Biomod/2011/TeamJapan/Sendai/Computational design/Simulation: Difference between revisions

From OpenWetWare
Jump to navigationJump to search
No edit summary
No edit summary
 
(45 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{:Biomod/2011/TeamJapan/Sendai/Header}}
{{:Biomod/2011/TeamJapan/Sendai/HeaderSimulation}}


<html>
<table width=800 border="0" align="center" vertical-align: middle;>
<tr><td><center><div id="red">3D simulation movie</div></center></td></tr></table>
</html>


<table border="0" align="center" vertical-align: middle;>
<tr>
  <td>
<youtube align="left" width="800" height="500">LtnN_Usj1Pw&border=1</youtube>
<div style="clear:both;"></div>
</td>
</tr>
</table>
== Outline ==
<html>
<table width=800 border="0" align="center" vertical-align: middle;>
<tr><td></br><img src="http://openwetware.org/images/b/b7/Simulation_abstract.png" width="800"></td></tr></table>
</html>


== 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 is represented as mass points and moves by following the Langevin equation. Hybridizing between robot legs and substrates on the field, and cleaving the substrates by legs, are described by a potential shift.  
In this simulation, the robot consists of mass points and we used the Langevin equation to describe the motion of each mass point.  
Situations between robot legs and substrates on the field , like sticking and cleaving , are described by change of potential.


This simulation had done by C language programing.
The program code was written entirely in C and OpenGL.


== Model and Methods ==
== Model and Methods ==
In this simulation, we composed the structure by binding extracted representative points.


First of all, we did the simulation of molecular spider robot. Following figure is representing correspondence of each part of the real spider and the spider in simulation. Left one is the real spider and right one is the one in simulation.  
In this simulation, we described the system as a coarse-grained model<sup>(1)</sup>. In a coarse-grained model, representative points of the structures are extracted. In our case, these representative points were connected by springs and strings, and their potentials associated with them.


At the spider in the simulation, blue points are representing selected mass points of the structure, green points are representing top of spider legs, and yellow lines are representing bonds.
For example, see Fig.1, which represents extraction of corresponding points from the molecular spider, and a scheme of potential to maintain structure. Streptavidine structures were maintained by a spring-type potential which keeps length among points and weakly affect angles among points. Deoxyrybozyme legs were connected with a string-type potential, which is taken into consideration 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.




Japanese:
[[Image:Spider001.gif‎|600px|left|thumb|Fig.1 Representation of the molecular spider in our simulation]]
[[[このシミュレーションでは構造の代表点を抜き出し、それらに長さ及び角度の拘束力を与えることで構造体を構成させている。
<html><div style="clear:both;"></div></html>
 
今回はじめに分子スパイダーを歩かせるシミュレーションを行ったが、実際のスパイダーとシミュレーション上のスパイダーモデルの対応は下図のようになっている。
 
下図右のシミュレーション上のモデルにおいて、青い点は構造体における代表点を、黄色の線は点同士の結合を、また緑色の点はスパイダーの足の先端部を示している。]]]
 
[[Image:Spider001.gif‎|600px]]
 
Each mass point is moving with effect of energy V.
 
This energy V is mainly composed of the energy by bond of distance or angle, and the potential of each substrate.
 
Potential of substrates changes by distance of leg and substrate ,and by substrate situation if it is cut or not.
 
 
Japanese:[[[各質点は代表点同士の結合による拘束力等によるポテンシャルの影響を受けて運動している。


そのポテンシャル V は以下式で表され、その値はばね結合によるポテンシャル、角度ばねによるポテンシャル、足と本体の結合によるポテンシャル、そして足がフィールド上のsubstrateと結合することにより生じるポテンシャルの合計となっている。
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. The potential of substrates is zero when legs are out of the 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.
 
ここで、スパイダーの足の先端がsubstrateとハイブリダイゼーションできる距離まで近づいた場合、その濃度は約0.83mMとなりK<sub>M</sub>=50nM より著しく大きい。そのため足の先端がsubstrateの影響範囲下に入った場合、速やかにポテンシャルが小さくなるように設定している。]]]


[[Image:potential.png|810px]]
[[Image:potential.png|810px]]
<html><div style="clear:both;"></div></html>


The whole motion of each mass point is described by Langevin Equation.
The motion of each mass point is described by the Langevin Equation<sup>(2)</sup>. 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 random force was obtained by the box-muller methods<sup>(3)</sup>. Distribution of the obtained random force is shown in Fig.2.


