ErbB tyrosine kinase receptors mediate mitogenic signal cascade by binding a variety of ligands and recruiting the different cassettes of adaptor proteins. In the present study, we examined heregulin (HRG)-induced signal transduction of ErbB4 receptor and found that the phosphatidylinositol 3'-kinase (PI3K)-Akt pathway negatively regulated the extracellular signal-regulated kinase (ERK) cascade by phosphorylating Raf-1 on Ser(259). As the time-course kinetics of Akt and ERK activities seemed to be transient and complex, we constructed a mathematical simulation model for HRG-induced ErbB4 receptor signalling to explain the dynamics of the regulation mechanism in this signal transduction cascade. The model reflected well the experimental results observed in HRG-induced ErbB4 cells and in other modes of growth hormone-induced cell signalling that involve Raf-Akt cross-talk. The model suggested that HRG signalling is regulated by protein phosphatase 2A as well as Raf-Akt cross-talk, and protein phosphatase 2A modulates the kinase activity in both the PI3K-Akt and MAPK (mitogen-activated protein kinase) pathways.