Multicellular Systems - Molecular Theory of the Living Cell - page 512

the hunchback mRNA, and (2) Bicoid and Nanos proteins are unevenly distributed
across the Drosophila egg.
The Bicoid, Hunchback, Nanos, and Caudal are transcription factors that regu-
late the transcription of gap genes such as Kr

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uppel, giant, tailless, and Knirps.
Gap genes are part of a larger family called the segmentation genes that determine
the segmental body plan of the embryo along the anterior-posterior axis. They are
called “gap genes” because their expression leads to the formation of gaps in
the normal pattern of structure or the formation of broad bands in the embryo.
The maternal effect genes, including bicoid and nanos , are required during
oogenesis. The transcripts or protein products of these genes are found in the egg
at fertilization, and form morphogen gradients. The pair-rule genes divide the
embryo into pairs of segments. These genes encode transcription factors that
regulate the expression of the segment polarity genes, whose role is to set the
anterior-posterior axis of each segment. The gap genes, pair-rule genes, and seg-
ment polarity genes are together called the segmentation genes, because they are
involved in segment patterning.
The order of the expression of the set of genes, maternal effect genes, gap genes,
pair-rule genes, and segment polarity genes leads to an increasingly differentiated
and diversified spatial compartmentation of the volume occupied by the Drosophila
embryo which in turn leads to increasing the “active” complexity of the
embryo,“ active” because such compartmentations would be impossible without
dissipating free energy. The concepts of “active” and “passive” complexities were
defined in Sect. 5.2.3 . Therefore, it appears logical to define what may be referred to
as “the active complexity of the embryo” (ACE) as the number of bits in the shortest
string of symbols that describes the geometric compartmentation of an embryo,
including the body segmentations:

¼

Active Complexity of Algorithmic Complexity of the Geometric

(15.1)

the Embryo ACE ð Þ Compartments of the Embryo

Once the concept of active complexity of embryo (ACE) is defined, it is simple
to take the next logical step and define what may be called the “information density
of the embryo” (IDE) as the ratio of ACE and the geometric volume of the
embryo (GVE):

Information Density of the Embryo ð IDE Þ
¼ Spatial Complexity of the Embryo (ACE) = Geometric Volume of the Embryo (GVE Þ
(15.2)

It is important to differentiate the IDE from what may be called the “information
density of the genome” (IDG), defined as the ratio of the algorithmic complexity of
the nucleotide sequences of the genome over the geometric volume of the genomic
DNA molecules, since embryo is dissipative structures (or dissipatons) and the
genome, as defined here, would be an equilibrium structures (or equilibrons)