In this equation, force '''F''' is derived from the energy V, -'''βv''' is the viscosity resistance, and η(t) is the white and Gaussian random force.
<big>'''Langevin Equation'''</big>


[[Image:Langevin.png]]
<html><div style="clear:both;"></div></html>


Japanese:[[[
[[Image:F=.png|100px]]
上記の様に各質点はポテンシャルの影響を受けながら運動しているが、この元となる運動はブラウン運動に従ったものとなっており、その運動はLangevin Equation(以下式)によって記述される。
 
この式において '''F''' はポテンシャル V による力を、-β'''v''' は粘性による抵抗を、η は時間により変化するランダム力を表しており、各質点はこの式にしたがって運動している。このランダム力は正規分布に従っている。]]]
[[Image:Langevin.png]]
 
<html><div style="clear:both;"></div></html>
<html><div style="clear:both;"></div></html>


またランダム力は下のような分布になっており、各成分がGaussian distributionにしたがっていることがわかる。
[[Image:Rforce.png|left|465px|thumb|Fig.2 Distribution of white Gaussian random force]]
 
[[Image:Rforce.png]]


<html><div style="clear:both;"></div></html>
<html><div style="clear:both;"></div></html>
Line 65: Line 59:
<table border="0" align="center" vertical-align: middle;>
<table border="0" align="center" vertical-align: middle;>
<tr>
<tr>
  <td>
 
<youtube align="left" >4gDTzqJRFUs&border=1&color1=0x6699&color2=0x54abd6 </youtube>
<youtube align="left" >4gDTzqJRFUs&border=1&color1=0x6699&color2=0x54abd6 </youtube>
<br>
[[Image:Field1.png|480px|thumb|Fig.3 Field in simulation]]
<html><div style="clear:both;"></div></html>
<html><div style="clear:both;"></div></html>
  </td>
 
   <td>
   <td>
シミュレーションの動作確認のため、論文"Molecular robots guided by prescriptive landscape"を参考にスパイダーの移動シミュレーションを行った。その結果が上の動画である。
In order to deduce parameters, we simulated movements of DNA spider robot in the DNA spider article (Lund et al. 2010)<sup>(4)</sup>. 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.
この動画中で赤い点は切断されていない足場を、青い点は切断された足場を表している。
この動画からスパイダーは足でsubstrateを切断しながらトラック上を歩いて行き、ゴールまでたどり着いていることが確認できる。
 
 
In order to perform a simulation of a DNA spider we used parameters provided by "Molecular robots guided by prescriptive landscape" (Lund ''et al'', 2010).
The red points in the simulation (see above video) are not yet cleaved scaffolds, but the blue ones. The green point represents the end of a robot's leg.
For simulation purpose, the legs are represented as inextensible cables.
   </td>
   </td>
</tr>
</tr>
Line 85: Line 75:


=== 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.]]


シミュレーション上でスパイダーがゴールまでたどり着けることが確認できたため、次に実際の実験との一定の整合性を確認するためのデータ収集を行った。
今回は参考論文P208 Figure2 の実験と同様の条件でシミュレーションを行い、データ収集を行った。
その実験とはスタートトリガーDNAを投入した後、各時間においてフィールド上に乗っているスパイダーがそれぞれどの位置にいるかの統計を取ったというものである。
シミュレーションでは合計100匹のスパイダーをスタートさせ、各時間においてフィールド上に残っているスパイダーに対してその位置を調べた。
[[Image:Spider_data5.png|565px|thumb|right|(左図)時間毎におけるフィールド上のスパイダーに対するゴールしたスパイダーの割合
(Left) Number of spiders that approach the goal (without including the ones that left the field) vs time<br />
(右図)時間毎におけるフィールド上のスパイダーに対するトラック上のスパイダーの割合
(Right) Number of spiders over the track (without including the ones that left the field) vs time]]
その結果が右図である。
右図はスタート後各時間においてフィールド上のスパイダーの何パーセントがその場所にいたのかということを示したグラフである。(このとき参考論文において常に一定数のスパイダーがスタートに見られたため、その数も考慮してある。)
このグラフより、シミュレーションにより得られたスパイダーの各時間における位置の割合は参考論文で得られている実験結果と同様の結果となっていることがわかった。
そのため、シミュレーションにおいてこの実験をある程度再現できたと言える。
また参考論文においてスパイダーがゴールするまでの時間は1本の足場が切断されるまでの時間の約21倍であったが、シミュレーションで得られた平均ゴール到達時間は設定した足場の切断時間の約20倍となり、こちらについてもほぼ同様の結果が得られた。
そのためこの結果からも参考論文における実験を再現できていたと言える。
The above figure describe quantitatively how many spiders reach the goal and how many are over the track with respect to time. This result is similar to previous experiments reported in the literature.




