Difference between revisions of "Team:Slovenia/CoiledCoilInteraction"

 
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                 </a>
 
                 </a>
 
                 <div class="ui vertical sticky text menu">
 
                 <div class="ui vertical sticky text menu">
                     <a class="item" href="#intro" style="margin-left: 10%">
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<i class="chevron circle left icon"></i>
                        <b>Project</b>
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<b>Modeling logic gates</b>
                    </a>
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</a>
                    <a class="item" href="#achievements" style="margin-left: 10%">
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                        <b>Achievements</b>
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<i class="selected radio icon"></i>
                    </a>
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<b>Coiled-coil interaction model</b>
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</a>
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                        <b>Medal requirements</b>
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<i class="selected radio icon"></i>
                    </a>
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<b>Achievements</b>
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                        <b>Idea</b>
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<b>Model</b>
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<b>Protease-based inducible secretion</b>
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</a>
 
                 </div>
 
                 </div>
 
             </div>
 
             </div>
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                 <!-- content goes here -->
 
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                 <div class="main ui citing justified container">
 
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<div>
                     <h1 class="ui left dividing header"><span id="intro" class="section"> &nbsp; </span>Coiled-coil interaction model</h1>
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                     <h1 class="ui left dividing header"><span id="intro" class="section colorize"> &nbsp; </span>Coiled-coil interaction model</h1>
 
<div class = "ui segment" style = "background-color: #ebc7c7; ">
 
<div class = "ui segment" style = "background-color: #ebc7c7; ">
<p><b><ul><li>
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<p><b><ul><li>We designed a two state model that describes the interactions of coiled coils within our inducible system.<li>The difference of affinities required for a favorable ratio of signal to noise ratio whereas determined using the model.
 
</ul></b></p>
 
</ul></b></p>
 
</div>
 
</div>
                     <div class="ui segment">
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</div>
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                     <div class="ui segment"><h5><span id="model" class="section colorize"> &nbsp; </span></h5>
 
                         <p>Logic operations in biological systems have been tested with several approaches
 
                         <p>Logic operations in biological systems have been tested with several approaches
 
                             <x-ref>Singh2014</x-ref>
 
                             <x-ref>Singh2014</x-ref>
 
                             . Our project
 
                             . Our project
                             relies on the reconstitution of split protein promoted by coiled-coil (CC) dimerization. The
+
                             relies on the reconstitution of split protein promoted by coiled coil (CC) dimerization. The
 
                             interaction between CC peptides can be finely tuned
 
                             interaction between CC peptides can be finely tuned
 
                             <x-ref>Woolfson2005, Gradisar2011, Negron2014</x-ref>
 
                             <x-ref>Woolfson2005, Gradisar2011, Negron2014</x-ref>
 
                             , thereby CCs offers a flexible and
 
                             , thereby CCs offers a flexible and
 
                             versatile platform in terms of designing logic operation <i>in vivo</i>. With the purpose of
 
                             versatile platform in terms of designing logic operation <i>in vivo</i>. With the purpose of
                             understanding the relation that underlies the interaction between coiled-coil peptides and
+
                             understanding the relation that underlies the interaction between coiled coil peptides and
                             therefore using them in logic gates, we designed the following model (
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                             therefore using them in logic gates, we designed the following model (<ref>5.4.1.</ref>). Our system is based on constructs that have been characterized in mammalian cells in the
                            <ref>5.4.1.</ref>
+
                            ). Our system is based on constructs that have been characterized in mammalian cells in the
+
 
                             context of <a href="https://2016.igem.org/Team:Slovenia/Protease_signaling/Logic">logic
 
                             context of <a href="https://2016.igem.org/Team:Slovenia/Protease_signaling/Logic">logic
 
                                 function
 
                                 function
                                 design</a>. Two orthogonal CC segment, <b>A</b> and <b>b</b>, fused together in on chain can bind each
+
                                 design</a>. Two orthogonal CC segments, <b>A</b> and <b>b</b>, fused together in one chain can bind each
                             other and form a stable CC pair. This complex exists in combination with the peptide <b>B</b>,
+
                             other and form a stable CC pair. This complex exists in equilibrium with the peptide <b>B</b>,
 
