Pros and Cons of different ODE modelling frameworks

In Systems Biology, there is no a perfect mathematical modelling framework perfectly fulfilling all the desirable features. Every kind of model shows strengths in some aspects and weakness in others. In the following table we compare different power-law models with other ODE-based models used in biochemical systems.

the legend of the table is included in the table. Here, green represents an excellent performance of the modelling framework analysed for the property studied. Light green means that these models are quite good, while yellow represents an intermediate acceptable performance. Orange means that this kind of models is not good enough (at the state-of-the art in experimental and computational techniques) with respect to the property considered; finally, with red the referred models present serious deficiencies in the cited aspect. In this comparison we assume that ODE models are valid for the biochemical systems considered (biochemical systems with stochastic events not considered). The properties analysed in this table refer to:

• Biophysical Realism: the model is able to precisely reproduce the biophysical reality of the system.

• Useful for any biochemical system: supposed valid the modeling of the system with ordinary differential equations, these models can be used to represent any kind of biochemical system.

• Interpretability: the parameters describing the model are easy to be interpreted

• Encoding of non-linearity: the equations are able to (separately) encode high non-linearity in the behaviour of the system (saturation, inhibition, cooperativity...).

• On-line data availability: available online databases offer estimations for the values of the model parameters.

• Model calibration techniques: there are fast, accurate, well-tested algorithms available for parameter estimation

• Use of quantitative data: the parameter estimation requires a suitable reduced amount of quantitative data to obtain satisfactory results

• Scalability: the mathematical models scale well in highly dimensional biochemical networks.

• Computability: there are available fast algorithms for simulation, steady-state analysis, stability analysis, bifurcation analysis...

When modelling, the right choice is always to choose the framework that fit better with the case analysed: type of biochemical system investigated, available experimental data, accessible, known computational methods, etc. Two examples to illustrate this idea.