Team:HIT-Harbin/Modeling

For our perspectives, there are some significant issues and stuffs we can never neglect for the modeling of synthetic biology.

A.Whether the relative reactions will be influenced by the metabolism of the adopted cells(i.e. E.coli, yeast)?

B.Whether the established modeling can characterize related features of corresponding projects. For instance, for the project “sensor”, whether the model can accurately deal with every biochemistry step and then precisely output two essential scales of the “sensor”, namely sensitivity range and response time?

C.Is the model valid, whose equations stand in the special reaction environment(minimal space for reactions, the quantized number of molecules)?

D.Is it necessary to consider the effect of noise? If so, then does the divece possess noise immunity and robustness?

E.Can the established model be simulated by current computing devices?

Considering all the elements above, the models are given in two sections. For different issues, related models are discussed step by step. The integration of three models is expected so as to reflect the reality of the reaction given by relative devices, and instruct our design and experiments.

SectionⅠ: Software Simulation for Core Circuit

Parts&Pools is a software especially for modeling based on Pops, written by our advisor Prof. Mario. With this software, the whole metabolism course of related parts and bacterium like E.coli, yeast can be rapidly generated in MDL. So it is convenient to give out precise mathematical model on the cell metabolism level.

We spent a whole day to design and simulate related devices with this software and ProMoT. Ultimately, we got...(10月17日给出) The models reflect several problems:

a)The influence the metabolism system has on our genetic circuit is quite small. We have built up some models for corresponding reactions by Hill Equation. It turns out that their results are similar to others. So the models given by Law of Mass Action will not deviate too much from the reality.

b)The period of time to achieve homeostasis: 25h with memory system; 38h without memory system;

c)After adding memory system, the time for GFP to be steady become significantly shorter. Meanwhile, after eliminating dioxin, GFP produced by device without memory system will attenuate to 50%. But for those devices with memory system, the attenuation of GFP will be less than 10%.

d)Memory system has a process of positive feedback. Thus, just a trace of leakage of promoters can cause a lot of GFP being transcribed and end up interfering the result. That’s the reason why we add in insulating parts.

Section Ⅱ: Differential Equation Model for Supplementary Circuit

Originally, we intended to keep on utilizing Prof. Mario’s software to model for our supplementary project. However, it is limited by the processing capacity of computers. As is shown in the previous models, our device can neglect the metabolism system of yeast. Hence, we turn to the approach of differential equation.

a)Relevant Parameters

b) Assumptions

1)All the reactions follow the Law of Mass Action

2)Adjacent genes have the same speed of transcription

3)Terminator and LexA have no leakage

4)All of LexA-CYC1 are equivalent

5)All LexA regulatory factors degrade naturally

c) Model Simplification

One significant parameter of “sensor” is the response time. So the negligible biochemical reaction period in traditional systematic biologic model need to be taken into consideration.

1)Is the time of synthesis of mRNA negligible?

2)Is the time of synthesis of GFP/LexA negligible?

3)Can the concentration of dioxin+LexADBD be approximated as the concentration of pure dioxin?

1) The influence from the time of synthesis of mRNA

Suppose the concentration of mRNA is cmr, the synthesis rate is s, and the half life of mRNA is T. Then we have: Solving the differential equation, we can obtain the result:

According to the statistics from bionumbers, mRNA’s half life is around 2mins, while its synthesis time is less than 5s. There’s no harm to assume that mRNA’s synthesis rate is 0.01mol/s. By computing with C program, we can observe that after 9s, the corresponding change of concentration of mRNA is less than 0.1%. Comparing with the synthesis time for protein which is more than 3mins, it is less than 10%. So basically, the concentration of mRNA during the phase of synthesis of protein is fixed and it satisfies: , which is

2) The influence from the time of synthesis of regulatory factors GFP/LexA

In accordance with the result of search, the half life of GFP/LexA is around one hour, while synthesis takes about 2mins. By using qtiplot, we can see the whole process with C programing. The result shows that, it makes little difference whether considering the reaction process or not.

Hence, basically, the time of synthesis of regulatory factors GFP/LexA can be neglected for related reactions.

d) Construction of Model

cactd=d czifp=ced=cactg=cgfp=lhill(actd+actg) cmp=zhill(czifp)

e) Result

1. The realtionship between the dioxin and the GFP concentration is nearly linear, which is perfect for the signal transformation.

2. The quorum sensing speed is quite rapid, which is suitable for the dioxin's enrichment

3. The efficiency of dioxin degrading enzyme does not meet our expectation. But its presence shortens the settling time of the concentration of GFP of sensor to 30000s, which is largely faster than current methods.