Difference between revisions of "Team:Freiburg/Delivery"

 
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<h5 style="text-align:center"> Results - Drug Delivery</h5>
 
<div class="team_pic_div"> <img style="width:55%;float:left;margin-top:4%;" src="https://static.igem.org/mediawiki/2016/0/0e/T--Freiburg--DeliverySummary.png">  
 
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<span style="font-size:14px"><b>Figure 1: Depiction of GST displaying spores.</b> <br>Conversion process of CDNB and GSH to G-SDNB by GST displaying spores.</span>
 
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<span style="font-size:14px"><b>Figure 1:</b> Depiction of GST displaying spores. Conversion process of CDNB and GSH to G-SDNB by GST displaying spores.</span>
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Displaying a functional enzymatic moiety on the surface of the spores represents an essential feature for the activation of prodrugs. We evaluated glutathione-S-transferase (GST) displaying spores as potential carrier for the activation of azathioprine and verified their functionality in a colorimetric GST assay. The spores displaying GST exhibited an increased enzymatic activity in the conjugation of reduced glutathione(GSH) to 1-chloro-2,4-dinitrobenzene (CDNB) compared to unmodified spores and therefore provide evidence for their feasibility as a carrier for targeted drug delivery.
+
Displaying a functional enzymatic moiety on the surface of the spores represents an essential feature for the activation of prodrugs. We evaluated glutathione-S-transferase (GST) displaying spores as potential carrier for the activation of azathioprine and verified their functionality in a colorimetric GST assay.<br>
 +
The spores displaying GST exhibited an increased enzymatic activity in the conjugation of reduced glutathione (GSH) to 1-chloro-2,4-dinitrobenzene (CDNB) compared to unmodified spores and therefore provide evidence for their feasibility as a carrier for targeted drug delivery.
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The treatment of ulcerative colitis with the prodrug azathioprine and the conversion to its active form 6-mercaptopurine in the liver by glutathione S-transferase results in a systemic drug dispersion throughout the whole body, greatly harming healthy tissues as well as diseased cells. As a base analog 6-mercaptopurine inhibits the nucleic acid synthesis by inhibition of the purine metabolism, thus leading to apoptosis of highly proliferating cells. To ensure the local activation of the prodrug we modified the spores of B. subtilis to display a functional GST on their surface, which facilitates the activation of azathioprine. This approach provides that the enzymatic activity can be delivered to the affected sites in the gut and promotes the local treatment. Therefore, considerably lower amounts of the prodrug can be administered resulting in a reduction of systemic side effects. In order confirm the feasibility of those modification analysis of the proper display of GST and its functionality is required.
+
The treatment of ulcerative colitis with the prodrug azathioprine and the conversion to its active form 6-mercaptopurine in the liver by glutathione S-transferase results in a systemic drug dispersion throughout the whole body, greatly harming healthy tissues as well as diseased cells. As a base analog 6-mercaptopurine inhibits the nucleic acid synthesis by inhibition of the purine metabolism, thus leading to apoptosis of highly proliferating cells.<br>
 +
To ensure the local activation of the prodrug we modified the spores of <i>B. subtilis</i> to display a functional GST on their surface, which facilitates the activation of azathioprine. This approach provides that the enzymatic activity can be delivered to the affected sites in the gut and promotes the local treatment. Therefore, considerably lower amounts of the prodrug can be administered resulting in a reduction of systemic side effects. In order to confirm the feasibility of those modifications, analysis of the proper display of GST and its functionality is required.
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<h5 style="text-align: center"> Our Approach </h5>
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<h5 style="text-align: center"> Results </h5>
 
