Modeling Response of Biological Signal Pathways Using a Hybrid Boolean Framework

Mathematical models in systems biology are often constructed by either Ordinary Differential Equation (ODE) modeling or logical (Boolean) modeling. We develop a Hybrid Boolean Model (ODE+Boolean) for biological signal pathways with postulated epigenomic feedback. The basic idea in this model is to combine continuous dynamical systems (an ODE model for already well-known parts of the network) with a discrete transition system (Boolean, for postulated but largely unknown components). We use the existing or well-known ODE model to “trigger” signal pathways represented by a Boolean model. This framework is easier to validate than a complete ODE model for large and complex signal pathways, for example to find unknown pathways to match the response to experimental data. The advantage of using a Boolean model for the unknown parts of the network is that relatively few parameters are needed. Thus, the framework avoids over-fitting, covers a broad range of pathways and easily represents various experimental conditions. The overall goal of the hybrid model is to predict the behavior of biological signal pathways, thus helping to understand unknown parts of the pathway between experimental results and qualitative/quantitative results. Extensions are discussed, and numerical examples in biological systems and one engineering example are provided.