Biomod/2012/UTokyo/UT-Komaba/Simulation: Difference between revisions

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[[image:Komaba2012-bistable.jpg|400px]]  [[image:Biomod-2012-UTkyo-UTKomaba-math8.png|400px]]
[[image:Komaba2012-bistable.jpg|400px]]  [[image:Biomod-2012-UTkyo-UTKomaba-math8.png|400px]]
The bistable system amplifies the small difference.
So, if you want to change the state from "A" to "B", all you have to do is to add more B than A which is in equilibrium.
This graph shows such operations at t=300 and t=600.


==DNA tablet==
==DNA tablet==

Revision as of 01:11, 30 August 2012

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Bistable system

Using the bistable system, you can realize two different states, state"A" and state"B".

State"A" has many staple strands of type A and few of type B.

In contrast, "B" has few staple strands of type A and many of type B.

Please note that we'll represent state"X" as "X", and staple strands of type X as X.


So, how do concentrations of A and B change?

In this section, we will show you the results of the simulations.

Bistable simulation without "switch"

　

As you can see, there is only small difference between [A] and [B] at the start.

But the bistable system amplifies the difference, and finally only A survives.

How to set up equations

All the reactions are here.

But as you'll see later, these are simplified.

If you have no idea about these reactions, please refer to"Idea" section.

For example, left of the top reaction formula shows A is doubled by template [math]\displaystyle{ T_{A} }[/math]

You should care that, A, B, iA, and iB naturally decreases because exonuclease gradually decomposes these staple strands.

To set up equations, let's close up some reactions.

First of all, let's consider the reactions among A, iA and [math]\displaystyle{ T_{A} }[/math]

[math]\displaystyle{ T_{A} }[/math] has three states.

So, the sum is constant.

We considered A increases in proportion to [math]\displaystyle{ AT_{A}/n }[/math]

By these equations, you can get this conclusion.

This is the equation we showed at the top of this subsection.

You can get the other equations the same way we showed.

Bistable simulation with "switch"

The bistable system amplifies the small difference.

So, if you want to change the state from "A" to "B", all you have to do is to add more B than A which is in equilibrium.

This graph shows such operations at t=300 and t=600.

DNA tablet

5×5 origami simulation

{{#widget:YouTube|id=BLX8pDfZ2Ek}}


15×15 origami simulation

{{#widget:YouTube|id=5PmS2_7T44A}}
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