# Biomod/2012/TeamSendai/Simulation

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

Results

Results

Team Sendai Top

## 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 produced by DNA, we can not ignore the influence of the Coulomb force.
So we calculate the electric potential near the gate.

## Model

Sets the coordinates　as follows.

Point-charge model is used.
Assumesd　the phosphate groups negative charge,and
negative charge circles the axis of the double helix once every 10.4 base pairs like DNA.
And we use follow fomula to calculate electric potential.

Debye–Hückel equation

Debye length

Add all potential by negative charge DNA which compose gate have.
(used C language to output the numbers)

Condition
Temperature 298[K]
Na+ 50mM

## Results

Electric potential changing z-axis at x-axis and y-axis is 0.

the length of the gate is 88bp, 30nm. Target base pair 25 を点電荷と仮定する

## MD Simulation

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

## DNA Model

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
＜＜モデル載せる＞＞

The potential energy of the system includes 5 distinct contributions.
＜＜ポテンシャル載せる＞＞

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.
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.
Constants of these potentials are achieved from references.
The force on bead i is given by a Langevin equation

Langevin equation

The first term donates a conservative force derived from the potential U 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.
Langevin equation is integrated using a Velocity-Verlet method.

Toehold displacement of dsDNA
In order to test predictive capability of the model, here we carried out a simulation
of Toehold displacement between two strands.
Length of strands and simulation situation was as follows.

Target strand/Toehold A/Toehold B : 25nt / 9nt (+10nt spacer) / 13nt (+10nt spacer)
Temperature : 300K
Time-step size / simulation length : 0.01ps / 100ns
Ion concentration : 50mM Na+

results
＜＜後ほど＞＞

## Comparison of capture ability

One of constructional features of our structure ”Cell-Gate” is the use of new strand displacement method.
By comparing our selector strand and a toehold strand, the most popular method for
strand displacement, we show the effectiveness our structure in terms of capture ability.

Model and Method
According to the design of experiment section, we designed models as below of the
selector strand and the toehold strand.
＜＜モデル載せる＞＞

Hex-cylinder is represented as the assembly of electrically-charged mass points
fixed on the field.
＜＜モデル載せる＞＞

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

## DNA Model

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.

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 “tether like structure”, only bond interactions are active 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.

Parameters of these potentials were fit to reference literatures.

The force on bead i is given by a Langevin equation

The first term donates a conservative force derived from the potential U 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.
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 situation was as follows.
Target strand/Toehold A/Toehold B : 25nt / 9nt (+10nt spacer) / 13nt (+10nt spacer)
Temperature : 300K
Time-step size / simulation length : 0.01ps / 100ns
Ion concentration : 50mM Na+

## Results

＜＜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.

## Comparison of capture ability

One of constructional features of our structure ”Cell-Gate” is the use of new 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.

## Model and Method

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

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

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

## Results

＜＜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 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.
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.
We run 5 simulations for each 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 the selector strand, we originally designed, provides a high capture ability to our system “Cell-Gate”.

## Reference

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 ()
5. Cafemol manual ( http://www.cafemol.org/ )
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/ )