Line 166: | Line 166: | ||
<p>We plotted the 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 (Figure 2) show that in order to obtain a large | <p>We plotted the 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 (Figure 2) show that in order to obtain a large | ||
difference | difference | ||
− | between signal and leakage the affinity of coil <b>B</b> for coil <b>A</b> needs to be strong (low $Kd_B$). On the other hand, the affinity of the autoinhibitory coil <b>b</b> should be slightly lower, ($Kdb$ \gt $Kd_B$), but not so low that it would allow too much leakage in the pre-cleavage state (<ref>5.4.2.</ref>, right panel).</p> | + | between signal and leakage the affinity of coil <b>B</b> for coil <b>A</b> needs to be strong (low $Kd_B$). On the other hand, the affinity of the autoinhibitory coil <b>b</b> should be slightly lower, ($Kdb$\gt$Kd_B$), but not so low that it would allow too much leakage in the pre-cleavage state (<ref>5.4.2.</ref>, right panel).</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."> |
Revision as of 08:04, 19 October 2016
Coiled-coil interaction model
Logic operations in biological systems have been tested with several approaches
![](https://static.igem.org/mediawiki/2016/9/98/T--Slovenia--5.4.1.png)
The two state system is considered at inducible by activity of TEV protease and signal both before and after cleavage is represented as reconstitution on split firefly luciferase reporter.
The relationship between the signal before and after cleavage by proteases 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 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 = Kd_b * 4 * 10^{-3} M^{-1}
\end{equation}
This relation 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”)
We plotted the 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 (Figure 2) 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 $Kd_B$). On the other hand, the affinity of the autoinhibitory coil b should be slightly lower, ($Kdb$\gt$Kd_B$), but not so low that it would allow too much leakage in the pre-cleavage state (5.4.2., right panel).
![](https://static.igem.org/mediawiki/2016/7/76/T--Slovenia--5.4.2.png)
The plots display the difference (M) between the signal before after and the proteolytic cleavage (left) and the concentration of the species responsible for leakage [AB-b] (right) 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