We have been studying two signaling systems that regulate M-phase entry and progression. The first is the Mos- MEK-p42 MAPK cascade, which is an important element in the network that triggers Xenopus oocyte maturation. In oocytes, this cascade is embedded in two positive feedback loops--active p42 MAPK brings about the accumulation and activation of Mos and Raf-l--and this feedback allows the cascade to convert transient, graded stimuli into sustained, switch-like responses. Recently we identified a role for Mos outside of oocyte maturation: Mos is the long-sought-after mitotic activator of p42 MAPK in Xenopus egg extracts. Moreover, the activity of Mos was found to depend upon one or more Cdc2- cyclin B-dependent phosphorylations, a previously unrecognized level of Mos regulation. These findings provide the first evidence of a mitotic role for Mos, and the first evidence that Mos activity is post-translationally regulated. Here we propose: (1) to elucidate the mechanism through which Cdc2-cyclin B stimulates Mos activity. The second system we have been studying is the Cdc2/cyclin B-Wee1-Cdc25-APC network. Like the Mos-MEKp42 MAPK cascade, this network contains a system of interlocking positive feedback loops. The positive feedback loops function as a bistable trigger for mitosis, and together with a slower negative feedback loop that triggers cyclin destruction, function as a reliable biochemical oscillator. Here we propose: (2) To determine whether three "open loop" subcircuits of the Cdc2/cyclin B-Weel-Cdc25-APC network exhibits steeply sigmoidal responses, which recent theoretical work indicates should be important for robust bistability in "closed loop" feedback systems, and (3) To determine whether the bistability of Cdc2 activation is required for sustained cell cycle oscillations. Our overarching goals are to gain new insights into the biochemical circuits that regulate M-phase progression, and to better understand the design principles used by nature in the generation of sophisticated, systems-level biochemical behaviors.