Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models

A peripheral mononeuropathy was produced in adult rats by placing loosely constrictive ligatures around the common sciatic nerve. The postoperative behavior of these rats indicated that hyperalgesia, allodynia and, possibly, spontaneous pain (or dysesthesia) were produced. Hyperalgesic responses to noxious radiant heat were evident on the second postoperative day and lasted for over 2 months. Hyperalgesic responses to chemogenic pain were also present. The presence of allodynia was inferred from the nocifensive responses evoked by standing on an innocuous, chilled metal floor or by innocuous mechanical stimulation, and by the rats' persistence in holding the hind paw in a guarded position. The presence of spontaneous pain was suggested by a suppression of appetite and by the frequent occurrence of apparently spontaneous nocifensive responses. The affected hind paw was abnormally warm or cool in about one-third of the rats. About one-half of the rats developed grossly overgrown claws on the affected side. Experiments with this animal model may advance our understanding of the neural mechanisms of neuropathic pain disorders in humans.

Bifurcation mechanisms involved in the generation of action potentials (spikes) by neurons are reviewed here. We show how the type of bifurcation determines the neuro-computational properties of the cells. For example, when the rest state is near a saddle-node bifurcation, the cell can fire all-or-none spikes with an arbitrary low frequency, it has a well-defined threshold manifold, and it acts as an integrator; i.e. the higher the frequency of incoming pulses, the sooner it fires. In contrast, when the rest state is near an Andronov–Hopf bifurcation, the cell fires in a certain frequency range, its spikes are not all-or-none, it does not have a well-defined threshold manifold, it can fire in response to an inhibitory pulse, and it acts as a resonator; i.e. it responds preferentially to a certain (resonant) frequency of the input. Increasing the input frequency may actually delay or terminate its firing. We also describe the phenomenon of neural bursting, and we use geometric bifurcation theory to extend the existing classification of bursters, including many new types. We discuss how the type of burster defines its neuro-computational properties, and we show that different bursters can interact, synchronize and process information differently.

Spontaneous pain, a poorly understood aspect of human neuropathic pain, is indicated in animals by spontaneous foot lifting (SFL). To determine whether SFL is caused by spontaneous firing in nociceptive neurons, we studied the following groups of rats: (1) untreated; (2) spinal nerve axotomy (SNA), L5 SNA 1 week earlier; (3) mSNA (modified SNA), SNA plus loose ligation of the adjacent L4 spinal nerve with inflammation-inducing chromic gut; and (4) CFA (complete Freund's adjuvant), intradermal complete Freund's adjuvant-induced hindlimb inflammation 1 and 4 d earlier. In all groups, recordings of SFL and of spontaneous activity (SA) in ipsilateral dorsal root ganglion (DRG) neurons (intracellularly) were made. Evoked pain behaviors were measured in nerve injury (SNA/mSNA) groups. Percentages of nociceptive-type C-fiber neurons (C-nociceptors) with SA increased in intact L4 but not axotomized L5 DRGs in SNA and mSNA (to 35%), and in L4/L5 DRGs 1-4 d after CFA (to 38-25%). SFL occurred in mSNA but not SNA rats. It was not correlated with mechanical allodynia, extent of L4 fiber damage [ATF3 (activation transcription factor 3) immunostaining], or percentage of L4 C-nociceptors with SA. However, L4 C-nociceptors with SA fired faster after mSNA (1.8 Hz) than SNA (0.02 Hz); estimated L4 total firing rates were approximately 5.0 and approximately 0.6 kHz, respectively. Similarly, after CFA, faster L4 C-nociceptor SA after 1 d was associated with SFL, whereas slower SA after 4 d was not. Thus, inflammation causes L4 C-nociceptor SA and SFL. Overall, SFL was related to SA rate in intact C-nociceptors. Both L5 degeneration and chromic gut cause inflammation. Therefore, both SA and SFL/spontaneous pain after nerve injury (mSNA) may result from cumulative neuroinflammation.