Difference between revisions of "Team:CityU HK/Collaborations"

 
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<div class="paragraph" style="text-align:left;"><span style="">Partner team: Hong_Kong-CUHK</span><br><span style="">Project: Magneto-bacter vinelandii Magnetosome-forming&nbsp;</span><em style="">Azotobacter vinelandii</em><span style="">&nbsp;with Downstream Applications &nbsp;</span></div>
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<div class="paragraph" ><span style="">Partner team: Hong_Kong-CUHK</span><br><span style="">Project: Magneto-bacter vinelandii Magnetosome-forming&nbsp;</span><em style="">Azotobacter vinelandii</em><span style="">&nbsp;with Downstream Applications &nbsp;</span></div>
  
  
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<div class="paragraph" style="text-align:left;"><font size="4"><font color="#2a2a2a">In our collaboration work with the Chinese University of Hong Kong iGEM team, we were given the task to assist them with their project by doing a simulation that look into the interaction between GFP-nanobody to different concentrations of GFP.&nbsp;</font><font color="#2a2a2a">It is our honor to be able to collaborate and participate in their project. A wonderful experience we have gained through.</font></font></div>
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<div class="paragraph" ><font size="4"><font color="#2a2a2a">In our collaboration work with the Chinese University of Hong Kong iGEM team, we were given the task to assist them with their project by doing a simulation that look into the interaction between GFP-nanobody to different concentrations of GFP.&nbsp;</font><font color="#2a2a2a">It is our honor to be able to collaborate and participate in their project. A wonderful experience we have gained through.</font></font></div>
  
 
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<h2 class="wsite-content-title" style="text-align:left;">Background</h2>
 
<h2 class="wsite-content-title" style="text-align:left;">Background</h2>
  
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<div class="paragraph" style="text-align:left;"><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:#2a2a2a;mso-font-kerning:0pt"="" style=""><font color="#2a2a2a" size="4">The project of the CUHK iGEM team is to explore the use of magnetosome together with GFP-specific nanobody for immunoprecipitation. Magnetosome is an organelle with a magnetic iron crystal surrounded by a lipid bilayer. It is derived from magnetotactic bacteria which is used for navigation through sensing the Earth magnetic field. Biomolecules such as antibodies can be immobilized on magnetosomes for various scientific applications. One such applications is using magnetosomes together with nanobodies for immunoprecipitation reactions. To make the experiment measurable, green fluorescent protein (GFP)-specific nanobody was used (Figure 1).</font></span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:black;mso-font-kerning:0pt"="" style=""></span><br><span style=""></span><br><span style=""></span><span style=""></span></div>
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<div class="paragraph" ><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:#2a2a2a;mso-font-kerning:0pt"="" style=""><font color="#2a2a2a" size="4">The project of the CUHK iGEM team is to explore the use of magnetosome together with GFP-specific nanobody for immunoprecipitation. Magnetosome is an organelle with a magnetic iron crystal surrounded by a lipid bilayer. It is derived from magnetotactic bacteria which is used for navigation through sensing the Earth magnetic field. Biomolecules such as antibodies can be immobilized on magnetosomes for various scientific applications. One such applications is using magnetosomes together with nanobodies for immunoprecipitation reactions. To make the experiment measurable, green fluorescent protein (GFP)-specific nanobody was used (Figure 1).</font></span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:black;mso-font-kerning:0pt"="" style=""></span><br><span style=""></span><br><span style=""></span><span style=""></span></div>
  
 
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<div class="paragraph" style="text-align:center;"><span style="">Figure 1: Schematic diagram of a magnetosome (adsorbed with GFP-specific nanobodies) interacting with GFPs</span><strong style=""><u style=""><span style=""></span></u></strong><br><span style=""></span><br><span style=""></span></div>
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<div class="paragraph" style="text-align:center;"><span style="font-size:1em;">Figure 1: Schematic diagram of a magnetosome (adsorbed with GFP-specific nanobodies) interacting with GFPs</span><strong style=""><u style=""><span style=""></span></u></strong><br><span style=""></span><br><span style=""></span></div>
  