Fig.4 describes how many spiders reached the goal and how many did not at a certain time. We tuned simulation parameters to be consistence with the result in figure 2G of Lund et al. (''Nature'', 2010)<sup>(4)</sup>. In our simulation, the time for reaching the goal substrate was about 20 times longer than the time that DNAzyme cleaved substrate. The result matched very well to the time in the article (about 21 times longer).


<html><div style="clear:both;"></div></html>
<html><div style="clear:both;"></div></html>


== Simulation of the triangular prism robot ==
== Simulation of the triangular prism robot ==
Line 129: Line 91:
   </td>
   </td>
   <td>
   <td>
今回私たちが作製する三角柱ロボットが実際に競技フィールド上を移動するのかということを確かめるために、実際のスケールを元にしてシミュレーション上でロボット及び競技フィールドを作製し、ロボットの移動シミュレーションを行った。
We simulated whether our triangular prism robot can reach the goal of the field. The video in the left shows that our robot has high probability to reach the goal. We supposed that the triangular prism robot could reach the goal by only rotary motion. However, our simulation result indicated that the triangular prism moves forward by combination of, both, rotary motion and walking motion. This combined motion did not impede the robot efficiency for moving forward. Anyway, this design is satisfying our initial racing condition of reaching the goal.
その結果が上の動画である。
 
この動画からロボットはフィールド上を移動していき、最終的にゴールまでたどりつけていることがわかる。


当初自分たちの目標としていた回転運動のみでのゴールとはならなかったがブラウン運動による回転等の移動が随所に見られ、最終的にゴールまできちんとたどり着けるという結果が得られた。


そのため実際の三角柱ロボットでもsubstrateを切断しながらゴールまで到達できると考えられる。


In the above video we present the simulation of the movement for the molecular robot based on a triangular prism body.
In this simulation, the robot reached its goal when is placed over the obstacle origami field.
From initial design we supposed that the robot could reach the goal by only rotary motion.
This behavior is corroborated in the simulation where the robots show rotary motion driven by Brownian motion, and also forward translational motion. However, this combined motion does not impide the robot reach the goal point. Thus, we are inclined to believe that the performance of this robot over the field would be success.
   </td>
   </td>
</tr>
</tr>
</table>
</table>


== Comparison between the spider and triangular prism robot ==


== Comparison between the spider and triangular prism robot ==
<table border="0" align="center" vertical-align: middle;>
<tr>
<td>
<youtube align="left">QjchE3TR1UQ&border=1&color1=0x6699&color2=0x54abd6</youtube>
<youtube align="left">QjchE3TR1UQ&border=1&color1=0x6699&color2=0x54abd6</youtube>
<html><div style="clear:both;"></div></html>
  </td>
  <td>
私たちの作製する三角柱ロボットとスパイダーの移動速度の比較を行うため、同一スケールのフィールド上においてスパイダーと三角柱を同時に移動させるシミュレーションを行った。


このときsubstrateを配置する場所についてはスパイダーは参考論文におけるsubstrateの間隔を参考に配置し、また三角柱については私たちの設計と同様な位置に配置した。


この動画から三角柱はスパイダーよりも速い速度でゴールへと進んでいることがわかる。


今回のプロジェクトの目的は三角柱を用いることにより速いスピードで移動させるということだったので、このことからシミュレーション上ではこの目標を達成できたといえる。
[[Image:Speed1.png|258px|thumb|center|Fig.5 Speed of spider and triangular prism.]]
 
<html><div style="clear:both;"></div></html>
 


三角柱の方が早いという結果が得られたのは三角柱の方がスパイダーよりも大きな構造となっており、フィールドに生やすsubstrateの本数を減らすことができたためであると考えられる。


In this section we compare the times for reaching the same goal for each one of the two molecular robots.
In order to examine which of the robots (our triangular prism or DNA spider) is the fastest in reaching the goal, a simulation was carried out. Locations of the substrates for the molecular spider were determined by following the design of the substrates in the original DNA spider paper, those positions are seen in the video. Locations of the substrate for our triangular prism robot were considered to be the same as our field design. Since the body of the triangular prism robot is bigger than the spider body, we could reduce the number of substrates for the prism on the field. It can be seen from this video that the triangular prism robot reaches the goal faster than the DNA spider.
The substrate distribution pattern for the spider in the video is the same as spider paper. And, substrate position for triangular prism is our field design.
It can be seen from this video that the triangular prism robot reaches the goal faster than the spider because a bigger body.
Since the body of the triangular prism robot is bigger than the spider body, we could reduce the number of substrates on the field.
  </td>
</tr>
</table>


== Data of triangular prism simulation ==
== Data of triangular prism simulation ==


