Information theoretic analysis of pulmonary stretch receptor spike trains

Primary afferent neurons transduce physical, continuous stimuli into discrete spike trains. Investigators have long been interested in interpreting the meaning of the number or pattern of action potentials in attempts to decode the spike train back into stimulus parameters. Pulmonary stretch receptors (PSRs) are visceral mechanoreceptors that respond to deformation of the lungs and pulmonary tree. They provide the brain stem with feedback that is used by cardiorespiratory control circuits. In anesthetized, paralyzed, artificially ventilated rabbits, we recorded the action potential trains of individual PSRs while continuously manipulating ventilator rate and volume. We describe an information theoretic-based analytical method for evaluating continuous stimulus and spike train data that is of general applicability to any continuous, dynamic system. After adjusting spike times for conduction velocity, we used a sliding window to discretize the stimulus (average tracheal pressure) and response (number of spikes), and constructed co-occurrence matrices. We systematically varied the number of categories into which the stimulus and response were evenly divided at 26 different sliding window widths (5, 10, 20, 30,..., 230, 240, 250 ms). Using the probability distributions defined by the co-occurrence matrices, we estimated associated stimulus, response, joint, and conditional entropies, from which we calculated information transmitted as a fraction of the maximum possible, as well as encoding and decoding efficiencies. We found that, in general, information increases rapidly as the sliding window width increases from 5 to approximately 50 ms and then saturates as observation time increases. In addition, the information measures suggest that individual PSRs transmit more "when" than "what" type of information about the stimulus, based on the finding that the maximum information at a given window width was obtained when the stimulus was divided into just a few (usually <6) categories. Our results indicate that PSRs provide quite reliable information about tracheal pressure, with each PSR conveying about 31% of the maximum possible information about the dynamic stimulus, given our analytical parameters. When the stimulus and response are divided into more categories, slightly less information is transmitted, and this quantity also saturates as a function of observation time. We consider and discuss the importance of information contained in window widths on the time scales of an excitatory postsynaptic potential and Hering-Breuer reflex central delay.