ETHZ/Modeling Basics

From 2007.igem.org

Introduction

The functioning of our model depends mostly on protein concentrations. These proteins are produced within the E. coli cells based on genes that we introduced into the cell. To understand the system, it is crucial to model the gene expression and regulation accurately.

This Wiki page is intended to present the basic mechanisms and assumptions that went into the mathematical description of our iGEM model.

Constitutive Protein Production

The most simple parts in the system are genes that are continuously transcribed to produce a protein. At the same time, proteins have a certain half-life time, which means that they are degraded. This leads to the following simple model of protein production/degradation shown in Fig. 1.

Fig. 1: System of a constitutively produced protein P. Production rate is c^max and degradation rate is d_P.

To find the concentration of protein P (as a function of time), the system of Fig. 1 can be written as an ODE

This equation states that the change of protein concentration is a function of protein production (c^max) and protein degradation (d_P[P]).

It is worth looking at the protein production a bit closer. The production of protein P depends on the expression of a gene that codes for this protein. In the case of constant protein production, the gene can be modeled by a constitutive promoter and a coding region for the protein (Fig. 2).

Fig. 2: Model for the gene coding for protein P. The promoter of the gene is continuously expressed.