and the Jacobian is referred to as the Design Matrix for the linear-
ized approximation of the full model [20].
Sloppy models are characterized by a logarithmic hierarchy of
Fisher Information Matrix eigenvalues while unidentifiable models
have in general small eigenvalues. Even though sloppiness and
parameter identifiability are closely related, they should be consid-
ered as two distinct concepts [21]: sloppy models may be both
identifiable and not identifiable and the same appears for not sloppy
models.3 Methods
Here we present an experiment based on a three-step approach:
identifiability, sloppiness, and inverse problems. The aim of this
experiment is to have the elements to analyze a biology system
and to know if what we are analyzing is complete. If so, then we
are able to retrieve the main elements of the system.3.1 The Forward
Model
We have selected a simpler case of mitotic oscillator analyzed by
Tyson [22], but other models could be analyzed using the same
approach.
Tyson states that:
l The proteins cdc2 and cyclin form a heterodimer (maturation
promoting factor) that controls the major events of the cell cycle.
l A mathematical model for the interactions of cdc2 and cyclin is
constructed.
l Simulation and analysis of the model show that the control
system can operate in three modes: as a steady state with high
maturation promoting factor (MPF) activity, as a spontaneous
oscillator, or as an excitable switch.
l Solutions depend on the values assumed by the ten parameters in
the model.
l Nothing is known experimentally about appropriate values for
these parameters.
l The focus is on two parameters: k4, the rate constant describing
the autocatalytic activation of MPF by dephosphorylation of the
cdc2 subunit, and
l k6, the rate constant describing breakdown of the active cdc2-
cyclin complex.Inverse Problems in Systems Biology 77