Action potential initiation and conduction along peripheral axons is a dynamic process that displays pronounced activity dependence. In patients with neuropathic pain, differences in the modulation of axonal conduction velocity by activity suggest that this property may provide insight into some of the pathomechanisms. To date, direct recordings of axonal membrane potential have been hampered by the small diameter of the fibers. We have therefore adopted an alternative approach to examine the basis of activity-dependent changes in axonal conduction by constructing a comprehensive mathematical model of human cutaneous C-fibers. Our model reproduced axonal spike propagation at a velocity of 0.69 m/s commensurate with recordings from human C-nociceptors. Activity-dependent slowing (ADS) of axonal propagation velocity was adequately simulated by the model. Interestingly, the property most readily associated with ADS was an increase in the concentration of intra-axonal sodium. This affected the driving potential of sodium currents, thereby producing latency changes comparable to those observed for experimental ADS. The model also adequately reproduced post-action potential excitability changes (i.e., recovery cycles) observed in vivo. We performed a series of control experiments replicating blockade of particular ion channels as well as changing temperature and extracellular ion concentrations. In the absence of direct experimental approaches, the model allows specific hypotheses to be formulated regarding the mechanisms underlying activity-dependent changes in C-fiber conduction. Because ADS might functionally act as a negative feedback to limit trains of nociceptor activity, we envisage that identifying its mechanisms may also direct efforts aimed at alleviating neuronal hyperexcitability in pain patients.

A ketogenic diet is an alternative treatment of epilepsy in infants. The diet, rich in fat and low in carbohydrates, elevates the level of polyunsaturated fatty acids (PUFAs) in plasma. These substances have therefore been suggested to contribute to the anticonvulsive effect of the diet. PUFAs modulate the properties of a range of ion channels, including K and Na channels, and it has been hypothesized that these changes may be part of a mechanistic explanation of the ketogenic diet. Using computational modelling, we here study how experimentally observed PUFA-induced changes of ion channel activity affect neuronal excitability in CA1, in particular responses to synaptic input of high synchronicity. The PUFA effects were studied in two pathological models of cellular hyperexcitability associated with epileptogenesis. We found that experimentally derived PUFA modulation of the A-type K (KA) channel, but not the delayed-rectifier K channel, restored healthy excitability by selectively reducing the response to inputs of high synchronicity. We also found that PUFA modulation of the transient Na channel was effective in this respect if the channel's steady-state inactivation was selectively affected. Furthermore, PUFA-induced hyperpolarization of the resting membrane potential was an effective approach to prevent hyperexcitability. When the combined effect of PUFA on the KA channel, the Na channel, and the resting membrane potential, was simulated, a lower concentration of PUFA was needed to restore healthy excitability. We therefore propose that one explanation of the beneficial effect of PUFAs lies in its simultaneous action on a range of ion-channel targets. Furthermore, this work suggests that a pharmacological cocktail acting on the voltage dependence of the Na-channel inactivation, the voltage dependences of KA channels, and the resting potential can be an effective treatment of epilepsy.

A range of ionic currents have been suggested to be involved in distinct aspects of epileptogenesis. Based on pharmacological and genetic studies, potassium currents have been implicated, in particular the transient A-type potassium current (KA). Epileptogenic activity comprises a rich repertoire of characteristics, one of which is synchronized activity of principal cells as revealed by occurrences of for instance fast ripples. Synchronized activity of this kind is particularly efficient in driving target cells into spiking. In the recipient cell, this synchronized input generates large brief compound EPSPs. The fast activation and inactivation of KA lead us to hypothesize a potential role in suppression of such EPSPs. In this work, using computational modeling, we have studied the activation of KA by synaptic inputs of different levels of synchronicity. We find that KA participates particularly in suppressing inputs of high synchronicity. We also show that the selective suppression stems from the current's ability to become activated by potentials with high slopes. We further show that KA suppresses input mimicing the activity of a fast ripple. Finally, we show that the degree of selectivity of KA can be modified by changes to its kinetic parameters, changes of the type that are produced by the modulatory action of KChIPs and DPPs. We suggest that the wealth of modulators affecting KA might be explained by a need to control cellular excitability in general and suppression of responses to synchronicity in particular. We also suggest that compounds changing KA-kinetics may be used to pharmacologically improve epileptic status.

Following each action potential, C-fiber nociceptors undergo cyclical changes in excitability, including a period of superexcitability, before recovering their basal excitability state. The increase in superexcitability during this recovery cycle depends upon their immediate firing history of the axon, but also determines the instantaneous firing frequency that encodes pain intensity. To explore the mechanistic underpinnings of the recovery cycle phenomenon a biophysical model of a C-fiber has been developed. The model represents the spatial extent of the axon including its passive properties as well as ion channels and the Na/K-ATPase ion pump. Ionic concentrations were represented inside and outside the membrane. The model was able to replicate the typical transitions in excitability from subnormal to supernormal observed empirically following a conducted action potential. In the model, supernormality depended on the degree of conduction slowing which in turn depends upon the frequency of stimulation, in accordance with experimental findings. In particular, we show that activity-dependent conduction slowing is produced by the accumulation of intraaxonal sodium. We further show that the supernormal phase results from a reduced potassium current Kdr as a result of accumulation of periaxonal potassium in concert with a reduced influx of sodium through Nav1.7 relative to Nav1.8 current. This theoretical prediction was supported by data from an in vitro preparation of small rat dorsal root ganglion somata showing a reduction in the magnitude of tetrodotoxin-sensitive relative to tetrodotoxin -resistant whole cell current. Furthermore, our studies provide support for the role of depolarization in supernormality, as previously suggested, but we suggest that the basic mechanism depends on changes in ionic concentrations inside and outside the axon. The understanding of the mechanisms underlying repetitive discharges in recovery cycles may provide insight into mechanisms of spontaneous activity, which recently has been shown to correlate to a perceived level of pain.

Highly synchronized neural firing has been discussed in relation to learning and memory, for instance sharp-wave activity in hippocampus. We were interested to study how a postsynaptic CA1 pyramidal neuron would integrate input of different levels of synchronicity. In previous work using computational modeling we studied how the integration depends on dendritic conductances. We found that the transient A-type potassium channel K(A) was able to selectively suppress input of high synchronicity. In recent years, compartmentalization of dendritic integration has been shown. We were therefore interested to study the influence of localization and pattern of synaptic input over the dendritic tree of the CA1 pyramidal neuron. We find that the selective suppression increases when synaptic inputs are placed on oblique dendrites further out from the soma. The suppression also increases along the radial axis from the apical trunk out to the end of oblique dendrites. We also find that the K(A) channel suppresses the occurrence of dendritic spikes. Moreover, recent studies have shown interaction between synaptic inputs. We therefore studied the influence of apical tuft input on the integration studied above. We find that excitatory input provides a modulatory influence reducing the capacity of K(A) to suppress synchronized activity, thus facilitating the excitatory drive of oblique dendritic input. Conversely, inhibitory tuft input increases the suppression by K(A) providing a larger control of oblique depolarizing factors on the CA1 pyramidal neuron in terms of what constitutes the most effective level of synchronicity. Furthermore, we show that the selective suppression studied above depends on the conductance of the K(A) channel. K(A) , as several other potassium channels, is modulated by several neuromodulators, for instance acetylcholine and dopamine, both of which have been discussed in relation to learning and memory. We suggest that dendritic conductances and their modulatory systems may be part of the regulation of processing of information, in particular for how network synchronicity affects learning and memory.