Team:TU Delft-Leiden/Modeling/Landmine

Landmine Module

An important part of our iGEM project is a promoter sensitive to landmines, first described by Yagur-Kroll et al. [1]. We will use two of the promoters described in this paper, ybiJ and ybiFB2A1, in our project. Of these promoters, not much is known other than the fact that they have a DNT/TNT-dependent response curve (see figure 1). Our goal was to find a model which would be able to reproduce the response curves of both promoters.

Our first approach was to solve a system of Ordinary Differential Equations (ODEs) resembling the transcription and translation of a gene activated by the DNT-sensitive promoter. The ODEs were derived from the following system of reactions: $$ P_{R} + DNT \ \overset{k_{on}}{\underset{k_{off}}{\rightleftharpoons}} \ P_{A} \tag{1}$$ $$ P_{A} \ \xrightarrow{s_{A}} \ P_{A} + mRNA \tag{2}$$ $$ P_{R} \ \xrightarrow{s_{R}} \ P_{R} + mRNA \tag{3} $$ $$ mRNA \ \xrightarrow{s_{P}} \ mRNA + R \tag{4} $$ $$ mRNA \ \xrightarrow{d_{M}} \ \emptyset \tag{5} $$ $$ R\ \xrightarrow{d_{P}} \ \emptyset \tag{6} $$ In these reaction equations, \(P_{R}\) and \(P_{A}\) indicate respectively repressed and active promoters. DNT indicates DNT molecules, mRNA stands for an mRNA molecule transcribed from the gene behind the promoter and R is the reporter protein which is translated from the mRNA. \(k_{on}\) and \(k_{off}\) are the rates at which a promoter goes from the repressed to the active state and vice versa. \(s_{A}\) is the transcription rate from an active promoter. \(s_{R}\) is the transcription rate from a repressed promoter; this is also referred to as leakage. \(s_{P}\) is the translation rate. \(d_{M}\) and \(d_{P}\) are the mRNA and protein degradation rates.

Reaction (1) describes the activation and deactivation of a promoter in the presence of DNT. We assume that the activation mechanism can be described as the binding of the DNT to the repressed promoter, with the resulting complex being an active promoter. Reaction (2) describes transcription. Reaction (3) described transcription through leakage, i.e. transcription from a repressed promoter. Reaction (4) describes translation. Reactions (5) and (6) describe mRNA and reporter protein degradation respectively.

This system of reactions leads to the following system of ODEs: $$ \frac{d}{dt} [P_{R}] = \ -k_{on}[P_{R}][DNT] \ + \ k_{off}[P_{A}] \tag{7.1} $$ $$ \frac{d}{dt} [P_{A}] = \ k_{on}[P_{R}][DNT] \ - \ k_{off}[P_{A}] \tag{7.2} $$ $$ \frac{d}{dt} [DNT] = \ -k_{on}[P_{R}][DNT] \ + \ k_{off}[P_{A}] \tag{7.3} $$ $$ \frac{d}{dt} [mRNA] = \ s_{A}[P_{A}] \ + \ s_{R}[P_{R}] \ - \ d_{M}[mRNA] \tag{7.4} $$ $$ \frac{d}{dt} [R] = \ s_{P}[mRNA] \ - \ d_{P}[R] \tag{7.5} $$