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To determine the functionality of the displayed GST on the spores we first verified the localization on the surface of the spore. We assembled an integration vector containing a construct with GST fused to the spore coat gene cotG and a hemagglutinin epitope tag (<a target="_blank" href='http://parts.igem.org/Part:BBa_K2114011' style="color: #99ff33">BBa_K2114011</a>), which was driven by the PCotYZ-RBS promoter (<a target="_blank" href='http://parts.igem.org/Part:BBa_K2114000' style="color: #99ff33">BBa_K2114000</a>) and transformed them into <i>B. subtilis</i>.<br>
 +
After selection the resulting spores should display GST on their surface. We verified the proper localization of the fusion protein by immunostaining with anti-HA antibodies conjugated to Alexa Fluor 647 and flow cytometry (Figure 2). Spores bound by the conjugated antibody appeared at a higher fluorescence intensity in the scatter plot. We observed two distinguishable populations, suggesting the presence of different stages in the spores.
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<center><img class="something" src="https://static.igem.org/mediawiki/2016/7/7c/T--Freiburg--DeliveryResultsneu.png"> </center>
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<b>Figure 2: Scatter plot of immunostained spores displaying GST.</b><br>
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Spores transformed with the part BBa_K2114011 driven by the promoter PCotYZ-RBS (BBa_K2114000) displayed GST and an HA epitope tag on their surface, which could be verified by staining with anti-HA antibodies conjugated to Alexa Fluor 647. The stained spores exhibited a higher fluorescence intensity.
  
 
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To verify the functionality of the displayed GST we performed a colorimetric GST assay. This assay is based on the GST-catalyzed conjugation of the thiol group of reduced glutathione (GSH) to the GST substrate 1-chloro-2,4-dinitrobenzene (CDNB). The GST-catalyzed reaction produces a dinitrophenyl thioether which can be detected by a spectrophotometer at 340 nm.<br>
 +
The modified spores displaying GST were incubated with the substrates and the absorbance was monitored for a time course of 30 min (figure 3 A). We could verify that spores displaying GST had a significantly increased change of absorbance at 340 nm in comparison to unmodified wild type spores (figure 3 B). We calculated the enzymatic activity from the linear increase of the absorbance at 340 nm and could determine a turnover of the substrate at 1.5 nmol/ml/min.
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<center><img class="something" src="https://static.igem.org/mediawiki/2016/2/22/T--Freiburg--ResultsDeliveryFigure4.png"> </center>
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<b>Figure 3: GST assay with GST displaying spores compared to WT.</b><br>
 +
<b>(A)</b> The GST assay was performed with 25 million GST-displaying spores (BBa_K2114001). The absorbance at 340 nm was monitored for a time course of 30 min. Unmodified wild type spores were used as reference (WT). <br>
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<b>(B)</b> The increase of the absorbance in time is significantly higher for GST displaying spores compared to WT spores.
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We could verify that GST is located on the surface of the spores and functional as shown by flow cytometry analysis and a GST assay.
 +
During our experiments we observed that the spores unexpectedly exhibited two distinguishable populations in flow cytometry after staining with specific antibodies. We concluded that the spores most likely implicate distinct stages of sporulation, with different accessibility of the heterologous proteins that are displayed on the surface. Further optimization could increase the potential of
 +
<a target="_blank" style="color: #99ff33" href='https://2016.igem.org/Team:Freiburg/Production_Nanocillus' >Nanocillus</a>.
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Such as the improvement of the display efficiency, through synchronization of the sporulation process, thus avoiding the heterogeneity of the spores. The simultaneous utilization of additional coat proteins besides CotG for the display of GST would result in a higher amount of displayed enzyme on the spore surface and thus an increased overall activity of the Nanocillus.
 +
Nevertheless, due to their enormous versatility and modifiability we can conclude that our Nanocillus spores represent a promising approach for targeted drug delivery.
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<h5>Enzyme modelling:</h5>
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Michaelis-Menten kinetics provides a good theoretical basis to analyze the behavior of enzymes under different substrate conditions. Although the idea of the classical enzyme substrate complex is outdated and has been superseded by the idea of an “induced fit” the mathematical equations of Michaelis and Menten offer a good foundation to predict the amount of product produced by an enzyme under a certain substrate concentration<sup>1</sup>. <br> <br>
 +
 +
         
