  The ability to represent intracellular biochemical dynamics via deterministic
and stochastic modelling is one of the crucial components to move biological
sciences in the observe-predict-control-design knowledge ladder. Compared to
the engineering or physics problems, dynamical models in quantitative biology
typically dependent on a relatively large number of parameters. Therefore, the
relationship between model parameters and dynamics is often prohibitively
difficult to determine. We developed a method to depict the input-output
relationship for multi-parametric stochastic and deterministic models via
information-theoretic quantification of similarity between model parameters and
modules. Identification of most information-theoretically orthogonal biological
components, provided mathematical language to precisely communicate and
visualise compensation like phenomena such as biological robustness, sloppiness
and statistical non-identifiability. A comprehensive analysis of the
multi-parameter NF-$\kappa$B signalling pathway demonstrates that the
information-theoretic similarity reflects a topological structure of the
network. Examination of the currently available experimental data on this
system reveals the number of identifiable parameters and suggests informative
experimental protocols.