 
<h2 class="wsite-content-title" style="text-align:left;">Task</h2>
 
<h2 class="wsite-content-title" style="text-align:left;">Task</h2>
  
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<div class="paragraph" style="text-align:left;"><span style=""><font color="#2a2a2a" size="4">Simulate the binding dynamics of a fixed concentration of magnetosome with GFP specific nanobody expressed on its surface in different initial concentrations of antigens (GFP).&nbsp;</font></span><br><span style=""></span></div>
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<div class="paragraph"><span style=""><font color="#2a2a2a" size="4">Simulate the binding dynamics of a fixed concentration of magnetosome with GFP specific nanobody expressed on its surface in different initial concentrations of antigens (GFP).&nbsp;</font></span><br><span style=""></span></div>
  
 
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<h2 class="wsite-content-title" style="text-align:left;">Software - SimBiology<br><span style=""></span></h2>
 
<h2 class="wsite-content-title" style="text-align:left;">Software - SimBiology<br><span style=""></span></h2>
  
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<div class="paragraph" style="text-align:left;"><font color="#2a2a2a" size="4"><span style="">SimBiology is a toolbox in Matlab that enable us to model and simulate the dynamics of the association and dissociation between molecules. Most of the function can be utilized through its GUI (Graphical User Interface). </span><br><span style=""></span><br><span style=""></span>  <span style="">Once the model is constructed (i.e. the mathematic relationships between molecules are set up, parameters such as association constant, molarity of reagent, etc. are provided), we can simulate the reaction or even scan through one or more variables. The “scan” function enables us to simulate the dynamics of the system when some parameters, such as the initial concentration of the reagent, are at different values.</span><br></font><span style=""></span><br><span style=""></span></div>
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<div class="paragraph" ><font color="#2a2a2a" size="4"><span style="">SimBiology is a toolbox in Matlab that enable us to model and simulate the dynamics of the association and dissociation between molecules. Most of the function can be utilized through its GUI (Graphical User Interface). </span><br><span style=""></span><br><span style=""></span>  <span style="">Once the model is constructed (i.e. the mathematic relationships between molecules are set up, parameters such as association constant, molarity of reagent, etc. are provided), we can simulate the reaction or even scan through one or more variables. The “scan” function enables us to simulate the dynamics of the system when some parameters, such as the initial concentration of the reagent, are at different values.</span><br></font><span style=""></span><br><span style=""></span></div>
  
 
<h2 class="wsite-content-title" style="text-align:left;"><span "font-size:12.0pt;font-family:="" &quot;calibri&quot;,&quot;sans-serif&quot;;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:="" &#26032;&#32048;&#26126;&#39636;;mso-fareast-theme-font:minor-fareast;mso-hansi-theme-font:minor-latin;="" mso-bidi-theme-font:minor-latin;mso-ansi-language:en-us;mso-fareast-language:="" zh-tw;mso-bidi-language:ar-sa"="" style="">Assumptions</span></h2>
 
<h2 class="wsite-content-title" style="text-align:left;"><span "font-size:12.0pt;font-family:="" &quot;calibri&quot;,&quot;sans-serif&quot;;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:="" &#26032;&#32048;&#26126;&#39636;;mso-fareast-theme-font:minor-fareast;mso-hansi-theme-font:minor-latin;="" mso-bidi-theme-font:minor-latin;mso-ansi-language:en-us;mso-fareast-language:="" zh-tw;mso-bidi-language:ar-sa"="" style="">Assumptions</span></h2>
  
