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

Fig. 1 Snapshots of self-assembly process of
DNA on mica surface: (a) t=1×10 -4 s, (b)
1×10 -3 s, (c) 1×10 -2 s and (d) AFM image.
characteristic time is determined as 1.0×10 -5 s with respect to the characteristic length
and diffusion coefficients. The non-dimensional forms of Eqs. (1) and (2) can be
obtained by using these quantities.
4. RESULTS AND DISCUSSION
Figure 1 shows computational results and the atomic force microscope (AFM) images
of self-assembled structure of 50bp poly(dA)poly(dT) DNA fragments on mica and
HOPG surfaces. Bright regions present higher density of adsorbed molecules. The time
evolution of u shows the distribution in the self-assembled structure formation. The
density is distributed randomly at t 0 s, and the difference in the density becomes
clearer as time passes. In this case, F u, v
and G u, v
are given by
Fu, v
au bv
c , (3)
Gu, v
eu f , (4)
where a , b , c , e and f are parameters which are summarized in Table 1. The surface
8
is divided into 100 100 grids and x y
1.
010
m. The parameter, c and f are
the source terms. The characteristics of these patterns strongly depend on the difference
of constraints for F and G . For the case of mica surface, the condition is set to
0 F Pu
and v P G 0 , where u P and P v denote upper limits for interactions with
external systems as controlled by the source terms. On the other hand, for the case of
HOPG, the conditions of u P F and v P G are maintained. At the equilibrium
2
conditions, t 110
s, computational results are in qualitative agreement with
experimental ones. Differences between network patterns on mica and HOPG surfaces
can be represented precisely. The length of both the vertical and the horizontal sides is
1.0 μm and the order of length corresponds to the experimental scale.
Table 1 Parameters for the reaction-diffusion wave model in the non-dimensional units.
D u
Fig. 2 Snapshots of self-assembly process of
DNA on HOPG surface: (a) t=1×10 -4 s, (b)
1×10 -3 s, (c) 1×10 -2 s and (d) AFM image.
x
y
t
0.60 0.60 0.10 0.01 0.50 0.20 0.50
a
b
c
d
e
f
g
0.08 0.08 0.08 0.03 0.06 0.15 0.03
D v
P u
P v