Biomod/2012/UTokyo/UT-Komaba/Simulation
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Simulation
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.
How do concentrations of A and B change? In this section, we 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 magnifies the difference, and finally only A remains.
How to Set up Equations
The picture below shows all of the reactions. However, as you'll see later, these models of reactions are simplified. If you have no idea about these reactions, please refer to Idea.
For example, left of the top reaction formula shows that A is doubled by template [math]\displaystyle{ T_{A} }[/math]. Please note that A, B, iA, and iB naturally decreases because exonuclease gradually decomposes these staple strands.
To set up the 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.
The sum is constant.
We considered A increases in proportion to [math]\displaystyle{ \frac{AT_{A}}{n} }[/math]
The conclusion below is derived from these equations.
This is the equation we showed at the top of this subsection. You can get the other equations the same way we show.
Bistable Simulation with "Switch"
The bistable system magnifies the small difference. 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 the equilibrium. But, in this case, there are also many iB, so you have to add excessive amount of B.
This graph shows such operations at t=300 and t=600.
The Change Between Two Pictures
Next simulation is about the process of the change on the surface of the DNA tablet between the two states; "A" and "B". Let's note a hybridized strand as "1", and a non-hybridized strand strand as "0". On the surface of the tablet, two types of reaction occur; 1→0 and 0→1. Because denaturation occurs at a constant rate, the event probability of "1 to 0" does not change, while that of "0 to 1", i.e. hybridization, is proportional to the concentration of the complementary strands existing around the tablet.
Two simulations below: one is very simple, with a small tablet, only 5×5 pixels, and the other is with a larger one, 15×15. In the simulation movies, the blue points represent the hybridized strands "1". In these simulation, the concentration curves of every element are the same to those of the bistable simulation (look at the graph in the last section).
5×5 Origami Simulation
state A : "A" appears. state B : "B" appears.
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15×15 Origami Simulation
Can you see what is shown in each states in the movie below?
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9x12 Origami Simulation
- {{#widget:YouTube|id=Li2z7nJD5mA}}
This is the simulation of the DNA tablet with the actual design. One picture is "Tablet Boy" and the other is "I love DNA".
DNA Tablet with N-stable System and N-oscillate System
N-stable System Simulation
Successfully done.
N-oscillate System Simulation
Successfully done.
{{#widget:YouTube|id=1akkkwjjsis}}
In this short movie, the concentration change of the simulation above is applied. The state changes from "only A" to "B" to "C" to "A" ..., and the vertical line move to right from left.
