Biomod/2013/Titech/M&R Controlable Optical Makeup: Difference between revisions
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By changing the length of Crystallizer DNA complex, the distance between particles also changes. It result in changing the wavelength of incident wave to structural colors and a structural color changes. To confirm this, we firstly calculated the wavelength of light which applied to a structural color (<I>λ</I>) by using the spacing between the planes in the nanoparticle’s lattice (d) and the angle between the incident ray and the scattering planes (<I>θ</I>), and simulated the relation between them.</p> | By changing the length of Crystallizer DNA complex, the distance between particles also changes. It result in changing the wavelength of incident wave to structural colors and a structural color changes. To confirm this, we firstly calculated the wavelength of light which applied to a structural color (<I>λ</I>) by using the spacing between the planes in the nanoparticle’s lattice (<I>d</I>) and the angle between the incident ray and the scattering planes (<I>θ</I>), and simulated the relation between them.</p> | ||
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A particle’s plane in a three-dimension crystal structure intense the wavelength of light that enter the face by the Bragg reflection. When we put d = the spacing between the planes in the nanoparticle’s lattice, n = reflective index, <I>θ</I>= the angle between the incident ray and the scattering planes, <I>λ</I>= the wavelength of incident wave, <I>λ</I> is defined as follows:</p> | A particle’s plane in a three-dimension crystal structure intense the wavelength of light that enter the face by the Bragg reflection. When we put <I>d</I> = the spacing between the planes in the nanoparticle’s lattice, n = reflective index, <I>θ</I>= the angle between the incident ray and the scattering planes, <I>λ</I>= the wavelength of incident wave, <I>λ</I> is defined as follows:</p> | ||
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UV-Tuning Nano- Parasol</a></li>
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Controllable Optical Makeup</a></li></ul>
<li class="risuto"><a href = "http://openwetware.org/wiki/Biomod/2013/Titech/" class = "menu">supl.info </a></li> <li class="risuto"><a href = "http://openwetware.org/wiki/Biomod/2013/Titech/team" class = "menu">member</a></li> <li class="risuto"><a href = "http://openwetware.org/wiki/Biomod/2013/Titech/acknowledgement" class = "menu">Acknowledgement </a></li> </ul> </div>
<div id="haikei"> <a href="http://openwetware.org/wiki/Biomod">Biomod<a/>|<a href="http://openwetware.org/wiki/Biomod/2013">2013</a> <div style="width:900px"> <img src="https://upload.wikimedia.org/wikipedia/commons/3/34/%E3%81%A8%E3%81%A3%E3%81%B7%E3%81%8C.png" width="900"> </div>
<div style="width:700px;margin-right:100px;margin-left:100px;"> <!--haikei縺ｮ荳ｭ--> <p> </p> <h1><Controllable Optical Makeup></h1>
<p><a href = "http://openwetware.org/wiki/Biomod/2013/Titech/methods&results"><b>>>UV-Tuning Nano-parasol</b></a></p>
<p> Next, Controllable Optical Makeup system has following two target functions as the component of this system.</p> <p> </p>
<h2>1. Particle crystallizer</h2> <p> The gold nanoparticles(GNPs) with Handle DNA form the three-dimension crystal structure by connecting each other by Crystallizer DNA comlex. This three-dimension crystal structure makes a Bragg reflection to a light and it shows opal-like structural colors.</p><br>
<div align="center">
<img src="https://upload.wikimedia.org/wikipedia/commons/3/3c/Resolt_10-26_DNA%EF%BE%83%EF%BE%9E%E7%B5%90%E6%99%B6%E5%8C%96.png">
</div>
<p>We showed that “Particle crystallizer” function woks by following two steps.</p>
<div style="border:1px black solid;">
1.1.Make three-dimension crystal structure of polystyrene beads.<br>
1.2.Make three-dimension crystal structure of gold nanoparticles.
