Explaining pathological changes in axonal excitability through dynamical analysis of conductance-based models

Neurons rely on action potentials, or spikes, to relay information. Pathological changes in spike generation likely contribute to certain enigmatic features of neurological disease, like paroxysmal attacks of pain and muscle spasm. Paroxysmal symptoms are characterized by abrupt onset and short duration, and are associated with abnormal spiking although the exact pathophysiology remains unclear. To help decipher the biophysical basis for 'paroxysmal' spiking, we replicated afterdischarge (i.e. continued spiking after a brief stimulus) in a minimal conductance-based axon model. We then applied nonlinear dynamical analysis to explain the dynamical basis for initiation and termination of afterdischarge. A perturbation could abruptly switch the system between two (quasi-)stable attractor states: rest and repetitive spiking. This bistability was a consequence of slow positive feedback mediated by persistent inward current. Initiation of afterdischarge was explained by activation of the persistent inward current forcing the system to cross a saddle point that separates the basins of attraction associated with each attractor. Termination of afterdischarge was explained by the attractor associated with repetitive spiking being destroyed. This occurred when ultra-slow negative feedback, such as intracellular sodium accumulation, caused the saddle point and stable limit cycle to collide; in that regard, the active attractor is not truly stable when the slowest dynamics are taken into account. The model also explains other features of paroxysmal symptoms, including temporal summation and refractoriness.

[1]  J. Ochoa,et al.  Sensations evoked by intraneural microstimulation of single mechanoreceptor units innervating the human hand. , 1983, The Journal of physiology.

[2]  P. Cavallari,et al.  Motor neuron 'bistability'. A pathogenetic mechanism for cramps and myokymia. , 1994, Brain : a journal of neurology.

[3]  Z. Rappaport,et al.  Pathophysiology of trigeminal neuralgia: the ignition hypothesis. , 2002, The Clinical journal of pain.

[4]  M. Espir,et al.  Paroxysmal symptoms as the first manifestations of multiple sclerosis. , 1980, Journal of neurology, neurosurgery, and psychiatry.

[5]  S. Strogatz Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering , 1995 .

[6]  D. Burke,et al.  Excitability changes in human sensory and motor axons during hyperventilation and ischaemia. , 1997, Brain : a journal of neurology.

[7]  William H. Calvin,et al.  Can neuralgias arise from minor demyelination? Spontaneous firing, mechanosensitivity, and afterdischarge from conducting axons , 1982, Experimental Neurology.

[8]  G. Ermentrout,et al.  Analysis of neural excitability and oscillations , 1989 .

[9]  Stephen G. Waxman,et al.  Pathophysiology of demyelinated axons , 1995 .

[10]  Terrence J. Sejnowski,et al.  Biophysical Basis for Three Distinct Dynamical Mechanisms of Action Potential Initiation , 2008, PLoS Comput. Biol..

[11]  S G Waxman,et al.  Ionic mechanisms of anoxic injury in mammalian CNS white matter: role of Na+ channels and Na(+)-Ca2+ exchanger , 1992, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[12]  J. Rinzel,et al.  Dissection of a model for neuronal parabolic bursting , 1987, Journal of mathematical biology.

[13]  K. Smith,et al.  A mechanism for ectopic firing in central demyelinated axons. , 1995, Brain : a journal of neurology.

[14]  M. Devor,et al.  Ephaptic transmission in chronically damaged peripheral nerves , 1979, Neurology.

[15]  S G Waxman,et al.  Membranes, myelin, and the pathophysiology of multiple sclerosis. , 1982, The New England journal of medicine.

[16]  Stephen G. Waxman,et al.  Axonal conduction and injury in multiple sclerosis: the role of sodium channels , 2006, Nature Reviews Neuroscience.

[17]  P. Wall,et al.  Cross-excitation in dorsal root ganglia of nerve-injured and intact rats. , 1990, Journal of neurophysiology.

[18]  S. Dib-Hajj,et al.  Sodium channels in normal and pathological pain. , 2010, Annual review of neuroscience.

[19]  J. S. Coggan,et al.  Imbalance of ionic conductances contributes to diverse symptoms of demyelination , 2010, Proceedings of the National Academy of Sciences.

[20]  Michael Costigan,et al.  Neuropathic pain: a maladaptive response of the nervous system to damage. , 2009, Annual review of neuroscience.

[21]  H. E. Torebjörk,et al.  Paraesthesiae from ectopic impulse generation in human sensory nerves. , 1980, Brain : a journal of neurology.

[22]  M. Baker Axonal flip-flops and oscillators , 2000, Trends in Neurosciences.

[23]  S. Waxman The Axon : structure, function, and pathophysiology , 1995 .

[24]  S. Waxman,et al.  Mechanisms of paresthesiae, dysesthesiae, and hyperesthesiae: role of Na+ channel heterogeneity. , 1996, European neurology.

[25]  Ichiro Kanazawa,et al.  Positive symptoms in multiple sclerosis: their treatment with sodium channel blockers, lidocaine and mexiletine , 1999, Journal of the Neurological Sciences.

[26]  C. Westerberg,et al.  Paroxysmal attacks in multiple sclerosis. , 1975, Brain : a journal of neurology.

[27]  M. Brecht,et al.  Sparse and powerful cortical spikes , 2010, Current Opinion in Neurobiology.

[28]  C. Morris,et al.  Voltage oscillations in the barnacle giant muscle fiber. , 1981, Biophysical journal.

[29]  W. Henderson Trigeminal neuralgia: the pain and its treatment. , 1967, British medical journal.

[30]  Eugene M. Izhikevich,et al.  Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .

[31]  Frederik Barkhof,et al.  Grey matter pathology in multiple sclerosis , 2008, The Lancet Neurology.

[32]  H Bostock,et al.  Changes in excitability of human motor axons underlying post‐ischaemic fasciculations: evidence for two stable states. , 1991, The Journal of physiology.

[33]  Bard Ermentrout,et al.  Simulating, analyzing, and animating dynamical systems - a guide to XPPAUT for researchers and students , 2002, Software, environments, tools.

[34]  E. Tüzün,et al.  Paroxysmal attacks in multiple sclerosis , 2001, Multiple sclerosis.