Systems Biology (Methods in Molecular Biology)

simple six coupled linear differential equations model approximat-

ing the gene regulatory network of repressing genes, they investi-

gated the key regulatory parameters that are required to produce

unstable steady-state, resulting in regular oscillations:

dXi

dt

¼Xiþ

k 1

1 þYjn

k 2 ð 24 Þ

dYi

dt

¼k 3 YjXi



ð 25 Þ

whereXi(i¼ lacl,tetR,cl) represent mRNAs (genes) andYj

(j¼λcl, Lacl, TetR) represent proteins concentrations. Figure9a

shows the oscillations in protein concentrations with time.

Subsequently, a plasmid encoding the repressilator and a

reporter protein were constructed and inserted into the bacteria.

50 a

cd

b

40

30

20

10

-10

-20

-30

80

40

60

20

-20

0

0

0

40

30

20

10

-10

0

20 40

Time (-) Time (-)

Time (-) Time (-)

60 80 100

0 200 400 600 800 1000 0 200 400 600 800 1000

0 200

200

150

100

50

-50

0

400

s

600 800 1000

Fig. 8Simple and Complex Goodwin dynamics. Simulations with single oscillator with parameters (a)X 0 ¼7,
Y 0 ¼10,k 1 ¼72,k 2 ¼36,k 3 ¼1,k 4 ¼2,k 5 ¼1,k 6 ¼0, and coupled oscillators (b)X 10 ¼7,Y 10 ¼10,
X 20 ¼7,Y 20 ¼10,k 11 ¼k 12 ¼360,k 21 ¼36,k 22 ¼43,k 31 ¼1.0,k 32 ¼0,k 41 ¼0.1,k 42 ¼1,k 51 ¼5,
k 52 ¼5,k 1 ¼0.5,k 2 ¼0,k 3 ¼0.6,k 4 ¼0, (c)k 31 ¼0.5,k 41 ¼0.2,k 51 ¼8,k 52 ¼8, (d)k 31 ¼0.1,k 32 ¼1.
Only parameters that are different from (b) are listed for (c)and(d).x-axis represents time andy-axis represents
concentration in arbitrary units.X 1 isredwhileX 2 isbluefor (a),X 1 isdark bluewhileX 2 islight blueforb–d

186 Kumar Selvarajoo