Biology Reference
In-Depth Information
In some circumstances, the core features of those simplifications can be gen-
erated by quantitative investigations and represented by mathematical equations
that are formally analogous to what we find in the Euclidean types of theories
discussed in Section 1. But they lack that very broad universality, and instead
serve their functions by being prototypes for analogical modeling to similar pro-
totypes, albeit in this case, analogical modeling to other quantitative prototypes.
In addition, they are not usually uni-level, but instead mix levels of aggregation.
In the H and H work, the discussion is focused on current flows and potential
difference changes because of ions and inferred ion channels, but as situated in
an axon of a particular species. Further reflection of the H and H systems-level
methodology may provide important generalizable heuristics that can inform
biology pursued at the level of general systems.
4. A NEUROSCIENTIFIC ACCOUNT OF BEHAVIOR IN
C. ELEGANS
An interesting comparison with the above H and H account can be found in a
recent essay by Ferrée and Lockery. Whereas the typical study of the behavior of
the model organism,
C. elegans
, tries to identify genes and molecular sequences
that are characterized as 'causes' of behaviors, the example to be discussed in
this section is more akin to the H and H inquiry and their mode of modeling. For
an example of the more typical approach to worm behavior modeling, see Mario
de Bono and Cori Bargmann's (1998)
Cell
paper with their focus on a DNA
nucleotide change as the 'cause' of a behavioral phenotype involving social
versus solitary feeding. Ferrée and Lockery, in contrast, provide an analysis
that attempts to model the factors and interactions that govern the neurons not
the genes. Ferrée and Lockery's general task was to determine 'the behavioral
strategy for chemotaxis in
C. elegans
', and their specific approach was to 'derive
a linear neural network model of the chemotaxis control circuit' in
C. elegans
,
and then to 'demonstrate that this model is capable of producing nematode-like
chemotaxis' (Ferrée & Lockery, 1999, p. 2). This then is a simulation study, but
one based on a considerable amount of empirical work. The following account
is adapted from Schaffner (2000), but here is updated and placed in a different
context - that of exploring systems theory in biology and the extent and nature
of mathematical equations in that area.
Ferrée and Lockery utilized a 'candidate neural network' based on Bargmann's
earlier work on the worm (see Fig. 2). Lockery's own investigations (Goodman
et al., 1998) have shown that the neural signals in
C. elegans
are encoded
by graded electrical potentials (not by classic sodium action potentials). The
individual neurons display nonlinear transfer functions, but Ferrée and Lockery
