Team:Dundee/Project/ProductionExport

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<H2>Model predicts failure of basic mop </h2>
<H2>Model predicts failure of basic mop </h2>
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<p>As discussed above, the model predicts that 3.3g of  the basic mop would be required  to clean up one litre of contaminated water as defined by WHO regulations. This equates to an impractically  large quantity. Moreover, with these basic  cells the Wet Team started testing the ToxiMop. 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. </p>
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<p>As discussed above, the model predicts that 3.3g of  the basic mop would be required  to clean up one litre of contaminated water as defined by WHO regulations. This equates to an impractically  large quantity. Moreover, with these basic  cells the Wet Team started testing the ToxiMop. 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. We tried to get an understanding of why the tests were unsuccessful. </p>
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<Br><br>We tried to get an understanding of why the tests were unsuccessful.
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The model predicted that 5.75g of cells would be required to clean up the toxin present in the experimental sample.  Hence the 1g of cells used was vastly  insufficient.  We recommended the use of 5.75g of cells in a repetition of the same experiment. However, this was viewed  as being unpractical and hence the Team decided to pursue ways of improving the efficiency of the mop. </div>
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As detailed in (6), the model predicted that 5.75g of cells would be required to clean up the toxin present in the experimental sample.  Hence the 1g of cells used was vastly  insufficient.  We recommended the use of 5.75g of cells in a repetition of the same experiment. However, this was viewed  as being unpractical and hence the Team decided to pursue ways of improving the efficiency of the mop. </div>
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Revision as of 12:04, 3 October 2013

iGEM Dundee 2013 · ToxiMop

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 to better understand PP1 production and export. This was crucial as we hypothesised that microcystin binding would predominantly take place with periplasmic PP1.

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 (PP1cyto) 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 PP1export. PP1export is then exported into the periplasm (PP1peri), 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. 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

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 this repository [4]. The program v1_odes_solver_PP1Production solves this system numerically.

Our model predicts that we will produce approximately 1200 net PP1 in steady state in the cytoplasm of each E. coli chassis. This gives an initial indication of how many cells are required to mop up given concentrations of microcystin. We used 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 was easily achievable by our Wet Team.



Figure 3: PP1 production. Solutions of equation (3).

Figure 4: PP1 produced per cell division. Solutions of equation (3).

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-1s-1
Recognition unbinding K2 8E3 M-1.s-1
Assembly association K3 200E4 M-1s-1
Assembly disassociation K4 0.00167 s-1
Export K5 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 regular 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 approximately 200 PP1 molecules would be exported to the periplasm. This was less than we anticipated. Indeed , based on these figures, 3.3g of cells would be required to clean up one litre of contaminated water as defined by WHO regulations.

Figure 5: PP1 production & export

Figure 6: 202 PP1 are exported to the periplasm and 1164 remain in the cytoplasm

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 PP1 numbers, we formulated and analysed a stochastic model.

The stochastic model, although better representing the random nature associated with such processes, did not produce significantly different results. Instead the model showed that because the 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: PP1cyto Stochastic mean & realisations [7]

Figure 8: PP1peri Stochastic mean & realisations [7]

Figure 9: PP1cyto Stochastic realisations & Deterministic Solution [8]

Figure 10: 2PP1peri Stochastic realisations & Deterministic Solution [8]

Model predicts failure of basic mop

As discussed above, the model predicts that 3.3g of the basic mop would be required to clean up one litre of contaminated water as defined by WHO regulations. This equates to an impractically large quantity. Moreover, with these basic cells the Wet Team started testing the ToxiMop. 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. We tried to get an understanding of why the tests were unsuccessful.







As detailed in (6), the model predicted that 5.75g of cells would be required to clean up the toxin present in the experimental sample. Hence the 1g of cells used was vastly insufficient. We recommended the use of 5.75g of cells in a repetition of the same experiment. However, this was viewed as being unpractical and hence the Team decided to pursue ways of improving the efficiency of the mop.

Increasing Tat machinery

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. 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 11: PP1cyto Stochastic means for the corresponding number of TatA Assemblies [9]

Figure 12: PP1peri Stochastic means for the corresponding number of TatA Assemblies [9]

Figure 13: Change in number of PP1peri with increasing TatA Assemblies [9]

Figure 14: 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. 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 15: PP1cyto Stochastic means for the corresponding number of TatB-C Complexes [10]

Figure 16: PP1peri Stochastic means for the corresponding number of TatB-C Complexes [10]

Figure 17: Change in number of PP1peri with increasing TatB-C Complexes [10]

Figure 18: 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 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 19: PP1cyto Increasing TatA assemblies & TatB-C

Figure 20: PP1peri Stochastic means for the corresponding TatB-C Complex-TatA Assembly combinations [11]




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