</div>
<p> </p>
<h3>1.1. Make three-dimension crystal structure of polystyrene beads</h3>
<h4>
We suceeded in observing the three-dimension crystal structure of polystyrene beads and observing its structural colors.</h4>
<div align="center">
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Resolt_10-26%E3%83%9D%E3%83%AA%E3%82%B9%E3%83%81%E3%83%AC%E3%83%B3%E3%83%93%E3%83%BC%E3%82%BA%E3%81%AE%E7%B5%90%E6%99%B6%E5%8C%96.png/800px-Resolt_10-26%E3%83%9D%E3%83%AA%E3%82%B9%E3%83%81%E3%83%AC%E3%83%B3%E3%83%93%E3%83%BC%E3%82%BA%E3%81%AE%E7%B5%90%E6%99%B6%E5%8C%96.png" width="300">
</div>
<p>
At the beginning, we did an experiment using polystyrene beads to confirm that the three-dimendion crystal structure of nano-sized particles shows structural colors by Bragg reflection. The diameter of polystyrene beads we used are 200 nm, we constructed three-dimension crystal structure of these beads on the surface of a cover glass and observed its structural colors. First, we put colloidal suspension of polystyrene beads on the cover glass, and covered it by sillicon oil. After drying it at 55°C for one night, polystyrene beads were arraied regularly. The detail of materials is mentioned in supl.info.</p>
<p>
Fig. 13.1. shows the scheme and the result of the above experiment. The picture in Fig. 13.1. shows that the crystal structure of polystyrene beads shows deep blue structural color when they are totally dried. And Movie. 1. shows a movie of the transformation of polystyrene beads showed in Fig. 13.1. It is clear that the crystal structure of polystyrene beads shows a structural color according to the time course. So it is estimated that polystyrene beads are arraied regularly and form three-dimension crystal structure as the scheme in Fig. 13.1.</p>
<p>
To make sure that polystyrene beads forms the three-dimension crystal structure, we observed the colloidal suspension of polystyrene beads by Scanning Electron Microscopy (SEM). Fig. 13.2. shows the image of that polystyrene beads by SEM. It shows that polystyrene beads are arraied regularly and forms the three-dimension crystal structure.</p>
<table> <tr> <td width="340"> <img src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/28/Results%26Methods_Fig._1._1.1.png/769px-Results%26Methods_Fig._1._1.1.png" width="300"> </td> <td width="360"> <iframe width="350" height="263" src="http://www.youtube.com/embed/_J0YQTaxygM" frameborder="0" allowfullscreen></iframe> </td> </tr> <tr> <td><b>Fig. 13.1. A crystal structure of<br>
polystyrene beads</b><br>
the scheme and the result of<br>
the experiment. </td> <td><b>Movie. 1. Three-dimension crystal<br>
structure by polystyrene beads</b>
</td> </tr> </table>
<p> </p>
<table align="center">
<tr>
<td width="420"> <div align="center"> <img src="https://upload.wikimedia.org/wikipedia/commons/8/87/Results%26Methods_Fig._1._1.2.png" width="400"> </div> </td> </tr> <tr> <td width="420"><strong>Fig. 13.2. Polystyrene beads</strong><br> the image of polystyrene beads <br> which arraied regularly on the <br> cover glass by SEM </td> </tr> </table> <p> We confirmed that polystyrene beads form the three-dimension crystal structure and that structure shows structural colors.<br> <strong>So we concluded that nano-sized particles form a three-dimension crystal structure and show structural colors.</strong></p>
<p style="text-align:right;"><a href="http://openwetware.org/wiki/Biomod/2013/Titech/SMM1">>>see more methods</a></p>
<p> </p> <h3>1.2.Make three-dimension crstal structure of gold nanoparticles</h3> <h4>We succeeded in connecting the gold nanoparticles together by DNA and foming gold nanoparticles into crystal structure.</h4>
