IN PROGRESS 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 set up 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.
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”)The results have been plotted varying the $K_d$ for the interaction of A with both B and b, 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 between signal and leakage a high affinity of the coil B for the coil A (low $Kd_B$) is required, while on the other hand an excessive destabilization of the autoinhibitory coil b (high $Kd_b$) would prevent the signal to be visible ( 5.4.2. ).
![](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.
This relationship suggested to try using a different version of the coiled-coils available in
the
toolset already used by the Slovenian iGEM 2009
team