 +
 +
Our goal was to generate a simple but effective model that could be included in the wet lab work for more easy and efficient planning and evaluation. <br> <br>
 +
 +
 +
We thought the easiest way to approach such a goal was to display the data by graphical visualization. <br> <br>
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 +
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<center><img class="something" src="https://static.igem.org/mediawiki/2016/5/55/T--Freiburg--Modeling1.png"> </center> <br>
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<b>Figure 4: Visualization of Michaelis-Menten kinetic.</b> <br> <br>
 +
 +
         
 +
 +
Using this visualization, we can set the differential equations to simulate the enzyme-substrate interaction. <br> <br>
 +
 +
Equation 1: <br>
 +
 +
<center><img class="something" src="https://static.igem.org/mediawiki/2016/5/54/T--Freiburg--Modeling5.png"> </center> <br>
 +
<b>Figure 5: First part of Michaelis-Menten kinetic.</b> <br> <br>
 +
<center><img class="something" src="https://static.igem.org/mediawiki/2016/5/50/T--Freiburg--Modeling27.png"> </center> <br>
 +
<b>Figure 6:</b> [k1=association constant of E and S to ES, k-1=dissociation constant of ES into E and S, [E]=enzyme concentration, [S]=substrate concentration, [ES]=enzyme-substrate-complex concentration] <br> <br>
 +
 +
 +
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Equation 2:
 +
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<br> <br>
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<center><img class="something" style="width:70%" src="https://static.igem.org/mediawiki/2016/8/89/T--Freiburg--Modeling6.png"> </center> <br>
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<b>Figure 7: Second part of Michaelis-Menten kinetic.</b> <br>
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 +
<center><img class="something" src="https://static.igem.org/mediawiki/2016/d/d4/T--Freiburg--Modeling28.png"> </center> <br>
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<b>Figure 8:</b> [k2=dissociation constant of ES into E and P, k-2= association constant of E and P to ES, [E]=enzyme concentration, [P]=product concentration, [ES]=enzyme-substrate-complex concentration] <br> <br>
 +
 +
With these equations we can calculate the change of the different components over time. <br> <br>
 +
 +
<center><img class="something" style="width:50%"src="https://static.igem.org/mediawiki/2016/d/dd/T--Freiburg--Modeling29.png"> </center> <br>
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<b>Figure 9:
 +
 +
System of the equations of Michaelis-Menten kinetic </b>
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<br><br>
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<br><br>
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<br><br>
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<center><img class="something" src="https://static.igem.org/mediawiki/2016/4/43/T--Freiburg--Modeling14.png"> </center> <br>
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<b>Figure 10:
 +
 +
Here you can see the increase of product [P] (yellow line graph) and decrease of substrate [S] (blue line graph).</b> <br>
 +
 +
 +
{k1=5, k2=0, k3=5,k4=0, E[0] = 50, S[0] = 2000, ES[0] = 0, P[0] = 0, concentration in mM, time in hours}
 +
<br><br>
 +
However our system is more complex than the equations mentioned above would describe. <br>
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<center><img class="something" src="https://static.igem.org/mediawiki/2016/7/75/T--Freiburg--Modeling7.png"> </center>
