J. Plasma Fusion Res. SERIES, Yol.2 (1999) 25-27

Complexity in a Molecular String
YOSHIKAWA Kenichi
Department of Physics, Graduate School of Science
Kyoto University, Kyoto 606-8502, Japan(Received: 8 December 1998 / Accepted: 6 May 1999)

Abstract
It is shown that a single molecular string, or a linear macromolecule, exhibits rich variety ofmorphologies in its folded compact structure. Experimental evidence on nanometer-size ordered structure
is given as the folding products from giant DNAs. Numerical simulation has been carried out, together
with theoretical analysis, and phase diagram is proposed for the morphological variation in a molecularstring.

Keywords:
folding transition, coil-globule transition, giant DNA, polyelectrolyte

1. Physics of a Giant DNA

long DNA chains and generalized theoretical discussion
for a molecular string.

In living cells both for prokaryote and eukaryote,individual double-stranded DNA chains usually exist ina highly packed state []. For example, in mammaliancells, individual DNA chains have a contour length or
full-stretch length, l, on the order of a centimeter, andthey are stored within the space on the order ofmicrometer. The persistence length, ,1, of DNA isusually on the order of 50nm in aqueous environment.
Thus, a DNA chain with L = I cm corresponds to alinear, freely jointed polymer chain with N = 105segments, where N = L/(21).If DNA chains act as ideal(l) Through the observation on the conformation ofindividual long DNA chains, it has become clear that theDNAs undergo large discrete transition between
elongated coiled state and collapsed compact state on
the level of the individual chains. i.e.. the transition is

first-order phase transition [2,3). On the contrary, thephysico-chemical parameters on the ensemble averageof the chains are always continuous with the transition,i.e., the transition on large number of molecular chains
does not belong to any kind of phase transition.
(2) The process of nucleation & growth has been
observed on the level of the single DNA chain [4,5]. As
the product of the crystallization on the single DNAs,various kinds of morphologies, such as toroid, rod, andspherical structures, are formed [6-10]. (See Fig.1)(3) On the mechanism of the phase transition in giant
DNAs, it is shown that the change in the translationalentropy of the counter ions exhibits the significant
contribution to the free energy [3,] l].

linear chains, the average end-to-end distance is <R> 2)J,'ltn - 30pm. This means that DNAs in natural origins

behave as flexible molecular string with the course
graining of the order of micrometer, whereas they look
stiff rod on the length scale of nanometer. In spite of therecent development of molecular biology, the problem
how the long DNAs are folded in a compact space
without entanglement has not been solved yet.
In the present paper, we describe such a problemfrom both points of view; experimental features with@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Research25

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Fig. 2 Schematic representation of the phase diagram in

the morphological change of a single polymer
chain with the parameters of chain stiffness andtemperature. (Partly modified from Ref.9) The
temperature axis can be translated into themanner of pairwise interaction between thesegments. where high and low temperatures

Sqlcbr= [00mcorrespond to repulsive and attractive

Fig. 1 Morphologies of T4DNAS (contour length: 57 pml
as were observed with transmission electron
microscopy. (Modified from Refs. 6, 8, 9, 11, 121A) With aminated polyethyleneglycol (PEG-A) atintermediated concentrations, the DNA chain
exhibits intrachain segregated state, and B) withinteractions, respectively.

chains, the transition has the nature similar to gas-liquid

the increase of PEG-A concentration, nearlyphase transition. On the other hand, for stiff chains

spherical product is generated. C) With a trivalentcation, spermidine, toroidal form is observed, andD) an anticancer drug, daunomycine, changes thetoroidal morphology into fragmented barrelstructure. E) With spermidine, rod structure is also

several kinds of solid-like states are generated. From theexperiments on the giant DNA chains, we have actually

lipospermine, the DNA takes spool-like structure.

3. Future Problem

observed the morphologies such as toroid, rod andspherical.

obtained in addition to the toroid. F) WithThe next research target would be the experimental
studies to make sure such kinds of phase diagram forvarious polymer chains beside DNAs.

2. Phase Diagram in a Molecular String
As has been described in the above section, wehave confirmed that individual isolated giant DNAs

Reference

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a thick line in the figure, condensed phases exist atlower temperatures. It is noted that liquid-like state isfound for the region of flexible chain. Thus, for flexible

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