<div align="center"> <img src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/44/Resolt_10-26_DNA%E3%81%8F%E3%82%8A%E3%81%99%E3%81%9F%E3%82%89%E3%81%84%E3%81%96%E3%83%BC.png/799px-Resolt_10-26_DNA%E3%81%8F%E3%82%8A%E3%81%99%E3%81%9F%E3%82%89%E3%81%84%E3%81%96%E3%83%BC.png" width="400"> </div>
<p> By using “Crystallizer DNA complex”, the gold nanoparticles connect together and form a crystal structure. Crystallizer DNA complex consists of a longer strand and a shorter strand, which binds to the middle region of the longer strand to form a stiff double-stranded structure for allowing precise positioning.</p>
<div align="center"> <img src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/92/Resolt_and_Method_%E9%87%91%E3%83%8A%E3%83%8E%E6%9E%B6%E6%A9%8B.png/800px-Resolt_and_Method_%E9%87%91%E3%83%8A%E3%83%8E%E6%9E%B6%E6%A9%8B.png" width="400"> </div>
<p> In the 1.1, we confirmed that nano-sized particles form a three-dimension crystal structure and it shows the structural colors. So if we can confirm that that gold nanoparticles connect together by DNA and form three-dimension structure, it is estimated that a crystal structure of gold nanoparticles shows a structural color by the Bragg reflection.</p> <p> To confirm that gold nanoparticles form a three-dimension structure, we compared two kinds of solution, one contains gold nanoparticles and Crystallizer DNA complex (Fig. 14. (a)), and the other is a control solution that doesn’t contain Crystallizer DNA complex (Fig. 14. (c)). If gold nanoparticles are crystallized, they precipitate and we can observe them. [1]</p> <p> We prepared these two solutions in micro tube, and put them at 55°C. Then, we cooled them from 55°C to 23°C (annealing). The pase of annealing is 1°C / 2min . By this annealing, gold nanoparticles combine together by Crystallizer DNA complex. The detail of materials is mentioned in suppl.info.</p>
<p> Fig. 14. shows the result of the above experiment. Fig. 14.(b) shows that there is black precipitation at the bottom of the micro tube. On the other hand, in the Fig. 14. (d), there is no precipitation.<b> So we concluded that the gold nanoparticles form a crystal structure by Crystallizer DNA complex.</b></p>
<table align="center"> <tr> <td width="550"> <div align="center"> <img src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Results%26Methods_Fig._1._2.png/686px-Results%26Methods_Fig._1._2.png" width="500"> </div> </td> </tr> <tr> <td> <b>Fig. 14. A crystal structure of gold nanoparticles</b><br> <b>(a)</b>A soluson that contains gold nanoparticles and Crystallizer DNA complex<br> <b>(b)</b> (a) after annealing<br> <b>(c)</b> A control soluson that doesn't contains CrystallizerDNA complex<br> <b>(d)</b> (c) after annealing </td> </tr> </table> <p> This time, we used 102 bp Crystallizer DNA complex in the experiment, but in fact, it should be at least 354 bp to observe the Bragg reflection in a visible light resion. The reason why we used 102 bp is that it is preliminary experiment and the possibility of succeeding the experiment becomes higher if we use 102 bp DNA. We are planning to make three-dimension crystal structure using over 354 bp Crystallizer DNA complex.</p> <p> As it is showed in Fig. 14., we could confirm that gold nanoparticles form a crystal structure, but couldn’t confirm that they form a three-dimension crystal structure. In order to observe a three-dimension crystal structure, we need Transmission Electron Microscope (TEM). So we are going to observe the three-dimension crystal structure of gold nanoparticles by TEM.</p> <p> [1]<i>Nanoparticle Superlattice Engineering with DNA Robert J. Macfarlane et al. Science 334, 204 (2011)</i></p>
<p style="text-align:right;"><a href="http://openwetware.org/wiki/Biomod/2013/Titech/SMM2">>>see more methods</a></p>