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<b>Figure 11: Rapid equilibrium random sequential bi-bi mechanism of GST.</b> <br> <br>
 +
 +
As you can see in the illustration above the reaction catalysed by GST consists of two substrates<sup>2</sup>.      <br>   
 +
 +
So the next step consisted of collecting information about the exact reaction mechanism. Our literature search revealed that it is the reaction mechanism of a rapid equilibrium random sequential bi-bi mechanism<sup>3</sup>.        <br>
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 +
 +
Using a visualization we can set the differential equations to simulate the enzyme-substrate interactions.<br>
 +
 +
<center><img class="something" style="width:80%" src="https://static.igem.org/mediawiki/2016/5/57/T--Freiburg--Modeling8.png"> </center><br>
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<b>Figure 12: Visualization of a rapid equilibrium random sequential bi-bi mechanism.</b>
 +
<br><br>
 +
 +
Equation 1:
 +
<br>
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<center><img class="something" style="width:25%" src="https://static.igem.org/mediawiki/2016/d/d7/T--Freiburg--Modeling9.png"> </center><br>
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<b>Figure 13: First part of the rapid equilibrium random sequential bi-bi mechanism.</b><br><br>
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 +
<center><img class="something" src="https://static.igem.org/mediawiki/2016/d/dc/T--Freiburg--Modeling30.png"> </center><br>
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<b>Figure 14:</b> → [A] has no direct influence on the reaction between [B] and [E]<br><br>
 +
 +
 +
[k1= association constant of E and B into EB , k-1=dissociation constant of EB into E and B, [E]=enzyme concentration, [B]=concentration of substrate B, [EB]=enzyme-substrate-B-complex concentration]
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<br><br>
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Equation 2:
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<br>
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<center><img class="something" src="https://static.igem.org/mediawiki/2016/a/ad/T--Freiburg--Modeling10.png"> </center><br>
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<b>Figure 15: Second  part of the rapid equilibrium random sequential bi-bi mechanism.</b>
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<br>
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<center><img class="something" src="https://static.igem.org/mediawiki/2016/3/3b/T--Freiburg--Modeling31.png"> </center><br>
 +
<b>Figure 16:</b> → [B] has no direct influence on the reaction between [A] and [E]<br><br>
 +
 +
 +
[k2= association constant of E and A into EA , k-2=dissociation constant of EA into E and A, [E]=enzyme concentration, [A]=concentration of substrate A, [EA]=enzyme-substrate-A-complex concentration]<br><br>
 +
 +
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Equation 3:
 +
<br><br>
 +
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<center><img class="something" src="https://static.igem.org/mediawiki/2016/c/c5/T--Freiburg--Modeling11.png"> </center><br>
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<b>Figure 17:</b> Third part of the rapid equilibrium random sequential bi-bi mechanism.<br>
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 +
