Team:NJAU China/Writein

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Fundamental Modeling: Write-in System

Conjugation and traI

As is described in project,we use Hfr with traI knocked out.The gene was then added in the biobrick under control of blue-light sensor.Now that we’ve already known necessity of traI on the process of conjugation^[1],it’s critical that we build a model for it.

These functions below are directly from UCSF 2013^[2].

[D] represents for the concentration of donor cells
[R] represents for the concentration of recipient cells
[T] represents for the concentration of transconjugant cells
γrepresents for conjugation rate
φ represents for cell growth rate

However,we have a more complex situation.The parameterγ become a variant because of traI. We consider traI as kind of a catalyzer in this reaction and get the following

One thing to mention,here we made assumption that [traI] always dominates the rate of conjugation,but this may not be true.It’s highly possible that traI is not the speed-limiting enzyme.Then after a critical moment,γbecomes steady and reach its maximum.To prove this may need lots of experiments and data,and makes little difference to the result.

Assumption of stepped expression

In this section,we are going to discuss about the producing curve of GFP after conjugation.First we need to figure out the concentration of GFP in single cell.

Functions are

[mGFP] represents for the concentration of mRNA
V represents for the maximum transcription rate of promoter
D represents for the degration rate

The convolution method

At most of the time,we choose single cell model to simulate the situation of whole system.Cells grow different but we can still find a statistical average for them.But the single cell model may not fit situation of conjugation,because transconjugation cells of different time has different state of producing GFP,and is difficult to find an average.So we use convolution method to simulate it.

The expression of GFP is stepped,every single cell conjugated at different time shows a different state of producing GFP. The raw function is

Modeling for whole process

We made every step of the write-in system together to estimate the controlling efficiency of our system.We assume that the biological reaction share most of the features with chemical reaction,so we use mass-action functions and Hill functions to estimate the whole process.

Functions Figure This video is done by Processing,and is out of our model.The figure shows much similarity with the model we give.