Biology Reference
In-Depth Information
Natural system:
Abstract set of states
M
= {
p
}
Synthetic model:
s
(
M
) =
j
a
(
O
j
)
Analytic model:
a
(
M
) =
∏
i
i
[
M
]
On the basis of the material presented here, Rosen defines a natural system as
a 'simple system' or mechanism if all of its models are simulable. In Chapters 7
and 8 of his topic
Life Itself
, he then argues that 'there exist modes of
organisation
whose material realizations cannot be simple'. ( organisms). While simulation
is what machines do, more often than not a biological system is a 'complex
system'. In Chapter 8, Rosen summarises his argument: If a natural system M is
a mechanism, then the category of all analytical and synthetic models of M has a
unique largest model
max
. This model captures all that is knowable about M.If
a natural system is a mechanism, then there is a necessarily finite set of minimal
models
min
and the maximal model
max
is equivalent to the direct sum of the
minimal ones
=
i
max
min
which means the maximal model is a synthetic model.
The uncertainty principle of systems biology states that as the complexity
of a system increases, our ability to make precise and yet general statements
diminishes. If we wish to understand the general principles of cell functions
(say cell differentiation), independent of cell type or organism, then we need
to generalise rate equations or automata and move a level up in abstraction.
The relationship between state-variables and observable is also the subject of
the recent book of the Netsruev group (Netsruev, 2003). The underlying idea
of Rosen's discussion of observables (Rosen, 1991), as well as more recent
texts on smooth manifolds (Netsruev, 2003), is to show whether it is possible to
replace a set of states, M, for a system with a set of real-valued mappings from
M to
(observables) on M. In (Netsruev, 2003) the Netsruev group discusses
the possibility that every statement about M can be turned into a statement
about the set of observables. Applied to modelling of dynamic systems, this
work is closely related to recent developments in the setting of hybrid systems
(Haghverdi et al., 2003; Tabuada et al., 2004; Tabuada & Pappas, 2005). Progress
in this area is going to be important for dynamic pathway modelling in systems
biology.