<center><img class="something" src="https://static.igem.org/mediawiki/2016/0/00/T--Freiburg--Modeling32.png"> </center><br>
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<b>Figure 18:</b> [k3= association constant of EB and A into EAB , k-3=dissociation constant of EAB into EB and A, [EAB]=enzyme-substrate-A-B-complex concentration, [A]=concentration of substrate A, [EB]=enzyme-substrate B-complex concentration]
 +
<br><br>
 +
 +
 +
 +
Equation 4:<br><br>
 +
 +
<center><img class="something" style="width:30%" src="https://static.igem.org/mediawiki/2016/6/6e/T--Freiburg--Modeling12.png"> </center><br>
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<b>Figure 19: Fourth part of the rapid equilibrium random sequential bi-bi mechanism.</b><br><br>
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 +
 +
 +
<center><img class="something" src="https://static.igem.org/mediawiki/2016/c/c8/T--Freiburg--Modeling33.png"> </center><br>
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<b>Figure 20:</b> [k4= association constant of EA and B into EAB , k-4=dissociation constant of EAB into EA and B, [EAB]=enzyme-substrate-A-B-complex concentration, [B]=concentration of substrate B, [EA]=enzyme-substrate-A-complex concentration]
 +
 +
<br><br>
 +
Equation 5:<br><br>
 +
 +
<center><img class="something" src="https://static.igem.org/mediawiki/2016/d/d8/T--Freiburg--Modeling13.png"> </center><br>
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<b>Figure 21: Five part of the rapid equilibrium random sequential bi-bi mechanism.</b><br><br>
 +
 +
 +
<center><img class="something" src="https://static.igem.org/mediawiki/2016/d/df/T--Freiburg--Modeling34.png"> </center><br>
 +
<b>Figure 22:</b> [k5=dissociation constant of EAB into E, P and Q , k-3=association constant of E, P and Q to EAB, [EAB]=enzyme-substrate-A-B-complex concentration, [Q]=concentration of product Q, [P]=concentration of product P]
 +
 +
<br><br>
 +
Again with these equations we can calculate the change of the different components over the time.<br><br>
 +
 +
<center><img class="something" style="width:30%" src="https://static.igem.org/mediawiki/2016/5/52/T--Freiburg--Modeling35.png"> </center><br>
 +
<b>Figure 23:
 +
 +
System of the equations of rapid equilibrium random sequential bi-bi mechanism. </b>
 +
<br><br>
 +
<br><br>
 +
<br><br>
 +
<center><img class="something" src="https://static.igem.org/mediawiki/2016/7/79/T--Freiburg--Modeling15.png"> </center><br>
 +
<b>Figure 24:
 +
Here you can see the increase of product one  [P] (blue line graph) and  product two [Q] (yellow line graph).</b> <br>
 +
{k1=0.5, k-1=0.03, k2=0.4, k-2=0.01, k3=0.6, k-3=0.02, k4=0.7, k-4=0.001, k5=0.5, k-5=0.0001,  A[0] = 30, B[0] = 20, E[0] = 5, EB[0] = 10, EA[0] = 5, EAB[0] = 0,P[0] = 10,Q[0] = 0, concentration in mM, time in hours}
 +
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1.  Kostland, D.E.,Application of a Theory of Enzyme Specificity to Protein Synthesis ,  Proceedings of the National Academy of Sciences of the United States of America, Vol. 44, No. 2 (Feb. 15, 1958), pp. 98-104
 +
<br>
 +
 +
2. Jakonbon, IN., A Steady-State-Kinetic Random Mechanism for Glutathione S-Transferase A from Rat Liver , (Received October 14, 1976/March 18, 1977
 +
<br>
 +
3.  A rapid equilibrium random sequential bi-bi mechanism for human placental glutathione S-transferase, Biomolecular Resource Centre, University of California, San Francisco 94143-0541
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Latest revision as of 03:11, 20 October 2016