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<div class="paragraph" style="text-align:left;"><font size="4"><font color="#2a2a2a"><span "font-size:10.0pt;font-family:="" &quot;arial&quot;,&quot;sans-serif&quot;;mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:#2a2a2a;mso-font-kerning:="" 0pt;mso-ansi-language:en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"="">1). All nanobodies are bound on the surface of a magnetosome, i.e. no free floating nanobodies. </span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:black;mso-font-kerning:0pt;mso-ansi-language:="" en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"=""><br> </span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:#2a2a2a;mso-font-kerning:0pt;mso-ansi-language:="" en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"="">2). Each magnetosome has the same number of GFP-specific nanobodies adsorbed on its surface.&nbsp;</span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;mso-fareast-font-family:="" &#26032;&#32048;&#26126;&#39636;;color:black;mso-font-kerning:0pt;mso-ansi-language:en-us;mso-fareast-language:="" zh-tw;mso-bidi-language:ar-sa"=""><br> </span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:#2a2a2a;mso-font-kerning:0pt;mso-ansi-language:="" en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"="">3). A magnetosome does not interact directly with GFP molecules nor interfere with the reactions between GFP-specific nanobodies and GFPs.</span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;mso-fareast-font-family:="" &#26032;&#32048;&#26126;&#39636;;color:black;mso-font-kerning:0pt;mso-ansi-language:en-us;mso-fareast-language:="" zh-tw;mso-bidi-language:ar-sa"=""><br> </span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:#2a2a2a;mso-font-kerning:0pt;mso-ansi-language:="" en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"="">4). The GFP-specific nanobodies on the surface of a magnetosome have the same association and dissociation rate constant to GFP when compared with the GFP-specific nanobody alone.</span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:black;mso-font-kerning:0pt;mso-ansi-language:="" en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"=""><br> </span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:#2a2a2a;mso-font-kerning:0pt;mso-ansi-language:="" en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"="">5). The binding of GFP with GFP-specific nanobody is in a one-to-one ratio.</span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;mso-fareast-font-family:="" &#26032;&#32048;&#26126;&#39636;;color:black;mso-font-kerning:0pt;mso-ansi-language:en-us;mso-fareast-language:="" zh-tw;mso-bidi-language:ar-sa"=""><br> </span></font><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:#2a2a2a;mso-font-kerning:0pt;mso-ansi-language:="" en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"=""><font color="#2a2a2a">6). The reaction follows the law of mass action, which means the reaction rate is proportional to the concentration of the reagents.</font></span></font><br><span style=""></span></div>
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<div class="paragraph" ><font size="4"><font color="#2a2a2a"><span "font-size:10.0pt;font-family:="" &quot;arial&quot;,&quot;sans-serif&quot;;mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:#2a2a2a;mso-font-kerning:="" 0pt;mso-ansi-language:en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"="">1). All nanobodies are bound on the surface of a magnetosome, i.e. no free floating nanobodies. </span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:black;mso-font-kerning:0pt;mso-ansi-language:="" en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"=""><br> </span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:#2a2a2a;mso-font-kerning:0pt;mso-ansi-language:="" en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"="">2). Each magnetosome has the same number of GFP-specific nanobodies adsorbed on its surface.&nbsp;</span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;mso-fareast-font-family:="" &#26032;&#32048;&#26126;&#39636;;color:black;mso-font-kerning:0pt;mso-ansi-language:en-us;mso-fareast-language:="" zh-tw;mso-bidi-language:ar-sa"=""><br> </span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:#2a2a2a;mso-font-kerning:0pt;mso-ansi-language:="" en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"="">3). A magnetosome does not interact directly with GFP molecules nor interfere with the reactions between GFP-specific nanobodies and GFPs.</span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;mso-fareast-font-family:="" &#26032;&#32048;&#26126;&#39636;;color:black;mso-font-kerning:0pt;mso-ansi-language:en-us;mso-fareast-language:="" zh-tw;mso-bidi-language:ar-sa"=""><br> </span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:#2a2a2a;mso-font-kerning:0pt;mso-ansi-language:="" en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"="">4). The GFP-specific nanobodies on the surface of a magnetosome have the same association and dissociation rate constant to GFP when compared with the GFP-specific nanobody alone.</span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:black;mso-font-kerning:0pt;mso-ansi-language:="" en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"=""><br> </span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:#2a2a2a;mso-font-kerning:0pt;mso-ansi-language:="" en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"="">5). The binding of GFP with GFP-specific nanobody is in a one-to-one ratio.</span><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;mso-fareast-font-family:="" &#26032;&#32048;&#26126;&#39636;;color:black;mso-font-kerning:0pt;mso-ansi-language:en-us;mso-fareast-language:="" zh-tw;mso-bidi-language:ar-sa"=""><br> </span></font><span "font-size:10.0pt;font-family:&quot;arial&quot;,&quot;sans-serif&quot;;="" mso-fareast-font-family:&#26032;&#32048;&#26126;&#39636;;color:#2a2a2a;mso-font-kerning:0pt;mso-ansi-language:="" en-us;mso-fareast-language:zh-tw;mso-bidi-language:ar-sa"=""><font color="#2a2a2a">6). The reaction follows the law of mass action, which means the reaction rate is proportional to the concentration of the reagents.</font></span></font><br><span style=""></span></div>
  
