From 2009.igem.org

Revision as of 03:37, 22 October 2009

Introduction

We developed a mathematical model to simulate the response of the testing circuit (Fig. 1).

Figure 1 - Genetic Circuit to test CIS and TRANS' mRNA functionality

Mathematical Model

Transcription and translation processes are considered similar to a second order kinetics like an enzymatic reaction: RNA polymerase and ribosome perform enzymes' role, while gene promoter and RBS sequence act as substrates. The binding between enzyme and substrate leads to the formation of a complex, yielding to the final product: mRNA for the polymerase-promoter complex and protein for the ribosome-RBS complex.

Reactions

All the biochemical reactions occurring in the testing circuit are listed in Fig. 2, Fig. 3 and Fig. 4

Figure 2: GFP transcription and GFP translation (left); LacI transcription, LacI translation and LacI dimerization (right)

Figure 3: Other Chemical Reactions

Figure 4. Trans-Reactions

Symbol definitions are listed in Table 1

Table 1. Legend

Differential Equations

The differential equations describing the above biochemical reaction are obtained appling the law of mass action.

Figure 5. Differential Equations

Figure 6. Differential Equations

Figure 7: Equilibrium Constants

Figure 8: Algebraic Constrains

Table 2. Model parameters; Value of parameter was taken from the literature or obtained from experimantal data

Simulations

To simulate the model we implemented the equation in Simulink (Figure 3 and Figure 4).

Figure 9: Simulink Model

Results of the model simulations are shown in the wet lab parts characterization.

• Recent changes
• What links here
• Related changes
• Special pages
• My preferences

• Printable version
• Permanent link
• Privacy policy
• Disclaimers