S6-1

Structure Formation by Electrostatic Forces in Biological Systems
生体高分子の強い静電気力による構造形成
Motohiko Tanaka
田中基彦
Institute for Fusion Science, Toki 509-5292, Japan
Email: mtanaka@nifs.ac.jp, URL http://dphysique.nifs.ac.jp/
土岐市下石町 322-6 核融合科学研究所 連携研究推進センター
Electrostatics plays an important role in making structures of soft condensed
matters (polymers, gels, colloids) when the Coulombic (electrostatic) energye2/εa dominates over thermal energy kT. This happens in liquids of normalpressure and room temperature, including hydration of molecules and DNA
stacking under hydrogen bonds. Here, we present the aggregation of
like-charged macromolecules in salted liquid, and the translocation of DNA
through a nano-sized pore permeated in a low-dielectric constant membrane.

1. Ionic Soft Matters and Biological Systems
It is not well recognized that the Coulombic
forces are contributing a great deal in making
structures of biological materials. For example,
DNA is a strongly charged polymer (one unit
charge per 3.4 Angstroms stack) for whichhydrogen bonds between oxygen, nitrogen andhydrogen atoms stabilize the double helix ofDNA. Cell membrane is again an assembly ofpolymers having ionic (hydrophilic) heads andhydrophobic tails. Bare charges, if present, areusually dressed by salt ions such as sodium,potassium and chloride, and electric fields arealmost not visible in some distances away.
Two extremes of ionized “soft” matters are
high- temperature ionized gases (plasmas) andionic soft matters including charged polymers
and living cells. The criterion of forming thelatter matter is whether the electrostatic
energy is greater than thermal (entropic)
energy that smears out specific structures,

Q 2 / ε R > kT

(1)

where Q and R are the charge content and sizeof an object, ε is dielectric constant of medium(solvent), and T is the temperature.
The length for which the Coulomb andthermal energies become equal, a= Q2/εkT, iscalled the Bjerrum length, which is about thesize of molecular objects, i.e. 7 Angstroms inwater (note εw=80). In such circumstances,
molecules should be treated as objects of finite
sizes and their collisional encounters areimportant. Peculiar structure formations ofcharged polymers [1] and over-screening forcharged macromolecule [2] take place in thisregime. On the other hand, in high-temperature plasmas reversed inequality Q2 / εR <<kT holds. Then, the Bjerrum length isextremely shorter than characteristic plasma
sizes, and the complete Debye shieldingsmoothes out specific structures; collective
phenomena are the central issue of plasmas.
We use the molecular dynamics simulations
to trace the motion of particles (monomers andions) with the Newton equations of motion.
The forces on particles are calculated by Fi=-grad φ with the potential given by

φ (r ) = ∑ q q / ε r + 4ε LJ (σ / r )12 − (σ / r )6 ijijijijij(2)
where rij=|ri - rj|, σ is the sum of radii of two
encountering particles; the Lennard-Jones
potential of the second term is truncated at
the bottom, thus provides only the volume
exclusion effects and no attraction forces.
2. Merging of Like-Charged Macromolecules
Oppositely charged objects repel each otherand should keep large distances in vacuum. InFig.1: Aggregation of like-charged macromoleculesby mediation of multivalent counterions (smallspheres), for trivalent (left) and monovalent (right)
cases. Solvent particles are not shown.

liquid with salt ions, oppositely charged macro
molecules can aggregate! This counterintuitive behavior is made possible if (i) theCoulombic energy prevails over thermalenergy (inequality (1)), and (ii) counterions ofmulti-valency are present in the liquid. Figure
1 shows the result of the molecular dynamics
simulations for two macromolecules (Q=-10eon each) and small ions under e2 /εRkT=10;
small ions are multivalent counterions Ze (Z=1or 3) and monovalent coions (–e). These ions
are immersed in the solvent which is modeledby large number of neutral particles anddielectric constant ε= 80. The figure showsthat the macroions aggregate when thevalency of counterions are multivalent Z > 1for monovalent salt ions.
3. DNA in a Nanopore
The RNA string goes through a nano-sizepore of the nuclear membrane after beingtranscripted from DNA in nuclei. Also asynthetic pore-membrane can be used as theDNA sensor by measuring the pore current.
We are studying translocation of a singlestranded DNA through the pore by moleculardynamics simulations [3]. Our model consistsof upper and lower compartments and the poreof a nanometer radius, which are filled withsolvent (water, dielectric constant ε= 80) andmonovalent salt of 1M/l concentration. The
central part of the system is a membrane oflow dielectric constant εm= 2.
Figure 2 shows the ssDNA and ions in thepore (denoted by a cylinder) at steady phase.
Large spheres represent DNA monomers ofFig.2: ssDNA in a nano-size radius pore.
Counterions condense on charges of DNA forelectroneutrality while coions are depleted
from the pore to reduce ion energy which isenhanced by low dielectric membrane..

neutral sugar rings, bases and charged phosphate groups. Due to enhancement of electrostatic energy by low dielectric membranesurrounding the pore, charged groups of DNA
are repelled from the pore wall. (Free) coions
are depleted from the pore for which bothelectrostatics and volume exclusion of bulky
DNA monomers play their roles. Counterions
condense on the DNA without penalty ofelectrostatic energy increase and the pore is
kept charge neutral.
Finally, we mention quite high efficiency of aPC cluster machine equipped with low-latency
communication software GAMMA combinedwith commercial Fortran/C compilers [4].
Acknowledgments: This work was supported
by Grant in Aid No.16032217 from Japan
Ministry of Education, Science and Culture.
References:[1] M.Tanaka, Toyoichi Tanaka et al., Phys.Rev.
E56, 5798 (1997); ibid. E62, 3803 (2000).
[2] M.Tanaka and A.Grosberg, J.Chem.Phys.
115, 567 (2001); Europhys.J.E7, 371 (2002);
Phys.Rev. E68, 061501 (2003).
[3] Y.Rabin and M.Tanaka, submitted.
[4] M.Tanaka, LANL, physics /0407152 (2004);
Japan Physical Soc. Butsuri 59, 898 (2004).