Characterization of reliability of spike timing in spinal interneurons during oscillating inputs

The spike timing in rhythmically active interneurons in the mammalian spina l locomotor network varies from cycle to cycle. We tested the contribution from passive membrane properties to this variable firing pattern, by measur ing the reliability of spike timing, P, in interneurons in the isolated neo natal rat spinal cord, using intracellular injection of sinusoidal command currents of different frequencies (0.325-31.25 Hz). P is a measure of the p recision of spike timing. In general, P was low at low frequencies and ampl itudes (P = 0-0.6; 0-1.875 Hz; 0-30 pA), and high at high frequencies and a mplitudes (P = 0.8-1; 3.125-31.25 Hz; 30-200 pA). The exact relationship be tween P and amplitude was difficult to describe because of the well-known l ow-pass properties of the membrane, which resulted in amplitude attenuation of high-frequency compared with low-frequency command currents. To formali ze the analysis we used a leaky integrate and fire (LIF) model with a noise term added. The LIF model was able to reproduce the experimentally observe d properties of P as well as the low-pass properties of the membrane. The L IF model enabled us to use the mathematical theory of nonlinear oscillators to analyze the relationship between amplitude, frequency, and P. This was done by systematically calculating the rotational number, N, defined as the number of spikes divided by the number of periods of the command current, for a large number of frequencies and amplitudes. These calculations led to a phase portrait based on the amplitude of the command current versus the frequency-containing areas [Arnold tongues (ATs)] with the same rotational number. The largest ATs in the phase portrait were those where N was a whol e integer, and the largest areas in the ATs were seen for middle to high (> 3 Hz) frequencies and middle to high amplitudes (50-120 pA). This correspon ded to the amplitude- and frequency-evoked increase in P. The model predict ed that P would be high when a cell responded with an integer and constant N. This prediction was confirmed by comparing N and P in real experiments. Fitting the result of the LIF model to the experimental data enabled us to estimate the standard deviation of the internal neuronal noise and to use t hese data to simulate the relationship between N and P in the model. This s imulation demonstrated a good correspondence between the theoretical and ex perimental values. Our data demonstrate that interneurons can respond with a high reliability of spike timing, but only by combining fast and slow osc illations is it possible to obtain a high reliability of firing during rhyt hmic locomotor movements. Theoretical analysis of the rotation number provi ded new insights into the mechanism for obtaining reliable spike timing.