Polarized molecular activities play important roles in guiding the cell toward persistent and directional migration. In this study, the polarized distributions of the activities of phosphatidylinositol 3-kinase (PI3K) and the Rac1 small GTPase were monitored using chimeric fluorescent proteins (FPs) in cells constrained on micro-patterned strips, with one end connecting to a neighboring cell (junction end) and the other end free of cell-cell contact (free end). The recorded spatiotemporal dynamics of the fluorescent intensity from different cells was scaled into a uniform coordinate system and applied to compute the molecular activity landscapes in space and time. The results revealed different polarization patterns of PI3K and Rac1 activity induced by the growth factor stimulation. The maximal intensity of different FPs, and the edge position and velocity at the free end were further quantified to analyze their correlation and decipher the underlying signaling sequence. The results suggest that the initiation of the edge extension occurred before the activation of PI3K, which led to a stable extension of the free end followed by the Rac1 activation. Therefore, the results support a concerted coordination of sequential signaling events and edge dynamics, underscoring the important roles played by PI3K activity at the free end in regulating the stable lamellipodia extension and cell migration. Meanwhile, the quantification methods and accompanying software developed can provide a convenient and powerful computational analysis platform for the study of spatiotemporal molecular distribution and hierarchy in live cells based on fluorescence images.