Biology Reference
In-Depth Information
challenge. However, progress is unlikely to involve
a dramatic solution that starts with a DNA sequence and
infers the underlying mechanism; indeed, it can be argued
that there is insufficient information and knowledge of the
constraints required to reduce the degrees of freedom
necessary to accomplish such a feat. Rather, progress will
be made, as in the past, by top-down high-throughput
measurements and statistical analysis combined with
bottom-up molecular characterization of subsystems
involving hard physical and chemical constraints. This is
the first of the two fundamental problems in bridging the
chasm between genotype and phenotype that was
mentioned in the introduction to the Phenotype Section.
The second fundamental problem, the task of going from
the model of a system to the elucidation of its phenotypic
repertoire, is the long-term challenge being addressed by
the system design space approach.
The system design space approach described in this
chapter is applicable currently to any relatively small
subsystem for which the molecular mechanisms have been
identified. To deal with the size and subtleties of larger
systems, future development of this approach will likely
advance on three fronts. First, it should be possible to
develop rules for producing the design space of a composite
system by augmenting an existing design space with a newly
acquired design space for an additional subsystem. In this
way one could in principle move incrementally to larger
system design spaces by building on the knowledge of
constraints and design principles acquired earlier in the
study of the constituent subsystems. Second, it should be
possible to develop more efficient means of visualizing the
enormous amount of data generated. In the lambda example,
we have simply provided representative results for a single
phenotype (Case 11); similar results are available for all of
the realizable qualitatively distinct phenotypes. However, at
this point more of the same types of figures and tables are
overwhelming. Third, it should be possible to develop more
efficient algorithms for identifying and analyzing pheno-
types in system design space based on well-established
theory. In general, the boundaries between phenotypes in the
system design space are always straight lines (hyper-planes)
in logarithmic space and the slopes are rational functions of
the exponents in generalized mass action models. Algebraic
geometry provides the theoretical foundation for this type of
analysis, and there are opportunities for automating much of
the analysis based on this linear theory.
As an example of what can be done with regard to this
third opportunity is the set of algorithms already developed
and assembled into a Matlab application called Design Space
Toolbox
[77]
, and there is the potential for much further
automation. Establishing dominance is a standard mathe-
matical problem in linear algebra that is solved everyday for
problems of enormous size (e.g., scheduling in the airline
industry), so solving each case is not a problem. Nevertheless,
scale-up becomes an issue because of the large number
of potential phenotypes, which is determined by the number
of combinations of terms in the original equations, many of
which will be invalid but still must be checked. This is an
obviously parallizable problem yet to be implemented. As
should be clear from these conclusions, the analysis of system
design space is in its infancy and there are still abundant
challenges and opportunities for further development.
ACKNOWLEDGEMENTS
I thank Rick Fasani for assistance in constructing the system design
spaces, and Pedro Coelho, Dean Tolla, and Jason Lomnitz for fruitful
discussions. This work was supported in part by US Public Health
Service Grant R01-GM30054 and by a Stanislaw Ulam Distinguished
Scholar Award from the Center for Nonlinear Studies of the Los
Alamos National Laboratory.
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