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. 2022 Dec 15:10:e14516.
doi: 10.7717/peerj.14516. eCollection 2022.

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

Affiliations

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

Emilia M Wysocka et al. PeerJ. .

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 dynamics, acquired through model simulations. In line with previous reports, we confirm that the Kappa model recapitulates the general dynamics of its ODE counterpart with minor differences. These occur when molecules have multiple sites binding the same interactor. Furthermore, activation of these molecules in the RB model is slower than in the ODE one. As reported for other molecular systems, we find that, also for the DARPP-32 reaction network, the RB representation offers a more expressive and flexible syntax that facilitates access to fine details of the model, easing model reuse. In parallel with these analyses, we report a refactored model of the DARPP-32 interaction network that can serve as a canvas for the development of more complex dynamic models to study this important molecular system.

Keywords: Addiction; Context and reward-related learning; DARPP-32; Dopamine-dependent synaptic plasticity; Kappa language; Modeling molecular dynamics; Molecular interactions; Molecular signalling; Ordinary differential equations; Rule-based modelling.

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Conflict of interest statement

Matthew Page and James Snowden are employees of UCB Celltech.

Figures

Figure 1
Figure 1. Approach to comparison of ODE and RB modelling frameworks.
Figure 2
Figure 2. Reaction diagrams showing (A) the DARPP-32 network included in the ODE model by Fernandez et al. (2006) Nodes: DARPP-32 (cyan), second messengers (magenta), kinases/phosphatases (white).
Edges: inhibition reactions (blue), activation reactions (red); (B) the observables with the greatest divergence between trajectories of the ODE and RB models. These observables are connected in a chain of mutually dependent activation reactions triggered by the influx of calcium ions (Ca2+).
Figure 3
Figure 3. Time-courses of the ODE model for DARPP-32 isoforms triggered by a pulse of cAMP followed by a train of Ca2+ spikes obtained with (A) a deterministic solver, and (B) a stochastic simulation.
Trajectories of the stochastic simulation were obtained from calculating mean value (line) and standard deviation (shade) based on 40 simulations. (C) RB model (stochastic simulation). Variable isoforms of DARPP-32: ���D”—unphosphorylated; “D137”—Ser137 phosphorylated; “D75”—Thr75 phosphorylated; “D34”—Thr34 phosphorylated.
Figure 4
Figure 4. (A-O) Superimposed time courses of stochastic variants of the ODE and RB models in the baseline condition.
Note that the scales on the y-axis are different to closely compare the traces of the observables. Trace colour: ODE (red), RB (black).
Figure 5
Figure 5. (A-M) Traces of 13 pairs of molecular species containing Ca2+, selected to match the ODE model.
The largest disparity lies in the “PP2BinactiveCa2” variable—summation result of six entities representing an inactive form of PP2B in the RB model.
Figure 6
Figure 6. Comparison of the constitutive Ser137 mutation induced in (A) ODE model in deterministic setting; (B) RB model in stochastic setting; and the Ser137Ala mutation in (C) ODE model in deterministic setting; (D) RB model in stochastic setting; The same interference performed on rate constants of the two models caused similar dynamics.

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