Biomod/2012/TeamSendai/Simulation

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<!-- Menu --> <ul id="menu"> <li><a href="http://openwetware.org/wiki/Biomod/2012/Tohoku/Team_Sendai ">Top</a></li> <li><a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Idea ">Project</a></li> <li><a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Simulation">Simulation</a> </li> <li><a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Design">Design</a> </li> <li> <a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Experiment ">Experiment</a> <ul> <li><a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Method">Method</a> <ul> <li> <a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Result#Porter">Porter</a> <li> <a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Result#Cylinder">Cylinder</a> </li> <li> <a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Result# Vesicle">Vesicle</a> </li> </ul> </li> <li> <a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Result">Result</a> <ul> <li> <a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Result#Porter">Porter</a> <li> <a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Result#Cylinder">Cylinder</a> </li> <li> <a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Result# Vesicle">Vesicle</a> </li> </ul> </li> </ul> </li> <li> <a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Achievement">Achievement</a> </li> <li> <a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Diary">Diary</a> </li> <li> <a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/Team ">Team</a> </li> <li> <a href=" http://openwetware.org/wiki/Biomod/2012/TeamSendai/FAQ">FAQ</a> </li> </ul>

<!--目次 --> <div id="mokuji"> <h2>Contents</h2> <ol> <li><a href="#Numerical Calculation for Electric Potential">Electric Potential Numerical Calculation</a></li> <ol> <li><a href="#Model">Model</a></li> <li><a href="#">Results</a></li> </ol>

<li><a href="#MD Simulation">MD Simulation</a></li> <ol> <li><a href="#DNA Model">DNA Model</a></li> <ol> <li><a href="#Results">Results</a></li> </ol>

<li><a href="#Comparison of capture ability">Comparison of capture ability</a></li> <ol> <li><a href="#Results">Results</a></li> </ol> <li><a href="#Reference">Reference</a></li> </ol>

</ol> </div>

<p> <br><br>


</p>

<a name="Numerical Calculation"></a><h2>Numerical Calculation</h2> <p>

A phosphodiester bond make up the backbone of each helical strand of DNA. <br> The phosphate groups in the phosphodiester bond are negatively-charged.<br> Because gate is produced by DNA, we can not ignore the influence of the Coulomb force.<br> So we calculate the electric potential near the gate.

</p>

<a name="Model"></a><h2>Model</h2> <p> <br> Sets the coordinates as follows.<br>

<img src="http://openwetware.org/images/9/90/Cy.png" width="350px" height="300px"> <img src="http://openwetware.org/images/6/66/Lin.jpg" width="420px" height="300px"><br> <br><br><br>

Point-charge model is used.<br> Assumesd the phosphate groups negative charge,and<br> negative charge circles the axis of the double helix once every 10.4 base pairs like DNA.<br>

And we use follow fomula to calculate electric potential.<br><br> Debye–Hückel equation<br> <img src="http://openwetware.org/images/e/ec/Potential_fomula.png" width="300px" height="90px"><br> <br> Debye length<br> <img src="http://openwetware.org/images/f/f9/Debyelen.png" width="400px" height="250px"><br><br>



Add all potential by negative charge DNA which compose gate have.<br>

(used C language to output the numbers)<br><br>

<img src="http://openwetware.org/images/4/45/Helix.gif" width="500px" height="290px"><br>


Condition<br> Temperature 298[K]<br> Na+ 50mM<br>

<img src="http://openwetware.org/images/f/fc/Add2.png" width="500px" height="180px"><br>


</p>

<a name="Results"></a><h2>Results</h2> <p> <br> Electric potential changing z-axis at x-axis and y-axis is 0.<br>

<img src="http://openwetware.org/images/0/09/1014x0y0potential.png" width="620px" height="450px"><br> the length of the gate is 88bp, 30nm.

Target base pair 25 を点電荷と仮定する </p>


<a name="MD Simulation"></a><h2>MD Simulation</h2> <p> We carried out molecular dynamics simulation to examine the the mechanism and the effectiveness of our structure “Cell Gate”.

</p>

<a name="DNA Model"></a><h2>DNA Model</h2> <p> For simplicity, course-grained DNA model is used in our simulation. <br> One DNA nucleotide is represented by one bead in the model and each bead can be<br> hybridized with complementary bead.<br>   <<モデル載せる>><br><br> The potential energy of the system includes 5 distinct contributions.<br>   <<ポテンシャル載せる>><br><br><br> The first three terms are intramolecular interactions , bonds , bond angles, and<br> dihedral angles. In order to express “tether like structure”, only bond interactions<br> are active in our DNA model.<br> And the latter two are non-bonded interactions. Coulomb interactions are taken into<br> account using the Debye-Huckel approximation which enables to internalize<br> counterions contribution.<br> Constants of these potentials are achieved from references.<br> The force on bead i is given by a Langevin equation<br><br><br>

Langevin equation<br><br>

<img src="http://openwetware.org/images/1/11/Langevin.png" width="220px" height="80px"><br><br> <img src="http://openwetware.org/images/2/23/F%3D.png" width="150px" height="80px"><br>

The first term donates a conservative force derived from the potential U and the<br> second is a viscosity dependent friction.<br> The third term is a white Gaussian noise and effects of solvent molecules are<br> internalized in this term.<br> Langevin equation is integrated using a Velocity-Verlet method.<br><br><br> Toehold displacement of dsDNA<br> In order to test predictive capability of the model, here we carried out a simulation<br> of Toehold displacement between two strands.<br> Length of strands and simulation situation was as follows.<br><br> Target strand/Toehold A/Toehold B : 25nt / 9nt (+10nt spacer) / 13nt (+10nt spacer)<br> Temperature : 300K<br> Time-step size / simulation length : 0.01ps / 100ns<br> Ion concentration : 50mM Na+<br><br> results<br> <<後ほど>>

</p>

<a name="Comparison of capture ability"></a><h2>Comparison of capture ability</h2> <p> One of constructional features of our structure ”Cell-Gate” is the use of new strand displacement method.<br> By comparing our selector strand and a toehold strand, the most popular method for<br> strand displacement, we show the effectiveness our structure in terms of capture ability.<br><br><br> Model and Method<br> According to the design of experiment section, we designed models as below of the<br> selector strand and the toehold strand.<br> <<モデル載せる>><br><br><br> Hex-cylinder is represented as the assembly of electrically-charged mass points<br> fixed on the field.<br> <<モデル載せる>><br><br><br> Simulation was carried out at the following condition.<br> Temperature : 300K<br> Ion concentration : Na+ 50mM<br> Box size : 20nm×20nm×20nm (periodic boundary condition)<br> Time-step size / simulation length : 0.01ps / 10ns<br> Results<br> <<後ほど>><br>

</p>

<a name="Reference"></a><h2>Reference</h2> <p> 1. Thomas A. Knotts et al. A coarse grain model of DNA , J.Chem.Phys 126,084901(2007)<br> 2. Carsten Svaneborg et al. DNA Self-Assembly and Computation Studied with a Coarse-Grained Dynamic Bonded Model, DNA 18,LNCS 7433, pp.123-134, 2012<br> 3. Xhuysn Guo & D.Thirumalai, Kinetics of Protein Folding: Nucleation Mechanism, Time Scales, and Pathways, Biopolymars, Vol.36, 83-102 (1995)<br> 4. GROMACS manual ()<br> 5. Cafemol manual ( http://www.cafemol.org/ )<br>

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