                             which
 
                             which
 
                             can also bind the peptide <b>A</b> and has a different affinity from the peptide <b>b</b>. The linker that
 
                             can also bind the peptide <b>A</b> and has a different affinity from the peptide <b>b</b>. The linker that
                             connects <b>A</b> and <b>b</b> can be cleaved by a generic protease (e.g. TEVp), this irreversible reaction
+
                             connects <b>A</b> and <b>b</b> can be cleaved by a generic protease (e.g. TEVp). This irreversible reaction
                             shift the equilibrium towards a state in which all of the three peptides are free in
+
                             shifts the equilibrium towards a state in which all three peptides are free in
 
                             solution
 
                             solution
 
                             and therefore compete for binding. In our experiments, a similar system as the generic coils
 
                             and therefore compete for binding. In our experiments, a similar system as the generic coils
 
                           <b>A</b>
 
                           <b>A</b>
 
                             and <b>B</b> was fused to the <a
 
                             and <b>B</b> was fused to the <a
                                     href="https://2016.igem.org/Team:Slovenia/Protease_signaling/Reporters">split
+
                                     href="https://2016.igem.org/Team:Slovenia/Protease_signaling/Reporters#cle">split
 
                                 reporter
 
                                 reporter
 
                                 firefly luciferase</a>.
 
                                 firefly luciferase</a>.
 
                         </p>
 
                         </p>
  
                         <div style="float:left; width:100%">
+
                         <div style="margin-left:auto; margin-right:auto; width:75%">
 
                             <figure data-ref="5.4.1.">
 
                             <figure data-ref="5.4.1.">
 
                                 <img
 
                                 <img
 
                                         src="https://static.igem.org/mediawiki/2016/9/98/T--Slovenia--5.4.1.png">
 
                                         src="https://static.igem.org/mediawiki/2016/9/98/T--Slovenia--5.4.1.png">
 
                                 <figcaption><b> Scheme representing the CC interaction model </b><br/>
 
                                 <figcaption><b> Scheme representing the CC interaction model </b><br/>
<p style="text-align:justify">The two state
+
<p style="text-align:justify">The two-state
 
                                     system
 
                                     system
                                     is considered at inducible by activity of TEV protease and signal both before and
+
                                     is considered inducible by activity of TEV protease and the signal, both before and
 
                                     after
 
                                     after
                                     cleavage is represented as reconstitution on split firefly luciferase reporter.
+
                                     cleavage, is represented as reconstitution on split firefly luciferase reporter.
 
</p>
 
</p>
 
                                 </figcaption>
 
                                 </figcaption>
 
                             </figure>
 
                             </figure>
 
                         </div>
 
                         </div>
                         <p>The relationship between the signal before and after cleavage by proteases is represented by
+
                         <p>The relationship between the signal before and after cleavage is represented by
 
                             the
 
                             the
 
                             difference [AB] - [AB-b]. In order to understand the optimal combination of dissociation
 
                             difference [AB] - [AB-b]. In order to understand the optimal combination of dissociation
                             constant required to obtain a good signal we solved two systems of equations set up
+
                             constant required to obtain a good signal we solved two systems of equations that describe the two separate states of the system, Before cleavage (eq. 1) and After cleavage (eq. 6). The two states are modeled as separate equilibria, with proteolytic cleavage considered as an irreversible and complete reaction.</p>
                            considering
+
                            the two state of the reaction scheme, Before cleavage and After cleavage, (1) and (6) respectively, as separate
+
                            phases
+
                            of the reaction and additionally, considering cleavage as an irreversible and complete
+
                            reaction.</p>
+
 
                         <p>Given values for total concentrations and Kd (from 10<sup>-9</sup> to 10<sup>-3</sup> M) the
 
                         <p>Given values for total concentrations and Kd (from 10<sup>-9</sup> to 10<sup>-3</sup> M) the
 
                             equations, for the
 
                             equations, for the
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                         Kd_B &= \frac{[A-b] * [B]}{[AB - b]} \\
 
                         Kd_B &= \frac{[A-b] * [B]}{[AB - b]} \\
 
                         c_B &= [B] + [AB-b]\\
 
                         c_B &= [B] + [AB-b]\\
                         c_A-b &= [A-b]+[Axb]+[AB-b] \label{2.1-2}
+
                         c_A-_b &= [A-b]+[Axb]+[AB-b] \label{2.1-2}
 