<h2>2.Color variation</h2> <p> By changing the length of Crystallizer DNA complex that connects gold nanoparticles together, the wavelength of incident wave also changes. It brings the changes of structural colors.</p>
<p>To confirm the proposed function, we implemented the following experiments.</p> <div style="border:1px black solid;">
2.1. Simulating that a structural color changes by changing the length of <br> Crystallizer DNA complex. <br> 2.2. Change of the particle’s distance and structural colors.<br> 2.3. Simulation of “Permutation Output system”.</div><br><br>
<h3>2.1.Simulating that a structural color changes by changing the length of Crystallizer DNA complex.</h3> <h4> We confimed by simulation that structural colors change according to the number of Crystallizer DNA complex's bases and obseerving angle.</h4>
<div align="center"> <img src="https://upload.wikimedia.org/wikipedia/commons/7/7e/%E3%81%84%E3%82%8D%E3%82%93%E3%81%AA%E8%89%B2%E3%81%AB%E3%83%BC%E3%83%BC%E3%83%BC.png" width="500"> </div>
<p>
By changing the length of Crystallizer DNA complex, the distance between particles also changes. It result in changing the wavelength of incident wave to structural colors and a structural color changes. To confirm this, we firstly calculated the wavelength of light which applied to a structural color (<I>λ</I>) by using the spacing between the planes in the nanoparticle’s lattice (<I>d</I>) and the angle between the incident ray and the scattering planes (<I>θ</I>), and simulated the relation between them.</p>
<div style="float:right;"> <img src="https://upload.wikimedia.org/wikipedia/commons/a/a8/Resolt_10-26%E3%83%96%E3%83%A9%E3%83%83%E3%82%B0%E5%8F%8D%E5%B0%84.png" width="300"> </div>
<p style="line-height:120%"> A particle’s plane in a three-dimension crystal structure intense the wavelength of light that enter the face by the Bragg reflection. When we put <I>d</I> = the spacing between the planes in the nanoparticle’s lattice, n = reflective index, <I>θ</I>= the angle between the incident ray and the scattering planes, <I>λ</I>= the wavelength of incident wave, <I>λ</I> is defined as follows:</p>
<div align="center">
<img src="https://upload.wikimedia.org/wikipedia/commons/e/e0/Ramuda%3D2ndsin.png">
</div>
<p>
And by using the length of DNA and a radius of a gold nanoparticle, d is described as follows:
</p>
<div align="center">
<img src="https://upload.wikimedia.org/wikipedia/commons/6/6b/%E3%81%93%E3%81%93%E3%81%93%E3%81%93%E3%81%93%E3%81%93%E3%81%93%E3%81%93%EF%BD%8B%E6%95%B0%E5%BC%8F%E3%81%82%E3%81%84%E3%81%A0.png" align="center">
</div>
<p> (0.255 is the length of DNA per one base, B is the number of bases, R is the radius of a gold nanoparticle ) This equation shows that the distance between particles changes if the length of DNA which connects particles together changes.So ① is described as follows:</p>
<div align="center"> <img src="https://upload.wikimedia.org/wikipedia/commons/8/86/%E3%82%93%E3%82%93%E3%82%93%E3%82%93%E3%82%93%EF%BD%8E%E6%95%B0%E5%BC%8F%E2%91%A1.png"align="center"> </div> <p> We made the graph of equation② in Fig. 15. (a)(b)(c).<br> Fig.15.(a) shows that the relation between <I>λ</I> and the number of bases of DNA which connects particles together changes. It is clear that the wavelength of light which applied to the Bragg reflection changes if the length of DNA which connects particles together changes.</p> <p> </p>
<p> </p> <div align="center"></div> <table>
<tr>
<td width="402" rowspan="2">(a)<img src="https://upload.wikimedia.org/wikipedia/commons/f/f1/Results%26Methods_Fig.2.1.%28a%29.png" width="400"></td> <td width="282">(b)<img src="https://upload.wikimedia.org/wikipedia/commons/9/95/Results%26Methods_Fig.2.1.%28b%29.png" width="280" height="200"></td> </tr> <tr> <td>(c)<img src="https://upload.wikimedia.org/wikipedia/commons/0/06/Results%26Methods_Fig.2.1.%28c%29.png" width="280" height="200"> </td> </tr>