[[Image:Tri_data1.png|480px|thumb|right|1種類、3種類の足の三角柱のゴールに到達した個体の割合及び平均到達時間]]
[[Image:Tri_data1.png|480px|thumb|right|Fig.6 Goal time and percentage of 1 leg type and 3 leg types robot]]
三角柱において足の種類を増やし移動方向を指定することで移動速度が大きくなるのかということを検証するため3種類の足を用いた三角柱と1種類の足を用いた三角柱でデータ収集を行った。


その結果が右図のグラフであるである。


このグラフを見ると足の種類によるゴール到達時間すなわち速度の変化はないがゴールする割合が3種類の足を用いたものの方が1種類のものよりも少なくなっていることがわかる。
To check the effect of the number of leg-types over the time to reach the goal, 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. The goal time of both cases are very similar, but the percentage of the triangle prism was different. 1 leg type robot has a higher goal probability. Thus, we concluded that the 1 leg type robot could be better.
 
このことから私たちの設計した三角柱においては3種類の配列の足を用いるよりもすべて同じ配列の足を用いた方がよいと考えられる。


<html><div style="clear:both;"></div></html>
<html><div style="clear:both;"></div></html>


== Other data ==
== Other data ==
=== Cleavage rate and spider speed ===
=== Cleavage rate and spider speed ===
[[Image:Spider_data1.png|479px|thumb|right|Correlation between cleavage time and percentage of spiders reached the goal substrate ,and goal time]]
[[Image:Spider_data1.png|482px|thumb|right|Fig.7 Correlation between cleavage time and percentage of spiders reached the goal substrate ,and goal time]]


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.
To verify effects of cleavage rates of DNAzyme, simulation of the molecular spider was done by changing cleavage time. Fig.7 is the result from our simulation. Increase of cleaving rate facilitated speed in reaching the goal, but percentage of spiders which reached goal reduced. Therefore, there is a trade-off between increasing the cleaving rate and the percentage of robots that reaches the goal.


From this figure , we can see that percentage of spiders reached to the goal substrate and time to get to the goal substrate from the start increase 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.
<html><div style="clear:both;"></div></html>
 
=== Field design and spider speed ===
[[Image:Spider_data3.png|725px|thumb|left|Fig.8 Design of spider fields. All of these fields are based on the field we used in spider simulation (base field). (a)1 Substrate line is removed from the base field every 2 line. (b) 2 Substrate lines are removed every 3 line. (c) Upper substrates are removed. (d) The base field.]]


<html><div style="clear:both;"></div></html>
<html><div style="clear:both;"></div></html>


=== Field design and spider speed ===
[[Image:Spider_data2.png|452px|thumb|right|Fig.9 Correlations between the number of substrates and moving data of spiders]]
[[Image:Spider_data3.png|725px|thumb|left|Design of spider fields. All of these fields are based on the field we used in spider simulation(base field). (a)1 Substrate line is removed from the base field every 2 line. (b)2 Substrate lines are removed every 3 line. (c)Upper substrates are removed. (d)The base field.]]
Fig.8 shows design of fields and moving data of spider over each field. Designs of these fields were based on the field used in the molecular spider article (figure 1d in Lund et al. Nature 2010))<sup>(4)</sup>. Substrates in the field (a), (b), (c) are removed in a different pattern.
 
The results by the simulation are shown in the right figure. Less substrates gained speed to reach goal, and decreased probability of goal. But the goal probability depends on not only the number of substrates but also on the location of the substrates.
 
These suggested that it is better to reduce substrates on the field as much as possible to gain robot's speed.
 
<html><div style="clear:both;"></div></html>
 
=== Body size and leg size ===


<html><div style="clear:both;"></div></html>
<html><div style="clear:both;"></div></html>


[[Image:Spider_data2.png|422px|thumb|right|Correlations between the number of substrates and moving data of spiders]]
[[Image:Tri spider1.png|466px|thumb|right|Fig.10 These robot's size is the same.]]
 
 
In this section, both robots, triangular prism and a modified molecular spider, were chased in silico on the same field. On this simulation, spider robot has longer legs, while design of triangular prism was the same as the one we used above. Right figure shows moving data of each robot. As a result, the molecular spider with long legs was slower than our robots, although it had more goal probability. It might be due to difference in the body size, leg length and the number of legs. Longer leg increases the probability to reach the goal, making more molecular spiders reach goal. And if the structure has more legs, it can cleave more substrates in the same time. Therefore, when the design of the fields is the same, robots with many legs are fast. This notion explained why the triangular prism was faster when comparing with the molecular spider.


