ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

APPLICATION OF REACTION-DIFFUSION WAVE TO SELF-
ASSEMBLED NETWORK STRUCTURES OF DNA
1. ABSTRACT
Kentaro Doi 1 , Yukihiro Toyokita and Satoyuki Kawano
Recently, it is reported that DNAs tend to form self-assembled structures on several
kinds of substrate surface and that peculiar network patterns can be observed. In this
study, we develop a theoretical model to simulate a self-assembly network formation of
DNA by using reaction-diffusion wave. The network patterns on two kinds of solid
surfaces are obtained and are compared with the experimental results of AFM images.
2. INTRODUCTION
DNA has attracted much attention from technological aspects due to functional properties
such as electric conductivity, double strand structures, and base complementarity. Selfassembly
is one of the most interesting characteristics of DNA, but the mechanism has
not been elucidated enough yet. In the present study, we have applied a reactiondiffusion
wave model to the self-assembled network formation of DNA on twodimensional
substrate surfaces. A reaction-diffusion system consisting chemical
reactions and molecular diffusion is adapted for modeling the adsorption phenomenon
on the surfaces. In particular, peculiar self-assembled structures on mica and highly
oriented pyrolytic graphite (HOPG) surfaces can be simulated well. It is found that the
difference of surface conditions is taken into account by constraints for the stacking
structures and source terms which denote the provision of DNA near the surfaces.
3. REACTION-DIFFUSION WAVE MODEL
In this model, dissociated or adsorbed states of DNA above a substrate surface are
represented by reaction-diffusion equations:
u
2
Du
u du Fu,
v,
(1)
t
v
2
Dv
v gv Gu,
v,
(2)
t
where u and v are the number density of adsorbed and desorbed DNA, respectively,
and u D and D v are the diffusion coefficient for u and v , respectively. The reaction rate
constants are presented by d and g , and the more higher order terms are usually
presented by functional F u, v
and G u, v.
Solving Eqs. (1) and (2), peculiar structures
are obtained at the equilibrium conditions. Using this method, the self-assembly of
DNA is discussed in detail. In this study, the characteristic length is set to 1.7×10 -8 m
based on the length of a 50bp DNA fragment employed in our experiments, and the
1 Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science,
Osaka University, Machikaneyama-cho 1-3, Toyonaka, Osaka 560-8531, Japan