Information theoretic analysis of dynamical encoding by four identified primary sensory interneurons in the cricket cercal system

1. The stimulus/response properties of four identified primary sensory interneurons in the cricket cercal sensory system were studied using electrophysiological techniques. These four cells are thought to represent a functionally discrete subunit of the cercal system: they are the only cells that encode information about stimulus direction to higher centers for low intensity stimuli. Previous studies characterized the quantity of information encoded by these cells about the direction of air currents in the horizontal plane. In the experiments reported here, we characterized the quantity and quality of information encoded in the cells' elicited responses about the dynamics of air current waveforms presented at their optimal stimulus directions. The total sample set included 22 cells. 2. This characterization was achieved by determining the cells' frequency sensitivities and encoding accuracy using the methods of stochastic systems analysis and information theory. The specific approach used for the analysis was the "stimulus reconstruction" technique in which a functional expansion was derived to transform the observed spike train responses into the optimal estimate (i.e., "reconstruction") of the actual stimulus. A novel derivation of the crucial equations is presented. The reverse approach is compared with the more traditional forward analysis, in which an expansion is derived that transforms the stimulus to a prediction of the spike train response. Important aspects of the application of these analytical approaches are considered. 3. All four interneurons were found to have identical frequency tuning, as assessed by the accuracy with which different frequency components of stimulus waveforms could be reconstructed with a linear expansion. The interneurons encoded significant information about stimulus frequencies between 5 and 80 Hz, which peak sensitivities at approximately 15 Hz. 4. All four interneurons were found to have identical stimulus/response latencies. The mean latency between a stimulus component and the corresponding elicited spike was 17 ms. All four interneurons also had identical integration times. The integration time, measured by the duration of stimulus, which could affect the probability of spiking, was approximately 50 ms. 5. The accuracy of the encoding can be expressed as a signal-to-noise ratio, where the noise is a scaled difference between the original signal and the best estimate of the signal. Peak signal-to-noise ratios of approximately 1 were obtained for the cells across all stimulus power levels, using only the linear expansion term. Analysis of the data indicated that the consideration of second-order nonlinear transformations of the stimulus would not have increased the calculated encoding accuracy. 6. The encoding accuracy also can be expressed in the information theoretic units of bits/second, which characterizes the information transmission rate of the cell. Bits/second values varied between 10 and 80 for the 22 different cells in our experimental set. The information rate values were highly correlated with the mean spike rates of the interneurons, but were not correlated with the stimulus power levels. However, normalizing the absolute information rates by the mean spike rate in each case yielded a measure of bits/spike that was remarkably invariant across all experiments. The measured bits/spike rate was approximately 1 for all experiments. This result is discussed in the context of recent theoretical studies on optimal encoding. 7. Although the dynamic sensitivities of the four interneurons were identical, their directional sensitivities are known to be orthogonal. Thus the cells are complementary to one another from a functional standpoint: whereas a particular cell will be insensitive to air currents from some directions, one or more of the other three cells will be sensitive to stimuli from those directions...