MicroRNAs and Robustness in Biological Regulatory Networks. A Generic Approach with Applications at Different Levels: Physiologic, Metabolic, and Genetic - Systems Biology of Metabolic and Signaling Networks - page 74

miR G 1 miR G 1 miR G 1

G 2 G 2 G 2

Negative circuit Positive circuits

G 3 G 3 G 3

miR G 1 G 2 G 3 miR G 1 G 2 G 3 miR G 1 G 2 G 3

0
0
0
0

1
0
1
0

1
0
1
0

1
0
1
0

0
0
0
0

1
0
0
1

1
0
1
1

1
1
0
1

0
0
0
0

1
1
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1

1
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1
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miR G 1 G 2 G 3 miR G 1 G 2 G 3 miR G 1 G 2 G 3

miR- > G3 + (miR- < G3 +)

1
1
1
1

1
00
11
1

11 1

1

111 111 1

0 0 0 1 1

1
1

0 (1)
0 (0)

00

0
0

1011
1011

1 (0) 0 (1)

0 0 (1) 1 0 (1)

Fig. 4.9 Dynamic behavior of circuits inhibited by the microRNA miR. Left : negative circuit
whose limit cycle is canceled by miR and replaced by a fixed configuration. Middle : positive
circuit whose limit cycle is canceled by miR and replaced by a fixed configuration. Right : positive
circuit whose limit cycle is not canceled by miR

inhibitory activity the cortex exerts on the sub-cortical structures, which leaves
effective only the sufficiently activated neural networks, as well as the anatomically
identified subthalamic nuclei involved in motor control (Benabid et al. 1992 ), when
they are co-activated by voluntary conscious and/or sensory unconscious inputs.
Neural versus genetic metaphor seems pertinent because of the structural and
functional analogy of their mathematical models.
We will use to compare microRNAs the normalized circular Hamming distance
(equal to the number, divided by 22, of mismatches, i.e., the number of pairs
different of A-U, U-A, C-G, G-C, G-U, and U-G, the classical pairs due to the
Crick-Watson antisense hybridization, cf. Table 4.1 ) to the reference palindromic
sequence AL. AL is close to the Archetypal Levin's tRNA loops sequence
(Demongeot and Moreira 2007 ) and barycenter of a set of RNA rings of length
22 (like the microRNAs), whose the main characteristics is containing all the amino
acids triplets, then constituting a “matrimonial agency” for amino acids favoring
peptidic bonds as an ancestral ribosome (Hobish et al. 1995 ; Demongeot et al.
2009b , c ). More, AL falls in the 5 % lowest tail part of the distribution of
normalized circular Hamming distances to Rfam, a collection of multiple sequence
alignments covering noncoding RNA families (Griffiths-Jones et al. 2005 ). Prox-
imity to AL of microRNAs of Tables 4.1 and 4.2 is significant for a distance strictly