Systems Biology (Methods in Molecular Biology)

5 Reaction-Diffusion Models

So far, we have considered only temporal biochemical reaction

systems that can generate complex dynamics. In certain situations,

spatial effects are also important for investigation, such as for the

understanding of self-organized pattern formation during the

developmental process. For example, how does a butterfly develop-

ment produce beautiful symmetric shapes on its wings, the spots

derived in leopard skins? Naturally, the analysis of spatial properties

should carry the spatial coordinates.

50

a

cd

[Y] [X] b [Y] [X]

[Y] [X] [Y] [X]

plot_1

plot_1 plot_1

plot_1

40

30

20

10

-10

-20

-8 -6 -4 -2 0 -15 -10 -5 0 5 10 15

mmol/ml

mmol/ml mmol/ml

mmol/ml

2468

-30

(^40200)
150
100
50
-50
-20 -15 -10 -5 0 5 10 15 20
0
30
35
25
20
10
15
-5
-10 -5 0
mmol/ml mmol/ml
510
mmol/ml
5
0
0
50
60
70
80
40
30
20
10
0
Fig. 12Goodwin phase-space plots from model with parameters of (a) Fig.8a,(b) Fig.8b,(c) Fig.8c,(d)
Fig.8d.x- andy-axes represent concentration in arbitrary units
194 Kumar Selvarajoo