Signal transduction through MAPK-like cascades: ligand activates receptor, which sequentially activates kinases via phosphorylation. Each step amplifies and filters the signal.
MAPK cascade model:
Each layer: dX*_i/dt = k₁·S·X_{i-1}·(1−X*_i)^n/(K_m^n+(1−X*_i)^n) − kp·X*_i
where X*_i is the phosphorylated fraction, n is Hill cooperativity.
Key features: Signal amplification (each layer boosts gain), ultrasensitivity (Hill n>1), adaptation, and noise filtering. Real MAPK cascades (Raf→MEK→ERK) achieve ~1000-fold amplification with switch-like responses controlling cell growth and differentiation.