Biomod/2012/TeamSendai/Simulation: Difference between revisions

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<div id="Container">
<div id="Container">
<h2>Numerical Calculation</h2>
<h1>Numerical Calculation</h1>
A phosphodiester bond make up the backbone of each helical strand of DNA. The phosphate groups in the phosphodiester bond are negatively-charged. Because GATE is made of DNA, we can not ignore the influence of the Coulomb force. So we calculate the electric potential inside and outside the GATE.
A phosphodiester bond make up the backbone of each helical strand of DNA. The phosphate groups in the phosphodiester bond are negatively-charged. Because GATE is made of DNA, we can not ignore the influence of the Coulomb force. So we calculate the electric potential inside and outside the GATE.


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<h2>MD Simulation</h2>
<h1>MD Simulation</h1>
We carried out molecular dynamics simulation to examine the capturing mechanism and
We carried out molecular dynamics simulation to examine the capturing mechanism and
the effectiveness of our structure “Cell Gate”.
the effectiveness of our structure “Cell Gate”.
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<h2>DNA Model</h2>
<h2>DNA Model</h2>
[[Image: Format_DNA_rasen.jpg |center|638px]]
[[Image: Format_DNA_rasen.jpg |center|638px]]
For simplicity, course-grained DNA model is used in our simulation. One DNA nucleotide is represented by one bead in the model and each bead can be hybridized with complementary bead.
For simplicity, a course-grained DNA model is used in our simulation. One DNA nucleotide is represented by one bead in the model and each bead can be hybridized with a complementary bead.


The potential energy of the system includes 5 distinct contributions.
The potential energy of the system includes 5 distinct contributions.
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{{-}}


The first three terms are intramolecular interactions, bonds, bond angles, and dihedral angles. In order to express “tether like structure”, only bond interactions  are active in our DNA model.  
The first three terms are intramolecular interactions, bonds, bond angles, and dihedral angles. In order to express the “tether like structure”, only bond interactions  are considered in our DNA model.  


And the latter two are non-bonded interactions. Coulomb interactions are taken into account using the Debye-Huckel approximation which enables to internalize  counterions contribution.
And the latter two terms are non-bonded interactions. Coulomb interactions are taken into account using the Debye-Huckel approximation which enables to internalize  counterions contribution.


Parameters of these potentials were fit to reference literatures.
Parameters of these potentials were fit to reference literatures(1).


The force on bead i is given by a Langevin equation
The force on bead i is given by a Langevin equation
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The first term donates a conservative force derived from the potential U and the second is a viscosity dependent friction.
The first term donates a conservative force derived from the potential Vtot and the second is a viscosity dependent friction.


The third term is a white Gaussian noise and effects of solvent molecules are internalized in this term.
The third term is a white Gaussian noise and effects of collision with solvent molecules which causes brownian motion are internalized in this term.


Langevin equation is integrated using a Velocity-Verlet method.
Langevin equation is integrated using a Velocity-Verlet method.




<h1> Toehold displacement of dsDNA</h1>
<h2> Toehold displacement of dsDNA</h2>
[[Image: Format_toea_toeb.jpg |right|490px]]
[[Image: Format_toea_toeb.jpg |right|490px]]
In order to test the model, here we carried out a simulation of Toehold displacement between two strands.
In order to test the model, here we carried out a simulation of Toehold displacement between two strands.


Length of strands and simulation situation was as follows.
Length of strands and simulation condition were as follows:


Target strand/Toehold A/Toehold B : 25nt / 9nt (+10nt spacer) / 13nt (+10nt spacer)
Target strand/Toehold A/Toehold B : 25nt / 9nt (+10nt spacer) / 13nt (+10nt spacer)


Temperature : 300K
Temperature : 300K
Time-step size / simulation length : 0.01ps / 100ns
Time-step / simulation length : 0.01ps / 100ns
Ion concentration : 50mM Na+
Ion concentration : 50mM Na+


<h2>Results</h2>
<h3>Results</h3>
＜＜動画＞＞
＜＜動画＞＞


Movie 1 shows the trajectory of each strands from the simulation. The target strand moves from Toehold A strand to Toehold B strand which are fixed on the field. This result agrees with the energy gradient.
Movie 1 shows the trajectory of each strand from the simulation. The target strand moves from Toehold A strand to Toehold B strand which are fixed on the field. This result agrees with the energy gradient.




<h2> Comparison of capture ability</h2>
<h2> Comparison of capture ability</h2>
One of constructional features of our structure ”Cell-Gate” is the use of new strand displacement method.
One of constructional features of our structure ”Cell-Gate” is the use of a novel strand displacement method.


