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 86

then we have:

2 2 P 2 H

x 2 2

Im ξ ¼ðΔ P Þ 4 ð C ð P Þþ C ð H Þþ@ =@ x 1 @ x 2 ð@ =@

j

1 = 2

2 H

x 1 2

2 H 2 P

x 1 2

2 P

x 2 2

@ =@ Þþ@ =@ x 1 @ x 2 @ =@ :@ =@ = 2 ;

2 P

x 1 2

2 P

x 2 2 is the Laplacian of P and C

2 P

x 1 2

2 P

where Δ P ¼@ =@ þ@ =@ ð P Þ¼@ =@ @ =

2 is the mean Gaussian curvature of the surface P , both taken
at the stationary state of the differential system.
Concerning the energy balance in neurons, if the apparent V max of the PFK is
diminished in astrocytes due to a lack of ATP (used to inactivate via phosphoryla-
tion the neurotransmitter receptors), then the oscillatory behavior is less frequent
and the production rate of lactate from pyruvate is more important than in neuron,
creating a flux of lactate to neurons. The neurons consume the lactate coming from
the extracellular space, partially replenished by the astrocytes production. That
gives to neurons an ATP level higher than in astrocytes, with an extra-pyruvate
production from lactate, and extra-oxygen and glucose consumption theoretically
predicted and experimentally observed.
This ATP level depends on ATPase and Translocase concentrations, which are in
human under the negative control of 3 miRNAs, the hsa-miR-136, 34 (common), and
301 (cf. Table 4.3 ) acting as boundary control nodes (http://microrna.sanger.ac.uk)
by regulating the neuronal oxidative system efficacy. These enzymes are located
on the mitochondrial inner membrane surface whose protein content can generate
the ATP/GTP turnover (Bier et al. 1996 ), as well as the proton leak (Mourier
et al. 2010 ).

@ x 2 2 ð@

2 P

=@ x 1 @ x 2 Þ

4.4.5 MicroRNAs, Morphogenesis, and Cell Cycle

The Engrailed gene is required for the proper segmentation and maintenance of the
posterior compartment of the Drosophila embryo (Almeida and Demongeot 2012 ),
but also the Engrailed gene efficiently activates the gene Elk, necessary for the
control of K + ion channels in excitable cells, and the human Engrailed homologues
encode homeo-domains containing proteins and are implicated in the control of the
pattern formation during the development of the central nervous system. On the top
of Fig. 4.14 , we have represented the action of the gene Elk, which controls for
example positively the ability of CA3 cells Yi's to express their negative feedback
upon the CA1 cells Xi's inside the hippocampus (Tonnelier et al. 1999 ), showing
that the same set of genes can be involved from the development phase until the
control of a high level function as the hippocampus memory ability.