<html><div style="clear:both;"></div></html>
<html><div style="clear:both;"></div></html>
==Reference==
(1) Fumiko Takagi ''et al''. How protein thermodynamics and folding mechanisms are altered by the chaperonin cage: Molecular simulations, PNAS. 100, 11367 (2003)<br />
(2) [http://en.wikipedia.org/wiki/Langevin_equation http://en.wikipedia.org/wiki/Langevin_equation]<br />
(3) [http://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform http://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform]<br />
(4) Lund ''et al''. Molecular robots guided by prescriptive landscapes, Nature. 465, 206 (2010)<br />

Latest revision as of 08:08, 2 November 2011

<html>

<style rel="stylesheet" type="text/css"> 

      .clear {clear:both;}
 #verticalmenu {

/*this .CSS is inspired by http://www.javascriptkit.com/ */ font-family: "Comic Sans MS" , "Brush Script MT",serif, sans-serif, monospace, cursive, fantasy; list-style:none;}

  1. verticalmenu a:hover {

color: #aa1d1d; /* color when the click is over the main menu text-transform: uppercase; font-size: 10px; */


}

a:visited { color:#00a5ea; text-decoration: none }

.glossymenu, .glossymenu li ul{ list-style-type: none; margin: 0; padding: 0; width: 250px; /*WIDTH OF MAIN MENU ITEMS*/ border: 1px solid black; list-style:none; }

.glossymenu li{ position: relative; }

.glossymenu li a{ background: white url(http://openwetware.org/images/a/a7/Glossyback2.jpg) repeat-x bottom left; font: bold 17px Verdana, Helvetica, sans-serif; color: white; display: block; width: auto; padding: 10px 0; padding-left: 10px; text-decoration: none; }

.glossymenu li ul{ /*SUB MENU STYLE*/ position: absolute; width: 200px; /*WIDTH OF SUB MENU ITEMS*/

left: 0; top: 0; display: none; }

.glossymenu li ul li{ float: left; }

.glossymenu li ul a{ width: 190px; /*WIDTH OF SUB MENU ITEMS - 10px padding-left for A elements */ }

.glossymenu .arrowdiv{ position: absolute; right: 2px; background: transparent url(http://openwetware.org/images/6/69/Arrow.gif) no-repeat center right; }

.glossymenu li a:visited, .glossymenu li a:active{ color: white; }

.glossymenu li a:hover{ background-image: url(http://openwetware.org/images/5/50/Glossyback.jpg); }

/* Holly Hack for IE \*/

  • html .glossymenu li { float: left; height: 1%; }
  • html .glossymenu li a { height: 1%; }

/* End */

</style>

<script type="text/javascript">

/***********************************************

  • CSS Vertical List Menu- by JavaScript Kit (www.javascriptkit.com)
  • Menu interface credits: http://www.dynamicdrive.com/style/csslibrary/item/glossy-vertical-menu/
  • This notice must stay intact for usage
  • Visit JavaScript Kit at http://www.javascriptkit.com/ for this script and 100s more
                                                                                              • /

var menuids=new Array("verticalmenu") //Enter id(s) of UL menus, separated by commas var submenuoffset=-2 //Offset of submenus from main menu. Default is -2 pixels.

function createcssmenu(){ for (var i=0; i<menuids.length; i++){ 

 var ultags=document.getElementById(menuids[i]).getElementsByTagName("ul")
   for (var t=0; t<ultags.length; t++){
   var spanref=document.createElement("span")

spanref.className="arrowdiv" spanref.innerHTML="&nbsp;&nbsp;" ultags[t].parentNode.getElementsByTagName("a")[0].appendChild(spanref) 

   ultags[t].parentNode.onmouseover=function(){
   this.getElementsByTagName("ul")[0].style.left=this.parentNode.offsetWidth+submenuoffset+"px"
   this.getElementsByTagName("ul")[0].style.display="block"
   }
   ultags[t].parentNode.onmouseout=function(){
   this.getElementsByTagName("ul")[0].style.display="none"
   }
   }
 }

} if (window.addEventListener) window.addEventListener("load", createcssmenu, false) else if (window.attachEvent) window.attachEvent("onload", createcssmenu) </script>

<table border="0" align="center" vertical-align: middle;> <tr> 

 <td>

<ul id="verticalmenu" class="glossymenu"> <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Sendai">Home</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Sendai/Strategy">Strategy</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Sendai/Design">Design</a></li> <li><a href="#">Experiments</a> 

   <ul>
   <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Sendai/Results/Electrophoresis">Electrophoresis</a> 
   <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Sendai/Results/Atomic_Force_Microscope">AFM</a> 
   </ul>

</li> <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Sendai/Computational_design/Simulation" >Simulation</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Sendai/Notes">Notes</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Sendai/Team">Team</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Sendai/Resources">Resources</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2011/TeamJapan/Sendai/Sitemap">Sitemap</a></li>


