Signal transduction pathways control cellular responses to stimuli, but it is unclear how molecular information is processed as a network. We constructed a systems model of 7980 intracellular signaling events that directly links measurements to 1440 response outputs associated with apoptosis. The model accurately predicted multiple time-dependent apoptotic responses induced by a combination of the death-inducing cytokine tumor necrosis factor with the prosurvival factors epidermal growth factor and insulin. By capturing the role of unsuspected autocrine circuits activated by transforming growth factor-alpha and interleukin-1alpha, the model revealed new molecular mechanisms connecting signaling to apoptosis. The model derived two groupings of intracellular signals that constitute fundamental dimensions (molecular "basis axes") within the apoptotic signaling network. Projection along these axes captures the entire measured apoptotic network, suggesting that cell survival is determined by signaling through this canonical basis set.