A mathematical tool for exploring the dynamics of biological networks

Barbano et al. 10.1073/pnas.0709955104.

Supporting Information

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The Full Network with 102 Components

The DARPP-32 network depicted in Fig. 1 highlights 45 key species. The full network includes a number of enzyme-substrate complexes such as PKA-cAMP bound to DARPP-32-T75P. These species account for the increase in the number of chemical species present from 45 to 102. For clarity, these additional species are indicated with the annotation "complex" in the list below. (Free phosphate is assumed to be in abundance and not considered as a separate variable.)

The list of components below contains a few molecules that were not included in Fig. 1 as parts of the network. They were introduced because the four enzymes regulating the Ser-97 and Ser-130 phosphorylation states of DARPP-32, namely, CK1-P, PP-1, CK2, and PP2C, were treated inconsistently in the available model. More precisely, while CK1-P is regulated by the transient impulse of glutamate, the other three enzymes were uncoupled from either of the neurotransmitters being studied. We, therefore, chose to create several artificial activators: Dummy-Activator-PP1, Dummy-Activator-CK2, and Dummy-Activator-PP2C. In the absence of these dummy activators, DARPP-32 was overwhelmingly driven to the Ser102P phosphorylation state, leaving meaningful variation only between the Thr-34 and Thr-75 phosphorylation sites, instead of all four sites present in the model. The three dummy activators correct this imbalance. In essence, the three "unregulated" enzymes are provided with artificial activation impulses that mimic the specified impulses of dopamine and glutamate.

Component list:

1 DARPP-32-T75P

2 DARPP-32

3 DARPP-32-T34P

4 PP2A-P

5 PP2A

6 PKA-cAMP

7 PKA-cAMP-DARPP-32-T75P (complex)

8 Cdk5-P

9 PP2B-Ca2+

10 DARPP-32-T75P-PP2A-P (complex)

11 DARPP-32-Cdk5-P (complex)

12 DARPP-32-PKA-cAMP (complex)

13 DARPP-32-T34P-PP2B-Ca2+ (complex)

14 PP2A-PKA-cAMP (complex)

15 PKA

16 cAMP

17 ATP

18 Ga

19 D1R

20 Dopamine

21 Cdk5

22 CK1-P

23 CK1

24 PP2B

25 Ca2+

26 IP3

27 PIP2

28 PLC-Gq

29 PLC

30 Gq

31 mGluR

32 Glutamate

33 Cdk5-CK1-P (complex)

34 PP2B-Ca2+ -CK1 (complex)

35 PLC-Gq-PIP2 (complex)

36 PP-1

37 PP-1-DARPP-32-T34P (complex)

38 Adenylyl Cyclase

39 Adenylyl Cyclase-Ga

40 Adenylyl Cyclase-Ga-ATP (complex)

41 DARPP-32-S97P

42 CK2-P

43 CK2-P-DARPP-32 (complex)

44 PP-1-DARPP-32-S97P

45 DARPP-32-T75P-S97P

46 Cdk5-P-DARPP-32-S97P (complex)

47 PP2A-DARPP-32-T75P-S97P (complex)

48 CK2-P-DARPP-32-T75P (complex)

49 PP-1-DARPP-32-T75P-S97P (complex)

50 PKA-cAMP-DARPP-32-T75P-S97P (complex)

51 DARPP-32-T34P-S97P

52 PKA-cAMP-DARPP-32-S97P (complex)

53 PP2B-Ca2+ -DARPP-32-T34P-S97P (complex)

54 CK2-P-DARPP-32-T34P (complex)

55 PP-1-DARPP-32-T34P-S97P (complex)

56 PP-1-DARPP-32-T34P-S97P

57 DARPP-32-S130P

58 PP2C

59 CK1-P-DARPP-32 (complex)

60 PP2C-DARPP-32-S130P (complex)

61 DARPP-32-T75P-S130P

62 Cdk5-P-DARPP-32-S130P (complex)

63 PP2A-P-DARPP-32-T75P-S130P (complex)

64 CK1-P-DARPP-32-T75P (complex)

65 PP2C-DARPP-32-T75P-S130P (complex)

66 PKA-cAMP-DARPP-32-T75P-S130P

67 DARPP-32-T34P-S130P

68 PKA-cAMP-DARPP-32-S130P (complex)

69 PP2B-Ca2+ -DARPP-32-T34P-S130P (complex)

70 CK1-P-DARPP-32-T34P (complex)

71 PP2C-DARPP-32-T34P-S130P (complex)

72 PP-1-DARPP-32-T34P-S130P

73 DARPP-32-T75P-S97P-S130P

74 CK1-P-DARPP-32-T75P-S97P (complex)

75 PP2C-DARPP-32-T75P-S97P-S130P (complex)

76 CK2-P-DARPP-32-T75P-S130P (complex)

77 PP-1-DARPP-32-T75P-S97P-S130P (complex)

78 PKA-cAMP-DARPP-32-T75P-S97P-S130P

79 DARPP-32-T34P-S97P-S130P

80 CK1-P-DARPP-32-T34P-S97P (complex)

81 PP2C-DARPP-32-T34P-S97P-S130P (complex)

82 CK2-P-DARPP-32-T34P-S130P (complex)

83 PP-1-DARPP-32-T34P-S97P-S130P (complex)

84 PP-1-DARPP-32-T34P-S97P-S130P

85 DARPP-32-S97P-S130P

86 CK1-P-DARPP-32-S97P (complex)

87 PP2C-DARPP-32-S97P-S130P (complex)

88 CK2-P-DARPP-32-S130P (complex)

89 PP-1-DARPP-32-S97P-S130P (complex)

90 PP2A-P-DARPP-32-T75P-S97P-S130P (complex)

91 Cdk5-P-DARPP-32-S97P-S130P (complex)

92 PP2B-Ca2+ -DARPP-32-T34P-S97P-S130 (complex)

93 PKA-cAMP-DARPP-32-S97P-S130P (complex)

94 PP1-inactive

95 Dummy-Activator-PP1

96 PP1-Dummy (complex)

97 CK2-inactive

98 Dummy-Activator-CK2

99 CK2-Dummy (complex)

100 PP2C-inactive

101 Dummy-Activator-PP2C

102 PP2C-Dummy (complex)

MATLAB or C codes for setting up the random parameters and solving the system of ordinary differential equations are available by request from the authors (greengard@courant.nyu.edu or spivak.marina@gmail.com).

This Article

  1. Published online before print November 21, 2007, doi: 10.1073/pnas.0709955104 PNAS December 4, 2007 vol. 104 no. 49 19169-19174
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