 
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<h2 class="wsite-content-title" style="text-align:left;">Model</h2>
  
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<div class="paragraph" style="text-align:left;"><span style=""><font color="#2a2a2a" size="4">Figure 1 shows the model constructed in SimBiology. The blue rounded rectangles represent the reagents, including antigens (GFP), GFP specific nanobody and the nanobody-antigens-complex. The yellow circle represents the binding reaction. The arrow points toward the nanobody-antigens-complex indicate that the complex is the product of the forward reaction. The double arrows above the yellow circle “binding” indicate that the reaction is reversible.</font></span><br></div>
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<div class="paragraph" ><span style=""><font color="#2a2a2a" size="4">Figure 1 shows the model constructed in SimBiology. The blue rounded rectangles represent the reagents, including antigens (GFP), GFP specific nanobody and the nanobody-antigens-complex. The yellow circle represents the binding reaction. The arrow points toward the nanobody-antigens-complex indicate that the complex is the product of the forward reaction. The double arrows above the yellow circle “binding” indicate that the reaction is reversible.</font></span><br></div>
  
  
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<div class="paragraph" style="text-align:left;"><strong style=""><span style="">Figure 2</span></strong><span style="">. Interaction between antigens (GFP) and GFP specific nanobody to form the nanobody-antigen complex</span><br><span style=""></span></div>
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<div class="paragraph" ><strong style=""><span style="">Figure 2</span></strong><span style="">. Interaction between antigens (GFP) and GFP specific nanobody to form the nanobody-antigen complex</span><br><span style=""></span></div>
  
  
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<div class="paragraph" style="text-align:left;"><span style=""><font color="#2a2a2a" size="4">By using the scan function of SimBiology, the dynamic of the system was simulated with changing the initial concentration of the antigen (the green line) from 0 M to 1.6x10-6 M with an interval of 2x10-7 M.</font></span><br><span style=""></span></div>
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<div class="paragraph" ><span style=""><font color="#2a2a2a" size="4">By using the scan function of SimBiology, the dynamic of the system was simulated with changing the initial concentration of the antigen (the green line) from 0 M to 1.6x10-6 M with an interval of 2x10-7 M.</font></span><br><span style=""></span></div>
  
