Contents 1 Single Cell Model 1.1 Overview 1.2 Receptor Activation 1.3 Overview

Single Cell Model

The single-cell model of our system is composed of 4 interconnected modules. The design of the modules were based on the papers [] and on the feedback received from the experimentalists on the expected behaviour of the pathway and also taking into consideration only the aspects relevant to our project. The single-cell model helped us understand in detail whether and how our synthetic circuit works, especially to explore the characteristics of the GFP band and get a feeling of how it is related to concentration of our input substance.

Overview

The single cell mathematical model is developed on a scheme favouring the temporal order of processes. The changes in the species concentrations in time is given by a system of non-linear ordinary differential equations. The parameters used in the model were derived from literature supported by experimental evidence and was simulated using numerical Matlab solvers. The description of the individual modules and their use within the scope of the project is given in the sections below.

Receptor Activation

The ligand binds to the specific receptor and renders it active. The ligand concentration is obtained from the diffusion model. The receptor concentration is assumed to be constant based on the information gathered from the experimentalists. The activated receptor can now interact with the G subunit of the G-Protein.

Overview

The single cell mathematical model is developed on a scheme favouring the temporal order of processes. The changes in the species concentrations in time is given by a system of non-linear ordinary differential equations. The parameters used in the model were derived from literature supported by experimental evidence and was simulated using numerical Matlab solvers. The description of the individual modules and their use within the scope of the project is given in the sections below.

\begin{equation}

  E = mc^2

\end{equation}