The present invention relates to methods based on the interactions of thrombin as a biological regulator. More specifically, the invention relates to the interactions of thrombin with regard to Notch signaling, Jagged1, PAR1, and cellular effects mediated thereby. The invention relates to the discovery that thrombin cleaves Jagged1 to produce non-membrane soluble Jagged1 (sJ1). The soluble Jagged1 protein can affect Notch signaling and, among other things, mediate the release of FGF-1 and/or IL-1α from a cell. The invention further relates to the role(s) of thrombin and signaling via Notch proteins and the effect on thrombosis, angiogenesis, and/or differentiation, among other processes. Moreover, the invention relates to discovery that thrombin, sJ1, and TRAP mediate, inter alia, rapid non-classical release of FGF-1, and proteins associated therewith (e.g., p40 Syn1 and S100A13, among others), and the effect growth and proliferation of a stem cell without loss of differentiation potential. Thus, the present invention relates to methods of clonally expanding a pluripotent stem cell while preserving the differentiation potential of the cell, a process termed “stamatogenesis.”