Identification of Molecular Pathologies Sufficient to Cause Neuropathic Excitability in Primary Somatosensory Afferents Using Dynamical Systems Theory

Pain caused by nerve injury (i.e. neuropathic pain) is associated with development of neuronal hyperexcitability at several points along the pain pathway. Within primary afferents, numerous injury-induced changes have been identified but it remains unclear which molecular changes are necessary and sufficient to explain cellular hyperexcitability. To investigate this, we built computational models that reproduce the switch from a normal spiking pattern characterized by a single spike at the onset of depolarization to a neuropathic one characterized by repetitive spiking throughout depolarization. Parameter changes that were sufficient to switch the spiking pattern also enabled membrane potential oscillations and bursting, suggesting that all three pathological changes are mechanistically linked. Dynamical analysis confirmed this prediction by showing that excitability changes co-develop when the nonlinear mechanism responsible for spike initiation switches from a quasi-separatrix-crossing to a subcritical Hopf bifurcation. This switch stems from biophysical changes that bias competition between oppositely directed fast- and slow-activating conductances operating at subthreshold potentials. Competition between activation and inactivation of a single conductance can be similarly biased with equivalent consequences for excitability. “Bias” can arise from a multitude of molecular changes occurring alone or in combination; in the latter case, changes can add or offset one another. Thus, our results identify pathological change in the nonlinear interaction between processes affecting spike initiation as the critical determinant of how simple injury-induced changes at the molecular level manifest complex excitability changes at the cellular level. We demonstrate that multiple distinct molecular changes are sufficient to produce neuropathic changes in excitability; however, given that nerve injury elicits numerous molecular changes that may be individually sufficient to alter spike initiation, our results argue that no single molecular change is necessary to produce neuropathic excitability. This deeper understanding of degenerate causal relationships has important implications for how we understand and treat neuropathic pain. Author Summary: Neuropathic pain results from damage to the nervous system. Much is known about the multitude of molecular and cellular changes that are triggered by nerve injury (and which correlate with development of neuropathic pain), but little is understood about how those changes cause neuropathic pain. Rather than identifying what changes occur after nerve injury (which has already been the focus of countless studies), our study focuses on identifying which changes are functionally important. Specifically, we explain how certain molecular changes, acting alone or in combination, cause a triad of neuropathic changes in primary afferent excitability. Through computational modeling and nonlinear dynamical analysis, we demonstrate that the entire triad of excitability changes arises from a single switch in the nonlinear mechanism responsible for spike initiation. Going further, we demonstrate that many distinct molecular changes are sufficient to produce that switch but that no single molecular change is necessary if more than one sufficient change co-occurs after nerve injury, which appears to be the case. The issue becomes whether molecular changes combine to reach some tipping point whereupon cellular excitability is qualitatively altered. This highlights the importance of nonlinearities for neuropathic pain and the need for more computational pain research.