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From 2009.igem.org

Contents 1 Oscillator Modelling 1 1.1 Variables Used 1.2 Formulas used 1.3 Conclusion 1.4 References

Oscillator Modelling 1

• TetR concentration
• CII concentration.
• 1/3min intervals.

Variables Used

	Protein Name	Half-life (min)	Promoter	Promoter Strength (relative)
Inducer	CII	8 [1]	pRE	0.025 (est)
Repressor	TetR	40 (est due to LVA tag)	pTet	1
Reporter	GFP	2160 [2]

Time segment used for the calculation: 1/3mins Maximum amount of Repressors that can stop promoter activity: 10 (an arbitrary number)

Formulas used

Calculating the strength of the pTet promoter when there are repressors around:

pTetcurrent = pTetmax*1-1/Tetmax*[TetR]     ----- (1)

Calculate the amount of each protein produced:

CII = pTetcurrent     ----- (2)

TetR = [CII] * pREmax     ----- (3)

GFP = [CII] pTetcurrent     ----- (4)

The calculation of amount of substrates remaining w.r.t the half lives:

[CII] = [CII] x 0.5(Δt / CII-t1/2)     ----- (5)

[TetR] = [TetR] x 0.5(Δt / TetR-t1/2)     ----- (6)

[GFP] = [GFP] x 0.5(Δt / GFP-t1/2)     ----- (7)

Conclusion

The only variables are:

• The relative strength of pRE relative to pTet (since it has not been measured yet)
  • the weaker pRE is relative to pTet, the slower the oscillator dampens.
• Maximum amount of repressor such that adding more repressors will not affect the strength of pTet anymore.
  • Amplitude of TetR oscillation is directly proportional.

References

[1] Shotland, et al: Proteolysis of Bacteriophage λ CII by Escherichia coli FtsH (HflB). J Bacteriol. 2000, 182(11): 3111–3116

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