</ul> </td> 

 <td>

<img src="http://openwetware.org/images/9/93/Simulationh.png" width="650"> </br></br></br></br></br> </td> </tr> </table> </html> <html> <head> <style type="text/css">

  1. content {padding-left: 10px;width: 970px;}}

h3 {font-decoration: none;} h1.firstHeading {display: none; } </style> </head> </html>

<html> <style rel="stylesheet" type="text/css"> /*このスタイルシートの著作権はテンプレート工房TAKEにあります*/ /*ページのレイアウト用css*/

body{ background:#F5F5DC; /*壁色と壁紙設定*/ background-repeat:repeat;/*繰り返さない場合はno-repeatに変更*/ font:"メイリオ", "ＭＳ Ｐゴシック", Osaka, "ヒラギノ角ゴ Pro W3"; color: #333333; margin:0px; padding:0px; }

  1. contents{
     width:900px;

margin:0 auto; background-color: #FFFFFF ;/*コンテンツ内の背景(サイズをぴったりにすること）*/ background-repeat:repeat-y; /*縦に繰り返し*/ border:solid 1px #666666;/*サイトに枠を付ける設定,色の変更可*/ 

     position:relative;
     font-size:80%;

}


/*ヘッダー部分の設定*/

  1. header{

background-image:url(http://openwetware.org/images/c/c4/TeamSendai-logo3.png) ;/*ヘーダー*/ background-repeat:repeat-x; /*縦に繰り返し*/ background-position:top right; height:140px; /*ヘーダーの高さ*/ }

  1. header p {

font-size: 26px; 

       color:#333333;

padding-top: 15px; padding-left: 20px; }


/*上部メニューボタンの設定*/

  1. navbar{
     background-color:#FFFFFF; 
     width: 100%;
     height:40px;
     position:margine;
     top:100px;
     left:0px;
     border-top:solid 1px #FFFFFF;
     border-bottom:solid 1px #FFFFFF; 
     }


  1. navbar ul{
         margin:0;

padding:0; list-style-type:none; font-family:Arial, Helvetica, sans-serif; font-size: 12px; line-height:40px; letter-spacing:2px; }

  1. navbar li{
     background-color:#000099;  /*上部メニューのボタンの背景*/

float:left; width:146px; /*メニューボタンの幅*/ text-align:center; padding:0; border-right:solid 1px #ffffff; }

  1. navbar ul a:hover{
  	background-color:#0033cc;	/*メニューボタンにカーソルが来た時に背景*/

width:146px; /*メニューボタンの幅*/ }

  1. navbar a{
     color:#ffffFF;/*メニューボタンの文字の色*/

display:block; }

  1. navbar a:hover{
  color:#999999; /*メニューの文字がカーソルが来た時、この色に変わる*/
  }



/*サイドメニューの設定*/

  1. side{

background-color:#ddffff; 

     width:220px;/*サイドの幅（変更するときはコンテンツ背景も変更すること）*/

position:margin; top:600px;/*上からの位置*/ left:12px; }

  1. side h3 {

font-size: 90%; border: double 3px #FFFFFF; color:#ffffff; text-align: center; background-color:#999999; 

     width:190px;

line-height: 30px; margin-top: 10px; margin-left: 5px; margin-bottom: 5px; }

  1. side h3 a {
     color:#ffffff;

font-weight:normal; }

  1. side ul{
     font-size:100%;

line-height:220%; /*サイドの文字と文字の行間設定*/ background-color: #ddffff; margin:0px; padding-left:10px; }

  1. side ul a:hover {
     width:180px;

background-color: #99ffff; /*サイドのカーソルオーバー時の背景色*/ color: #999999; /*サイドのカーソルオーバー時の文字色*/ }

  1. side ul{
    list-style-type:none;

padding-left:2px; }

  1. side li{

padding-left:15px;　/*文字の左端からの位置*/ }

  1. side li a{
    color:#333333;/*サイドの文字色*/
    width:180px;
    display:block;

}

  1. side .ad_list li{
    background-image:none;

padding-left:0; }



/*右側メイン部分の設定*/

  1. main{
     width:630px;
     padding-top:15px;
     margin-left:240px;

}



/*下部のフッター部分の設定*/ address{ font-size:80%; font-style:normal; text-align:center; padding-top:5px; }

address{ 

     background-color:#000066;
     color:#ffffff;
         width:882px;

padding-bottom:10px; border:none; } address a{ 

     color:#ff9999;

