Using activity time windows and logical representation to reduce the complexity of biological network models: G1/S checkpoint pathway with DNA damage

Biological systems are difficult to understand complex systems. Scientists continue to create models to simulate biological systems but these models are complex too; for this reason, new reduction methods to simplify complex biological models into simpler ones are increasingly needed. In this paper, we present a way of reducing complex quantitative (continuous) models into logical models based on time windows of system activity and logical (Boolean) models. Time windows were used to define slow and fast activity areas. We use the proposed approach to reduce a continuous ODE model into a logical model describing the G1/S checkpoint with and without DNA damage as a case study. We show that the temporal unfolding of this signalling system can be broken down into three time windows where only two display high level of activity and the other shows little or no activity. The two active windows represent a cell committing to cell cycle and making the G1/S transition, respectively, the two most important high level functions of cell cycle in the G1 phase. Therefore, we developed two models to represent these time windows to reduce time complexity and used Boolean approach to reduce interaction complexity in the ODE model in the respective time windows. The developed reduced models correctly produced the commitment to cell cycle and G1/S transfer through the expected behavior of signalling molecules involved in these processes. As most biological models have a large number of fast reactions and a relatively smaller number of slow reactions, we believe that the proposed approach could be suitable for representing many, if not all biological signalling networks. The approach presented in this study greatly helps in simplifying complex continuous models (ODE models) into simpler models. Moreover, it will also assist scientists build models concentrating on understanding and representing system behavior rather than setting values for a large number of kinetic parameters.