Results - Drug Delivery
Figure 1: Depiction of GST displaying spores.
Conversion process of CDNB and GSH to G-SDNB by GST displaying spores.
Displaying a functional enzymatic moiety on the surface of the spores represents an essential feature for the activation of prodrugs. We evaluated glutathione-S-transferase (GST) displaying spores as potential carrier for the activation of azathioprine and verified their functionality in a colorimetric GST assay.
The spores displaying GST exhibited an increased enzymatic activity in the conjugation of reduced glutathione (GSH) to 1-chloro-2,4-dinitrobenzene (CDNB) compared to unmodified spores and therefore provide evidence for their feasibility as a carrier for targeted drug delivery.
Introduction
The treatment of ulcerative colitis with the prodrug azathioprine and the conversion to its active form 6-mercaptopurine in the liver by glutathione S-transferase results in a systemic drug dispersion throughout the whole body, greatly harming healthy tissues as well as diseased cells. As a base analog 6-mercaptopurine inhibits the nucleic acid synthesis by inhibition of the purine metabolism, thus leading to apoptosis of highly proliferating cells.
To ensure the local activation of the prodrug we modified the spores of B. subtilis to display a functional GST on their surface, which facilitates the activation of azathioprine. This approach provides that the enzymatic activity can be delivered to the affected sites in the gut and promotes the local treatment. Therefore, considerably lower amounts of the prodrug can be administered resulting in a reduction of systemic side effects. In order to confirm the feasibility of those modifications, analysis of the proper display of GST and its functionality is required.
Results
To determine the functionality of the displayed GST on the spores we first verified the localization on the surface of the spore. We assembled an integration vector containing a construct with GST fused to the spore coat gene cotG and a hemagglutinin epitope tag (BBa_K2114011), which was driven by the PCotYZ-RBS promoter (BBa_K2114000) and transformed them into B. subtilis.
After selection the resulting spores should display GST on their surface. We verified the proper localization of the fusion protein by immunostaining with anti-HA antibodies conjugated to Alexa Fluor 647 and flow cytometry (Figure 2). Spores bound by the conjugated antibody appeared at a higher fluorescence intensity in the scatter plot. We observed two distinguishable populations, suggesting the presence of different stages in the spores.
Figure 2: Scatter plot of immunostained spores displaying GST.
Spores transformed with the part BBa_K2114011 driven by the promoter PCotYZ-RBS (BBa_K2114000) displayed GST and an HA epitope tag on their surface, which could be verified by staining with anti-HA antibodies conjugated to Alexa Fluor 647. The stained spores exhibited a higher fluorescence intensity.
To verify the functionality of the displayed GST we performed a colorimetric GST assay. This assay is based on the GST-catalyzed conjugation of the thiol group of reduced glutathione (GSH) to the GST substrate 1-chloro-2,4-dinitrobenzene (CDNB). The GST-catalyzed reaction produces a dinitrophenyl thioether which can be detected by a spectrophotometer at 340 nm.
The modified spores displaying GST were incubated with the substrates and the absorbance was monitored for a time course of 30 min (figure 3 A). We could verify that spores displaying GST had a significantly increased change of absorbance at 340 nm in comparison to unmodified wild type spores (figure 3 B). We calculated the enzymatic activity from the linear increase of the absorbance at 340 nm and could determine a turnover of the substrate at 1.5 nmol/ml/min.
Figure 3: GST assay with GST displaying spores compared to WT.
(A) The GST assay was performed with 25 million GST-displaying spores (BBa_K2114001). The absorbance at 340 nm was monitored for a time course of 30 min. Unmodified wild type spores were used as reference (WT).
(B) The increase of the absorbance in time is significantly higher for GST displaying spores compared to WT spores.
We could verify that GST is located on the surface of the spores and functional as shown by flow cytometry analysis and a GST assay. During our experiments we observed that the spores unexpectedly exhibited two distinguishable populations in flow cytometry after staining with specific antibodies. We concluded that the spores most likely implicate distinct stages of sporulation, with different accessibility of the heterologous proteins that are displayed on the surface. Further optimization could increase the potential of Nanocillus. Such as the improvement of the display efficiency, through synchronization of the sporulation process, thus avoiding the heterogeneity of the spores. The simultaneous utilization of additional coat proteins besides CotG for the display of GST would result in a higher amount of displayed enzyme on the spore surface and thus an increased overall activity of the Nanocillus. Nevertheless, due to their enormous versatility and modifiability we can conclude that our Nanocillus spores represent a promising approach for targeted drug delivery.
Enzyme modelling:
Michaelis-Menten kinetics provides a good theoretical basis to analyze the behavior of enzymes under different substrate conditions. Although the idea of the classical enzyme substrate complex is outdated and has been superseded by the idea of an “induced fit” the mathematical equations of Michaelis and Menten offer a good foundation to predict the amount of product produced by an enzyme under a certain substrate concentration1.

