Distributional invariance and proportional scaling in axonal conduction

Conduction velocity along axons reflects geometric and biophysical influences whose joint statistical organization remains largely uncharacterized. Using high-resolution time-of-arrival measurements along hundreds of identified axonal branches in vitro, we quantified how propagation speed changes along trajectories. The ratio between terminal and initial velocities, ρ=v_end/v_start, follows a right-skewed distribution whose shape remains invariant across branch lengths, positions within neurons, and hierarchical aggregation levels. Local conduction profiles reveal a predominantly progressive deceleration along branches. These observations indicate a simple and robust statistical organization of slowdown, suggesting that proportional modulation of propagation speed is a consistent feature of axonal signaling in structurally variable substrates.