How synaptic noise may affect cross-correlations.

The relationship between a postsynaptic potential (the 'test PSP') and the profile of the cross-correlation that it produces in a repetitively discharging mammalian motoneuron, with and without synaptic noise, has been explored by computer stimulation. In a noiseless motoneuron the cross-correlation profile represents the first derivative of PSP shape except where 'shadowing' occurs (Eqn. 1a-c). When synaptic noise is present the relationship changes. When the amplitude of spike-like 'noise PSPs' occurring at regular intervals reaches a critical value (Eqn. 2), all threshold crossings involve noise PSPs. Under these circumstances termed 'just maximally effective synaptic noise', the cross-correlation represents test PSP directly (Eqn. 3a). When the interval between noise PSPs is shortened the relationship reverts to the first differential (Eqn. 4a-c). If the amplitude of the noise PSPs is less than the critical value (Eqn. 5) the cross-correlation profile is represented in a complex way by a combination of the first derivative of the upper part and the direct representation of the lower part of the test PSP. The area of the cross-correlation peak above baseline provides the most reliable estimate of EPSP amplitude in a noiseless motoneuron (Eqn. 6a). This area may fall to half for the same triangular test EPSP in the presence of just maximally effective synaptic noise (Eqn. 7a). In general, the presence of synaptic noise leads to underestimation of EPSP amplitude. These general principles remain valid for physiological noise consisting of randomly occurring EPSPs and allow certain experimental findings in cat motoneurons to be understood.