Biomod/2011/TeamJapan/Sendai/Computational design/Simulation: Difference between revisions
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== About simulation == | == About simulation == | ||
We did 3D simulation of the molecular rolling robot over the DNA origami field using molecular dynamics. | We did 3D simulation of the molecular rolling robot over the DNA origami field using molecular dynamics. In this simulation, the robot represented as mass points, and moves by followed to Langevin equation. Hybridizing between robot legs and substrates on the field, and cleaving the substrates by legs, are described by potential shift. | ||
In this simulation, the robot | |||
Programs of our simulation were written in C language. | |||
== Model and Methods == | == Model and Methods == | ||
In this simulation, we used coarse-grained model (reference). As a coarse-grained model, representative points of structures were extracted, and structures were maintained by spring and string potentials. | |||
For example, see Fig.1, which represents extraction of corresponding points from real spider, and a scheme of potential to maintain structure. Streptavidine structures were maintained by spring-type potential which keeps length among points and weakly affect angles among points. Deoxyrybozyme legs were connected with string-type potential, which appears when points go beyond the determined length. On the spider simulation, blue points, green points, and yellow lines, represent mass points of the structure, top of spider legs, lines represents bonds, respectively. | |||
[[Image:Spider001.gif|600px|left|thumb|Fig.1 Spider in simulation]] | [[Image:Spider001.gif|600px|left|thumb|Fig.1 Spider in simulation]] | ||
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Each mass point is moving under influence of energy V. | Each mass point is moving under influence of energy V. The energy V is sum of potential energy for maintaining structure, and that for binding substrates on field. Potential of substrates is zero when legs are out of effective area (as cut-off), and changes by distance between legs and substrates when legs enter effective area. The force from differentiation of the substrate potential is proportional to the distance. | ||
Potential of substrates changes by distance of | |||
[[Image:potential.png|810px]] | [[Image:potential.png|810px]] | ||
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The motion of each mass point is described by Langevin Equation. | The motion of each mass point is described by Langevin Equation. | ||
In this equation, force '''F''' | The motion of each mass point is described by Langevin Equation. In this equation, acceleration is determined by sum of force '''F''' from the differentiation of energy '''V''', viscosity resistance -β'''v''' , and white Gaussian random force η(t). White Gaussian force was obtained by box-muller methods (reference). Distribution of the obtained random force is shown in Fig.2. | ||
'''Langevin Equation''' | |||
[[Image:Langevin.png]] | [[Image:Langevin.png]] | ||
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[[Image:Rforce.png|left|465px|thumb|Fig.2 Distribution of white Gaussian random force]] | |||
[[Image:Rforce.png|left|465px|thumb|Fig.2 | |||
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In order to deduce parameters, we simulated movements of DNA spider robot in the DNA spider article (Lund et al, 2010). Red points and blue points represent uncleaved substrates and cleaved substrates, respectively. See the above movie, in which spider goes toward goal with cleaving substrates. | |||
In order to | |||
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=== Simulation data === | === Simulation data === | ||
[[Image:Spider_data5.png|565px|thumb|right|Fig.4 (Left) Percentages of spiders that reached goal (without including the ones that left the field) (Right) Percentages of spiders which did not reach goal (which does not includes robots that was apart from field of DNA origami by brownian motion) These are resulted from 100 DNA spider simulation.]] | |||
Fig.4 describes how many spiders reached goal and how many did not at certain time. We tuned parameters on simulation to consist with the result in the figure 2G of DNA spider paper (Lund et al. 2010). On our simulation, the time for reaching the goal substrate was about 20 times longer than the time that DNAzyme cleaves substrate. The result matched very well to the time in the article (about 21 times longer). | |||
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We simulated whether our robot of triangular prism can reach goal of the field. Above videos shows our robot has a potential to reach goal. We supposed that our robot could reach the goal by only rotary motion, but however, our simulation result indicated that the triangular prism moves forward by corroboration manner of rotary motion with walking motion. This combined motion did not impede efficiency of moving forward. Anyway, simulation results reinforced us to consider our robots can reach goal. | |||
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To examine which is faster to reach goal, our triangular prism or DNA spider, simulation was done. Locations of substrates for the DNA spider were determined in above video by following the design of substrate in DNA spider paper. Locations of substrate field for triangular prism were followed to our field design. Since the body of the triangular prism robot is bigger than the spider body, we could reduce the number of substrates on the field. It can be seen from this video that the triangular prism robot reaches goal faster than the DNA spider. | |||
Since the body of the triangular prism robot is bigger than the spider body, we could reduce the number of substrates on the field. | |||
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[[Image:Tri_data1.png|480px|thumb|right|Fig.6 Goal time and percentage of 1 leg type and 3 leg types robot]] | [[Image:Tri_data1.png|480px|thumb|right|Fig.6 Goal time and percentage of 1 leg type and 3 leg types robot]] | ||
To check the effect of the number of leg-types, speeds of triangular prism with 3 types of legs and with 1 type of legs were calculated by our simulation. The right part of Fig.6 shows the results. Goal time of both are very similar, but the percentage of triangle prism was different. 1 leg type robot has higher goal probability. Thus, we concluded that the 1 leg type robot is better. | |||
The right | |||
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About simulation
We did 3D simulation of the molecular rolling robot over the DNA origami field using molecular dynamics. In this simulation, the robot represented as mass points, and moves by followed to Langevin equation. Hybridizing between robot legs and substrates on the field, and cleaving the substrates by legs, are described by potential shift.