                         \end{align}
 
                         \end{align}
 
                         After cleavage
 
                         After cleavage
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                         \end{align}
 
                         \end{align}
  
                        The two systems are connected by the relation between the dissociation constants $Kd_b$ and
+
                      <p>The two systems are connected by the relation between the dissociation constants $Kd_b$ and
 
                         $Kd_x$,
 
                         $Kd_x$,
 
                         \begin{equation}
 
                         \begin{equation}
                         Kd_x = Kd_b * 4 * 10^{-3} M^{-1}
+
                         Kd_x = \frac{Kd_b}{4 * 10^{-3}M}
 
                         \end{equation}
 
                         \end{equation}
                         This relation approximates the higher affinity between the coils A and b when they are
+
                         This relation (12) approximates the higher affinity between the coils <b>A</b> and <b>b</b> when they are
 
                         covalently
 
                         covalently
 
                         linked by a short peptide (as in the system “Before cleavage”)
 
                         linked by a short peptide (as in the system “Before cleavage”)
                         <x-ref>Moran1999, Zhou2004</x-ref>
+
                         <x-ref>Moran1999, Zhou2004</x-ref>.</p>
                         .
+
                          
                         <p>The results have been plotted varying the $_Kd for the interaction of <b>A</b> with both <b>B</b> and <b>b</b>,
+
                         <p>We plotted the difference [AB] - [AB-b], where [AB] is considered the signal after cleavage and [AB-b] the signal before cleavage (leakage), against different combinations of Kd for the interaction of <b>A</b> with both <b>B</b> and <b>b</b> ($Kd_B$ and $Kd_b$). Our calculations show that in order to obtain a large
                            against
+
                            the difference [AB] - [AB-b], where [AB] is considered the signal after cleavage and [AB-b]
+
                            the
+
                            signal before cleavage (leakage). The system revealed that in order to obtain a high
+
 
                             difference
 
                             difference
                             between signal and leakage a high affinity of the coil <b>B</b> for the coil <b>A</b> (low $Kd_B$) is
+
                             between signal and leakage the affinity of coil <b>B</b> for coil <b>A</b> needs to be strong (low $Kd_B$) (<ref>5.4.2.</ref> A). On the other hand, the affinity of the autoinhibitory coil <b>b</b> for <b>A</b> should be slightly lower than the affinity of <b>B</b> ($ Kd_b \gt Kd_B $), but not so low that it would allow too much leakage in the pre-cleavage state (<ref>5.4.2.</ref> B).</p>
                            required,
+
                            while on the other hand an excessive destabilization of the autoinhibitory coil <b>b</b> (high
+
                            $Kd_b$)
+
                            would prevent the signal to be visible (
+
                            <ref>5.4.2.</ref>
+
                            ).
+
                        </p>
+
 
                         <div style="float:left; width:100%">
 
                         <div style="float:left; width:100%">
 
                             <figure data-ref="5.4.2.">
 
                             <figure data-ref="5.4.2.">
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                                 <figcaption><b> Difference between [AB] and [AB-b] depending on the ratio of Kd
 
                                 <figcaption><b> Difference between [AB] and [AB-b] depending on the ratio of Kd
 
                                     values.</b><br/>  
 
                                     values.</b><br/>  
<p style="text-align:justify">The plots display the difference (M) between the signal before
+
<p style="text-align:justify">The plots display the difference between the signal before and after proteolytic cleavage (A) and the concentration of the species responsible
                                    after
+
                                    and the proteolytic cleavage (left) and the concentration of the species responsible
+
 
                                     for
 
                                     for
                                     leakage [AB-b] (right) in a range of different Kd values.
+
                                     leakage [AB-b] (B) in a range of different Kd values.
 
