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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 | ||
− | 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.e. 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 | + | 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.e. 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 |
P3mS | P3mS | ||
and it turned out that, as in the model described above, an excessive destabilization | and it turned out that, as in the model described above, an excessive destabilization |
Revision as of 16:39, 19 October 2016
Coiled-coil interaction model
Logic operations in biological systems have been tested with several approaches
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”)
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).
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