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*'''Christos''': 1. Add gifs concerning the simulations
*''''Christos'''': 1. Add gifs concerning the simulations

Revision as of 19:18, 7 October 2007

Eth zh logo 2.png
Main Page      Biology Pespective      Engineering Perspective      Meet the Team      Team Notes      Pictures!

.:: EducatETH E. coli - Engineering Perspective ::.

.:: Introduction ::.

In order to understand if it is possible to create the learning system that we wanted, we had to run some initial simulations, to see if we could reach the desirable steady states. After creating a basic framework on which to work on, we refined the parameters by searching the available literatures. In the next, we are presented the coupled differential equations that model our system, their parameters and the values that we picked, the results of our simulations, and lastly, we provide our references. For an introduction to system modeling in synthetic biology, please read our modeling tutorial here.

.:: System Model ::.

Following the guidelines presented in our modeling guide, we divided the biological system into subsystems, each of which was modelled with a system of differential equations. According to what presented in the Biology Perspective, our system is composed the following three subsystems:

  1. A subsystem of constitutively produced proteins (see Fig. 1),
  2. The learning part (see Fig. 2), and
  3. The reporting subsystem (see Fig. 3).
The first two subsystems interact, and thus, they should be considered together. The third subsystem has no feedback with the other two, as it is only used for producing the appropriate fluorescent proteins. The subsystem with the constitutively produced proteins serves as a regulatory system, and can be modeled with three decoupled partial differential equations (see Fig. 1):
Subsystem 1: Constitutively produced proteins (Fig. 1)

The second subsystem is the main part of the biological model. This subsystem stores the information concerned the learned chemical, and drives the production of the appropriate reporter, during the recognition phase. It is actually a toggle switch, that reaches a steady state depending on the chemical that it is exposed to (see Fig. 2):

Subsystem 2: Basic learning subsystem (toggle) (Fig. 2)

The third subsystem reports the state that our system is, during the different phases of learning and recognition. During the learning phase, this subsystem reports which chemical the cells are exposed to, and during the recognition phase, it reports if the cells recognize the chemicals that they are currently exposed to (see Fig. 3):

Subsystem 3: Reporting subsystem (Fig. 3)

Note that the three constitutively produced proteins LacI, TetR and LuxR exist in two different forms; as free proteins and in complexes they build with IPTG, aTc and AHL, respectively. We need to model this complex-forming procedure, with another set of differential equations (Fig. 4):

Allosteric regulation (see Fig. 4)

In order to have meaningful results from our simulations, we browsed through the literature in order to find appropriate values for our parameters. We reduced our parameter space by joining parameters together, and we gave reasonable estimates, for the values that could not be extracted from available publications. Since this is a hard part that every team has to face, we present the table with the chosen parameters below:

Parameters of the model (Fig. 5)
Parameter Value Description References
c1max 0.01 [mM/h] max. transcription rate of
constitutive promoter
(per gene)
c2max 0.01 [mM/h] max. transcription rate of
luxR-activated promoter
(per gene)
lhi 25 high-copy plasmid number Estimate
llo 5 low-copy plasmid number Estimate
ap22cII,LacI 0.1 - 0.2 basic production of
p22cII/LacI-inhibited genes
ap22cII 0.1 - 0.2 basic production of
p22cII-inhibited genes
acI,TetR 0.1 - 0.2 basic production of
cI/TetR-inhibited genes
acI 0.1 - 0.2 basic production of
cI-inhibited genes
ap22cII,TetR 0.1 - 0.2 basic production of
p22cII/TetR-inhibited genes
acI,LacI 0.1 - 0.2 basic production of
cI/TetR-inhibited genes
dLacI 2.31e-3 [pro sec] degradation of lacI [10]
dTetR 1e-5 [pro sec]/2.31e-3 [pro sec] degradation of TetR [9], [10]
dLuxR 1e-3 - 1e-4 [per sec] degradation of LuxR [6]
dcI 7e-4 [per sec] degradation of cI [7]
dp22cII degradation of p22cII
dYFP 6.3e-3 [per min] degradation of YFP suppl. mat. to Ref. [8]
dGFP 6.3e-3 [per min] degradation of GFP in analogy to YFP
dRFP 6.3e-3 [per min] degradation of RFP in analogy to YFP
dCFP 6.3e-3 [per min] degradation of CFP in analogy to YFP
KLacI 1.3e-3 - 2e-3 [mM/h] lacI repressor
dissociation constant
[2], [5]
KIPTG 1.5e-10 [mM/h] IPTG-lacI repressor
dissociation constant
KTetR 5.6 (+-2) [nM-1] tetR repressor
dissociation constant
KaTc 1120 (+-400) [nM-1] aTc-tetR repressor
dissociation constant
[1], [3]
  • 0.003 [mM/s]
  • 55 - 520 [nM]
luxR activator
dissociation constant
  • 0.009 [mM/s] - 0.1 [mM/s]
  • 0.09 - 1 [µM]
AHL-luxR activator
dissociation constant
KcI 2e-3 [mM/h] cI repressor
dissociation constant
Kp22cII p22cII repressor
dissociation constant
nLacI 1 lacI repressor
Hill cooperativity
nIPTG 2 IPTG-lacI repressor
Hill cooperativity
nTetR 3 tetR repressor
Hill cooperativity
naTc 2 (1.5-2.5) aTc-tetR repressor
Hill cooperativity
nLuxR 2 luxR activator
Hill cooperativity
nAHL 1 AHL-luxR activator
Hill cooperativity
ncI 1.9 cI repressor
Hill cooperativity
np22cII p22cII repressor
Hill cooperativity

.:: Simulations ::.
.:: References ::.

[1] Weber W., Stelling J., Rimann M., Keller B., Daoud-El Baba M., Weber C.C., Aubel D., and Fussenegger M., "A synthetic time-delay circuit in mammalian cells and mice", Proceedings of the National Academy of Sciences, vol. 104, no. 8, pp. 2643, 2007.
[2] Setty Y., Mayo AE, Surette MG, and Alon U., "Detailed map of a cis-regulatory input function", Proceeding of the National Academy of Sciences, vol. 100, no. 13, pp. 7702--7707, 2003.
[3] Braun D., Basu S., and Weiss R., "Parameter Estimation for Two Synthetic Gene Networks: A Case Study", IEEE Int'l Conf. Acoustics, Speech, and Signal Processing 2005, vol. 5, 2005.
[4] Fung E., Wong W.W., Suen J.K., Bulter T., Lee S., and Liao J.C., "A synthetic gene--metabolic oscillator", Nature, vol. 435, no. 7038, pp. 118--122, 2005, supplementary material.
[5] Iadevaia S., and Mantzaris N.V., "Genetic network driven control of PHBV copolymer composition", Journal of Biotechnology, vol. 122, no. 1, pp. 99--121, 2006.
[6] Goryachev AB, Toh DJ, and Lee T., "Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants", Biosystems, vol. 83, no. 2-3, pp. 178--187, 2006.
[7] Arkin A., Ross J., and McAdams H.H., "Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-Infected Escherichia coli cells", Genetics, vol. 149, no. 4, pp. 1633--1648, 1998.
[8] Colman-Lerner A., Chin T.E., and Brent R., "Yeast Cbk1 and Mob2 Activate Daughter-Specific Genetic Programs to Induce Asymmetric Cell Fates", Cell, vol. 107, no. 6, pp. 739--750, 2001.
[9] Becskei A., and Serrano L., "Engineering stability in gene networks by autoregulation", Nature, vol. 405, no.6786, pp.590--593, 2000.
[10] Tuttle L.M., Salis H., Tomshine J., and Kaznessis Y.N., "Model-Driven Designs of an Oscillating Gene Network", Biophysical Journal, vol. 89, no. 6, pp. 3873--3883, 2005.

.:: To Do ::.
  • 'Christos': 1. Add gifs concerning the simulations