<tr> <td colspan="2"> <strong>Fig. 15. A relation between the number of bases and scattering angle <br> for a wavelength</strong><br> <b>(a)</b> a graph focused on the relation between <I>λ</I> and bp <br> <b>(b)</b> a graph focused on the relation between <I>λ</I> and <I>θ</I> <br> <b>(c)</b> a graph focused on the relation between <I>θ</I> and bp</td> </tr> </table> <p style="text-align:left;"><a href="http://openwetware.org/wiki/Biomod/2013/Titech/SMM4">">>see more methods</a> </p> <p> <b>So we concluded that a structural color changes according to the number of base of Crystallizer DNA complex.</b></p> <p> </p> <p> </p> <h3>2.2. Change of the particle's distance and structural colors</h3> <h4> We succeeded that transform the three dimension orderded structure of polystyrene beads and observe their structural colors</h4>
<div align="center"> <img src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/60/Resolt_10-26%E3%81%BD%E3%82%8A%E3%81%99%E3%81%A1%E3%82%8C%E3%81%88%E3%81%88%E3%81%88%E3%82%93.png/800px-Resolt_10-26%E3%81%BD%E3%82%8A%E3%81%99%E3%81%A1%E3%82%8C%E3%81%88%E3%81%88%E3%81%88%E3%82%93.png" width="400"> </div>
<p> As it is mentioned in 2.1, a structural color also changes by changing a distance between particles. To confirm this, we secondly constructed a three-dimension crystal structure and transformed its structure, and observed its structural colors.</p>
<p> First we fixed polystyrene beads arranged regularly in three-dimension space by elastmeric matrix made of poly-dimethylsiloxane (PDMS). By adding organic solvent to this elastmeric matrix, the distance between particles becomes bigger. In this experiment, we used cyclohexane as an organic solvent. We observed the change of a structural color at 1 minutes, 3 minutes, 5 minutes, 7 minutes and 10 minutes. The detail of materials is mentioned in suppl.info. </p>
<p> Fig. 16.(a) shows the scheme of the experiment. It shows that the distance between particles changes by adding PDMS. And Fig. 16. (b) ~ (g) shows that a structural color changes by adding PDMS. It is clear that a structural color changes from a deep blue to light blue, green, yellow, orange and red by adding organic solvent. And Movie. 2. shows that a structural color changes according to an angle(<I>θ</I>) that we observe that structure.</p> <p> <b>So we concluded that a structural color change by changing the particle’s distance. </b></p>
<table>
<tr>
<td colspan="6">(a)<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Resolt_10-26%E3%81%99%E3%81%86%E3%81%87%E3%83%AA%E3%83%B3%E3%82%B0.png/800px-Resolt_10-26%E3%81%99%E3%81%86%E3%81%87%E3%83%AA%E3%83%B3%E3%82%B0.png" width="600">
</td>
</tr>
<tr>
<td>(b)<img src="https://upload.wikimedia.org/wikipedia/commons/1/1b/Results%26Methods_Fig.2.2.%28a%29.png" width="110">
</td>
<td>(c)<img src="https://upload.wikimedia.org/wikipedia/commons/4/4a/Results%26Methods_Fig.2.2.%28b%29.png" width="110">
</td>
<td>(d)<img src="https://upload.wikimedia.org/wikipedia/commons/2/20/Results%26Methods_Fig.2.2.%28c%29.png" width="110">
</td>
<td>(e)<img src="https://upload.wikimedia.org/wikipedia/commons/d/d7/Results%26Methods_Fig.2.2.%28d%29.png" width="110">
</td>
<td>(f)<img src="https://upload.wikimedia.org/wikipedia/commons/4/4d/Results%26Methods_Fig.2.2.%28e%29.png" width="110">
</td>
<td>(g)<img src="https://upload.wikimedia.org/wikipedia/commons/e/e9/Results%26Methods_Fig.2.2.%28f%29.png" width="110">
</td>
</tr>
<tr>
<td colspan="6"><strong>Fig. 16. Change the particle's distance and structural colors <br> by adding cyclohexane.</strong> <br>
<b>(a)</b> the scheme of the experiment.
