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Understanding how a biological neuron works has been a major goal in neuroscience. Under the Poisson-excitation assumption, results from earlier study by Suksompong and Berger on the timing jitter in the leaky integrate-and-fire (LIF) model of neurons are used to determine families of neural thresholding functions that are appropriate in certain interesting senses. Next, the neuron is treated as a communication channel for which information-theoretic quantities can be calculated. In particular, the optimal distribution of the Poisson excitation intensity is numerically evaluated along with the corresponding capacity using the Blahut-Arimoto algorithm. Simple formulas which approximate the optimal intensity distribution are given. Furthermore, the Jimbo-Kunisawa algorithm is used to explore energy-efficient operations for neuron. Finally, a rate-matching argument leads to a unique operating condition which turns out to agree with experimentally observed rate.