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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.


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)

Temperature 298[K]
Na+ 50mM


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
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.
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+


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.

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


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 ( )

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