By comparing our selector strand and a toehold strand, the most popular method for strand displacement, we looked at the effectiveness of our structure in terms of capture ability.
By comparing our selector strand to toehold strand, the most popular method for strand displacement, we looked at the effectiveness of our structure in terms of it's strand capturing ability.


<h2> Model and Method</h2>
<h3> Model and Method</h3>
[[Image: Format_selector.jpg |left|445px]]
[[Image: Format_selector.jpg |left|445px]]
According to the design of experiment section, we designed models of the selector strand and the toehold strand as below.  
According to the design of the experiment section, we modeled the selector strand and the toehold strand as shown below.  
{{-}}
{{-}}




Hex-cylinder is represented as the assembly of electrically-charged mass points fixed on the field.
Hex-cylinder is represented as the assembly of fixed electrically-charged mass points.
[[Image: Format_Hexagon.jpg |left|265px]]
[[Image: Format_Hexagon.jpg |left|265px]]


Simulation was carried out at the following condition.
Simulation was carried out at the following condition:
Temperature : 300K
Temperature : 300K
Ion concentration : Na+ 50mM
Ion concentration : Na+ 50mM
Box size : 20nm×20nm×20nm (periodic boundary condition)
Box size : 20nm×20nm×20nm (periodic boundary condition)
Time-step size / simulation length : 0.01ps / 10ns
Time-step / simulation length : 0.01ps / 10ns
{{-}}
{{-}}




<h2>Results</h2>
<h3>Results and Conclusion</h3>
＜＜動画＋グラフ（一応）後ほど＞＞
＜＜動画＋グラフ（一応）後ほど＞＞


Movie2 and 3 shows the result of each simulation, selector-target and toehold-target.
Movie2 and 3 shows the result of each simulation, selector-target and toehold-target.


We note that this simulation was carried out under periodic boundary condition where the size of the box is 20nm×20nm×20nm, the distance between the target strand and the Hex-cylinder is maintained virtually constant.
We note that this simulation was carried out under a periodic boundary condition, where the size of the simulation box is 20nm×20nm×20nm. Then, the distance between the target strand and the Hex-cylinder is maintained virtually constant.
 
One of the advantages of the selector strand is shrinking ability. The selector strand hybridizes to the target making a loop which makes it possible to extend the strand length without changing the final structure's length.


One of the advantages of the selector strand is shrinking ability. The selector strand hybridizes to the target with making loop which makes it possible to extend the strand length without changing hybridized structure's length.Z


Results obtained from this simulation show that the selector strand can catch the target strand exists outside of the Hex-cylinder and hybridize completely while the toehold strand never hybridize to the target strand in simulation time.
Results obtained from this simulation show that the selector strand can catch the target strand exists outside of the Hex-cylinder and hybridize completely while the toehold strand never hybridize to the target strand in simulation time.


We run 5 simulations for each under the same conditions and results were almost the same as we first obtained.
We run 5 simulations for each capturing mechanism under the same conditions and results were almost the same as we first obtained.
 


By considering results of electrostatic potential calculation around the hex-cylinder and MD simulation, it is clear that the electrostatic field prevents the entrance of DNA strands into the Hex-cylinder and the selector strand helps it to get into the cylinder.
By considering results of electrostatic potential calculation around the hex-cylinder and MD simulation, it is clear that the electrostatic field prevents the entrance of DNA strands into the Hex-cylinder and the selector strand helps it to get into the cylinder.


Therefore, we concluded that the selector strand, we originally designed, provides a high capture ability to our system “Cell-Gate”.
Therefore, we concluded that our novel selector strand provides a high capture ability to our system “Cell-Gate”.
 
 


<h1>References</h1>
<h2>References</h2>
1. Thomas A. Knotts et al. A coarse grain model of DNA , J.Chem.Phys
1. Thomas A. Knotts et al. A coarse grain model of DNA , J.Chem.Phys 126,084901(2007)
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)
2. Carsten Svaneborg et al. DNA Self-Assembly and Computation Studied with a
3. Xhuysn Guo & D.Thirumalai, Kinetics of Protein Folding: Nucleation Mechanism, Time Scales, and Pathways, Biopolymars, Vol.36, 83-102 (1995)
Coarse-Grained Dynamic Bonded Model, DNA 18,LNCS 7433, pp.123-134,
4. GROMACS manual ( http://www.gromacs.org/ )
2012<br>
5. Cafemol manual  ( http://www.cafemol.org/ )
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>
6. Thomas A. Knotts et al.  A coarse grain model of DNA , J.Chem.Phys 126,084901(2007)
7. 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)
8. Xhuysn Guo & D.Thirumalai, Kinetics of Protein Folding: Nucleation Mechanism, Time Scales, and Pathways, Biopolymars, Vol.36, 83-102 (1995)
9. GROMACS manual ( http://www.gromacs.org/ )
10. Cafemol manual  ( http://www.cafemol.org/ )




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Numerical Calculation

A phosphodiester bond make up the backbone of each helical strand of DNA. The phosphate groups in the phosphodiester bond are negatively-charged. Because GATE is made of DNA, we can not ignore the influence of the Coulomb force. So we calculate the electric potential inside and outside the GATE.

