Model
As discussed in the Project, we can consider some basic variables of interest in our project: Synthetase (S), HSL (H), Receptor (R) and Protein of interest (R), which can be considered as the variables of the systems. Also we can consider the complex formed between the HSL and the Receptor (C). NOTE: For a simplified visualization, we adopt, during the whole discussion of the modelling, the letters indicated between parentheses as representation of the variables.
Before starting the model, itself, we need to stablish some assumptions:
- The population, during the measurements, is at dynamic equilibria, therefore we can consider it as a constant;
- Transcription, when constitutive, and translation events are very low effected by stochastic effects;
- Also, considering the transcription and translation can be coupled in a single term of an equation, due to a linear relation between mRNA and protein (I.e. the translation is not limited by ribosomes in the cell)
We can, then, propose the following reactions:
$$ \begin{align} &\rightarrow S \\ S &\rightarrow \\ S & \rightarrow H\\ H &\rightarrow \\ &\rightarrow R \\ R &\rightarrow\\ H + R &\leftrightarrow C\\ C &\rightarrow\\ C & \rightarrow P\\ P &\rightarrow \\ \end{align}$$