</p>
 
</p>
 
                                 </figcaption>
 
                                 </figcaption>
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                         </div>
 
                         </div>
  
                         <p>This relationship suggested to try using a different version of the coiled-coils available in
+
                         <p>Based on these results, we decided to use as <b>B</b> one of the peptides from the previously characterized coiled coil toolset used by the <a href="https://2009.igem.org/Team:Slovenia">Slovenian iGEM 2009
                            the
+
                            toolset already used by the <a href="https://2009.igem.org/Team:Slovenia">Slovenian iGEM 2009
+
 
                                 team</a>
 
                                 team</a>
                             <x-ref>Gradisar2011</x-ref>. In order to
+
                             <x-ref>Gradisar2011</x-ref>, P3. In order to
 
                             obtain a detectable signal for <a
 
                             obtain a detectable signal for <a
 
                                     href="https://2016.igem.org/Team:Slovenia/Protease_signaling/Logic">logic operation
 
                                     href="https://2016.igem.org/Team:Slovenia/Protease_signaling/Logic">logic operation
                                 in
+
                                 <i>in
                                 vivo </a> we decided
+
                                 vivo</i> </a> we decided
                             to use an inhibitory coiled-coil, which would be displaced by the second coiled-coil with
+
                             to use an inhibitory coiled coil, which would be displaced by the second coiled coil with
 
                             higher
 
                             higher
 
                             affinity, only once is cleaved off its partner ($ Kd_B \lt Kd_b $). In doing so we selected
 
                             affinity, only once is cleaved off its partner ($ Kd_B \lt Kd_b $). In doing so we selected
                             P3 as
+
                             P3mS as <b>b</b>, this coiled coil peptide binds AP4 (<b>A</b>) with lower affinity than P3 (<b>B</b>) since it presents few substitutions (<i>i.e.</i> Gln and Ser instead of Ala in <i>b</i> and <i>c</i> positions) which confer a higher solubility than P3 (<b>b</b>). We also tried differently destabilized versions of
                            <b>B</b> and
+
                             P3mS
                            P3mS as <b>b</b>, these two coiled-coil peptides present only few substitutions and the higher
+
                             and it turned out that, as in the model described above, an excessive destabilization
                            solubility of P3mS (<b>b</b>), which presents Gln and Ser instead of Ala in <i>b</i> and <i>c</i> position of the
+
                             (obtained by substituting <i>a</i> and <i>d</i> positions with Ala) leads to a small difference of the
                            heptads, would favour the dissociation. We also tried differently destabilized versions of
+
                             P3
+
                             and it turned out that, as in the forehead described model, an excessive destabilization
+
                             (obtained by substituting a and d positions with Ala) leads to a small difference of the
+
 
                             signal
 
                             signal
                             before and after cleavage. Using a slightly destabilized coiled-coil (P3mS-2A), which
+
                             before and after cleavage. Using a slightly destabilized coiled coil (P3mS-2A), which
 
                             presents
 
                             presents
 
                             only 2 alanines in the second heptad, the signal after cleavage reached its maximum of 16
 
                             only 2 alanines in the second heptad, the signal after cleavage reached its maximum of 16
 
                             folds (<a href="https://2016.igem.org/Team:Slovenia/Protease_signaling/Logic#autoinhibitory">Logic Figure 10</a>).</p>
 
                             folds (<a href="https://2016.igem.org/Team:Slovenia/Protease_signaling/Logic#autoinhibitory">Logic Figure 10</a>).</p>
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Latest revision as of 18:25, 19 October 2016

Model Logic

  Coiled-coil interaction model

  • We designed a two state model that describes the interactions of coiled coils within our inducible system.
  • The difference of affinities required for a favorable ratio of signal to noise ratio whereas determined using the model.

 

Logic operations in biological systems have been tested with several approaches Singh2014 . Our project relies on the reconstitution of split protein promoted by coiled coil (CC) dimerization. The interaction between CC peptides can be finely tuned Woolfson2005, Gradisar2011, Negron2014 , thereby CCs offers a flexible and versatile platform in terms of designing logic operation in vivo. With the purpose of understanding the relation that underlies the interaction between coiled coil peptides and therefore using them in logic gates, we designed the following model (5.4.1.). Our system is based on constructs that have been characterized in mammalian cells in the context of logic function design. Two orthogonal CC segments, A and b, fused together in one chain can bind each other and form a stable CC pair. This complex exists in equilibrium with the peptide B, which can also bind the peptide A and has a different affinity from the peptide b. The linker that connects A and b can be cleaved by a generic protease (e.g. TEVp). This irreversible reaction shifts the equilibrium towards a state in which all three peptides are free in solution and therefore compete for binding. In our experiments, a similar system as the generic coils A and B was fused to the split reporter firefly luciferase.

