Overview

The single cell model is a mathematical model of the species involved in our synthetic system of a single SmoColi cell. The change of the species concentrations in time is given by non-linear ordinary differential equations (ODEs), most of which follow Hill kinetics. The parameters we used in the model are derived from literature supported by experimental evidence. Some of the parameters are slightly adjusted to meet our own experimental approaches. The single cell model was simulated using numerical Matlab solvers.

Our model has several important strengths which are:

1. MODULARITY

Our system consists of three modules:

Sensor Module
Band Detector Module
Filter (Alarm) Module

The modules are almost independent, related between each other just by a single species. Most of the parameter values used within the modules do not depend on the other modules as well. The independence of the three modules enables their reusage in other systems. So if we want for example to add another sensor module to the existing band detector, the only thing we should change in the band detector is few parameter values for the linker species. This important property allows us to use the band detector + alarm with different sensors, making our synthetic cells a biological quantifiers of a range of substances.

2. ROBUSTNESS

We did a robustness analysis for our system and found out that it is indeed robust. This means that even upon parameter variation, the GFP band do not dissapear, just gets shifted or varies in its thickness. Each of our species eventually end up in a single stable steady states, there are no bufurcations nor oscillations in our system. So, we can freely vary the parameters found in literature to meet our experimental approaches and we can be sure that our system will still show the same global behaviour.

3. CONSISTENCY WITH BIOLOGY (will have to make sure this is correct)

Sensors

The sensor module of our system detects toxic substance found in cigarette smoke. Upon binding of the substance to the sensor molecule, series of downstream gene regulation events take place. We are dealing with two toxic substances (acetaldehyde and xylene). These two are detected by different sensor molecules with different mechanisms of action. Therefore, we designed two models, one for acetaldehyde detection, other for xylene detection. The models differ only by their sensor module, the band detector and the filter modules are same for both.

Acetaldehyde Sensor

As the name says, this sensor detects acetaldehyde from the air. Acetaldehyde binds to the transcriptional repressor AlcR, inhibiting TetR, which further inhibits CI and LacI production. Thus, the acetaldehyde binding to AlcR leads to CI and LacI expression (double inhibition leads to activation).

There has been experimental evidence about the AlcR repression activity when it binds to acetaldehyde [5]. However, the exact mechanism of acetaldehyde binding to AlcR is not known. In Weber et al. [5] the acetaldehyde-inducible gene expression was assessed by measuring the expression of acetaldehyde adjustable SEAP for different acetaldehyde concentrations. We fitted the experimental data points for SEAP expression to the Hill equation and used the parameter values that were obtained from the fit to describe the repression kinetics of TetR. The ODE for TetR is the following:

Equation system 1: ODE for TetR

TetR gene is repressed by the AlcR-acetaldehyde complex (AlcR_AcA). The input acetaldehyde concentration is implicitly considered in the equation, due to the fitting procedure.

The meaning and the values of the parameters are summarized in the Parameters section.

Xylene Sensor

The sensor that detects xylene is XylR. It is a hexamer which gets activated upon binding of xylene. Active XylR triggers CI and LacI expression. We model both active and inactive Xylene (Xyli and Xyla). Xylene is found in two forms in our system: bound to XylR and free xylene. We consider the free xylene as a state (Xyl) and the initial xylene concentration as an input parameter (Xyl_ini). Thus, the bound xylene concentration can be found by substracting the free xylene concentration from the initial one (Xyl_ini - Xyl).

The ODEs for active and inactive XylR, as well as for xylene are given below:

Equation system 2: ODEs for the states involved in the xylene sensor. XylRi stands for inactive XylR, XylRa for active XylR, Xyl for unbound xylene

Same as for the acetaldehyde sensor, the meaning and the values of the parameters are summarized in the Parameters section.