Production solves this system numerically.

The production model predicts that we will produce approximately 1200 net PP1 in the cytoplasm of each E. coli cell. This gives us initial indications of the amount of PP1 we can produce per cell and allows us to determine how many cells are required to mop up fixed concentrations of microcystin. We use this information to examine the practicality of the ToxiMop. For example, if we assume all the PP1 is exported to the periplasm and exploit the one-to-one binding of microcystin with PP1, then 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. The production of this mass of cells is highly achievable for our Wet team to produce.

Figure 4: PP1 production graph - Figure 5: 1173 PP1 are produced per cell division

Production & Export

Combining our separate schemes for protein production (2) and Tat transport (1), we built a model that describes PP1 Production & Export.

Reaction name	Constant	Value
Transcription	KTc	0.03833 nM.s-1
mRNA degradation	Kmdeg	0.0077 s-1
Translation	KTl	0.75 s-1
PP1 degradation	Kpdeg	0.0192 s-1
Recognition binding	K1	8E3 M-1.s--1
Recognition unbinding	K2	8E3 M-1.s--1
Assembly association	K3	200E4 M--1.s--1
Assembly disassociation	K4	0.00167 s-1
Export	K5	10 s-1

Figure 6: Table 1 - PP1 production & export rate constants [2].

Deterministic Model

To solve this system of ODE’s (5) we applied the appropriate initial conditions. The only non-zero initial conditions are the number of TatB-C complexes and TatA proteins. There are 15 TatB-C complexes and 600 TatA proteins in a regular E. coli cell [4]. With our previous assumptions and in terms of our variables, our model implements 15 TatB-C complexes and 30 TatA assemblies.

The program v1_odes_solver_PP1_TatProduction_export solves this system. The deterministic model predicted that approximately 200 PP1 would be exported to the periplasm. This was less than we would expect. Based on these figures we would now require 3.3g of cells to clean up one litre of contaminated water. In realistic applications, we would have many litres of contaminated water requiring large amounts of cells. Producing such amounts would be practically unachievable for our Wet Team. Therefore, to ensure the construction of our ToxiMop was viable, we needed to investigate options that would increase the number of PP1 being exported into the periplasm.

Figure 7: PP1 production & export - Figure 8: 202 PP1 are exported to the periplasm and 1164 remain in the cytoplasm

Stochastic Model

The first option we investigated was using the deterministic model as a basis to develop a stochastic model [5]. For given initial conditions, a deterministic model produces the same results each time while a stochastic model produces different results due to its incorporation of randomness through probability distributions. Therefore, we examined the results from our stochastic model for fluctuations that exported higher numbers of PP1 into the periplasm. This would allow us to justify a reduction in the mass of cells needed, down closer to an attainable amount to produce.

The stochastic model, although representing the random nature associated with such processes, did not provide this justification. Instead the model showed that because the high and low fluctuations cancel each other out, the deterministic solutions were good approximations of the PP1cyto and PP1peri stochastic means. In the current construction, our models conclude that the ToxiMop cells export 200 PP1 to the periplasm and retain approximately 1200 PP1 in the cytoplasm.

Figure 9: PP1_cyto Stochastic mean & realisations [6] - Figure 10: PP1_peri Stochastic mean &

Figure 11: PP1_cyto Stochastic realisations & Deterministic Solution [7] - Figure 12: 2PP1_peri Stochastic realisations & Deterministic Solution [7]

With these cells the Wet Team started testing the ToxiMop. Their main 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 were then added to the solution in a dialysis bag. Early results indicated that the ToxiMop was ineffective in mopping up the microcystin.

However, after some simple calculations that made use of the previous models, we tried to get an understanding of why the tests were unsuccessful.

Based on the high number of microcystin molecules present and having 200 PP1_peri per cell, the experiment would require a minimum of 5.75g of cells to clean up the toxin. Due to this, 1g of cells was an insufficient amount to positively confirm the mopping of microcystin. We recommended the use of 5.75g of cells in a repetition of the same experiment. In addition, if we could increase the number of PP1 in the periplasm we would increase the probability of binding microcystin and improve the effectiveness of the ToxiMop. For use in realistic applications, such an increase in PP1 would reduce the total mass of cells required for clean-up, making our solution more feasible. Therefore, increasing the number of PP1 being exported into the periplasm continued to be our main focus.

Increasing Tat machinery

As discussed, the second option we investigated was increasing the number of PP1 being exported into the periplasm. We attempted to achieve this by increasing the amount of Tat machinery per cell. Our models predicted that the cells retain 1200 PP1 in the cytoplasm which have no contribution in our ToxiMop application. By increasing the Tat machinery, we target transporting these excess proteins which results in greater PP1 numbers in the periplasm. The options we considered were; increasing TatA assemblies, increasing TatB-C complexes or simultaneously increasing both TatA assemblies & TatB-C complexes.

