Axonal delay dispersion decides whether a neuron detects an event or a sequence, and predicts cortical column diameter

Abstract: Cortical neurons fire sparsely -- often fewer than one spike per sensory window -- making rate coding insufficient and temporal coding a necessity. That conduction delays convert firing order into synchrony is long established. What governs which class of temporal feature a neuron detects -- one volley of coincident input, or two in a particular order -- has not been examined. We propose a delay-signature framework in which the axonal conduction delays converging on a dendritic branch constitute a physical key: only input sequences whose spike-time differences the delays compensate arrive synchronously, and coincidence detection, via calcium plateau thresholds, converts that synchrony into an all-or-none output. In simulations of an integrator-neuron model we report three results. First, a single physical scalar -- the dispersion of the delay set -- moves a population from event detection to order-selective sequence detection. The transition is emergent under random delays and connectivity: at narrow dispersion sequence detectors do not exist, and the dispersion at which they overtake event detectors tracks the inter-event interval with a slope statistically indistinguishable from one. This maps a computational distinction onto the anatomical one between myelinated and unmyelinated projections, making myelination a switch on what a neuron computes, not only a regulator of speed. Second, the same dispersion sets the code's limits: it bounds the longest codable interval and fixes an absolute timing tolerance of about a millisecond, with slowing better tolerated than speeding. Third, that millisecond window and horizontal conduction velocity together predict cortical column diameter, and the two areas with direct measurements fall where the relation puts them. One anatomically measurable parameter thus sets what a neuron detects and the limits of what it can represent.