reconciliation of the underlying hypothesis with experimental data.
In the context of systems biology, this implies, in most of the cases,
the necessity of identifying unknown kinetic parameters by data
fitting. In this concern, Gutenkunst [3] and Gutenkunst et al.
[4–6] suggest that dynamic systems biology models are universally
sloppy and, thus, parameters cannot be uniquely estimated.
Karlsson et al. [7], Anguelova et al. [8], Raue et al. [9], Oana
et al. [10] however, have shown how models regarded as sloppy are
structurally identifiable: it means that, in principle, parameters can
be given unique values. In the case of structural identifiability, it is
only a matter of the experimental constraints and noise that the
quality of the parameter estimates may be limited. In this sense, can
be analyzed how sloppiness is affected by the experimental setup
and experimental noise and can be illustrated, with a number of
examples related to biochemical networks, how sloppy models are
indeed practically identifiable.
Results indicate that sloppiness does not mean that parameters
cannot be estimated and a complete identifiability analysis provides
the tools to estimate ranges of parameters which are coherent with
experimental data and can then be used to assess quality of
predictions.
The notion of identifiability of systems is fundamentally a
problem of uniqueness of solutions for specific attributes of certain
classes of mathematical models. The identifiability problem usually
has meaning in the context of unknown parameters of the model. It
is clearly a critical aspect of the modelling process, especially when
the parameters are analogs of physical attributes of interest and the
model is needed to quantify them.
A parameterization of a subclass of dynamic systems will be
called identifiable if, for any finite but sufficiently long time series of
observed input–output trajectories, there exists a unique element in
the subclass of systems which represents those observations.2 Materials
2.1 Forward Model
Formulation
In systems biology the forward model, in general, is represented
from an ensemble of chemical reactions, see, for instance, Dila ̃o and
Muraro [11] or Shapiro et al. [12]. Then we may write:νi 1 A 1 þþνimAm!ri
μi 1 A 1 þþμimAm ð 1 Þwherei¼1,...,n. TheAj, forj¼1,...,m, represent, as for
example, chemical substances. The constantsνijandμijare the
stoichiometric coefficients, in general, non-negative integers, and
the constantsriare the rate constants. If νij¼ μij > 0, the
corresponding substance Aj is a catalyst, while ifμij > νij>
0,Ajis an autocatalyst.Inverse Problems in Systems Biology 71