Biology Reference
In-Depth Information
Interactions between the system chosen in this way and its
environment will remain, but the number will have been
minimized. Thus, the identification of environmental
interactions is facilitated and, when these are disrupted to
study the system in isolation, the effects of the normal
environment on the system can be most easily approxi-
mated by experimental means.
By this criterion for the delineation of a system, a cell
constitutes a well-delineated system because the semi-
permeable plasma membrane tends to minimize the inter-
actions between the cytoplasm and the extracellular milieu.
On the other hand, a cell with a disrupted membrane would
have greatly increased numbers of interactions between
its cytoplasm and the extracellular milieu, and the system
no longer would retain the properties characteristic of
a whole cell.
Temporal Simplifications
There is generally a vast difference in the relaxation times
or time constants that characterize the dynamic response of
a system. Early on, biologists distinguished three levels of
activity in time: evolutionary, developmental, and
biochemical
[4]
. With the refinement of instrumentation,
a fourth level was added: biomolecular. The time constants
for evolutionary change in a given type of organism would
be measured in terms of generations. Developmental
change takes place within an organism's lifetime.
Biochemical change has a relaxation time typically in the
range of seconds to minutes, whereas biomolecular tran-
sitions can occur within millisecond and faster
time
constants.
This temporal separation of phenomena can simplify
greatly the analysis of complex systems. The variables in
such a system that respond much faster than the phenomena
of interest can be assumed to be at their steady-state values;
those variables responding more slowly than the
phenomena of interest can be assumed to be constants or
slowly varying parameters. For instance, if one is interested
in the temporal behavior of a simple biochemical pathway
responding to changes in the concentration of a specific
ligand, then the molecular transitions of an enzyme mole-
cule and the binding of ligand will typically occur much
more rapidly than the time course of the overall reaction.
Under these conditions the two processes could be assumed
to be in steady state with respect to the rate of the overall
reaction. At the other end of the temporal spectrum,
changes in the total concentration of an enzyme that might
occur during the course of development can be ignored,
because such changes are so slight on the timescale of the
overall reaction. Simplifications such as these have a long
history of use in the physical sciences and are probably best
illustrated quantitatively by the circuit theory approxima-
tion to time-varying electromagnetic phenomena
[5]
.
Although the separation of timescales greatly simplifies
the analysis of complex systems, the phenomena operating
at the different scales remain integrated through constraints
that are implicit in the parameters that characterize the
system at any particular scale. For example, it is well
known that the parameters that characterize the rational
functions of steady-state enzyme kinetics on the bio-
chemical timescale (Michaelis constants, maximal veloci-
ties, inhibition constants, Haldane relationships, etc.) are
functions of the parameters that characterize the power-law
functions of the underlying chemical kinetics on the
biomolecular time scale (rate constants, kinetic orders,
detailed balance, conservation constraints, etc.). Indeed, the
systems approach is concerned specifically with under-
standing relationships that span interconnected scales by
revealing the constraints between them and exploiting these
constraints to simplify the analysis of the integrated system.
Feasibility and the Limitation of Complexity
While the requirement of wholeness urges us to consider
more and more interactions in describing a given system,
time, resources, insight, and the precision of instruments
place limits on the number of interactions that can be
considered. The amount of detailed consideration that can
be given to the environment on the one hand, and to the
subsystems on the other, is limited. Fortunately, there are
at least three different types of simplification
spatial,
e
temporal, and functional
that arise naturally to limit the
complexity of systems and make their analysis feasible.
e
Spatial Simplifications
Spatial or topological constraints are abundant in natural
systems. For example, the relative specificity of enzymes
for their reactants tends to limit the possible interactions
among the molecules of a biochemical system. Thus, the
enzymes of biochemical systems are natural subsystems at
this level of organization. The formation of multi-enzyme
complexes among the consecutive enzymes of a metabolic
pathway, which results in 'channeling' of the intermediates,
is another mechanism for spatially restricting the interac-
tion among molecules. This leads to subsystems at a higher
level of cellular organization. Channeling may be consid-
ered one of the simplest examples of compartmentalization
[3]
, which is common among eukaryotic organisms. The
mitochondria in such organisms provide one of the best-
known illustrations of a spatially separate compartment in
which certain metabolites have only limited access to the
remainder of the cytoplasm. Cellular compartments form
subsystems on a still higher level of organization. Such
compartmentalization often permits these systems to be
described by ordinary differential equations, whereas large
distributed systems would require partial differential
equations for their description.
