Living cells compute with chemistry, not silicon: a genetic AND/OR/XOR gate reads two input molecule concentrations at a central promoter and fires an output protein only when the combined signal crosses a Hill-function threshold:
s(t) = A(t) ⊕ B(t) (⊕ = AND / OR / XOR combine rule)
out = 1 if s(t) > threshold, else 0
[A],[B] diffuse toward sensor at rate D·∇²C
- Input A / B concentration — source strength of each diffusing chemical species (blue and red molecules).
- Reaction threshold — the combined-signal level the central sensor needs to flip the genetic output on.
- Diffusion rate — how fast molecules random-walk from their inlets toward the sensor at the cell's centre.
- AND / OR / XOR — which Boolean combination rule the synthetic promoter implements.
This mirrors real synthetic-biology "genetic circuits" used to make engineered bacteria sense two inputs (e.g. a toxin and a pH signal) and only activate a therapeutic or reporter gene when both conditions are met.