Template:NYMU-2015project-drylab-Oscillation

• FYVE
• Oscillation
• Epidemic

• HOME
• OVERVIEW
  • Background
  • Collaboration
  • Achievement
  • Parts
  • Attributions
• PROJECT
  • Experiment
  • Modeling
  • Functional
    Prototype
• POLICY PRACTICES
• BIOSAFETY
• NOTEBOOK
  • Calendar
  • Lab
  • Protocol
• TEAM

• 
• 
  • Background
  • Collaboration
  • Achievement
  • Parts
  • Attributions
• 
  • Experiment
  • Modeling
  • Functional
    Prototype
• 
• 
• 
  • Calendar
  • Lab
  • Protocol
• 

Oscillation

We construct a Lux/Aiia quorum-sensing oscillator so that S. oneidensis-MR1 will generate oscillating current which can help farmers tell if the potatoes are infected. We build two models to characterize the outcome of the genetic oscillator. The first model is used to predict whether the genetic oscillator will work. Since it is possible that some of the engineered S. oneidensis we inoculated on anode won’t survive, the second model is used to predict whether the gene expression will oscillate when there are only a few bacteria left on the anode.

Population simulation with delay differential equation

Since our circuit design is based on the circuit published by Danino et al.[1] our first model is a slight modification of the equation from the supplementary information. This model consists of four delay differential equation. We added one more delay differential equation to this model to simulate the expression of MtrB gene.

Parameters

Description	Parameter	Value
CA	Synthesis constant of Aiia	1
CI	Synthesis constant of LuxI	4
CmtrB	Synthesis constant of MtrB	1(assume)
δ	Hill function constant	10-3
α	Hill function constant	2500
k1	Hill function constant	0.1
τ	Time delay of the production of LuxR::AHL	10
k	Kinetic constant of AHL synthesis	1
b	Synthesis rate of AHL	0.06
γA	Enzymatic degradation rate of Aiia	15
γI	Enzymatic degradation rate of LuxI	24
γH	Enzymatic degradation rate of AHL	0.01
γmtrB	Enzymatic degradation rate of MtrB	0.007(assume,[3])
D	AHL membrane diffusion	2.5
f	0.3
g	Kinetics constant of AHL degradation	0.01
d0	Maxium cell density	0.88

Conclusion

As you can see in the graph, the production of Aiia and LuxI will oscillate as the time goes by. However, the production of MtrB will build up instead of oscillating. This is because MtrB is too stable and it is not totally degraded before the next period of oscillation. Thus, it is necessary to be targeted for proteolysis by adding a degradation tag in MtrB coding sequence.

Single cell simulation with ODE

If we inoculate the engineered S. oneidensis MR-1 into the anode of our SMFC, chances are that some of the bacteria will not survive in soil. Thus, it is necessary to simulate if the oscillator will work with only a single bacteria or a small population of bacteria.

With a small amount of bacteria, there will not have a significant time delay, and that’s why we chose a set of ODE to simulate the genetic oscillator.

Conclusion

As we can see in this model, even if there is only a small amount of bacteria left on the anode, the oscillator can still work. However, the current output will be much lesser than that of a large population of bacteria.

Parameters

Descriptions	Parameter	Units	Value
Basal production rate LuxI AiiA	a0LI a0A	μM/min μM/min	7.79x10-6 6.18x10-6
Active production rate LuxI AiiA mtrB	kpLI kpLA kpmtrB	μM μM μM	0.9 0.84 0.33(assume[4])
Cell reaction rate AHL production rate LuxR AHL association rate LuxR AHL dissociation rate AHL::Aiia catalytic rate AHL conc. adjustsment for environment AHL membrane diffusion constant	kp2 kr1+ kr1− kcataA ηenv ηcell	1/min μM/min 1/min 1/min 1/min 1/min	16 5.99x10-5 6x10-6 7x103 3x10-5 3
Michaelis-Menten constants LuxR::AHL complex Aiia complex	KmLA KmaA	μM μM	1.00x10-2 1.4977x103
Degradation related parameters LuxR::AHL complex AHL	τLA τA/τA˜	1/min 1/min	2.40x10-2 2.76x10-3
Enzymatic degradation Inverse of KMclx Vmax × ET OT / KMclx for LuxI Vmax × ET OT / KMclx for Aiia	f δ1 δ2 δ3	1/μM 1/μM.min 1/μM.min 1/μM.min	4.12x10-2 7.16x10-1 2.50x10-2 0.99x10-2 (assume[4])

Reference

1. Danino. T, Mondragon-Palomino, O, Tsimring, L. & Hasty, J. “A synchronized quorum of genetic clocks.” Nature 463, 326-330 (2010).
2. Petros Mina, Mario di Bernardo, Nigel J. Savery, Krasimira Tsaneva-Atanasova. “Modelling emergence of oscillations in communicating bacteria: a structured approach from one to many cells.” Published 7 November 2012
3. Danino. T, Mondragon-Palomino, O, Tsimring, L. & Hasty, J. “A synchronized quorum of genetic clocks.” Nature 463, 326-330 (2010).