Modularisation of published and novel models toward a complex KIR2DL4 pathway in pbNK cell

KIR2DL4 is an interesting receptor expressed on the peripheral blood natural killer (pbNK) cell as it can be either activating or inhibitory depending on the amino acid residues in the domain. This model uses mathematical modelling to investigate the downstream effects of natural killer cells’ activation (KIR2DL4) receptor after stimulation by key ligand (HLA-G) on pbNK cells. Development of this large pathway is based on a comprehensive qualitative description of pbNKs’ intracellular signalling pathways leading to chemokine and cytotoxin secretion, obtained from the KEGG database (https://www.genome.jp/pathway/hsa04650). From this qualitative description we built a quantitative model for the pathway, reusing existing curated models where possible and implementing new models as needed. This model employs a composite approach for generating modular models. The approach allows for the construction of large-scale complex model by combining component of sub-models that can be modified individually. This large pathway consists of two published sub-models; the Ca²⁺ model and the NFAT model, and a newly built FCεRIγ sub-model. The full pathway was fitted to published dataset and fitted well to one of two secreted cytokines. The model can be used to predict the production of IFNγ and TNFα cytokines.•

Development of pathway and mathematical model

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Reusing existing curated models and implementing new models

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Model optimization and analysis

A system of recurrent neural networks for modularising, parameterising and dynamic analysis of cell signalling networks

In this paper, we show how to extend our previously proposed novel continuous time Recurrent Neural Networks (RNN) approach that retains the advantage of continuous dynamics offered by Ordinary Differential Equations (ODE) while enabling parameter estimation through adaptation, to larger signalling networks using a modular approach. Specifically, the signalling network is decomposed into several sub-models based on important temporal events in the network. Each sub-model is represented by the proposed RNN and trained using data generated from the corresponding ODE model. Trained sub-models are assembled into a whole system RNN which is then subjected to systems dynamics and sensitivity analyses. The concept is illustrated by application to G1/S transition in cell cycle using Iwamoto et al. (2008) ODE model. We decomposed the G1/S network into 3 sub-models: (i) E2F transcription factor release; (ii) E2F and CycE positive feedback loop for elevating cyclin levels; and (iii) E2F and CycA negative feedback to degrade E2F. The trained sub-models accurately represented system dynamics and parameters were in good agreement with the ODE model. The whole system RNN however revealed couple of parameters contributing to compounding errors due to feedback and required refinement to sub-model 2. These related to the reversible reaction between CycE/CDK2 and p27, its inhibitor. The revised whole system RNN model very accurately matched dynamics of the ODE system. Local sensitivity analysis of the whole system model further revealed the most dominant influence of the above two parameters in perturbing G1/S transition, giving support to a recent hypothesis that the release of inhibitor p27 from Cyc/CDK complex triggers cell cycle stage transition. To make the model useful in a practical setting, we modified each RNN sub-model with a time relay switch to facilitate larger interval input data (≈20min) (original model used data for 30s or less) and retrained them that produced parameters and protein concentrations similar to the original RNN system. Results thus demonstrated the reliability of the proposed RNN method for modelling relatively large networks by modularisation for practical settings. Advantages of the method are its ability to represent accurate continuous system dynamics and ease of: parameter estimation through training with data from a practical setting, model analysis (40% faster than ODE), fine tuning parameters when more data are available, sub-model extension when new elements and/or interactions come to light and model expansion with addition of sub-models.