}


/*文字の設定*/ h1{ font-size:60%; letter-spacing: 2px; padding-left:10px; margin: 0px; }

h1 a{ 

     color:#FFFFFF;

font-weight:normal; }


h2{ 

     font-size:140%;

border-left: 10px solid #000066; 

         border-bottom:solid 1px #000099;/*文字の下に線を入れる設定*/
         width:900px;

padding-left: 5px; color:#333333; margin-top: 15px; margin-bottom: 5px; }

h3{ 

     font-size:120%;

border: solid 1px #111111; 

       color:#ffffff;

background-color:#4682B4 ; line-height: 30px; padding-left:10px; margin-top: 10px; margin-bottom: 1px; }

p{ 

     font-size:90%;/*全体の文字サイズ*/

line-height:150%;/*全体で使う、文字と文字の行間*/ 

         margin-left:5px;

}

p img{ 

     float:left;
         margin-top:5px;  /*写真の左にスペースを空ける*/
         margin-left:5px;  /*写真の左にスペースを空ける*/

margin-right:10px; /:写真と文字の間隔*/ }


/*リンク文字の設定*/ a{ 

    color:#000099;
     text-decoration:none;

} a:hover { color: #FF0000;/*リンクの文字の上にマウスが来た時この色に変わる*/ text-decoration: none; }

  1. purple{
     font-size:120%;

border: solid 1px #111111; 

       color:#ffffff;

background-color:#9370DB; line-height: 40px; padding-left:10px; margin-top: 10px; margin-bottom: 1px; }

h5{ 

     font-size:120%;

border: solid 1px #111111; 

       color:#ffffff;

background-color:#FFA500; line-height: 30px; padding-left:10px; margin-top: 10px; margin-bottom: 1px; }

h6{ 

     font-size:120%;

border: solid 1px #111111; 

       color:#ffffff;

background-color:#006400; line-height: 30px; padding-left:10px; margin-top: 10px; margin-bottom: 1px; }

  1. red{
     font-size:120%;

border: solid 1px #111111; 

       color:#ffffff;

background-color:#DC143C; line-height: 40px; padding-left:10px; margin-top: 10px; margin-bottom: 1px; }

  1. blue{
     font-size:120%;

border: solid 1px #111111; 

       color:#ffffff;

background-color:#191970; line-height: 40px; padding-left:10px; margin-top: 10px; margin-bottom: 1px; }

</style> </html>

<html> <table width=800 border="0" align="center" vertical-align: middle;> 

<tr><td><center><div id="red">3D simulation movie</div></center></td></tr></table>

</html>

EmbedVideo received the bad id "LtnN_Usj1Pw&border=1" for the service "youtube".

Outline

<html> <table width=800 border="0" align="center" vertical-align: middle;> 

<tr><td></br><img src="http://openwetware.org/images/b/b7/Simulation_abstract.png" width="800"></td></tr></table>

</html>

About simulation

We did 3D simulation of the molecular rolling robot over the DNA origami field using molecular dynamics. In this simulation, the robot is represented as mass points and moves by following the Langevin equation. Hybridizing between robot legs and substrates on the field, and cleaving the substrates by legs, are described by a potential shift.

The program code was written entirely in C and OpenGL.

Model and Methods

In this simulation, we described the system as a coarse-grained model(1). In a coarse-grained model, representative points of the structures are extracted. In our case, these representative points were connected by springs and strings, and their potentials associated with them.

For example, see Fig.1, which represents extraction of corresponding points from the molecular spider, and a scheme of potential to maintain structure. Streptavidine structures were maintained by a spring-type potential which keeps length among points and weakly affect angles among points. Deoxyrybozyme legs were connected with a string-type potential, which is taken into consideration 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.


Fig.1 Representation of the molecular spider in our simulation

<html><div style="clear:both;"></div></html>

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. The potential of substrates is zero when legs are out of the 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.

<html><div style="clear:both;"></div></html>

The motion of each mass point is described by the Langevin Equation(2). 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 random force was obtained by the box-muller methods(3). Distribution of the obtained random force is shown in Fig.2.

Langevin Equation

<html><div style="clear:both;"></div></html>

<html><div style="clear:both;"></div></html>

Fig.2 Distribution of white Gaussian random force

<html><div style="clear:both;"></div></html>

Spider simulation

EmbedVideo received the bad id "4gDTzqJRFUs&border=1&color1=0x6699&color2=0x54abd6" for the service "youtube".


Fig.3 Field in simulation

<html><div style="clear:both;"></div></html>

In order to deduce parameters, we simulated movements of DNA spider robot in the DNA spider article (Lund et al. 2010)(4). 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 (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 the goal and how many did not at a certain time. We tuned simulation parameters to be consistence with the result in figure 2G of Lund et al. (Nature, 2010)(4). In our simulation, the time for reaching the goal substrate was about 20 times longer than the time that DNAzyme cleaved substrate. The result matched very well to the time in the article (about 21 times longer).