Programs of our simulation were written in C language.
Model and Methods
In this simulation, we used coarse-grained model (reference). As a coarse-grained model, representative points of structures were extracted, and structures were maintained by spring and string potentials.
For example, see Fig.1, which represents extraction of corresponding points from real spider, and a scheme of potential to maintain structure. Streptavidine structures were maintained by spring-type potential which keeps length among points and weakly affect angles among points. Deoxyrybozyme legs were connected with string-type potential, which appears when points go beyond the determined length. On the spider simulation, blue points, green points, and yellow lines, represent mass points of the structure, top of spider legs, lines represents bonds, respectively.
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Each mass point is moving under influence of energy V. The energy V is sum of potential energy for maintaining structure, and that for binding substrates on field. Potential of substrates is zero when legs are out of effective area (as cut-off), and changes by distance between legs and substrates when legs enter effective area. The force from differentiation of the substrate potential is proportional to the distance.
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The motion of each mass point is described by Langevin Equation.
The motion of each mass point is described by Langevin Equation. In this equation, acceleration is determined by sum of force F from the differentiation of energy V, viscosity resistance -βv , and white Gaussian random force η(t). White Gaussian force was obtained by box-muller methods (reference). Distribution of the obtained random force is shown in Fig.2.
Langevin Equation
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Spider simulation
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In order to deduce parameters, we simulated movements of DNA spider robot in the DNA spider article (Lund et al, 2010). Red points and blue points represent uncleaved substrates and cleaved substrates, respectively. See the above movie, in which spider goes toward goal with cleaving substrates. |
Simulation data
Fig.4 describes how many spiders reached goal and how many did not at certain time. We tuned parameters on simulation to consist with the result in the figure 2G of DNA spider paper (Lund et al. 2010). On our simulation, the time for reaching the goal substrate was about 20 times longer than the time that DNAzyme cleaves substrate. The result matched very well to the time in the article (about 21 times longer).
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Simulation of the triangular prism robot
EmbedVideo received the bad id "z6_fWsgRH7A&border=1&color1=0x6699&color2=0x54abd6" for the service "youtube".
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We simulated whether our robot of triangular prism can reach goal of the field. Above videos shows our robot has a potential to reach goal. We supposed that our robot could reach the goal by only rotary motion, but however, our simulation result indicated that the triangular prism moves forward by corroboration manner of rotary motion with walking motion. This combined motion did not impede efficiency of moving forward. Anyway, simulation results reinforced us to consider our robots can reach goal.
|
Comparison between the spider and triangular prism robot
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To examine which is faster to reach goal, our triangular prism or DNA spider, simulation was done. Locations of substrates for the DNA spider were determined in above video by following the design of substrate in DNA spider paper. Locations of substrate field for triangular prism were followed to our field design. Since the body of the triangular prism robot is bigger than the spider body, we could reduce the number of substrates on the field. It can be seen from this video that the triangular prism robot reaches goal faster than the DNA spider.
Data of triangular prism simulation
To check the effect of the number of leg-types, speeds of triangular prism with 3 types of legs and with 1 type of legs were calculated by our simulation. The right part of Fig.6 shows the results. Goal time of both are very similar, but the percentage of triangle prism was different. 1 leg type robot has higher goal probability. Thus, we concluded that the 1 leg type robot is better.
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Other data
Cleavage rate and spider speed
To verify the effect of cleavage rate of substrate, we did spider simulation with changing cleavage time.
The following figure is the result we got from our simulation.
From this figure , we can see that percentage of spiders reached to the goal substrate increases and robot speed decreases if cleavage time increases.
This shows that increase of cleavage rate causes increase of spider speed and decrease of probability to reach the goal substrate.
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Field design and spider speed
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Above figure shows design of fields and moving data of spider over each field. Design of these fields are based on the field used in the spider article.(field of figure(d)) Substrates in field (a),(b),(c) is removed in different pattarn.
By looking each data from the viewpoint of the number of substrates, we got results in right figure. From this figure, we can see less substrates provides faster speed of robot. And we can also see the goal probability becomes higher if the number of substrates increases. But the goal probability seems to be strongly effected not only by the number but by its design too.
From these factors, we concluded that it is better to reduce substrates on the field as much as possible if we want to speed the robot.
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Body size and leg size
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In this section, whole size of both robots ,triangular prism and spider, are set up to be the same.
Design of triangular prism doesn't differ to the one we used above, while spider robot has longer legs.
Right figure shows moving data of each robot. From this figure, we can see the spider using long legs has more goal probability and goal time. This is thought to be due to the difference of body size, leg length and the number of legs. And faster speed in triangular prism robot can be seen in this simulation, too. If the robot has more legs, it can cleave more substrates in the same time, and then if the number of the substrates on the field is the same, robot has more legs will be faster. Thus, if the design of fields are the same, the robot has more legs is faster and this is why the triangular prism was faster in this simulation.
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