The size-principle: a deterministic output emerges from a set of probabilistic connections.

Orderly, size-related recruitment of motoneurones (MNs) illustrates how hundreds of cells operate as a functional entity to produce a highly deterministic output. The coherent action of the pool depends largely on the distribution of input to its members through the connections of afferent fibres. Three types of spike-triggered averaging have been utilized to study these connections. Impulses in individual Ia afferents elicit excitatory postsynaptic potentials ('single-fibre' EPSPs) in about 80% of homonymous MNs. After spinal transection 100% may respond, suggesting that Ia fibres project anatomically to all homonymous MNs. Functionally absent Ia connections are due to transmission failure. The sum of all the EPSPs elicited in a large population of MNs was recorded electrotonically from ventral roots. The mean amplitudes of these 'postsynaptic population potentials' (PSPPs) were correlated with the conduction velocities (CVs) of the Ia or spindle group II fibres. The greater the distance between the spinal entry point of a Ia fibre and the ventral root, the smaller was the PSPP. Tape recording of multiple afferents and the responses of up to 24 MNs permitted study of as many as 264 possible connections in a single, acute experiment. Construction of wiring diagrams and connectivity matrices from the data showed that functional connectivity is influenced by afferent fibre size, the effect of branching on fibre size, MN size and probably transmission failure, but that on a cell-to-cell level, connectivity does not follow strict, deterministic rules. The results raise the question of how probabilistic connections between afferent fibres and MNs give rise to deterministic outputs from the whole pool.