Higher-order non-linear phenomena in Renshaw cell responses to random motor axon stimulation

Renshaw cell responses to random motor axon stimulation exhibit second-order non-linearities in that they depend on the occurrence of a preceding stimulus, although these non-linearities are not strong enough to significantly depress the coherence. However, higher-order non-linearities have not been checked for so far. This is carried out here. Lumbosacral Renshaw cells were recorded with micropipettes in anaesthetized cats. Their responses to random (pseudo-Poisson) stimulation of motor axons in peripheral nerves or ventral roots were quantified by calculating peristimulus-time histograms of various sorts, conventional and conditional. Conventional peristimulus-time histograms were computed with respect to all the stimuli in a train. Conditional peristimulus-time histograms were calculated with respect to "test" stimuli which were sorted out (by computer) from the original stimulus train when they were preceded by "conditional" stimuli at average intervals of delta 1 or delta 2 or both. These conditioned responses were compared with those to be expected from hypothetical linear superposition. Renshaw cell responses showed small third-order non-linearities to pairs of conditioning stimuli at small intervals (up to some tens of milliseconds before the test stimuli). These third-order effects were smaller than each of the second-order non-linearities elicited by any of the single-conditioning stimuli. Also, further higher-order non-linearities were apparent, but of little average significance. Hence, the non-linearities in Renshaw cell responses to random inputs are essentially of second-order and fairly small.