Team:Tsinghua-A/Modeling

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Revision as of 15:37, 4 October 2011

Modeling Section

Overview | Accurate Model | Simplified Model | Dimensionless Model | Quorum-sensing Effect | Reference

PART 0 Intro

In our project, we are dedicated to design a quorum-sensing oscillator which consists of two types of cells. Cells of the same type can fluctuate synchronously and certain designs were made to adjust the phase and the amplitude of oscillation. These are the things that our modeling part aims to simulate. We built and simplified our simulation system step by step and deepened into further characteristics of the system, which would provide firm evidence proving that our design does work.

PART 1 Accurate Model

construction | parameters | results

In our first step, we wanted to describe the system thoroughly without leaving out any seemingly unimportant actions and factors. As a result, the description of the system contains every possible mass actions as well as some hill kinetics, Henri-Michaelis-Menten. We came up a set of ODEs with 19 equations.

PART 2 Simplified Model

preparation | parameters | results

Although ODEs provide a thorough, precise description of the whole system, they contain too many equations and parameters which would act as a barrier for simulation and further analysis. A simplification of complicated ODEs is necessary. We simplify every single ODE according to certain appropriate assumptions. Finally, we came up with a set of DDE equations.

PART 3 Dimensionless Model

preparation | parameters | results

In order to make a further analysis on stability of the system, sensitivity of parameters, feedback factors-we manipulate all the arguments and parameters to make them dimensionless. Analysis of this part is crucial since parameters in vivo experiment may be different and even at odds with modeling ones but a proper dimensionless can reveal the mathematical essence of our model.

PART 4 Quorum-sensing Effect

results

What we have done insofar is focused on two-cell oscillation. Quorum-sensing oscillator is not simply a matter of expansion in magnitude, but a matter of robustness in allowing difference of each individual cell. Moreover, we test the adjustment of phase and amplitude of oscillation in this part.

PART 5 Reference

reference

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Analysis based on dimensionless model Read more

In order to make a further analysis on stability of the system, and sensitivity of parameters, we further simplified the model to make them dimensionless. In addition, we tried to introduce feedback to our system and made a brief analysis on different types of feedback we introduced.

Quorum Sensing Effect Read more

What we have analyzed so far is focused on two-cell oscillation. Quorum-sensing oscillator is not simply a matter of expansion in magnitude, but a matter of robustness in allowing difference of each individual cell. Moreover, we test the adjustment of phase and period of oscillation in this part.

As we all know, no two things in this world are exactly the same, so do cells. The major differences between individual cells that we take into consideration include:

● Each cell’s activity of promoter is varied, so each cell has different rate to generate AHL.

● The initial amount of AHL may be disproportionally distributed among cells.

<A NAME="OLE_LINK67"></A><A NAME="OLE_LINK66"></A> The rate of generating AHL is closely related to parameter m and n. Therefore, we introduce randomness to both parameters by letting them obey normal distribution, that is:

<A NAME="OLE_LINK77"></A><A NAME="OLE_LINK76"></A>m(i) = μ1+N(0,σ1);

n(i) = μ2+ N(0,σ2);

<A NAME="OLE_LINK63"></A><A NAME="OLE_LINK62"></A> μ1 and μ2 are the average ability of generating 30C6HSL and 3012CHSL, and normal distribution-- N(0,σ)--describes the fluctuations of AHL generating rate in individual cell. We then expanded our equations from 2 cells to a population of cells. Each cell share a mutual environment in which we assume that AHL in environment is proportionally distributed.

<IMG SRC="" NAME="图形11" ALT="说明: D:\b1.bmp" ALIGN=BOTTOM WIDTH=579 HEIGHT=430 BORDER=0>

The figures indicate that our system can oscillate synchronically being able to tolerate differences at certain range among a population of cells.

We also tested whether the oscillation is dependent on initial distribution of AHL by changing the initial amount drastically by letting them follow uniform distribution. That is:

Initial(i) = U(0,20);

Based on this distribution restraining the initial AHL concentration in each cell, we simulated out a figure as follows.

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The results demonstratively give evidence proving that our system can start to oscillate synchronically given variant initial starting status.

References

[1] Uri Alon, (2007). Network motifs: theory and experimental approaches. Nature.

[2] Chunbo Lou, Xili Liu, Ming Ni, et al. (2010). Synthesizing a novel genetic sequential logic circuit: a push-on push-off switch. Molecular Systems Biology.

[3] Tal Danino, Octavio Mondragon-Palomino, Lev Tsimring & Jeff Hasty (2010). A synchronized quorum of genetic clocks. Nature.

[4] Marcel Tigges, Tatiana T. Marquez-Lago, Jorg Stelling & Martin Fussenegger (2009). A tunable synthetic mammalian oscillator. Nature.

[5] Sergi Regot, Javio Macia el al. (2010). Distributed biological computation with multicellular engineered networks. Nature.

[6] Martin Fussenegger, (2010). Synchronized bacterial clocks. Nature.

[7] Andrew H Babiskin and Christina D Smolke, (2011). A synthetic library of RNA control modules for predictable tuning of gene expression in yeast. Molecular Systems Biology.

[8] Santhosh Palani and Casim A Sarkar, (2011). Synthetic conversion of a graded receptor signal into a tunable, reversible switch. Molecular Systems Biology.

[9] Nancy Kopell, (2002). Synchronizing genetic relaxation oscillation by intercell signaling. PNS

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