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<div id="navigation"> <div id="menu" style="position:static"> <ul> <li><a class="aMain" href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Tokyo">Home</a></li> <li><a class="aTeam" href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Tokyo/Team/Students">Team</a></li> <li><a class="aProject" href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Tokyo/Project">Project</a>  <li><font color="#ffffff">Results</font> <ul> <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Tokyo/Project/Results">Experiments</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Tokyo/Project/Simulations">Simulations</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Tokyo/Achievements/DNA_Devices">DNA Design</a></li> </ul></li>  <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Tokyo/Project/Achievements">Achievements</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Tokyo/Project/Future_works">Future works</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Tokyo/Notebook/Protocols">Protocols</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Tokyo/Notebook/Lab.notebook">Notes</a></li> <li><a class="aNotebook" href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Tokyo/Sponsors/">Sponsors</a></li> <li><a class="aSitemap" href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Tokyo/Sitemap">Sitemap</a></li>

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Simulation

3.Confirmation of directional walking on DNA tracks

Principles and methods of simulations

To confirm this mode, we simulated whether DNA ciliate moves intended direction on substrate DNAs track by cellular automaton framework. Cellular automaton framework is separate model. Its field is assumed that the width is infinite and cells are square-block type. Next time step state is calculated by present own value and neighbor’s value. In this simulation, probability for movement is determined by each cell’s free energy. Probability for moving to substrate is larger than moving to cleaved substrate because substrate’s energy is smaller than cleaved substrate’s energy.

This program is the simulation of DNA ciliate’s behavior, which works base on cellular-automaton framework.

A yellow cell represents DNA ciliate.
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 ciliate moves one micrometer by Brownian movement as following formula.

R: Gas constant. 8.3145[P/mol*K]

T: Temperature. 298[K].

Na=Avogadro number. 6.022141×10²³

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 assumption is that DNA ciliate moves with cleaving a ribose moiety to another cell in 120 seconds at a rate of 0.5. The other assumption is that DNA ciliate moves 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 dependent 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].

Results of simulations

Simulation movie

Execute a Simulation

To confirm“tracks walking mode”works correctly, we made line graphs movement of DNA ciliate based on cellular automaton. Please look at figure1 and figure2. The vertical axis shows the distance from origin. The horizontal axis shows the number of steps. Three lines are different in the DNA types of DNA track. The red line's DNA track is normal DNA track our made, so DNA ciliate moves with cleaving substrates by its legs. The blue line's DNA track is only cleaved substrate, so DNA ciliate moves without cleaving in this situation. The green line's DNA track is complementary strands for DNA ciliate’s leg, not substrate, which deoxyribozyme can't cleave, so DNA ciliate can hybridize with, but can't cleave the DNA.

From these graphs, we found that DNA ciliate moving on substrate moves faster and more directly than the others.

These graphs are mean square displacement of DNA ciliate’s movement. In mean square displacement, Brownian motion is presented by linear function and forced motion is presented by quadratic function. In this simulation, the moving distance on substrate field is presented by quadratic function. We confirmed DNA ciliate is forced directly and moves intended direction on substrate in this simulation.

In conclusion, we confirmed that DNA ciliate moves by directional force, not by Brownian motion in “track walking mode”.

[Program Source]

Conclusion

From thease results,we can

References

[1] [2]

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Biomod/2011/TeamJapan/Tokyo/Project/Simulations: Difference between revisions

Revision as of 09:34, 1 November 2011

Simulation

3.Confirmation of directional walking on DNA tracks

Principles and methods of simulations

Results of simulations

Simulation movie

Conclusion

References

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