Connectivity Based On Time Series Analysis Of Spike Sequences

A basic problem in neurophysiology has been to establish minimal models for neural connectivity, including excitatory and inhibitory connections, when recording from two or more functionally interconnected interneurons. It has been observed by the author (and many other workers) that certain interneurons in neuropile associated with sensory transduction fire in the absence of a stimulus. The stimulus might make them fire faster, or slower, but in every case alters the statistics of the zero-stimulus firing point process. For example, a neuron in the optic lobe of a grasshopper might fire fairly randomly in the absence of a stimulus, but given an appropriate visual stimulus, its firing would become faster and more regular (periodic). If the stimulus were moved in the opposite direction, the zero-stimulus firing would still remain random, but would fire more slowly, or not at all (Northrop, 1970). Some insight into how this behavior could arise can be inferred from repeating the experiment

FIGURE 8.0-4 A discrete, self-tuning system that can mimic (model) a biological system. The input is sampled, broadband noise [xk]. The L + 1 model weights {wjk} are adjusted iteratively by an LMS algorithm (Widrow and Stearns, 1985) until the model closely matches the behavior of the neuro-sensory system.

FIGURE 8.0-4 A discrete, self-tuning system that can mimic (model) a biological system. The input is sampled, broadband noise [xk]. The L + 1 model weights {wjk} are adjusted iteratively by an LMS algorithm (Widrow and Stearns, 1985) until the model closely matches the behavior of the neuro-sensory system.

and recording from two or three closely situated neurons that can be shown to interact functionally.

One of the tools that sidesteps the need to calculate various individual and joint statistical functions for each neuron is the use of the joint peri-stimulus time (JPST) histogram, introduced by Gerstein and Perkel (1969). The JPST diagram is a visual tool, and offers qualitative (and some quantitative) evidence for canonical neural interconnections. It is normally viewed as a two-dimensional dot density plot when characterizing two neurons, but can be extended to three-dimensional, dot volumes for three neurons. The JPST diagram is described in the next section.

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