# Simulation

## The mode of walking on tracks

### Simulation

Execute a Simulation
This program is simulation of DNA ciliate’s behavior, which works base on cellular-automaton framework.
• Yellow cells represent DNA ciliates.
• Blue cells represent oligodeoxynucleotide substrates with a single ribose moiety.
• Red cells represent oligodeoxynucleotide substrates without a ribose moiety.
• The size of each cell is one micro-meter.
• A Yellow cell makes a move depend on its located cell. The rate of moving on each cell is derived as following steps.
Firstly, we calculated the average time that DNA ciliates move one micro-meter by Brownian movement as following formula.
R: Gas constant. 8.3145[P/mol*K]
T: Temperature. 298[K].
η: Viscosity 0.00089[Pa/s]
a: Radius of DNA ciliate body. 0.5-6[m]
x: 10-6[m]
Next, we obtained the rate based on two assumptions. One is that DNA ciliates move with cleaving a ribose moiety to another cell in 120 seconds at a rate of 0.5. Another is that DNA ciliates move on substrates without a ribose moiety in 1.2 seconds at a rate of 0.5.
t: Average time to move one micro-meter. [s/μm]
y: Steps to move at rate 0.5. [s]
Then, each rate is following.
```    On the blue cells, yellow cells do not move at a rate of 0.9941.
On the red cells, yellow cells do not move at a rate of 0.555.
On the white cells, yellow cells do not move at a rate of 0 (means to move absolutely).
```
• Yellow cells can move to only adjacent cell at one step.
• The direction of yellow cell' movement is stochastically depend on the adjacent cells’ free-energy. The rates are derived as :following formula. Free-energy of blue cells is -19.02[KJ/mol]. Free-energy of red cells is 16.03[KJ/moc]. Blue cells are about 211 times more likely to move than red cells.
ΔG_n: An free energy of cell n which is adjacent;
R: Gas constant. 8.3145[P/mol*K]
T: Temperature. 298[K].
 Figure1:The result of the simulation. (The beads’diameter are 1um) Figure2:The result of the simulation.(The beads' diameter are 200nm)
To confirm“tracks walking mode”works correctly, we built into the simulation of DNA ciliate based on cellular automaton.Please look at figure1 and figure2.The vertical axis shows the distance from origin. And the horizontal axis shows the number of steps. The red line shows the movement of DNA ciliate which cut tracks. The green line shows the movement of DNA ciliate which moves on tracks cut by DNAzyme in advance. The blue line shows the movement DNA ciliate which moves on tracks not cut by DNAzyme.
From this graph, we found that the speed of DNA ciliate walking tracks mode is faster than other case which gives no direction. So, we showed that DNA ciliate moves something not brown motion in “racks walking mode” by using simulation.

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