Our goal was to generate a simple but effective model that could be included in the wet lab work for more easy and efficient planning and evaluation.

We thought the easiest way to approach such a goal was to display the data by graphical visualization.


Figure 4: Visualization of Michaelis-Menten kinetic.

Using this visualization, we can set the differential equations to simulate the enzyme-substrate interaction.

Equation 1:

Figure 5: First part of Michaelis-Menten kinetic.


Figure 6: [k1=association constant of E and S to ES, k-1=dissociation constant of ES into E and S, [E]=enzyme concentration, [S]=substrate concentration, [ES]=enzyme-substrate-complex concentration]

Equation 2:


Figure 7: Second part of Michaelis-Menten kinetic.

Figure 8: [k2=dissociation constant of ES into E and P, k-2= association constant of E and P to ES, [E]=enzyme concentration, [P]=product concentration, [ES]=enzyme-substrate-complex concentration]

With these equations we can calculate the change of the different components over time.


Figure 9: System of the equations of Michaelis-Menten kinetic






Figure 10: Here you can see the increase of product [P] (yellow line graph) and decrease of substrate [S] (blue line graph).
{k1=5, k2=0, k3=5,k4=0, E[0] = 50, S[0] = 2000, ES[0] = 0, P[0] = 0, concentration in mM, time in hours}

However our system is more complex than the equations mentioned above would describe.
Figure 11: Rapid equilibrium random sequential bi-bi mechanism of GST.

As you can see in the illustration above the reaction catalysed by GST consists of two substrates2.
So the next step consisted of collecting information about the exact reaction mechanism. Our literature search revealed that it is the reaction mechanism of a rapid equilibrium random sequential bi-bi mechanism3.
Using a visualization we can set the differential equations to simulate the enzyme-substrate interactions.

Figure 12: Visualization of a rapid equilibrium random sequential bi-bi mechanism.

Equation 1:

Figure 13: First part of the rapid equilibrium random sequential bi-bi mechanism.


Figure 14: → [A] has no direct influence on the reaction between [B] and [E]

[k1= association constant of E and B into EB , k-1=dissociation constant of EB into E and B, [E]=enzyme concentration, [B]=concentration of substrate B, [EB]=enzyme-substrate-B-complex concentration]

Equation 2:

Figure 15: Second part of the rapid equilibrium random sequential bi-bi mechanism.

Figure 16: → [B] has no direct influence on the reaction between [A] and [E]

[k2= association constant of E and A into EA , k-2=dissociation constant of EA into E and A, [E]=enzyme concentration, [A]=concentration of substrate A, [EA]=enzyme-substrate-A-complex concentration]

Equation 3:


Figure 17: Third part of the rapid equilibrium random sequential bi-bi mechanism.

Figure 18: [k3= association constant of EB and A into EAB , k-3=dissociation constant of EAB into EB and A, [EAB]=enzyme-substrate-A-B-complex concentration, [A]=concentration of substrate A, [EB]=enzyme-substrate B-complex concentration]

Equation 4:


Figure 19: Fourth part of the rapid equilibrium random sequential bi-bi mechanism.


Figure 20: [k4= association constant of EA and B into EAB , k-4=dissociation constant of EAB into EA and B, [EAB]=enzyme-substrate-A-B-complex concentration, [B]=concentration of substrate B, [EA]=enzyme-substrate-A-complex concentration]

Equation 5:


Figure 21: Five part of the rapid equilibrium random sequential bi-bi mechanism.


Figure 22: [k5=dissociation constant of EAB into E, P and Q , k-3=association constant of E, P and Q to EAB, [EAB]=enzyme-substrate-A-B-complex concentration, [Q]=concentration of product Q, [P]=concentration of product P]

Again with these equations we can calculate the change of the different components over the time.


Figure 23: System of the equations of rapid equilibrium random sequential bi-bi mechanism.






Figure 24: Here you can see the increase of product one [P] (blue line graph) and product two [Q] (yellow line graph).
{k1=0.5, k-1=0.03, k2=0.4, k-2=0.01, k3=0.6, k-3=0.02, k4=0.7, k-4=0.001, k5=0.5, k-5=0.0001, A[0] = 30, B[0] = 20, E[0] = 5, EB[0] = 10, EA[0] = 5, EAB[0] = 0,P[0] = 10,Q[0] = 0, concentration in mM, time in hours}
1. Kostland, D.E.,Application of a Theory of Enzyme Specificity to Protein Synthesis , Proceedings of the National Academy of Sciences of the United States of America, Vol. 44, No. 2 (Feb. 15, 1958), pp. 98-104
2. Jakonbon, IN., A Steady-State-Kinetic Random Mechanism for Glutathione S-Transferase A from Rat Liver , (Received October 14, 1976/March 18, 1977
3. A rapid equilibrium random sequential bi-bi mechanism for human placental glutathione S-transferase, Biomolecular Resource Centre, University of California, San Francisco 94143-0541

Posted by: iGEM Freiburg

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