Dealing with indetermination in biochemical networks

A main aspect in computational modelling of biological sys- tems is the determination of model structure and model pa- rameters. Due to economical and technical reasons, only part of these details are well characterized, while the rest are unknown. To deal with this difficulty, many reverse en- gineering and parameter estimation methods have been pro- posed in the literature, however these methods often need an amount of experimental data not always available. In this paper we propose an alternative approach, which overcomes model indetermination solving an Optimization Problem (OP) with an objective function that, similarly to Flux Balance Analysis, is derived from an empirical bio- logical knowledge and does not require large amounts of data. The system behaviour is described by a set of Or- dinary Differential Equations (ODE). Model indetermina- tion is resolved selecting time-varying coefficients that max- imize/minimize the objective function at each ODE inte- gration step. Moreover, to facilitate the modelling phase we provide a graphical formalism, based on Petri Nets, which can be used to derive the corresponding ODEs and OP. Fi- nally, the approach is illustrated on a case study focused on cancer metabolism.