...The transport of DNA with counterions and coions is studied where a narrow
nanopore along the z-direction seperates wide downside and upside regions
(Ref. 1). The cylinder of the pore is assumed 1.5 nm wide and 4.0 nm high,
embedded in 4.0 nm in x,y directions and 12.0 nm in the z direction. The
short-range Coulomb and Lennard-Jones forces are treated, i.e.,

.....m dv/dt = q'q/(Gamma *r^2) (grad r/r) - fgm *(2 r(i)-r(i+1)-r(i-1))
.....+ 48*(epsil_LJ/kT) grad[(sigma/r_ij)^12 -(sigma/r_ij)^6]　(1).

The long-range potential forces with the mesh (i,j,k) coordinates are solved
by the Poisson equation, i.e.,

.....div(eps(i,j,k) [grad pot(i,j,k)]) = - 4*pi *rho(i,j,k) 　(2).

The dielectric constant eps(i,j,k) is highly changed from eps=78 in water
to eps=3 within the pore region.

...There are large potentials of positive and negative drops at end plates, and
they are small otherwise. The simulation code is named @nanoporAPG.f03
(ca 9,900 lines with graphics), and the parameter file paramAPG.h and the
configuration file PORV11_config.start3. The major subroutines are: RUN_MD,
moldyn, sht-forces, LJ-forces, sprmul, reflect_endpl, init, poissn, emcof3,
cresmd, and graphics. There are many input parameters to run the code, like
the nanopore sizes, the number of DNA, counterions and coions, the Cartesian
meshes for the Poisson solver, a time step dt, the potential values of top and
bottom plates, and the Bjerrum length, etc. It has N_x=N_y=80 and N_z=120
meshes, ca. 14,000 particles. A test run takes 15 minutes /6 cores (3.0 GHz)
for the time t=800 with the time step dt=0.01 (x 10^-14 s, Ref. 2).

...The fileporv11.773.pdf for very small dielectric constant in the pore region
shows four plots of potentials, particles of DNA and ions, those of all particles
(every 5 water molecules), and the velocity distributions. One can see that
the DNA chain moves toward the positive z direction into the cell volume.
Moreover, the lowr dielectric constant eps(\r) in the pore region makes the
DNA blob more concentrated because counterions find negatively-charged
DNA easily, which accelerates it to inside the positive cell region (Ref. 3).

References
1. Y. Rabin and M. Tanaka, Phys.Rev.Lett., vol.94, 148103 (2005).
2. The simulation codes of this directory have been updated in 2025.
3. M.Tanaka, https://github.com/Mtanaka77/Electrostatic_molecular_
dynamics_simulation_for_living_human_cells, April, 2025.

「細胞における静電的分子動力学」

　皮膚膜孔をDNAが通過する問題を扱う。静電コードの基本方程式は，
運動方程式は

.....m dv/dt = q'q/(Gamma *r^2) (grad r/r) - fgm *(2 r(i)-r(i+1)-r(i-1))
.....+ 48*(epsil_LJ/kT) grad[(sigma/r_ij)^12 -(sigma/r_ij)^6]　(1),

ポテンシャル場は
.....div(eps(i,j,k) [grad pot(i,j,k)]) = - 4*pi *rho(i,j,k)　(2)

である。静電定数 eps は場所の関数であり，膜孔では小さい eps=3 とする。
コード名は @nanoporAPG.f03 で，一緒にパラメータファイルに paramAPG.h，
設定ファイルに PORV11_config.start3 を用いる。皮膚垂直に電場をかける
ことで，DNAが膜孔を通過してセル内へ輸送されることを示せる。

Go back to the homepage