All the options were simulated to examine their effects on the number of PP1 being exported. This allowed us to determine and inform the Wet Team which was the best option to pursue.

Theoretically our increases would 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 that correspond to the particular genes. Therefore our cells could produce 20 times as much of the targeted proteins. For example; to increase TatA assemblies, we insert the TatA gene into the plasmid, to increase TatB-C complexes, we insert the TatB and TatC genes, and to increase both TatA assemblies and TatB-C complexes we insert all three genes. The simulations are incremented from the current machinery amounts (30 TatA assemblies & 15 TatB-C complexes) to 20 times these values to reflect this potential increase.

Increasing TatA assemblies

Figure 13: PP1_cyto Stochastic means for the corresponding number of TatA Assemblies [8] - Figure 14: PP1_peri Stochastic means for the corresponding number of TatA Assemblies [8]

Figure 15:Change in number of PP1_peri with increasing TatA Assemblies [8] - Figure 16: Mass of Cells required for ToxiMop experiment based on the number of TatA Assemblies [8]

Increasing the number of TatA assemblies, marginally increases the number of PP1 being exported. 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

Figure 17: PP1_cyto Stochastic means for the corresponding number of TatB-C Complexes [9] - Figure 18: PP1_peri Stochastic means for the corresponding number of TatB-C Complexes [9]

Figure 19:Change in number of PP1peri with increasing TatB-C Complexes [9] - Figure 20: Mass of Cells required for ToxiMop experiment based on the number of TatB-C Complexes [9]

As shown in the figures above, increasing the number of TatB-C complexes allows up to 3500 PP1 to be exported into the periplasm. This change is significant and the number of PP1 in the periplasm of our cells is sufficiently increased to improve our ToxiMop cells. With such an increase, the mass of cells required for clean-up is highly reduced allowing us to suggest this approach.

Increasing TatA assemblies & TatB-C

Figure 21: PP1_cyto Increasing TatA assemblies & TatB-C - Figure 22: PP1_peri Stochastic means for the corresponding TatB-C Complex-TatA Assembly combinations [10]

As shown in the figures above, increasing the number of TatB-C complexes allows up to 3500 PP1 to be exported into the periplasm. This change is significant and the number of PP1 in the periplasm of our cells is sufficiently increased to improve our ToxiMop cells. With such an increase, the mass of cells required for clean-up is highly reduced allowing us to suggest this approach.

Increasing both the number of TatA assemblies and TatB-C complexes increases the number of PP1 in the periplasm up to 3900 proteins. Of the possible options, this gives us the greatest increase in PP1 exported to the periplasm of our ToxiMop cells. Of course, as with the previous case, the mass of cells required for application is also significantly reduced to an achievable amount.

From a numerical stance and with respect to PP1 number alone, this approach would produce the most efficient ToxiMop cells. However, when comparing the difference between the inclusion of TatB and TatC genes against their inclusion alongside TatA, considerations must also be made regarding the increased stress placed upon cells which must produce all three proteins.

In conclusion, increasing TatA assemblies alone does not provide a sufficiently significant change in the number of exported PP1. Combining this with an increased TatB-C complex number produces the highest potential for PP1 export. Therefore, for our ToxiMop experimental cells we recommended this option based upon its numeric merits. However, we instructed the Wet Team to consider the stress being placed upon the cells with these newly introduced protein productions.

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. 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.



• 3. MATLAB program repository: https://github.com/cdjohnston/CraigiGEM-MATLAB



• 4. Palmer, Tracy, and Ben C. Berks. "The twin-arginine translocation (Tat) protein export pathway." Nature Reviews Microbiology 10.7 (2012): 483-496.



• 5. Higham, Desmond J. "Modeling and simulating chemical reactions." SIAM review 50.2 (2008): 347-368.



• 6. https://github.com/cdjohnston/CraigiGEM-MATLAB/blob/master/Production%20%26%20Export/Stochastic%20Models/v1_ssa_PP1_TATproduction_export.m



• 7. https://github.com/cdjohnston/CraigiGEM-MATLAB/blob/master/Production%20%26%20Export/Stochastic%20Models/v2_ssa_PP1_TATproduction_export.m



• 8. https://github.com/cdjohnston/CraigiGEM-MATLAB/blob/master/Production%20%26%20Export/Stochastic%20Models/v6_ssa_PP1_TATproduction_export.m



• 9. https://github.com/cdjohnston/CraigiGEM-MATLAB/blob/master/Production%20%26%20Export/Stochastic%20Models/v7_ssa_PP1_TATproduction_export.m



• 10. https://github.com/cdjohnston/CraigiGEM-MATLAB/blob/master/Production%20%26%20Export/Stochastic%20Models/v8_ssa_PP1_TATproduction_export.m