<html><div style="clear:both;"></div></html>

Simulation of the triangular prism robot

EmbedVideo received the bad id "z6_fWsgRH7A&border=1&color1=0x6699&color2=0x54abd6" for the service "youtube".

<html><div style="clear:both;"></div></html>

We simulated whether our triangular prism robot can reach the goal of the field. The video in the left shows that our robot has high probability to reach the goal. We supposed that the triangular prism robot could reach the goal by only rotary motion. However, our simulation result indicated that the triangular prism moves forward by combination of, both, rotary motion and walking motion. This combined motion did not impede the robot efficiency for moving forward. Anyway, this design is satisfying our initial racing condition of reaching the goal.


Comparison between the spider and triangular prism robot

EmbedVideo received the bad id "QjchE3TR1UQ&border=1&color1=0x6699&color2=0x54abd6" for the service "youtube".


Fig.5 Speed of spider and triangular prism.

<html><div style="clear:both;"></div></html>


In order to examine which of the robots (our triangular prism or DNA spider) is the fastest in reaching the goal, a simulation was carried out. Locations of the substrates for the molecular spider were determined by following the design of the substrates in the original DNA spider paper, those positions are seen in the video. Locations of the substrate for our triangular prism robot were considered to be the same as our field design. Since the body of the triangular prism robot is bigger than the spider body, we could reduce the number of substrates for the prism on the field. It can be seen from this video that the triangular prism robot reaches the goal faster than the DNA spider.

Data of triangular prism simulation

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 over the time to reach the goal, 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. The goal time of both cases are very similar, but the percentage of the triangle prism was different. 1 leg type robot has a higher goal probability. Thus, we concluded that the 1 leg type robot could be better.

<html><div style="clear:both;"></div></html>

Other data

Cleavage rate and spider speed

Fig.7 Correlation between cleavage time and percentage of spiders reached the goal substrate ,and goal time


To verify effects of cleavage rates of DNAzyme, simulation of the molecular spider was done by changing cleavage time. Fig.7 is the result from our simulation. Increase of cleaving rate facilitated speed in reaching the goal, but percentage of spiders which reached goal reduced. Therefore, there is a trade-off between increasing the cleaving rate and the percentage of robots that reaches the goal.


<html><div style="clear:both;"></div></html>

Field design and spider speed

Fig.8 Design of spider fields. All of these fields are based on the field we used in spider simulation (base field). (a)1 Substrate line is removed from the base field every 2 line. (b) 2 Substrate lines are removed every 3 line. (c) Upper substrates are removed. (d) The base field.

<html><div style="clear:both;"></div></html>

Fig.9 Correlations between the number of substrates and moving data of spiders

Fig.8 shows design of fields and moving data of spider over each field. Designs of these fields were based on the field used in the molecular spider article (figure 1d in Lund et al. Nature 2010))(4). Substrates in the field (a), (b), (c) are removed in a different pattern.

The results by the simulation are shown in the right figure. Less substrates gained speed to reach goal, and decreased probability of goal. But the goal probability depends on not only the number of substrates but also on the location of the substrates.

These suggested that it is better to reduce substrates on the field as much as possible to gain robot's speed.

<html><div style="clear:both;"></div></html>

Body size and leg size

<html><div style="clear:both;"></div></html>

Fig.10 These robot's size is the same.


In this section, both robots, triangular prism and a modified molecular spider, were chased in silico on the same field. On this simulation, spider robot has longer legs, while design of triangular prism was the same as the one we used above. Right figure shows moving data of each robot. As a result, the molecular spider with long legs was slower than our robots, although it had more goal probability. It might be due to difference in the body size, leg length and the number of legs. Longer leg increases the probability to reach the goal, making more molecular spiders reach goal. And if the structure has more legs, it can cleave more substrates in the same time. Therefore, when the design of the fields is the same, robots with many legs are fast. This notion explained why the triangular prism was faster when comparing with the molecular spider.

<html><div style="clear:both;"></div></html>

Reference

(1) Fumiko Takagi et al. How protein thermodynamics and folding mechanisms are altered by the chaperonin cage: Molecular simulations, PNAS. 100, 11367 (2003)
(2) http://en.wikipedia.org/wiki/Langevin_equation
(3) http://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform
(4) Lund et al. Molecular robots guided by prescriptive landscapes, Nature. 465, 206 (2010)

Retrieved from "https://openwetware.org/mediawiki/index.php?title=Biomod/2011/TeamJapan/Sendai/Computational_design/Simulation&oldid=561022"