Each nanorobot is a run-and-tumble microswimmer, the same navigation strategy real chemotactic bacteria use — it cannot sense the gradient's direction directly, only how the local chemoattractant concentration C changes while it swims:
C(r) = C0 / (1 + (r / λ)^2) r = distance to tumor
dC/dt sampled via a slow running average (adaptation)
tumble rate: k = k0 · clamp(1 − S·dC/dt·scale, 0.15, 4)
P(tumble this step) = 1 − exp(−k·dt)
When concentration is rising (swimming up-gradient), the tumble rate drops and the run extends; when it is falling, tumbling becomes more frequent and a new random heading is picked. Averaged over many robots this asymmetric random walk produces a net drift toward the tumor even though no single robot ever "steers" — exactly the biased-random-walk model of bacterial chemotaxis (Berg & Purcell).
- Gradient steepness — sets λ, the range over which the tumor's secreted signal is detectable. A shallow (small λ) field only recruits nearby robots; a far-reaching one recruits the whole vessel.
- Chemotactic sensitivity S — how strongly the sensed derivative biases the tumble rate. At S = 0 the walk is unbiased (pure diffusion, no homing).
- Thermal / flow noise — rotational Brownian diffusion of the swim direction plus stray blood-flow turbulence, degrading how straight each run is.
- Docking — a robot that reaches the tumor surface (capture radius) stops, its pH-sensitive shell dissolves in the tumor's acidic microenvironment, and it releases its drug payload (the flash burst).
Real-world relevance: this is the same class of model researchers use for autonomous nanorobots that navigate the bloodstream toward a tumor using chemical rather than externally-applied fields (no magnet or ultrasound transmitter required), trading external control for a slower, statistically-driven homing rate.