Model

The coodinates are set as follows:

Condition: Temperature 298[K], Na+ 50mM


A point-charge model is used. We assume the phosphate groups have negative charge,and negative charge circles the axis of the double helix once every 10.4 base pairs. we use following fomulas to calculate electric potential.

Debye–Hückel equation:


Debye length


Summing up all the Electric Potential for every DNA phosphate presented on the DNA origami GATE. (used C language to output the numbers)


Results

Electric potential at the z-axis(x=0, y=0).

the length of the gate is 88bp, 30nm. Target base pair 25 を点電荷と仮定する もっときれいなグラフに出力できないか

MD Simulation

We carried out molecular dynamics simulation to examine the capturing mechanism and the effectiveness of our structure “Cell Gate”.


DNA Model

For simplicity, a course-grained DNA model is used in our simulation. One DNA nucleotide is represented by one bead in the model and each bead can be hybridized with a complementary bead.

The potential energy of the system includes 5 distinct contributions.


The first three terms are intramolecular interactions, bonds, bond angles, and dihedral angles. In order to express the “tether like structure”, only bond interactions are considered in our DNA model.

And the latter two terms are non-bonded interactions. Coulomb interactions are taken into account using the Debye-Huckel approximation which enables to internalize counterions contribution.

Parameters of these potentials were fit to reference literatures(1).

The force on bead i is given by a Langevin equation


The first term donates a conservative force derived from the potential Vtot and the second is a viscosity dependent friction.

The third term is a white Gaussian noise and effects of collision with solvent molecules which causes brownian motion are internalized in this term.

Langevin equation is integrated using a Velocity-Verlet method.


Toehold displacement of dsDNA

In order to test the model, here we carried out a simulation of Toehold displacement between two strands.

Length of strands and simulation condition were as follows:

Target strand/Toehold A/Toehold B : 25nt / 9nt (+10nt spacer) / 13nt (+10nt spacer)

Temperature : 300K Time-step / simulation length : 0.01ps / 100ns Ion concentration : 50mM Na+

Results

＜＜動画＞＞

Movie 1 shows the trajectory of each strand from the simulation. The target strand moves from Toehold A strand to Toehold B strand which are fixed on the field. This result agrees with the energy gradient.


Comparison of capture ability

One of constructional features of our structure ”Cell-Gate” is the use of a novel strand displacement method.

By comparing our selector strand to toehold strand, the most popular method for strand displacement, we looked at the effectiveness of our structure in terms of it's strand capturing ability.

Model and Method

According to the design of the experiment section, we modeled the selector strand and the toehold strand as shown below.


Hex-cylinder is represented as the assembly of fixed electrically-charged mass points.

Simulation was carried out at the following condition: Temperature : 300K Ion concentration : Na+ 50mM Box size : 20nm×20nm×20nm (periodic boundary condition) Time-step / simulation length : 0.01ps / 10ns


Results and Conclusion

＜＜動画＋グラフ（一応）後ほど＞＞

Movie2 and 3 shows the result of each simulation, selector-target and toehold-target.

We note that this simulation was carried out under a periodic boundary condition, where the size of the simulation box is 20nm×20nm×20nm. Then, the distance between the target strand and the Hex-cylinder is maintained virtually constant.

One of the advantages of the selector strand is shrinking ability. The selector strand hybridizes to the target making a loop which makes it possible to extend the strand length without changing the final structure's length.


Results obtained from this simulation show that the selector strand can catch the target strand exists outside of the Hex-cylinder and hybridize completely while the toehold strand never hybridize to the target strand in simulation time.

We run 5 simulations for each capturing mechanism under the same conditions and results were almost the same as we first obtained.


By considering results of electrostatic potential calculation around the hex-cylinder and MD simulation, it is clear that the electrostatic field prevents the entrance of DNA strands into the Hex-cylinder and the selector strand helps it to get into the cylinder.

Therefore, we concluded that our novel selector strand provides a high capture ability to our system “Cell-Gate”.


References

1. Thomas A. Knotts et al. A coarse grain model of DNA , J.Chem.Phys 126,084901(2007) 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) 3. Xhuysn Guo & D.Thirumalai, Kinetics of Protein Folding: Nucleation Mechanism, Time Scales, and Pathways, Biopolymars, Vol.36, 83-102 (1995) 4. GROMACS manual ( http://www.gromacs.org/ ) 5. Cafemol manual ( http://www.cafemol.org/ )



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