Biology offers many examples of large-scale, complex, concurrent systems: many processes take place in parallel, compete on resources and influence each other's behavior. The scalable modeling of biological systems continues to be a very active field of research. In this paper we introduce a new approach based on Event-B, a state-based formal method with refinement as its central ingredient, allowing us to check for model consistency step-by-step in an automated way. Our approach based on functions leads to an elegant and concise modeling method. We demonstrate this approach by constructing what is, to our knowledge, the largest ever built Event-B model, describing the ErbB signaling pathway, a key evolutionary pathway with a significant role in development and in many types of cancer. The Event-B model for the ErbB pathway describes 1320 molecular reactions through 242 events.