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

Abstract

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. The advantages of RB modelling over ODEs have been presented and discussed in numerous reviews. In this study, we conduct a direct comparison of the time courses of a molecular system founded on the same reaction network but encoded in the two frameworks. To make such a comparison, a set of reactions that underlie an ODE model was manually encoded in the Kappa language, one of the RB implementations. A comparison of the models was performed at the level of model specification and results were acquired through model simulations. Conforming to previous reports, we confirm 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. 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. As in previous reports on other molecular systems, we find that, also in the case of the DARPP-32 reaction network, the RB representation offers a more expressive and flexible syntax that facilitates access to fine details of the model, facilitating model reuse. In parallel with these analyses, this manuscript reports a refactored model of the DARPP-32 interaction network that can serve as a canvas for the development of a more complex interaction network to study this important molecular system.