NTU@iGEM Project Introduction Methodology Team Introduction Team background Notebook Dry Lab Introduction ODEs used Modeling Constructs Parameters used Deterministic Modeling Sensitivity Analysis Stochastic Modeling Wetlab Introduction Materials and Equipment Protocols Verification of Detection & Lysis System Our New Parts Characterization Introduction Standard Promoters Characterization of pLacI-GFP pLacI-GFP images and clips Characterization of pLsrA-YFP New characterization Proposal Parameter Estimation & Correlations Acknowledgements

Contents 1 ODEs used in modeling 1.1 Constant synthesis & Linear Synthesis 1.2 Linear Degradation 1.3 Simple Forward Reaction 1.4 Phosphorylation and Dephosphorylation

ODEs used in modeling

The following equations shows the break down of the different equations that will be used in this modeling exercise. By understanding this section, it would make the understanding of the system of ODEs used

Constant synthesis & Linear Synthesis

• Simple ode to describe constant synthesis
• Gives an explicit analytical solution
• Unique solution once a IC is posed

Linear Degradation

• Rate of degradation is proportional to how much of the molecule is present
• Gives an explicit analytical solution
• Constant half life

Simple Forward Reaction

This equation ignores the fact that dissociation of the complex occurs. We can do so if the dissociation is much slower than the formation.

• Single solvable equation for the unknown C
• Simple, unique solution available with I.C

Phosphorylation and Dephosphorylation

Assumptions:

• Linear kintic rate laws apply only if XT is much less than the Michaelis constants of both kinase and phosphotase

• Modeled after simple linear kinetics
• Gives a hyperbolic signal response curve when X plotted vs S

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