Table 1 Enumeration of the phenotypic repertoire and potential dynamic behaviors for the relaxation oscillator design

From: Elucidating the genotype–phenotype map by automatic enumeration and analysis of the phenotypic repertoire

Case no.

Case signa ture

No. of eigenvalues with positive real part

1

111111111111

0

7

111121111111

0

8

111121111121

0

13

211111111111

1

15

211111112111

0

17

211111113111

1

19

211121111111

1

20

211121111121

1

21

211121112111

0

22

211121112121

0

23

211121113111

2

24

211121113121

1

29

311111113111

0

35

311121113111

0

36

311121113121

0

  1. Each design has a unique System Signature defined by a pair of integers for each equation of the system; the first of each pair indicating the number of positive terms and the second the number of negative terms in each equation. The System Signature in this application is [311121113121]. Each potential phenotype has a Case Signature, analogous to the System Signature, with the first of each pair signifying a particular term among the positive terms and the second a particular term among the negative terms in each equation. The potential phenotypes are given arbitrary sequential Case Numbers according to conventional digital counting of their Signatures. In this application: Case 1, (111111111111); Case 2, (111111111121); Case 3, (111111112111); Case 4, (111111112121); Case 5, (111111113111); …; Case 36, (311121113121). Note that 21 of the 36 potential phenotypes are not realizable; e.g., Cases 2 through 6. The number of eigenvalues with positive real part indicates whether the phenotype is stable with zero, exponentially unstable with one, or oscillatory unstable with two that are complex conjugate. Eigenvalues are determined using the set of parameters automatically determined for each of the phenotypes. For further details see Supplementary Online Methods.
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