Biology Reference
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Indeed, this was involved in the origin of one of the more distinctive laws of
systems biology, i.e. the summation theorem as discovered by Jim Burns and
the late Henrik Kacser (Kacser, personal communication).
The emergence of properties from nonlinear systems depends on the values
of the parameters. The consequence has long been overlooked by theoretical
biologists and biologically inspired physicists. The latter supposed that it was
good enough to show that some, phenomenological model of the biological
system could produce the emergent property of interest. In this manner, Turing
modelled developmental biology (in a way that is now known to be wrong, even
though parts of the self-organization mechanisms may still act), and Nicolis
and Prigogine modelled glycolytic oscillations in yeast. They did find that in
such a phenomenological model (with oversimplified and in fact unrealistic
rate equations and rather arbitrarily chosen parameter values) the emergent
phenomena occurred. For different rate equations or different parameter values,
the emergent property did not emerge from the calculations. Hence, to verify
whether a proposed systems biology mechanism is indeed responsible for an
observed emergent property, the model must be precise in terms of its structure
and parameter values. Until recently the handicap was of course that such precise
parameter values were not available. (Consequently, the above should not be
taken to question the importance of this earlier work in biological physics and
theoretical biology.)
With the advance of experimental techniques and thanks to the effort of many
scientists, it is now becoming possible to make the required precise models.
We refer to these precise models as 'computer replicas' of the real network
of interactions or 'silicon cells' (Westerhoff, 2001). In a sense, the silicon
cell strategy is entirely reductionist, yet at the same time upwardly compatible
with holism (Snoep & Westerhoff, 2005). All the molecules known to act in a
network are represented by a computer replica. At present this most often takes
the form of a rate equation and a reaction equation for each enzyme. The rate
equations, i.e. the reaction equations as well as the values of the parameters
therein, should have been established experimentally (here we recognize the
irreducibility discussed above) and are all inserted into the computer replica
of the network. All the computer then does is let the replica behave through
the integration of the equations in time. Emergent properties, if any, should
then show up in the computer calculations ( modulo the statistical error in the
measurements).
In this manner, ordinary and partial differential equations may be used to
calculate life, i.e. to produce a silicon cell that will display the main properties
of the real cell, inclusive of the emergent properties. The implications are
unprecedented for the sciences: If there is any place in the natural world where
qualitatively new properties emerge, this is life.
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