 
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<div class="paragraph" style="text-align:left;"><font size="4"><font color="#2a2a2a"><span style="">Two observations were made from the simulation above. First, when the concentration of the antigen (GFP) is below that of the GFP specific nanobody (7.78 x10-7 M, given in the Calculation section above), as shown in Figure 3.1 to Figure 3.4, the antigen (GFP) becomes the limiting reagent and the final molarity of the nanobody-antigen complex (represented by a red line) equals to the initial molarity of the antigen. However, when the concentration of the antigen is higher than that of the GFP specific nanobody, as shown in Figure 3.5 to Figure 3.9, GFP specific nanobody becomes the limiting reagent, so the final molarity of the nanobody-antigen complex equals to the initial molarity of the GFP specific nanobody.</span><br><span style=""></span><br><span style=""></span>  </font><span style=""><font color="#2a2a2a">Another observation is that, as the concentration of the antigen increases, the rate of the reaction (i.e. formation of the nanobody-antigen complex) reaches equilibrium faster (Figure 3.5 to Figure 3.9). This can be explained by the increased forward reaction rate which depends on the concentration of the GFP specific nanobody and antigen (GFP).&nbsp;</font></span></font><br><span style=""></span></div>
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<div class="paragraph" ><font size="4"><font color="#2a2a2a"><span style="">Two observations were made from the simulation above. First, when the concentration of the antigen (GFP) is below that of the GFP specific nanobody (7.78 x10-7 M, given in the Calculation section above), as shown in Figure 3.1 to Figure 3.4, the antigen (GFP) becomes the limiting reagent and the final molarity of the nanobody-antigen complex (represented by a red line) equals to the initial molarity of the antigen. However, when the concentration of the antigen is higher than that of the GFP specific nanobody, as shown in Figure 3.5 to Figure 3.9, GFP specific nanobody becomes the limiting reagent, so the final molarity of the nanobody-antigen complex equals to the initial molarity of the GFP specific nanobody.</span><br><span style=""></span><br><span style=""></span>  </font><span style=""><font color="#2a2a2a">Another observation is that, as the concentration of the antigen increases, the rate of the reaction (i.e. formation of the nanobody-antigen complex) reaches equilibrium faster (Figure 3.5 to Figure 3.9). This can be explained by the increased forward reaction rate which depends on the concentration of the GFP specific nanobody and antigen (GFP).&nbsp;</font></span></font><br><span style=""></span></div>
  
 
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<h2 class="wsite-content-title" style="text-align:left;">Reference</h2>
 
<h2 class="wsite-content-title" style="text-align:left;">Reference</h2>
  
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<div class="paragraph" style="text-align:left;"><font size="4"><font color="#2a2a2a">Marta H. Kubala<span "font-family:pmingliu;mso-ascii-font-family:calibri;="" mso-ascii-theme-font:minor-latin;mso-fareast-font-family:pmingliu;mso-fareast-theme-font:="" minor-fareast;mso-no-proof:yes"="">†</span>Kovtun<span "font-family:pmingliu;mso-ascii-font-family:="" calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:pmingliu;="" mso-fareast-theme-font:minor-fareast;mso-no-proof:yes"="">†</span></font><font color="#2a2a2a">, Kirill Alexandrov* andBrett M. Collins*Oleksiy. (2010 September). Structural and thermodynamic analysis of the GFP:GFP-nanobody complex. Protein Science, Volume 19, Issue 12, Pages 2389-2401.</font><br></font><span style=""></span><br><span style=""></span></div></div>
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<div class="paragraph" ><span "font-family:pmingliu;mso-ascii-font-family:="" calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:pmingliu;="" mso-fareast-theme-font:minor-fareast;mso-no-proof:yes"=""><font size="4"><font color="#2a2a2a">Kubala, M. H., Kovtun, O., Alexandrov, K. and Collins, B. M. (2010). Structural and thermodynamic analysis of the GFP:GFP-nanobody complex. <i>Protein Science</i>. <b>19</b>(12): 2389-2401.</font></span></div></div>
 
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Latest revision as of 19:29, 18 September 2015

Partnership
Partner team: Hong_Kong-CUHK
Project: Magneto-bacter vinelandii Magnetosome-forming Azotobacter vinelandii with Downstream Applications  
In our collaboration work with the Chinese University of Hong Kong iGEM team, we were given the task to assist them with their project by doing a simulation that look into the interaction between GFP-nanobody to different concentrations of GFP. It is our honor to be able to collaborate and participate in their project. A wonderful experience we have gained through.