<b>(b)</b> first state
<b>(c)</b> 1 minute later <br>
<b>(d)</b> 3 minutes later
<b>(e)</b> 5 minutes later <br>
<b>(f)</b> 7 minutes later <b>(g)</b> 10 minutes later </td> </tr> </table> <p> </p> <table> <tr> <td>(a)<iframe width="300" height="225" src="http://www.youtube.com/embed/SRw7Wm4iYmk" frameborder="0" allowfullscreen></iframe> </td> <td>(b)<iframe width="300" height="225" src="http://www.youtube.com/embed/uUnUI8bg37U" frameborder="0" allowfullscreen></iframe> </td> </tr> <tr> <td colspan="2"><strong>Movie. 2. Change of a structural color according to an observing angle.</strong><br> <b>(a)</b> change of structural color from green to blue<br> <b>(b)</b> change of structural color from orange color to green </td> </tr> </table> <p> </p> <p> </p> <h3>2.3. Simulation of “Permutation color-directing system”</h3> <h4> We confirmed that “Permutation color-directing system” operates by simulation.</h4> <div align="center"> <img src="https://upload.wikimedia.org/wikipedia/commons/0/0f/Resolt_10-26%E9%A0%86%E7%95%AA%E3%82%B7%E3%82%B9%E3%83%86%E3%83%A0.png"width="230"> </div>
<p> This time, we are going to realize 3! different output DNA from three input DNA by changing its order. We designed the Input DNA(A, B, C) as three input DNA and Output complex (X, Y, Z) which make strand excange reaction with Input DNA and release output DNA(X, Y, Z) (Fig. 17.1) .</p> <table> <tr> <td> <img src="https://upload.wikimedia.org/wikipedia/commons/f/f7/%E9%A0%86%E7%95%AA%E3%82%B7%E3%82%B9%E3%83%86%E3%83%A0saisinnbann.png"width="650"> </td> </tr> <tr> <td> <strong><p>Fig. 17.1.The reaction between Input(A,B,C) and Output complex(X,Y,Z)</p></strong> </td> </tr> </table>
<p style="text-align:right;"><a href="http://openwetware.org/wiki/Biomod/2013/Titech/SMM2">>>see more methods</a></p>
<p> Besides that, the existence of input-A makes input-C invalid via hybridization, which occurs faster than the strand exchange, since the 5’ portion of input-A has a sequence complementary to the 3’ portion of input-C. Similarly, input-B and input-C trigger the release of output-Y and output-Z and inactivate input-A and input-B, respectively.</p>
<p> First, we confirmed that the hybridyzation of Input DNA (A, B, C) happens ealier than the strand displacement reaction between Input DNA (A, B, C) and Output complex (X, Y, Z). We calculated the rate of the strand exchange reaction between Input DNA (A, B, C) and Output complex (X, Y, Z). And we also calculated the rate of the hybridyzation of Input DNA (A, B, C) (Fig. 17.2.).</p>
<p>We postulated that the concentrations of input DNA (A, B, C) and Output complex (X, Y, Z) are the same.To calculate the reaction rate constants of Input DNA (A, B, C) and Output complex (X, Y, Z) (k1、k2、k3), we cited the equation below from a paper[1] and applied it to our sequences.</p> <img src="https://upload.wikimedia.org/wikipedia/commons/8/89/Jyunnbannsisutemusikki.png"width="700">
<p> From this equation, reaction rate constants were calculated as follows: k1= 2.2×10^-2、k2=1.9×10-2、k3=3.9×10^-3 [μM^-1・s^-1]</p>
<p> As for the reaction rate constants of each inhibition (k’1、k’2、k’3), we referred to another paper[2], and postulated that its rate constant is 1.0×10^1[μM^-1・s^-1].</p> <p> Since the concentrations of Input-A, Input-B and Output-X complex are the same, production rate and inhibition rate of Output-X are led as follows:</p>
