Comparison of rule- and ordinary differential equation-based dynamic model of DARPP-32 signalling network

Dynamic modelling has considerably improved our understanding of complex molecular mechanisms. Ordinary differential equations (ODEs) are the most detailed and popular approach to modelling the dynamics of molecular systems. However, their application in signalling networks, characterised by multi-state molecular complexes, can be prohibitive. Contemporary modelling methods, such as rule-based (RB) modelling, have addressed these issues. Although the advantages of RB modelling over ODEs have been presented and discussed in numerous reviews, no direct comparison of the time courses of a molecular system encoded in the two frameworks has been made before. To make such a comparison, a set of reactions that underlie an ODE model by Fernandez et al. [1] was manually encoded in the Kappa language, one of the RB frameworks. A comparison of the models was performed at the level of model specification and results were acquired through model simulations. We found that the Kappa model recapitulated the general dynamics of its ODE counterpart with minor differences. These differences occur whenever molecules have multiple sites binding the same interactor. The notation of such rules requires a complete listing of all possible binding configurations. Furthermore, activation of these molecules in the RB model is slower than in the ODE one but can be corrected by revision of the rate constants used in the relevant rules. We conclude that the RB representation offers a more expressive and flexible syntax that eases access to fine-grain details of the model, facilitating model reuse. In parallel with these analyses, this manuscript reports a refactored model of a DARPP-32 interaction network that can serve as a canvas for the development of a more complex interaction network to study this particular molecular system. ### Competing Interest Statement The authors have declared no competing interest.