Biology Reference
In-Depth Information
regulatory circuits can evolve increased robustness to
perturbations, and that cryptic variation
differ from it in no more than k regulatory interaction. The
distance D of two circuits can be defined as the fraction of
regulatory interactions in which they differ. For example,
two circuits would have a distance of D
genotypic vari-
ation without phenotypic effects in a given environment
e
e
might facilitate evolutionary adaptation
[76
80]
. Note that
circuits different from those discussed here, such as
signaling circuits, can show properties similar to those
highlighted below, which suggests that these properties
may be generic features of regulatory circuits
[71,81,82]
.
The genotype of a regulatory circuit comprises the
genomic DNA that encodes all regulatory molecules, as
well as the non-coding DNA that may help determine the
interactions between them. For a transcriptional regulation
circuit, this genotype typically includes the genes that
encode the circuit's transcriptional regulators, as well as the
regulatory DNA sequences that determine where a regu-
lator binds, and which therefore determine who regulates
who in the circuit. As in metabolism, there are more
compact representations of a circuit's regulatory genotype
than its DNA sequence. For example, one can represent the
regulatory genotype simply through a square matrix
w
¼
0.2, if they
differed in 20% of their interactions. They would have
a distance of D
¼
e
1 if they differed in every single inter-
action, that is, if no interaction that occurs in the first circuit
also occurs in the second circuit
[83,84]
.
The final class of systems to be discussed here are
protein and RNA macromolecules. Their genotype spaces,
also known as sequence spaces, have been studied for many
years
[85
¼
87]
. For protein strings of a given length N of
amino acids, genotype space comprises all amino acids
strings of length N, and thus a totality of 20
N
such strings,
because 20 different amino acids occur in most proteins.
For RNA molecules of N nucleotides, it comprises 4
N
possible RNA strings. As for metabolism and for regulatory
circuits, the sizes of these genotype spaces can be astro-
nomically large. Two protein and RNA molecules are
k-neighbors in genotype space if they differ in k nucleotides
or amino acids. The k-neighborhood of a molecule
comprises all of its neighbors. The distance of two protein
or RNA molecules can be defined in a variety of ways, one
of them being the fraction of monomers in which they
differ.
The phenotype of a protein or RNA molecule comprises
its secondary structure, its tertiary structure
e
(w
ij
), whose entries w
ij
reflect whether transcription
factor j regulates the expression of transcription factor i in
the circuit. In the simplest possible representation, this
matrix contains only information about whether
this
interaction is activating (w
ij
¼þ
1),
or absent. Even the simplest representation shows that the
number of circuit genotypes will be very large, even for
circuits with a modest number N of genes. That is, there are
3
N
2
possible circuits. In more complicated representations
of transcriptional regulation circuits, these interactions
could assume a larger or a continuous range of values.
Mutations in DNA that affect the regulatory interactions of
circuit genes can change this circuit genotype. For
example, a mutation in regulatory DNA that abolishes
binding of a transcription factor to this DNA may also
abolish regulation of a nearby gene by this transcription
factor, and thus eliminate one of the regulatory interactions
w
ij
of this circuit (w
ij
/
1), repressing (w
ij
¼
that is, its
e
three-dimensional fold in space
as well as its biochem-
ical function, be it catalytic, structural, or something else.
Over the last 40 years the genotypes and phenotypes of tens
of thousands of proteins have been characterized bio-
chemically. They provide a rich source of information to
study the relationship between genotype and phenotype
[88]
. Fewer RNA phenotypes are known, but for RNA
secondary structures algorithms exist that can predict RNA
phenotypes from genotypes
[89,90]
. Albeit not perfectly
accurate for any one sequence, the relevant algorithms are
sufficiently accurate (and also sufficiently fast) to charac-
terize thousands to millions of different RNA genotypes
and their phenotypes
[87,91
e
0).
The mutual regulatory interactions of molecules in such
a circuit will create a gene expression pattern. This
expression pattern is a circuit's phenotype. It typically
influences the expression of many genes downstream of the
circuit, genes that influence physiological or developmental
processes. Changes in such phenotypes caused by muta-
tions of the circuit's regulatory genotype can help create
new traits, some of which may become evolutionary
innovations.
To study the origin of new gene expression phenotypes
in such circuits systematically, one needs to think of any
one circuit as being part of a much larger genotype space of
circuits. This space contains all possible circuits of a given
number N of genes. In this genotype space, two circuits
are k-neighbors if they differ in k regulatory interaction.
The k-neighborhood of a circuit comprises all circuits that
93]
. Because RNA secondary
structure phenotypes are necessary for the functioning of
many molecules, they are interesting study objects in their
own right
[94
e
96]
.
e
Genotype Networks
The genotype spaces of metabolic networks, regulatory
circuits, and macromolecules are much too large to be
characterized exhaustively. However, they can be charac-
terized through (unbiased) sampling of genotypes or
phenotypes, or through exhaustive enumeration of geno-
types and phenotypes for small systems. These approaches
can identify generic properties of such spaces, that is,
properties that hold for typical genotypes and phenotypes.
