Towards abstraction of computational modelling of mammalian cell cycle: Model reduction pipeline incorporating multi-level hybrid petri nets.

Cell cycle is a large biochemical network and it is crucial to simplify it to gain a clearer understanding and insights into the cell cycle. This is also true for other biochemical networks. In this study, we present a model abstraction scheme/pipeline to create a minimal abstract model of the whole mammalian cell cycle system from a large Ordinary Differential Equation model of cell cycle we published previously (Abroudi et al., 2017). The abstract model is developed in a way that it captures the main characteristics (dynamics of key controllers), responses (G1-S and G2-M transitions and DNA damage) and the signalling subsystems (Growth Factor, G1-S and G2-M checkpoints, and DNA damage) of the original model (benchmark). Further, our model exploits: (i) separation of time scales (slow and fast reactions), (ii) separation of levels of complexity (high-level and low-level interactions), (iii) cell-cycle stages (temporality), (iv) functional subsystems (as mentioned above), and (v) represents the whole cell cycle - within a Multi-Level Hybrid Petri Net (MLHPN) framework. Although hybrid Petri Nets is not new, the abstraction of interactions and timing we introduced here is new to cell cycle and Petri Nets. Importantly, our models builds on the significant elements, representing the core cell cycle system, found through a novel Global Sensitivity Analysis on the benchmark model, using Self Organising Maps and Correlation Analysis that we introduced in (Abroudi et al., 2017). Taken the two aspects together, our study proposes a 2-stage model reduction pipeline for large systems and the main focus of this paper is on stage 2, Petri Net model, put in the context of the pipeline. With the MLHPN model, the benchmark model with 61 continuous variables (ODEs) and 148 parameters were reduced to 14 variables (4 continuous (Cyc_Cdks - the main controllers of cell cycle) and 10 discrete (regulators of Cyc_Cdks)) and 31 parameters. Additional 9 discrete elements represented the temporal progression of cell cycle. Systems dynamics simulation results of the MLHPN model were in close agreement with the benchmark model with respect to the crucial metrics selected for comparison: order and pattern of Cyc_Cdk activation, timing of G1-S and G2-M transitions with or without DNA damage, efficiency of the two cell cycle checkpoints in arresting damaged cells and passing healthy cells, and response to two types of global parameter perturbations. The results show that the MLHPN provides a close approximation to the comprehensive benchmark model in robustly representing systems dynamics and emergent properties while presenting the core cell cycle controller in an intuitive, transparent and subsystems format.

A comprehensive complex systems approach to the study and analysis of mammalian cell cycle control system in the presence of DNA damage stress.

Not many models of mammalian cell cycle system exist due to its complexity. Some models are too complex and hard to understand, while some others are too simple and not comprehensive enough. Moreover, some essential aspects, such as the response of G1-S and G2-M checkpoints to DNA damage as well as the growth factor signalling, have not been investigated from a systems point of view in current mammalian cell cycle models. To address these issues, we bring a holistic perspective to cell cycle by mathematically modelling it as a complex system consisting of important sub-systems that interact with each other. This retains the functionality of the system and provides a clearer interpretation to the processes within it while reducing the complexity in comprehending these processes. To achieve this, we first update a published ODE mathematical model of cell cycle with current knowledge. Then the part of the mathematical model relevant to each sub-system is shown separately in conjunction with a diagram of the sub-system as part of this representation. The model sub-systems are Growth Factor, DNA damage, G1-S, and G2-M checkpoint signalling. To further simplify the model and better explore the function of sub-systems, they are further divided into modules. Here we also add important new modules of: chk-related rapid cell cycle arrest, p53 modules expanded to seamlessly integrate with the rapid arrest module, Tyrosine phosphatase modules that activate Cyc_Cdk complexes and play a crucial role in rapid and delay arrest at both G1-S and G2-M, Tyrosine Kinase module that is important for inactivating nuclear transport of CycB_cdk1 through Wee1 to resist M phase entry, Plk1-Related module that is crucial in activating Tyrosine phosphatases and inactivating Tyrosine kinase, and APC-Related module to show steps in CycB degradation. This multi-level systems approach incorporating all known aspects of cell cycle allowed us to (i) study, through dynamic simulation of an ODE model, comprehensive details of cell cycle dynamics under normal and DNA damage conditions revealing the role and value of the added new modules and elements, (ii) assess, through a global sensitivity analysis, the most influential sub-systems, modules and parameters on system response, such as G1-S and G2-M transitions, and (iii) probe deeply into the relationship between DNA damage and cell cycle progression and test the biological evidence that G1-S is relatively inefficient in arresting damaged cells compared to G2-M checkpoint. To perform sensitivity analysis, Self-Organizing Map with Correlation Coefficient Analysis (SOMCCA) is developed which shows that Growth Factor and G1-S Checkpoint sub-systems and 13 parameters in the modules within them are crucial for G1-S and G2-M transitions. To study the relative efficiency of DNA damage checkpoints, a Checkpoint Efficiency Evaluator (CEE) is developed based on perturbation studies and statistical Type II error. Accordingly, cell cycle is about 96% efficient in arresting damaged cells with G2-M checkpoint being more efficient than G1-S. Further, both checkpoint systems are near perfect (98.6%) in passing healthy cells. Thus this study has shown the efficacy of the proposed systems approach to gain a better understanding of different aspects of mammalian cell cycle system separately and as an integrated system that will also be useful in investigating targeted therapy in future cancer treatments.