  Motivated by recent experimental work, we define and study a deterministic
model of the complex miRNA-based regulatory circuit that putatively controls
the early stage of myogenesis in human. We aim in particular at a quantitative
understanding of (i) the roles played by the separate and independent miRNA
biosynthesis channels (one involving a miRNA-decoy system regulated by an
exogenous controller, the other given by transcription from a distinct genomic
locus) that appear to be crucial for the differentiation program, and of (ii)
how competition to bind miRNAs can efficiently control molecular levels in such
an interconnected architecture. We show that optimal static control via the
miRNA-decoy system constrains kinetic parameters in narrow ranges where the
channels are tightly cross-linked. On the other hand, the alternative locus for
miRNA transcription can ensure that the fast concentration shifts required by
the differentiation program are achieved, specifically via non-linear response
of the target to even modest surges in the miRNA transcription rate. While
static, competition-mediated regulation can be achieved by the miRNA-decoy
system alone, both channels are essential for the circuit's overall
functionality, suggesting that that this type of joint control may represent a
minimal optimal architecture in different contexts.