Scheme representing the CC interaction model

The two-state system is considered inducible by activity of TEV protease and the signal, both before and after cleavage, is represented as reconstitution on split firefly luciferase reporter.

The relationship between the signal before and after cleavage is represented by the difference [AB] - [AB-b]. In order to understand the optimal combination of dissociation constant required to obtain a good signal we solved two systems of equations that describe the two separate states of the system, Before cleavage (eq. 1) and After cleavage (eq. 6). The two states are modeled as separate equilibria, with proteolytic cleavage considered as an irreversible and complete reaction.

Given values for total concentrations and Kd (from 10-9 to 10-3 M) the equations, for the reaction constants (2), (3) and (7), (8) and and for mass conservation (4), (5) and (9), (10), (11) were solved for the species at equilibrium.

Before cleavage \begin{equation} \ce{Axb + B <=>[Kd_x] A-b + B <=>[Kd_B] AB-b} \end{equation} \begin{align} Kd_x &= \frac{[A-b]}{[Axb]} \label{1.1-2}\\ Kd_B &= \frac{[A-b] * [B]}{[AB - b]} \\ c_B &= [B] + [AB-b]\\ c_A-_b &= [A-b]+[Axb]+[AB-b] \label{2.1-2} \end{align} After cleavage \begin{equation} \ce{Ab + B <=>[Kd_b] A + b + B <=>[Kd_B] AB + b} \end{equation} \begin{align} Kd_b &= \frac{[A] * [b]}{[Ab]} \label{1.3-4}\\ Kd_B &= \frac{[A] * [B]}{[AB]} \\ c_A &= [A]+[AB]+[Ab]\\ c_B &= [B] +[AB]\\ c_b &= [b] + [Ab] \label{2.3-5} \end{align}

The two systems are connected by the relation between the dissociation constants $Kd_b$ and $Kd_x$, \begin{equation} Kd_x = \frac{Kd_b}{4 * 10^{-3}M} \end{equation} This relation (12) approximates the higher affinity between the coils A and b when they are covalently linked by a short peptide (as in the system “Before cleavage”) Moran1999, Zhou2004.

We plotted the difference [AB] - [AB-b], where [AB] is considered the signal after cleavage and [AB-b] the signal before cleavage (leakage), against different combinations of Kd for the interaction of A with both B and b ($Kd_B$ and $Kd_b$). Our calculations show that in order to obtain a large difference between signal and leakage the affinity of coil B for coil A needs to be strong (low $Kd_B$) (5.4.2. A). On the other hand, the affinity of the autoinhibitory coil b for A should be slightly lower than the affinity of B ($ Kd_b \gt Kd_B $), but not so low that it would allow too much leakage in the pre-cleavage state (5.4.2. B).

Difference between [AB] and [AB-b] depending on the ratio of Kd values.

The plots display the difference between the signal before and after proteolytic cleavage (A) and the concentration of the species responsible for leakage [AB-b] (B) in a range of different Kd values.

Based on these results, we decided to use as B one of the peptides from the previously characterized coiled coil toolset used by the Slovenian iGEM 2009 team Gradisar2011, P3. In order to obtain a detectable signal for logic operation in vivo we decided to use an inhibitory coiled coil, which would be displaced by the second coiled coil with higher affinity, only once is cleaved off its partner ($ Kd_B \lt Kd_b $). In doing so we selected P3mS as b, this coiled coil peptide binds AP4 (A) with lower affinity than P3 (B) since it presents few substitutions (i.e. Gln and Ser instead of Ala in b and c positions) which confer a higher solubility than P3 (b). We also tried differently destabilized versions of P3mS and it turned out that, as in the model described above, an excessive destabilization (obtained by substituting a and d positions with Ala) leads to a small difference of the signal before and after cleavage. Using a slightly destabilized coiled coil (P3mS-2A), which presents only 2 alanines in the second heptad, the signal after cleavage reached its maximum of 16 folds (Logic Figure 10).

 References