<p align="center">v1=k1 ∗ [input − A] ∗ [Output − X complex] <br>v′1=k′1 ∗ [input − A] ∗ [input − B]</p> Similarly, the ratio of the reaction rate between strand displacement and inhibition is calculated respectively as Fig.17.2. <table> <tr> <td> <img src="https://upload.wikimedia.org/wikipedia/commons/d/d0/Jynnbannsisutemusiki2.png"width="600"> </td> </tr> <tr> <td> <p><strong>Fig. 17.2.</strong><b> Ratio of the reaction rate between strand displacement and inhibition</b></p> </td> </tr> </table> <p> You can find that the inhibition of Input-A by Input-B proceeds 450 times faster than the production rate of Output-X. This means that Input-B functions as an Inhibitor to Input-A, since Input-A reacts with Input-B before it reacts with output-X-complex. Likewise, other inhibitions, Input-C to Input-B and Input-A to Input-C, happen because of the difference in their reaction rate.</p>
<p> In addition, we confirmed that this system operates when we input three Input DNA (A, B, C) to a solution in defferent order. We calculated the final concentration of Output complex (X,Y,Z) when we input three Input DNA (A,B,C) to a solution from the rate of the reaction in Fig. 17.2. We confirmed that output changes according to the order of input (Fig. 17.3.).</p>
<p> Fig. 17.3. is a simulation which shows the expressing patterns of Output(X,Y,Z) corresponding to the adding order of Input(A,B,C).</p>
<p> Concidering the difference in the reaction rate between strand displacement and inhibition, we calculated the concentration of Output(X,Y,Z). The way to lead the equation of the graphs below is described in <a href="http://openwetware.org/wiki/Biomod/2013/Titech/SMM5">see more detail.</a></p>
<table align="center"> <tr> <td><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/27/Simu_ABC.png/659px-Simu_ABC.png" width="330"></td> <td><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/18/Simu_ACB.png/659px-Simu_ACB.png" width="330"></td> </tr> <tr> <td><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Simu_BAC.png/654px-Simu_BAC.png" width="330"></td> <td><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Simu_BCA.png/658px-Simu_BCA.png" width="330"></td> </tr> <tr> <td><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/07/Simu_CAB.png/659px-Simu_CAB.png" width="330"></td> <td><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Simu_CBA.png/659px-Simu_CBA.png" width="330"></td> </tr> <tr> <td colspan="2"><b>Fig. 17.3. Patterns of output corresponding to the adding order of Input.</b></td> </tr> </table>
<div style="float:right"> <img src="https://upload.wikimedia.org/wikipedia/commons/0/0f/Resolt_10-26%E9%A0%86%E7%95%AA%E3%82%B7%E3%82%B9%E3%83%86%E3%83%A0.png" width="300"> </div> <p> </p> <p> <b>We concluded that “Permutation color-directing system” can out put 3! = 6 different DNA by changing the order of three Input DNA.</b></p> <p> </p> <p> </p> <p> </p> <p style="clear:both"> <p> </p> <p> </p> [1]<i>David Yu Zhang and Eric Winfree,;J. AM. CHEM. SOC. 2009, 131 17303-17314</i> <br> [2]<i> Larry E. Morrison’ and Lucy M. Stols,; Biochemistry 1993, 32, 3</i></p>
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