Background

The project of the CUHK iGEM team is to explore the use of magnetosome together with GFP-specific nanobody for immunoprecipitation. Magnetosome is an organelle with a magnetic iron crystal surrounded by a lipid bilayer. It is derived from magnetotactic bacteria which is used for navigation through sensing the Earth magnetic field. Biomolecules such as antibodies can be immobilized on magnetosomes for various scientific applications. One such applications is using magnetosomes together with nanobodies for immunoprecipitation reactions. To make the experiment measurable, green fluorescent protein (GFP)-specific nanobody was used (Figure 1).

Figure 1: Schematic diagram of a magnetosome (adsorbed with GFP-specific nanobodies) interacting with GFPs

Task

Simulate the binding dynamics of a fixed concentration of magnetosome with GFP specific nanobody expressed on its surface in different initial concentrations of antigens (GFP). 

Calculation

Software - SimBiology

SimBiology is a toolbox in Matlab that enable us to model and simulate the dynamics of the association and dissociation between molecules. Most of the function can be utilized through its GUI (Graphical User Interface).

Once the model is constructed (i.e. the mathematic relationships between molecules are set up, parameters such as association constant, molarity of reagent, etc. are provided), we can simulate the reaction or even scan through one or more variables. The “scan” function enables us to simulate the dynamics of the system when some parameters, such as the initial concentration of the reagent, are at different values.

Assumptions

1). All nanobodies are bound on the surface of a magnetosome, i.e. no free floating nanobodies.
2). Each magnetosome has the same number of GFP-specific nanobodies adsorbed on its surface. 
3). A magnetosome does not interact directly with GFP molecules nor interfere with the reactions between GFP-specific nanobodies and GFPs.
4). The GFP-specific nanobodies on the surface of a magnetosome have the same association and dissociation rate constant to GFP when compared with the GFP-specific nanobody alone.
5). The binding of GFP with GFP-specific nanobody is in a one-to-one ratio.
6). The reaction follows the law of mass action, which means the reaction rate is proportional to the concentration of the reagents.

Model

Figure 1 shows the model constructed in SimBiology. The blue rounded rectangles represent the reagents, including antigens (GFP), GFP specific nanobody and the nanobody-antigens-complex. The yellow circle represents the binding reaction. The arrow points toward the nanobody-antigens-complex indicate that the complex is the product of the forward reaction. The double arrows above the yellow circle “binding” indicate that the reaction is reversible.
Figure 2. Interaction between antigens (GFP) and GFP specific nanobody to form the nanobody-antigen complex

Result and discussion of the simulation

By using the scan function of SimBiology, the dynamic of the system was simulated with changing the initial concentration of the antigen (the green line) from 0 M to 1.6x10-6 M with an interval of 2x10-7 M.
Figure 3. Simulation kinetics of the interaction between GFP-nanobody and antigen


Two observations were made from the simulation above. First, when the concentration of the antigen (GFP) is below that of the GFP specific nanobody (7.78 x10-7 M, given in the Calculation section above), as shown in Figure 3.1 to Figure 3.4, the antigen (GFP) becomes the limiting reagent and the final molarity of the nanobody-antigen complex (represented by a red line) equals to the initial molarity of the antigen. However, when the concentration of the antigen is higher than that of the GFP specific nanobody, as shown in Figure 3.5 to Figure 3.9, GFP specific nanobody becomes the limiting reagent, so the final molarity of the nanobody-antigen complex equals to the initial molarity of the GFP specific nanobody.

Another observation is that, as the concentration of the antigen increases, the rate of the reaction (i.e. formation of the nanobody-antigen complex) reaches equilibrium faster (Figure 3.5 to Figure 3.9). This can be explained by the increased forward reaction rate which depends on the concentration of the GFP specific nanobody and antigen (GFP). 

Reference

Kubala, M. H., Kovtun, O., Alexandrov, K. and Collins, B. M. (2010). Structural and thermodynamic analysis of the GFP:GFP-nanobody complex. Protein Science. 19(12): 2389-2401.