Analysis of physiological systems

http://www-users.med.cornell.edu/%7Ejdvicto/pdfs/vict05.pdf

Spike train metrics.

The effects of perturbing an on-going biological oscillation with a single brief stimulus are considered. If the time from some observable event before the stimulus to the next event after the stimulus is plotted as a function of the phase of the stimulus, then there may be discontinuities in this plot. The discontinuities reflect the size of the stimulus and the topological properties of the biological oscillation. The implications for experiments are discussed.

Discontinuities in phase-resetting experiments

A pattern grouping algorithm for analysis of spatiotemporal patterns in neuronal spike trains. 2. Application to simultaneous single unit recordings.

It is known (e.g., Perkel et al., 1964) that when a pacemaker neuron elicits IPSP's in another, there are domains called “paradoxical segments” where in the steady-state i) faster inhibitory discharges determine faster inhibited ones, and ii) pre- and postsynaptic spikes are “locked” in an invariant forward-and-backward positioning in time, spikes alternating in the ratios 1:1 (1 pere for 1 postsynaptic), 1:2, 2:1..., that are also the slopes of the synaptic rate-transformation. The present project examined the matter further in the inhibitory synapse upon the crayfish tonic stretch receptor neuron, confirming the above. In addition it showed that locking and alternation existed also in the segments interposed between the 1:2, 1:1 and 2:1 paradoxical segments, even though they were not as marked and apparent, and that when tests were close to each other their order became influential and hysteresis-like phenomena appeared. The main finding was that paradoxical rate-relations, locking and alternation persisted when the presynaptic train was irregularized up to interval coefficients of variation of around 0.20 (Figs. 2–5). Therefore, both phenomena may not simply be laboratory curiosities, but also have a role in natural operation where probably a substantial population of neurons exhibits that kind of irregularity. As presynaptic irregularity increased, the paradoxical segment slopes and widths decreased and locking and alternation became less clear-cut. With CV's of about 0.20, only a relatively narrow 1:1 paradoxical segment with about O slope and little locking and alternation remained (Figs. 2b, 3g, 4right, 5third row). With larger CV's, the rate relation decreased monotonically and there was no locking nor alternation (Figs. 2e, 3h, 5bottom row). The postsynaptic discharge was more regular and had fewer changes in the number of presynaptic spikes per post-synaptic interval within paradoxical segments (particularly in their centers) than in segments interposed between them (left vs. right-hand columns in Figs. 5, 6; Fig. 7): the contrast, remarkable for regular stimuli, attenuated as variability increased. The following conclusions are relevant to coding of spike trains across a synapse with IPSP's. i) With fairly regular discharges, the same postsynaptic rate may result from several presynaptic ones (e.g., may result from rates in the 1:1 and 2:1 paradoxical segments and in the interposed one, Fig.2): in some cases but not others, the precise presynaptic rate can be identified on the basis of postsynaptic CV's, interval histograms and cycle slips. ii) A small rate change in a regular presynaptic discharge will have very different postsynaptic consequences depending on where it happens: if across a paradoxical-interposed boundary, for instance, it will cause remarkable rate, pattern and correlation changes. iii) The trans-synaptic mapping of variability involves an increase for the more regular presynaptic discharges and a decrease for the more irregular ones. iv) The postsynaptic discharge was slower with IPSP's than without in most cases; however, when the control discharge was weak or absent, IPSP's accelerated it. Results are relevant also to the operation of periodically performing systems that involve neuronal correlates, indicating that it is necessary in every case to ask whether zigzag relations and locking occur. The “delay function” plots the arrival time of an IPSP (or IPSP burst) relative to the last postsynaptic spike, i.e., the “phase” (Φ in Fig. 1b), against the interval lengthening produced, i.e., the “delay” (δ). In all cases, most points clustered around a straight line (Fig. 8), whose slope and ordinate intercept were in the 0.43–0.87 and the 0.02–0.52 ranges, respectively, for single IPSP's. The slope reflects how the IPSP effectiveness depends on when it arrives in the cycle; the intercept reflects the IPSP effectiveness. Large phases often showed “aberrant” points whose ordinates were either large (and having special formal implications), or very small (perhaps reflecting conduction and synaptic delays), or clustered around a second straight segment with a large negative slope (when spontaneous rates were low) (Fig. 8c). Delay functions for widely separated pairs of IPSP's could be multi-valued, points clustering around 2 or 3 parallel straight lines. A mathematical model of pacemaker inhibitory synaptic interactions (Segundo, 1979) agreed with this embodiment insofar as some postulated properties are concerned (e.g., regular discharge, interval lengthening by IPSP's, linear delay functions with slopes around 0.7) and as to the main aspects of the preparation's behavior (i.e., zigzag rate relations and locking), but not in terms of some aspects of the postulates (e.g., interval variability, rebound) or behavior (e.g., segment boundaries, jitter in the locking, and hysteresis). The model was judged to be on the balance satisfactorily realistic.

Presynaptic irregularity and pacemaker inhibition

The nerve cell as an analyzer of spike trains.

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The nerve cell as an analyzer of spike trains.