Mathematical modeling of processive Ras activation by SOS reveals a general mechanism for digital signaling

How cells generate discrete signaling outputs from continuous biochemical reactions is a fundamental question in cell biology. Using a rule-based model of Ras activation, we demonstrate that SOS processivity—the ability of a single membrane-bound SOS molecule to catalyze the activation of many Ras molecules before dissociating—produces quantized Ras activation in confined membrane corrals without requiring bistability or positive feedback. Distinct SOS occupancy states each generate a characteristic RasGTP level, producing multimodal distributions whose peaks are predicted by a minimal activator–target framework. Four dimensionless conditions determine where peaks appear: low activator number, resolvable peak spacing, timescale separation, and unsaturated catalysis. This framework describes any system in which processive enzymes act on confined target pools. Positive feedback modulates peak weights without shifting positions, while eliminating processivity abolishes quantization and collapses distributions to mean-field behavior. These results establish processivity-driven quantization as a general mechanism for discrete signaling in localized enzymatic systems.