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MAPK Signal Transduction Cascade
Three-tier kinase cascade (MAPKKK → MAPKK → MAPK). A graded input becomes a switch-like (ultrasensitive) output through zero-order ultrasensitivity and signal amplification.
Input-Output transfer curve
MAPK cascade (Ras → Raf → MEK → ERK) is a canonical three-tier phosphorylation relay. At each level, a kinase is activated by phosphorylation (activation) and deactivated by phosphatase (inactivation). Ultrasensitivity arises when enzymes operate near saturation (zero-order regime, Goldbeter-Koshland 1981): the sigmoidal dose-response sharpens (Hill coefficient n>1). Cascading three tiers multiplies the sigmoidal exponent — a graded Ras signal becomes a near-switch ERK output. This enables the cell to make binary decisions (proliferate vs differentiate). The Hill coefficient n slider lets you tune from graded (n=1) to switch-like (n≫1).