Biology Reference
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order of models, there are maps between models, and we are thus in a posi-
tion to establish a modelling relation between models. In other words, there
is a means to discuss the modelling process itself! The totality of analyt-
ical models can be identified with the totality of equivalence relations on
M, as well as the totality of sets of observables, the set of all subsets of
HM
.
4. SYNTHETIC MODELLING
The key to analytical modelling was that we do not make any assumptions about
the abstract set of pure states of the natural system, represented by M. This is
clearly not what most projects in systems biology do. For most cases we assume,
construct or synthesise M but subsequently forget that this is no more than a
hypothesis. The traditional way of modelling is discussed in this section before
we compare the two approaches.
In synthetic modelling, we synthesise M from subsets O
j
in terms of the
disjoint union
j
O
j
=
M
(3)
where the equality is by construction. The process is shown in Fig. 6.
In the setting of category theory, we obtain a synthetic object as the coproduct
of the family of objects O
j
=
j
C
O
j
for which there exists a family of injections
j
O
j
→
C
Φ
1
j
M
O
j
Φ
1
j
[
O
j
]
q
j
O
j
×
Φ
2
j
Φ
2
j
[
O
j
]
Synthesis of
M
Figure 6
The synthesis of a natural system as a direct sum of subspaces.
