Biology Reference
In-Depth Information
kinds of change separately, in order to find out whether any
commonalities exist among them. Such commonalities
would point
GENOTYPE SPACES AND THE PHENOTYPES
THEREIN
to more general principles of phenotypic
variability.
This section discusses genotypes and phenotypes separately
for each of the three systems classes mentioned above.
The metabolic genotype of an organism is the totality of
its DNA that encodes metabolic enzymes. It is thus funda-
mentally a subset of its genome. While one can think of this
genotype as a DNA string, is often more expedient to
represent the genotype more compactly. Here is a compact
representation that is well suited to study innovation
systematically
[54]
. Consider the known universe of
biochemical reactions, that is, chemical reactions catalyzed
by an enzyme that are known to occur somewhere in some
organism. This known universe of biochemical reactions
currently comprisesmore than 5000 such reactions
[55]
. One
can write these reactions as a list, as shown in
Figure 13.1
a,
which represents each reaction by its stoichiometric equa-
tion. Any one organism, such as a human or the bacterium E.
coli, will have enzymes that catalyze some of these reactions
but not others. For reactions that are catalyzed in any one
organism, write 1 next to the stoichiometric equation shown
in
Figure 13.1
a. For every reaction that does not occur, write
0. The result of this procedure is a binary string that indicates
which reactions do or do not take place in the metabolism of
an organism. It is a compact description of a metabolic
genotype, comprising all the enzymatic reactions that take
place in a metabolic network. With this definition in mind,
the notions of metabolic genotype andmetabolic network are
used here synonymously.
The totality of all possible metabolic genotypes
TOWARDS A SYSTEMATIC
UNDERSTANDING OF INNOVATION
By themselves, examples of innovations like those just dis-
cussed may not help us answer whether broader principles of
innovation exist. To this end, it may be necessary to study
innovationmore systematically. Oneway to do that is to study
a 'space' of possible innovation in each of the three system
classes. This space is vast, too vast to understand exhaus-
tively. But even by examining small samples of this space it is
possible to learn about the structure of the entire space, and
thus about principles of innovability. I will next discuss such
a more systematic approach for each system class. Before
that, however, I want to highlight three goals that a systematic
understanding of innovation
an innovability theory
e
e
should achieve (others are highlighted elsewhere
[10]
).
The first goal reflects perhaps the most difficult problem
that the origin of new beneficial trait poses to our under-
standing of evolution. Most mutations that affect an
organism's genotype are deleterious, that is, their effects
harm rather than benefit their carrier. Such mutations
produce inferior phenotypes. Thus, to find new and superior
phenotypes organisms may have to explore many mutant
genotypes. At the same time, however, organisms need to
preserve existing, well-adapted phenotypes. In other words,
organisms have to be conservative and explore many new
phenotypes at the same time. How both objectives can be
achieved simultaneously is a question that a theory of
innovation would have to answer.
The second goal relates to the observation that many
innovations in the history of life have occurred more than
once
[6]
. Dissected leaves may have evolvedmultiple times;
so did antifreeze proteins; and so did many metabolic
innovations. For example, life has solved the metabolic
problem of incorporating atmospheric carbon (CO
2
) into
biomass at least three times in different ways, that is, through
the Calvin
e
Benson cycle, through the reductive citric acid
cycle, and through the hydroxypropionate cycle
[53]
.
A third goal relates to the observation that some inno-
vations seem to combine existing parts of a system to create
a new function. I mentioned a metabolic pathway that can
degrade pentachlorophenol, as well as the urea cycle, both
of which involve new combinations of existing enzymatic
reactions
the set
e
of all the binary strings defined above
constitutes a meta-
bolic genotype space, a collection of possible metabolic
genotypes. This space is vast, containing more than 2
5000
possible genotypes, more metabolisms than could ever be
realized on earth (and many of them surely useless to life as
we know it). It is the space of all possible metabolisms that
can be realized with a given set of biochemical reactions. To
understand metabolism and metabolic innovation system-
atically is to understand the structure of this space, and the
metabolic phenotypes that exist in it.
A few further concepts are useful in discussing meta-
bolic genotype space. The first is that of a neighbor.Two
metabolic networks are neighbors in genotype space if they
differ in a single chemical reaction. A neighborhood of
a metabolic network comprises all its 1-neighbors, all
metabolic genotypes that differ from it in a single reaction.
These concepts can be extended to k-neighbors, networks
that differ from a given network in k chemical reactions.
The distance of two metabolic networks indicates the
fraction of reactions in which they differ. Two metabolic
networks have a distance of D
e
parts of a metabolic system. Is this combina-
torial nature of innovations a peculiarity of some innova-
tions, or is it a more general phenomenon?
The framework I will discuss here suggests an answer to
all three questions.
e
¼
0 if they contain the same
reactions; a distance of D
0.5 if 50% of reactions that are
catalyzed by one network are not catalyzed by the other
¼
